Chem. Rev. 1990, 90. 33-72 93
The Sol-Gel Process
LARRY L. HENCH' and JON K. WEST
D q " n t of Materials Sc*mceand Enghwrhg, Advanced Materials Research Center,UnimrMy of Floryle. oakresville.Fknm 32611
Received May 16. 1989 (Revised Manuscript Received October 27, 1989)
Contents
1. Introduction
11. Sol-Gel Process Steps: An Overview
111. Hydrolysisand Polycondensation
IV. Gelation
VI. Aging
VII. Drying
V. Theoretical Studies
VIII. Stabilization
IX. Densification
XI. Conclusions
I. Infroducf/on
X. Physical Properties
33
35
37
40
46
49
51
58
65
67
68
Interest in the sol-gel processingof inorganic ceramic
and glass materialsbegan asearly asthe mid-1900swith
Ebelmanl,*and Graham's3 studies on silica gels. These
early investigators observed that the hydrolysis of tet-
raethyl orthosilicate (TEOS),Si(OC2H5),,under acidic
conditions yielded Si02in the form of a "glass-like
material".l Fibers could be drawn from the viscousgel,
and even monolithic optical lenses? or composites
formed? However, extremely long drying times of 1
year or more were necessary to avoid the silica gels
fracturing into a fine powder, and consequently there
was little technological interest.
For a period from the late 18008through the 19209
gels became of considerable interest to chemists stim-
ulated by the phenomenon of Liesegang Rings4&formed
from gels. Many noted chemists, including OstwaldE
and Lord Rayleigh,? investigated the problem of the
periodic precipitation phenomena that lead to the
formation of Liesegang rings and the growth of crystals
from gels. A huge volume of descriptive literature re-
sulted from these studiesg'O but a relatively sparse
understanding of the physical-chemical principles?
Roy and co-workersll-" recognized the potential for
achieving very high levels of chemical homogeneity in
colloidal gels and used the sol-gel method in the 19509
and 1960sto synthesize a large number of novel ceramic
oxide compositions, involving AI, Si, Ti, Zr, etc., that
could not be made using traditional ceramic powder
methods. During the same period Iler's pioneeringwork
in silica chemistry15led to the commercial development
of colloidal silica powders, Du Pont's colloidal Ludox
spheres. Stober et a1.I6extended Iler's findings to show
that using ammonia as a catalyst for the TEOS hy-
drolysisreaction could control both the morphologyand
size of the powders, yielding the so-called Stober
spherical silica powder.
The final size of the spherical silica powder is a
function of the initial concentration of water and am-
monia, the type of silicon alkoxide (methyl, ethyl,
c ,
Lany L. Hend, is a eadaduateResearch Professain tbCep"
01 Materials Science and Engineeringat the University of Florida.
where he has taught since 1964 after receiving B.S. (1961) and
Ph.D. (1964) degrees in Ceramic Engineering at The Ohm State
Universny. He is the Director of lha Boglass ResearchCenter and
CoDirectof of the Advanced Materials Research Center at the
University of Florida. He has published more than 250 research
articles and is the coauthor or coeditor of 12 books in the fields
of biomateriak. ceramic processing. ceramic characterization.
glass surfaces.electronicceramics. nuclear waste disposal,and
sol-gel processing.
r
4-7
Jon K. West received his Ph.D. at the Univerrity of FkMa in 1979
while wwking full limeas an engineeringmanager wilh tb Battery
Business Departmentof General ElectricCo. His cment position
is Associate-in-Engineering with the Department of Materials
Science and Engineeringat the University of Florida. His work in
sol-gel silica includes mechanical testing, process control and
instrumentation.and theoreticalstudies based on molecular wbtal
calculations. He is the author of eight publications Including the
recently published textbook Principles of Electronic Ceramics. by
Hench and West. from John Wilev 8 Sons.
pentyl, esters, e t 4 and alcohol (methyl, ethyl, butyl,
pentyl) mixture used,16and reactant tempe~ature.~'An
example of a typical colloidal silica powder is shown in
Figure la, made by the Stober process, and its uniform
distribution of particle sizes is shown in Figure l b from
Khadikar and Sacks work.ls
0009-2665/90/0790-0031$09.50/0 0 1990 American Chemical Society
34 Chemical Reviews. 1990. Vol. 90. No. 1
.J .n .. .E .5 .s .I
Figure I. Top SEMof Stober sphericalsilicapowders. Bottom:
Histogram (numberof particles in a given diameter classversus
particle diameter) of a typical batch of Stoher spherical silica
powders. Reprinted from ref 18: copyright 1988 University of
Florida.
PARnCtBDlAMETER @m)
O~erbeek'~3and SugimotoZ1showed that nucleation
of particles in a very short time followed by growth
without supersaturation will yield monodispersed col-
loidal oxide particles. Matijevic and c o - ~ o r k e r s ~ ~ - ~ ~
have employed these concepts to produce an enormous
range of colloidal powders with controlled size and
morphologies, including oxides (TiO,, a-FepO3,Fe304,
BaTiO,, Ce02),hydroxides (AIOOH,FeOOH, Cr(OH),),
carbonates (Cd(OH)CO,), Ce,O(CO3),, Ce(III)/Y
HC03),sulfides (CdS, ZnS), metals (Fe(III), Ni, Co),
and various mixed phases or composites (Ni, Co, Sr
ferrites), sulfides (Zn, CdS), (Pb, CdS), and coated
particles (Fe304with AKOH), or Cr(OH),).
The controlled hydrolysis of alkoxides has also been
used to produce submicrometer Ti0z,26doped Ti02.27
Zr0z,28and doped Zr0z,28doped SiOz,TJSrTiO,." and
even cordierite30powders.
Emulsions have been employed to produce spherical
powders of mixed cation oxides, such as yttrium alu-
minum garnets (YAG),and many other systems such
as reviewed in Hardy et al."
Sol-gel powder processes have also been applied to
fissile elements31where spray-formed sols of U02and
U02-PuO, were formed as rigid gel spheres during
passage through a column of heated liquid.
Both glass and polycrystalline ceramic fibers have
been prepared by using the sol-gel method. Compo-
sitions include TiOz-Si02 and Zr02-Si02 glass
high-purity SiO, waveguide f i b e r ~ ? ~ . ~ ~A120b ZrO,,
Hen& and West
Tho,, MgO, TiO,, ZrSiO,, and 3AI2O3.2SiOzfibers.-
Abrasivegrains based upon sol-gel-derived alumina are
important commercial products."
A variety of coatings and films have also been de-
veloped by using sol-gel methods. Of particular im-
portance are the antireflection coatings of indium tin
oxide (ITO) and related compositions applied to glass
window panes to improve insulation chara~teristics.~~
Other work on sol-gel coatings is reviewed by Schroe-
der,'8 Macken~ie,'~,"and Wenzel.S1 Mackenzie's re-
v i e ~ s ~ ~ 5 0include many other applications of the sol-gel
process, proven, possible, and potential.
The motivation for sol-gelprocessing is primarily the
potentially higher purity and homogeneity and the
lower processing temperatures associated with sol-gels
compared with traditional glass melting or ceramic
powder methods. Ma~kenzie'~flsummarizes a number
of potential advantages and disadvantages and the
relative economicsof sol-gel methods in general. Hench
and colleague^^^^" compare quantitatively the merits
of sol-gel-derived silica optics over the alternative
high-temperature processing methods.
During the past decade there has been an enormous
growth in the interest in the sol-gel process. This
growth has been stimulated by several factors. On the
basis of Kistler's early work,%several teams have pro-
duced very low density silica monoliths,called aerogels,
by hypercritical point drying.5BZarzycki, Prassas, and
P h a l i p p o ~ ~ ~ . ~demonstrated that hypercritical point
drying of silica gels could yield large fully dense silica
glass monoliths. Yoldassgshowed that large monolithic
pieces of alumina could be made by sol-gel methods.
These demonstrations of potentially practical routes for
production of new materials with unique properties
coincided with the growing recognition that powder
processing of materials had inherent limitations in ho-
mogeneity due to difficulty in controlling agglomera-
tion.60 ,
The first of a series of International Conferences on
Ultrastructure Processingwas held in 1983to establish
a scientific basis for the chemical-based processing of
a new generation of advanced materials for structural,
electrical, optical, and optoelectronic applications.
Support by the Directorate of Chemical and Atmos-
pheric Sciences of the Air Force Office of Scientific
Research (AFOSR)for the Ultrastructure Conferences
in 1983,6l 1985,6, 1987," and 198ga and the Materials
Research Society Better CeramicsThrough Chemistry
annual meetings in alternate years in 1984,6519S6,66and
198Sa has provided constant stimulation for the field.
In addition, AFOSR has provided a stable financialbase
of support for a number of university programs in
sol-gel sciencethroughout the 1980sunder the technical
monitoring of D. R. Ulrich.
The primary goal in these conferences and the
AFOSR research and development program was to es-
tablish a scientific foundation for a new era in the
manufacture of advanced, high-technology ceramics,
glasses, and composites. For millennia, ceramics have
been made with basically the same technology. Pow-
ders, either natural or man-made, have been shaped
into objectsand subsequently densified at temperatures
close to their liquidus. The technology of making glass
has also remained fundamentally the same since pre-
history. Particles are melted, homogenized,and shaped
The Sol-Gel Process Chemical Reviews, 1990,Vol. 90,No. 1 35
f
Figure 2. Change in the roles of physics and chemistry as ce-
ramics move toward ultrastructure processing. Reprinted from
ref 61; copyright 1984 Wiley.
into objects from the liquid.
The goal of sol-gel processing and ultrastructure
processing in general is to control the surfaces and in-
terfaces of materials during the earliest stages of pro-
duction.61 Long-term reliability of a material is usually
limited by localized variations in the physical chemistry
of the surface and interfaces within the material. The
emphasis on ultrastructure processing is on limiting and
controlling physical chemical variability by the pro-
duction of uniquely homogeneous structures or pro-
ducing extremely fine-scale (10-100 nm) second phases.
Creating controlled surface compositional gradients and
achieving unique physical properties by combining in-
organic and organic materials are also goals of ultra-
structure processing.
The concept ofmolecular manipulation of the pro-
cessing of ceramics, glasses, and composites requires an
application of chemical principles unprecedented in the
history of ceramics. Modern ceramics are primarily the
products of applied physics, as indicated in Figure 2.
During the past decade there has been enormous
progress made in the shifting of the emphasis of ceramic
science to include a larger overlap with chemistry, as
also illustrated in Figure 2.61 The extensive literature
represented by the conference proceedings cited
above6147contains excellent examples of this shift to-
ward chemical-based processing in materials science.
Another essential factor for the increased scientific
understanding of the sol-gel process is the availability
of new analytical and calculational techniques capable
of investigating on a nanometer scale the chemical
processes of hydrolysis, polycondensation, syneresis,
dehydration, and densification of materials. Many of
the concepts of molecular control of sol-gel processes
are a result of the use of nuclear magnetic resonance
(NMR),X-ray small-angle scattering (XSAS),Raman
spectroscopy, X-ray photoelectron spectroscopy (XPS),
differential scanning calorimetry (DSC),dielectric re-
laxation spectroscopy (DRS),etc., that have been de-
veloped during the past three decades.
The difference between the modern development of
sol-gel-derived materials, such as gel-silica o p t i ~ s , ~ ~ - ~ ~
and the classical work of Ebelman1*2is that now drying
of the monolithic silica optics can be achieved in days
rather than years. The primary problem that had to
be overcomewas crackingduring drying due to the large
shrinkage that occurs when pore liquids are removed
from the gels. For small cross sections, such as in
powders, coatings, or fibers, drying stresses are small
and can be accommodated by the material. For mon-
olithic objects greater than about 1 cm in diameter,
drying stresses developed in ambient atmospheres can
introduce catastrophic fracture. To prevent fracture
during drying, it is essential to control the chemistry
of each step of the sol-gel process carefully. Likewise,
to densify a dried gel monolith, it is essential to control
the chemistry of the pore network prior to and during
pore closure. The objective of this review is to describe
the chemistry of the seven steps of the sol-gel process
that can yield monoliths under ambient pressures. This
review also describes how sol-gel-derived monoliths can
be processed to result in fully dense components or with
precisely controlled and chemically stable porosities.
Most detail exists for Si02,and therefore the emphasis
in this review is on silica sol-gel processing. The pro-
cessing of silica monoliths by alkoxide methods will be
compared with more traditional colloidal sol-gel
methods.
The reader interested in the sol-gel processing of
compositional systems other than Si02or coatings, fi-
bers, powders, or aerogels is referred to the Conference
Proceedings cited above6147as well as an International
Workshop on Sol-Gel Processing@and special confer-
ences chaired by Sanders and Klein69and F r i ~ k e . ~ ~
Klein's volume on sol-gel techn~logy,~~emphasizing
thin films, fibers, hollow glass microspheres, and spe-
cialty shapes, illustrates many potential applications of
this field. A textbook on sol-gel science has recently
been completed by Brinker and S ~ h e r e r . ~ ~Other gen-
eral reviews on earlier work include those by Klein,71
Sakka and K a m i ~ a , ~ ~M ~ k h e r j e e , ~ ~Sakka,74i75and of
course Iler15976and O k k e r ~ e . ~ ~
II. Sol-Gel Process Steps: An Overview
Three approaches are used to make sol-gel monoliths:
method 1,gelation of a solution of colloidal powders;
method 2, hydrolysis and polycondensation of alkoxide
or nitrate precursors followed by hypercritical drying
of gels; method 3, hydrolysis and polycondensation of
alkoxide precursors followed by aging and drying under
ambient atmospheres.
Sols are dispersions of colloidal particles in a liquid.
Colloids are solid particles with diameters of 1-100
nm.78 A gel is a interconnected, rigid network with
pores of submicrometer dimensions and polymeric
chains whose average length is greater than a microm-
eter. The term "gel" embraces a diversity of combina-
tions of substances that can be classified in four cate-
gories as discussed by F10ry:~~(1)well-ordered lamellar
structures; (2) covalent polymeric networks, completely
disordered; (3) polymer networks formed through
physical aggregation, predominantly disordered; (4)
particular disordered structures.
A silica gel may be formed by network growth from
an array of discrete colloidal particles (method 1)or by
formation of an interconnected 3-D network by the
simultaneous hydrolysis and polycondensation of an
organometallic precursor (methods 2 and 3). When the
pore liquid is removed as a gas phase from the inter-
connected solid gel network under hypercritical con-
ditions (critical-point drying, method 2), the network
Hench and West
powders made by chemical vapor deposition (CVD)of
SiC14.52-54
The processing steps involved in making sol-gel-de-
rived silica monoliths for methods 1-3 are compared
below. A schematic illustration of these seven steps is
given in Figure 3 for methods 1and 3.
Step 1: Mixing. In method 1a suspension of col-
loidal powders, or sol, is formed by mechanical mixing
of colloidal particles in water at a pH that prevents
precipitation, as discussed in detail by Iler.15776In
methods 2 and 3 a liquid alkoxide precursor, such as
Si(OR),, where R is CH3,CzH5,or C3H7,is hydrolyzed
by mixing with water (eq 2).
36 Chemical Reviews, 1990, Vol. 90, No. 1
OCH, OH
hydrolysis:H,CO-Si--OCH, + 4(H20) + H-Si-OH + 4(CH30H)
RELATIVE TIME I I
AH
Figure 3. Gel-silica glass process sequence.
ACH,
TMOS + 4(H20) + Si(OH14 + 4(CHsOH) (2)
does not collapse and a low density aerogel is produced.
Aerogels can have pore volumes as large as 98% and
densities as low as 80 kg/m3.59p80
When the pore liquid is removed at or near ambient
The hydrated silica tetrahedra interact in a conden-
sation reaction (eq 3), forming =Si-O-Si= bonds.
PH
AH AH
pressure by thermal evaporation (called drying, used OH
in methods 1and 3) and shrinkage occurs, the monolith I
condensation:HO-Si-OH + HO-Si-OH +
is termed a xerogel. If the pore liquid is primarily
alcohol based, the monolith is often termed an alcogel.
The generic term gel usually applies to either xerogels
such. A gel is defined as dried when the physically
adsorbed water is completely evacuated. This occurs
between 100 and 180 "C.
The surface area of dried gels made by method 3 is
very large P400 m2/g),and the average pore radius is
very small (<IOnm). Larger pore radii can be Produced
by thermal treatment,220by chemical washing during
pore radii can lead to large capillary pressures (eq 1)
OH OH
I Ior alcogels, whereas aerogels are usually designated as HO-Si<-Si-OH + H,O (3)
AH AH
Linkage of additional =Si-OH tetrahedra occurs as
a polycondensation reaction (eq 4) and eventually re-
sults in a Si02network. The H20and alcohol expelled
from the reaction remains in the pores of the network.
HO-Si-O-Si --OH + 6 W W 4 +
I
OH OH
dH AH
aging,237or by additions of HF to the The small I I
during drying or when the dried gel is exposed to liquids
as described by Laplace's equation, discussed by Zar- OHHO
I
HO-Si-OH HO-Si-OH
zycki,81and developed extensively by S ~ h e r e r ~ ~ , * ~ - ~for
the drying of gels: I I
Ap = 2y(cos 0)/r (1)
where Ap = the pressure difference in the capillaries,
y = specificsurface energy of the vapor-liquid interface,
0 = contact angle, and r = pore radius.
A dried gel still contains a very large concentration
of chemisorbed hydroxyls on the surface of the pores.
Thermal treatment in the range 500-800 "C desorbs the
hydroxyls and thereby decreases the contact angle and
the sensitivity of the gel to rehydration stresses, re-
sulting in a stabilized gel.
Heat treatment of a gel at elevated temperatures
substantially reduces the number of pores and their
connectivity due to viscous-phase sintering. This is
termed densification. The density of the monolith in-
creases and the volume fraction of porosity decreases
during sintering. The porous gel is transformed to a
dense glass when all pores are eliminated. Densification
is complete at 1250-1500 "C for gels made by method
1 and as low as 1000"C for gels made by method 3.299
The densification temperature decreases as the pore
radius decreases and surface area of the gels increases,
as illustrated in Figure 3. Silica glass made by den-
sification of porous silica gel is amorphous and nearly
equivalent in structure and density to vitreous silica
made by fusing quartz crystals or sintering of Si02
HO o
I I
0 OH
1 I
HO-Si-O-Si~-Si-O-Si<H + 6(H20) (4)
HA d A AH
HO-&-OH HO-Li-OH
HA AH
The hydrolysis and polycondensation reactions ini-
tiate at numerous sites within the TMOS + H20solu-
tion as mixing occurs. When sufficient interconnected
Si-0-Si bonds are formed in a region, they respond
cooperatively as colloidal (submicrometer)particles or
a sol. The size of the sol particles and the cross-linking
within the particles (i.e.,density) depend upon the pH
and R ratio (R= [H,O]/[Si(OR),]) among other vari-
ables discussed in a later section.
Step 2: Casting. Since the sol is a low-viscosity liq-
uid, it can be cast into a mold. The mold must be
selected to avoid adhesion of the gel.
Step 3: Gelation. With time the colloidal particles
and condensed silica species link together to become a
three-dimensional network. The physical characteris-
tics of the gel network depend greatly upon the size of
particles and extent of cross-linking prior to gelation.
At gelation, the viscosity increases sharply, and a solid
object results in the shape of the mold. With appro-
The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, NO. 1 37
priate control of the time-dependent change of viscosity
of the sol, fibers can be pulled or spun as gelation oc-
curs.
Step 4: Aging. Aging of a gel, also called syneresis,
involves maintaining the cast object for a period of time,
hours to days, completely immersed in liquid. During
aging, polycondensation continues along with localized
solution and reprecipitation of the gel network, which
increases the thickness of interparticle necks and de-
creases the porosity. The strength of the gel thereby
increases with aging. An aged gel must develop suffi-
cient strength to resist cracking during drying.
Step 5: Drying. During drying the liquid is removed
from the interconnected pore network. Large capillary
stresses can develop during drying when the pores are
small (e20nm). These stresses will cause the gels to
crack catastrophically unless the drying process is
controlled by decreasing the liquid surface energy by
addition of surfactants or elimination of very small
pores (method l),by hypercritical evaporation, which
avoids the solid-liquid interface (method 2),or by ob-
taining monodisperse pore sizes by controlling the rates
of hydrolysis and condensation (method 3).
After hypercritical drying (method 1)the aerogel has
a very low density and is a very good thermal insulation
when sandwiched between glass plates and eva~uated.5~
Step 6: Dehydration or Chemical Stabilization. The
removal of surface silanol (Si-OH) bonds from the pore
network results in a chemically stable ultraporous solid.
Porous gel-silica made in this manner by method 3 is
optically transparent with interconnected porosity and
has sufficient strength to be used as unique optical
components when impregnated with optically active
polymers such as fluors, wavelength shifters, dyes, or
nonlinear p o l y m e r ~ . ~ ~ t ~ ~
Step 7: Densification. Heating the porous gel at high
temperatures causes densification to occur. The pores
are eliminated, and the density ultimately becomes
equivalent to fused quartz or fused silica. The densi-
fication temperature depends considerably on the di-
mensions of the pore network, the connectivity of the
pores, and surface area, as illustrated in Figure 3.89
Alkoxide gels (method 3) have been densified as low as
1000 "C by Klein and Garvey,2wwhereas gels made by
the commercial colloidal process developed by Shoupw
require 1500-1720 OC. However, colloidal silica gels
with very carefully controlled dense packing can also
be densified at low temperatures of 1000"C, as shown
by Sacks and T ~ e n g . ~ ' ~ ~ ~The purity and homogeneity
of dense gel-silica made by method 3 are superior to
other silica glass processing methods. The ability to
produce optics with nearly theoretical limits of optical
transmission, lower coefficients of thermal expansion,
and greater homogeneity, along with net shape casting,
represents major advances resulting from sol-gel pro-
cessing of monolith^.^^^^^
Details of these seven sol-gel processing steps follow.
The emphasis is on sol-gel-derived silica monoliths
made by the alkoxide process (method 3) processed
under ambient pressures.
I I I. Hydrolysis and Polycondensation
As shown in Figure 3 the structure of a gel is estab-
lished at the time of gelation. Subsequent processes
such as aging, drying, stabilization, and densification
all depend upon the gel structure. Since it is the rela-
tive rates of hydrolysis (eq 2) and condensation (eq 3)
that determine the structure of the gel, it is essential
to understand the kinetics of the hydrolysis and con-
densation reactions and the ratio of their rate constants
As discussed by Orcel et a1.,93-95Hench and Orce1,96
Klemperer et al,,w*98Scherer and Brinker,70and Artaki
et al.,%many factors influence the kinetics of hydrolysis
and condensation, and the systems are considerably
more complex than represented by the simplified eqs
2-4. Many species are present in the solution, and
furthermore, hydrolysis and polycondensation occur
simultaneously. The variables of major importance are
temperature, nature and concentration of electrolyte
(acid, base), nature of the solvent, and type of alkoxide
precursor. Pressure influencesthe gelation process also;
kH increases with pressure as shown by Artaki et
a1.,100-102but pressure is usually not a processing vari-
able.
There are relatively few studies of the dependence
of kH and kc on independent processing variables. In
fact many studies have reported the variation of the
gelation time, viscosity, or textural characteristics (e.g.,
specific surface area) of the gel as a function of exper-
imental conditions without determining kH or kc.102-107
However, several investigations do provide a scientific
foundation for understanding the processing depen-
dence of kH and kc.
Aelion's study of the influence of electrolyte concen-
tration on the hydrolysis of TEOS in different solvents
showed that kHincreases linearly with the concentration
of H+ or H30+ in acidic media and with the concen-
tration of OH- in basic medium.lo3 The reaction rate
varies from 4.12 X lo4 L mo1-ls-l for a 0.063 mol L-l
HC1 solution. This corresponds to a rate constant per
unit concentration of electrolyte of 0.091 mol L-l s-'
[H+]-l. Similar values are observed in basic media
where the rate constant is about 0.040 L mol-' s-l
[OH]-'. There is a variation in the concentration of
TEOS of 0.2mol L-l for the basic conditions versus 0.6
mol L-' for the acid-catalyzed sol. The increase in
[TEOS] can account for the increase in rate constant.
As discussed by OrceP the nature of the solvent
(dioxane,methanol, or ethanol) has a "secondary" effect
on kH,as well as the temperature dependence of the
reaction (10-fold increase when the temperature varies
from 20 to 45.5 "C). NMR experiments by Artaki,
Zerda, and Jonas'OO show that kH varies in the different
solvents as follows: acetonitrile > methanol > di-
methylformamide > dioxane > formamide, with kH-
(acetonitrile) being about 20 times larger than ItH(for-
mamide).
An increase of the R ratio (moles of water/moles of
TEOS) from 1.86 to 3.72 induces kH to increase from
0.042 to 0.059 L mol-' s-l [acid]-l.lo3 However, Schmidt
et al.lo4found that the hydrolysis rate decreases when
the R ratio increases from 0.5 to 2. Schmidt attributes
this to the "special experimental conditions and the
water acting as a proton acceptor which decreases the
proton activity".lo5
The nature of the alkoxy groups on the silicon atom
also influences the rate constant. As a general rule, the
longer and the bulkier the alkoxide group, the slower
the rate constant.105J08J09For example, in the case of
(kH/kC) *
38 Chemical Reviews, 1990, Vol. 90, No. 1
the hydrolysis of kH = 51 X L mol-l s-l
[H+]-' for R = C2H5and kH = 3 X 10" L mo1-ls-l [H+]-'
for R = (CH3)2CH(CH2)3CH(CH3)CH2.
From these results it is apparent that the dominant
factor in controlling the hydrolysis rate is the electrolyte
con~entration.~~However,the nature of the acid plays
an important role. As outlined above, a minute addition
of HCl induced a 1500-fold increase of kH. However,
Aleion reported "hydrolysis in glacial acetic acid as
solvent is not particularly fast".lo3
Although these have been called "secondary" effectslo3
and they are very small compared to those induced by
addition of electrolyte, they are relatively important
(e.g., the 10-fold increase of kH with a variation of the
processing temperature of 25.5 "C) and might be re-
sponsible for numerous observations in systems inves-
tigated in other works. For example,a systematic study
of Mackenzie shows that the type of acid catalyst and
nature of solvent have a large effect on TEOS gela-
tion.l1°
Although the polycondensation of silicic acids has
been studied extensively, as reviewed by Iler15376there
are little data on the rate constant of the condensation
reaction.93 A value of kc = 3.3 X lo+ L molW1s-l has
been reported by Artaki et al. for the dimerization of
monosilicic acid.lo2 However, no value of kHis available
for the same system. Artaki et al. showed that appli-
cation of a pressure of 5 kbar to the system increased
the polycondensation rate constant by a factor 10.'O2
There are many problems associated with the com-
putation of reaction rate constants and especially the
determination of the mechanisms of the reactions as
well as the order of the reactions with respect to the
constituents, as discussed by Schmidt et al.lo5 When
the order of the reaction varies with time, such as in
Uhlmann et al.'s experiments, determining the rate
constant becomes even more difficult.lW For short
periods of time, the order of the reaction can be con-
sidered constant. However, one must keep in mind that
there are several hydrolysis and condensation reactions
possible, each having its own rate c~nstant.~~~J''Con-
sequently,assumptions are necessary to allow the com-
putation of kHand kc, which limits the characterization
of the reactions to the early stages of the process.
Because of the above limitations, early studies of the
influence of the experimental factors on the sol-gel
process were primarily phenomenological, without
specific values of the ratio kH/kcbeing determined for
a single system. This situation has changed dramati-
cally in the past few years. Many investigators have
pursued the kinetics of silicon alkoxide hydrolysis using
29SiNMR. It is one of the most useful techniques to
follow the hydrolysis and first-stage polymerization of
silicon alkoxide, because it allows the determination of
the concentration of the different Si(Or),(OH), and
(OH),(OR),Si-0-Si(OR)x(OH),species. Each of the
monomer and dimer species has a specific chemical shift
with respect to the metal alkoxide.'12
employed 29SiNMR as early as
1977to investigate the condensationof aqueous silicates
at high pH. Their results indicate that a typical se-
quence of condensation products is monomer, dimer,
linear trimer, cyclic trimer, cyclic tetramer, and a higher
order generation of discrete colloidal particles which are
commonly observed in aqueous systems. This sequence
Engelhardt et
Hench and West
Figure 4. Variation of the concentration of M1 (Si(OH)(OCH,),)
and D1 ((OCH3),Si-O-Si(0CH3),) as a function of time for the
different solution^.^^
of condensation requires both depolymerization (ring
opening) and availability of monomers (species that
may be produced by depolymerization). However, in
alcoholic solutions especially at low pH the depolym-
erization rate is very low. Iler15speculates that under
conditions where depolymerization is least likely to
occur, so that the condensation is irreversible and si-
loxane bonds cannot be hydrolyzed once they are
formed, the condensation process may resemble clas-
sical polycondensation of polyfunctional organic mo-
nomers resulting in a three-dimensional molecular
network. Owing to the insolubility of silica under these
conditions, the condensation polymer of a siloxane
chain cannot undergo rearrangement into particles. In
sol-gel systems commonly employed for glass prepara-
tion, the water/alcohol ratio and pH are widely varied.
Thus the importance of the reverse reactions depends
on processing conditions, and it is anticipated that
condensation may result in a spectrum of structures
ranging from molecular networks to colloidal particles.
Yoldas114concluded that the hydrolysis reaction and
the condensation reaction are not separated in time but
take place simultaneously. It has been well established
that the presence of H30+in the solution increases the
rate of the hydrolysis reaction, whereas OH- ions in-
crease the condensation reaction.'15
Orcel et al.9*953116 explored the effect of acid catalysis
and formamide (a drying control chemical additive) on
the hydrolysis and polycondensation rates of a TMOS
silica system, using 29SiNMR. By plotting the variation
of the concentration of the species of interest from the
NMR data as a function of time (Figure 4),one can
obtain the rate constants for hydrolysis ( k H ) and poly-
condensation (k,) of the Si alkoxide, in this case TMOS.
Even though the assumptions involved in the com-
putation of the rate constants are crude, such as first-
order kinetics and no influence of the degree of sub-
stitution of Si atoms on the reaction rates, the order of
magnitude of kH and kc, Table I, demonstrates im-
The Sol-Gel Process
I / f d
d
Chemical Reviews, 1990, Vol. 90, No. 1 39
TABLE I. Physicochemical Characteristics of the
Different Gel Solutions
sample SW 55 SF 25 SF 50 SF 23
vol formamide/vol formamide + 0 25 50 25
MeOH
D1 D1 D1 p H = 3
12 I 2 25
H20
103kH,L mol" h-I
kc, L mol-' h'' 29 31 25 6
d, nm 2 2.2 2.5
portant differences. These data show that acid catalysis
increases the hydrolysis rate constant, kH,by a factor
of 2. The data also show that formamide decreases the
hydrolysis rate and slightly increases the condensation
rate. This can be attributed to the ability of HCONH2
to form hydrogen bonds and to its high dielectric con-
stant ( E = 110).ll6 The presence of formamide also
decreases the time of gelation (tg).Additional details
regarding the use of formamide and other drying control
chemical agents (DCCAs) are discussed in refs 93 and
117.
The studies of Klemperer and colleagues97~98provide
some of the most detailed evaluation of the extent of
hydrolysis and condensation of silica prior to the onset
of gelation. To identify the polysilicate intermediates
formed during sol-gel processing, Klemperer et al.97
used a protocol that combined quenching by diazo-
methane, fractionation using spinning band column
distillation, identification by capillary gas chromatog-
raphy, and structural characterization using 29Si(1Hj
NMR techniques (one-pulse, 1D-INADEQUATE, and 2D-
INADEQUATE) to provide structural assignments and
response factors for the components separated by gas
chromatography. Theyg8 showed that under acidic
conditions the polysilicate molecular size distributions,
expressed in terms of mole percent of total silicon
present as a function of degree of polymerization, ex-
hibit maxima near the number-average degree of po-
lymerization. There are mostly linear structures under
acidic conditions. In contrast, under basic conditions
the maximum of the distribution is at the monomer
percent and extends to very high molecular weights.
Thus, the distribution of polysilicate species is very
much broader for basic conditions of hydrolysis and
condensation, characteristic of branched polymers with
a high degree of cross-linking, whereas for acidic con-
ditions Klemperer et aLgsconclude that there is a low
degree of cross-linking due to steric crowding.
Raman spectroscopy is one means of assessing
qualitatively the size of particles or scale of struc-
ture1l8Jl9when gelation occurs. Since the Raman in-
tensity is proportional to the concentration of scatterers,
sols and gels prepared with different experimental
conditions can be compared by using a proper internal
standard. In the study of the Si02-formamide system,
methanol was used for calibration.9H5 According to the
NMR data, the concentration of CH30H is constant
after 0.7t at 23 "C, and the solvent is significantly
expelled hom the gel after -6tg. Thus the calibrated
Raman intensities are valid in the time frame 0.7tg-6t,.
Results for several gel solutions, with and without
formamide, under basic and acidic conditions, are given
in Figure Lg6These curves demonstrate that when
formamide is present, i.e., samples SF 50 and SF 25,
larger particles are formed at the gelation point. This
is in good agreement with the NMR result^.^^-^^ Since
formamide decreases the hydrolysis rate, fewer sites are
3001 . I - , , 1
a
Reduced time (t/tql
Figure 5. Variation with time of the relative Raman intensity
of the 830-cm-' band of the various gel solutions.%
available for condensation and larger particles are
formed in the so1.93J17
The reaction of silica colloids with molybdic acid, a
technique widely used for the characterization of soluble
silicates,120can also be used to assess the size of particles
developed in the sol. Si02particles depolymerize in an
acidic medium, and the monosilicic acid thus formed
gives a yellow complex with Mo,which can be measured
optically. A plot of the absorbance as a function of time
allows the computation of the depolymerization rate
constant, kD,as a function of time.93p96For example,
the values of kD at 0.5tg for several SO2-formamide
solutions can be used to calculate the particle diameter.
Ultimately, kD can be related to the particle diameter
d through an empirical law:
(5)
where a and b are constants (see Iler120)depending on
experimental conditions, mainly solution pH. Since the
solution pH of samples 55, 25, and 50 are nearly
equivalent, it is possible to compare relative particle
sizes by using eq 5 and assuming the values for a and
b from Iler.120 (Note: This is only an approximation
since Iler's values are based on a pH = 2, SiOpsolution.)
The calculated values at the gelation point, shown in
Table I, increase with increasing formamide concen-
tration.
It has been shown93194that the calibrated Raman in-
tensity I R is inversely proportional to kD Thus, I R can
be related to the sol particle size as
I R = Adlfb (6)
where A is a function independent of d. For the con-
ditions described by Iler" l / b = 3.48. The theoretical
basis for this value is developed in refs 93 and 94.
By use of l / b and the values of d (eq 5) calculated
from the Mo test, it is possible to compute an empirical
value of 6.8 for A in eq 6. By use of eq 6 and the
measured values of Raman intensity (Figure 5), the
time-dependent change in sol particle size can be cal-
culated. The results are shown in Figure 5 on the
right-hand particle-size axis. By the time of gelation,
the size of the sol particles grows to 2 nm without
formamide, and with 50% formamide they grow to 2.5
nm.
These findings are similar to those of Klemperer et
a1.97998in their studies of the effects of base vs acid
log d = a + b log kD
40 Chemical Reviews, 1990, Vol. 90, No. 1 Hench and West
TABLE 11. Chemical Characteristics of the TMOS
Solutions (from Ref 94)
loT3kH, vol fract CH30H gelation
soln mol h mol h in solv, 90 time, h
I 2 >32 50 6
I1 12 29 100 40
catalysis on the size of polysilicate species prior to the
onset of gelation.
Thus, Orcel et al.'s studiesg4show that the shape and
size of polymeric structural units are determined by the
relative values of the rate constants for hydrolysis and
polycondensation reactions (kH and kc, respectively).
Fast hydrolysis and slow condensation favor formation
of linear polymers; on the other hand, slow hydrolysis
and fast condensationresult in larger, bulkier, and more
ramified polymers.lMAs illustrated by the values of kH
and kc reported in Table 11,larger particles are antic-
ipated for solution 1(higher volume fraction CH30H
in the solvent), which implies a lower value for the
depolymerization rate constant: kI < hII.
By combination of these various analytical methods,
the particle diameter (PD) of the silica particles in the
sol at the different steps of the sol-gel process can be
estimated. The r e ~ u l t s ~ J ~ ~are given in Table 111,and
it is possible to conclude that the particles are about
20 A in diameter at the gelation point and larger par-
ticles are formed when formamide is present in the
solution, as discussed in the next section on gelation.
IV. Gelaflon
The gelation point of any system, including sol-gel
silica, is easy to observe qualitatively and easy to define
in abstract terms but extremely difficult to measure
analytically. As the sol particles grow and collide,
condensation occurs and macroparticles form. The sol
becomes a gel when it can support a stress elastically.
This is typically defined as the gelation point or gelation
time, tgel. There is not an activation energy that can
be measured, nor can one precisely define the point
where the sol changes from a viscous fluid to an elastic
gel. The change is gradual as more and more particles
become interconnected. All subsequent stages of pro-
cessing depend on the initial structure of the wet gel
formed in the reaction bath during gelation.
Brinker and SchererlZ1point out that the sharp in-
crease in viscosity that accompaniesgelation essentially
freezes in a particular polymer structure at the gel point.
At this point gelation may be considered a rapid soli-
dification process. This "frozen-in'' structure may
change appreciably with time, depending on the tem-
perature, solvent, and pH conditions or upon removal
of solvent.
A. Gelation Time
A number of investigators have shown that the time
of gelation changes significantly with the sol-gel chem-
10000
n20moa MOLL RATIO: 2 0
HN0,fTEOS MOLL RATIO: 0.01
0 SO 100 110 200 2 8 0 300
t I
SO 100 150 200 250 300
0.1
TIME lhrl
Figure 6. Loss tangent as a measureof gelation time (Sacksand
Sheu, 1986). (A) Plots of storage modulus and loss modulus vs
aging time for sol 1. (B) Plot of loss tangent vs aging time for
sol 1.
istry.15~95~117~122~1z3One of the most precise methods to
measure tgelwas developed by Sacks and Sheu.lZ4This
method measures the viscoelastic response of the gel as
a function of shear rate.
They measured the complex shear modulus, G, by
using a viscometer with a narrow gap. This ensures a
well-defined shear rate as the cylinder in the sol os-
cillates at a frequency w and a small amplitude y. The
complex shear modulus has the form
G = G'(w) + iG"(w) (7)
where G' = storage modulus and G" = loss modulus.
The storage modulus arises from the elastic component
of the sol-gel, while the loss modulus comes from the
viscous component.
The relative measure of the viscous energy losses to
the energy stored in the system is usually defined as the
loss tangent:
tan 6 = G"/G' (8)
Figure 6 shows the large change in the loss tangent
at the gelation time along with the changes in G rand
G"from Sacks and Sheu.lZ4The rapid increase in the
storage modulus near tgelis consistent with the concept
that the interconnection of the particles becomes suf-
TABLE 111. Structural and Textural Properties of the Gels (from Orcel et a1.Ls6)n
property PD, A PR, A PV, cm3/g SA, m2/g D1, 8, D2, 8, 4. -
soln I (with DCCA) 24 30 1.19 784 59 24 2.29
soln I1 (no DCCA) 20 12 0.356 607 58 20 2.25
"PD,particle diameter (Mo test); PR, pore radius; PV, pore volume; SA, specific surface area; D1,Guinier radius at gelation point; D2,
Guinier radius on film heated at 200 "C; df, fractal dimension at gelation point.
The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, No. 1 41
presence of HF, and in about 0.3 h at 70 OC.llo
Although it is important to know how t, varies with
various experimental parameters, the knowledge thus
developed is empirical and qualitative, and a better
description of the system is needed in order to optimize
the process.
B. Viscosity of the Sol-Gel System
The sol-gel process has the unique advantage of al-
lowing the preparation of the same composition, such
as silica, in markedly different physical forms, fibers,
coatings, monoliths, just by varying a few experimental
conditions. As reviewed by O r ~ e l , ~ ~the processing pa-
rameter that must be controlled is the viscosity of the
sol-gel system. For example, the casting density of a
sol was shown by Klein and Garvey to be the deter-
minant in the manufacture of monoliths (between1and
1.2 g/cm3 for acid-catalyzed TEOS).'29 Several inves-
tigators have shown that fibers can be drawn from a sol
only for a range of viscosity that is greater than 1Pa
s.73,75J3e133Coatings can be applied with the most ef-
ficiency when the concentration of oxides is within
certain limits (several tens of grams of oxide per liter)
which fix the v i s c o ~ i t y . ~ ~ J ~ ~ - ~ ~ ~Controlling these pro-
cesses requires understanding the rheological properties
of the sol-gel system. However, there are few quanti-
tative studies relating gelation to rheological variables.'%
Some attempts have been used to define the point of
gelation by associating gel formation with a sudden
increase of the viscosity or reaching a maximum of
The viscosity of a solution undergoing hydrolysis and
polycondensation is time dependent and is related to
the size of the particles. The larger the molecules, the
higher the viscosity. Thus, any variation of the pro-
cessing parameters that induces an increase of the ap-
parent size of the particles increases the viscosity. For
example, acid-catalyzed silica sol-gel samples have a
higher viscosity than neutral or base-catalyzed solu-
The effect of the concentration of water on viscosity
is more complex. OrceP reviews the general behavior
as follows: at low water content, an increase of the
amount of H20 increases viscosity, which reaches a
maximum and then decreases for a further increase of
the concentration of water.'42 A similar effect is ob-
tained by varying the concentration of silicon alk-
Sacks and Sheu's rheological studies124show that a
silica sol prepared with the alkoxide process goes from
a Newtonian behavior to shear thinning and, finally,
thixotropy, which is especially useful in describing the
sol-gel transition. Furthermore, they dem~nstrated'~~
that spinnability is possible only when the solution is
shear thinning or slightly thixotropic.
C. Sol Structure
The rheological data summarized in the preceding
section demonstrate that there is a major evolution of
structure during the sol-gel transition. The system
evolves from a sol, where there are individual particles
more or less weakly interacting with each other, to a gel,
which basically becomes a continuous molecule occu-
pying the entire volume. Consequently, it is important
to characterize the evolution of the structure of the sol
visCosity.l30,132,'40,141
tions.130,142
oxide.143,144
GELATION TIME
7 1
1 I
0 5 10 15 20 25
R
Figure 7. Variation of the gelation time with the R ratio.'%
ficient to support a load elastically.
There is at least one indication that gelation time (t,)
is not an intrinsic property of the sol: t, depends on
the size of the container. Furthermore, gelation may
occur at different extents of reaction completion. For
example, in the case of the polymerization of TMOS,
more silicon alkoxide must be hydrolyzed when the
experimental conditions favor a ramified polymer rather
than a linear one.
The dependence of t, on solution pH has not been
fully determined, but it appears from the work of Ya-
mane et al. that the curve t vs pH has a bell shape.'25
In other words, gelation canbe nearly instantaneous for
very acidic or basic solutions of metal alkoxides. This
behavior is very different from the gels prepared by
destabilization of a silica sol where the curve has a S
shape with the maximum around the isoelectric point
of silica (pH - 2) and a minimum near pH 5-6.15
However, it should be noted that two solutions with the
same pH may have different gelation times, depending
on the nature of the counterion, all other parameters
being equal. The anion and solvent also play a role in
the kinetics of gelation,"O and gelation can be either
acid or base c a t a l y ~ e d . ~ ~ J ~ ~ J ~ ~
It is difficult to separate the effect of the alkoxy group
from the effect of the solvent since gelation kinetics
depends on the quantity of the solvent concentration.
However, the trend is the longer and the larger the
solvent molecule, the longer the gelation time. Simi-
larly, Mackenzie has shown that the longer and the
larger is the alkoxy group, the longer is t,.ll0
The amount of water for hydrolysis has a dramatic
influence on gelation time (Figure 7) from Colby et al.'%
For a R ratio (molesof water/moles of silicon alkoxide)
of 2, t, is about 7 h (gelation process at 70 "C with HF
as catalyst) and decreases to 10min for R = 8.128For
low water contents, generally an increase of the amount
of hydrolysis water decreases the gelation time, al-
though there is a dilution effect. It can be predictedg3
that for higher water contents, the gelation time in-
creases with the quantity of water. The location of the
minimum in the curve t, vs R, such as shown in Figure
7, depends on the experimental conditions, such as
nature of the chemicals, catalyst, and temperature.
Polymerization reactions are usually thermally acti-
vated, and this is observed for the hydrolysis and po-
lycondensation of solutions of silicon alkoxides. For
example, Mackenzie has shown that a molar solution
of TEOS in methanol gels in 49 h at 4 "C, in the
42 Chemical Reviews, 1990, Vol. 90, No. 1
sw 55
Hench and West
I.75I- 0.40
-2.01 I I 1 I t 1 I I
-5 0 -2.25 -1.5 -0.75 0
Loo h
Figure 8. Variation with time of log I(h)vs log h curves for a
SW55 sample (no f ~ r m a m i d e ) . ' ~ ~
during the gelation process.
Only a few techniques are available to follow struc-
tural evolution at the nanometer scale of sol-gels. They
include small-angle X-ray scattering (SAXS),neutron
scattering, and light scattering, each of them giving
complementary information, and transmission electron
microscopy. Small-angle X-ray scattering allows the
determination of a characteristic length of the particle
(Guinier's radius of gyration, or electronic radius of
gyration)145-147 and a fractal dimension, which gives
some information on the structure of the polymer
(branched vs linear) and on the growth mechani~m.'~~
The application of SAXS to a number of gel systems
has been reported by various a ~ t h o r s . ~ ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~
Small-angle neutron scattering (SANS) has also been
applied to the study of silica ~ 0 l s . l ~ ~Results similar to
those from SAXS are obtained, but further develop-
ments of the SANS technique may produce additional
insight to the sol-gel process.158
Light scattering has been used for a long time to
characterize macromolecular solutions. Although this
technique should be useful in following the sol-gel
transition, it has received very little attention in the
sol-gel literature. However, the characteristic dimen-
sion probed by visible light scattering is >10 nm, and
therefore it cannot be used to characterize the early
stages of the gelation process.149Recent development
of short-wavelength UV lasers may make it possible to
extend light-scattering studies to the range of 3 nm and
thereby could follow most of the gelation process.
The major conclusion of the various scattering studies
is that acid-catalyzed sols develop a linear structure
with very little branching. In contrast, base-catalyzed
systems are characterized by highly ramified struc-
tures.150,?51
Figure 8 is a Porod plot showing SAXS scattering
curves typical of a sol prepared by hydrolyzing
TMOS.93J56The log of the scattering intensity, I, is
plotted as a function of the scattering factor h. The
scattering factor is defined as h = (4r/X) sin (8/2). As
time increases from the sol stage (t/t,= 0.11) toward
gelation (t/t,= 1.00),there is an increase in the size of
X-ray scatterers. However, after a critical time ( t / t ,
Figure 9. 2 = 3; N = total number of bond sites = 43; n = total
number of node bonds = 81: P = 0.7.
= 0.28) no new scattering centers are formed. When
formamide is present, the critical reduced time for
formation of scattering centers is longer.93 The fractal
nature of the network formed can be calculated from
the slope of the Porod plot and is discussed in a later
section, as are additional SAXS investigations.
D. Classical or Mean-Field Theory of Gelation
The classical or mean-field theory of polymerization
was developed by F10ry.~~The basis structure of this
model looks like a tree and is called a Cayley tree or
Bethe lattice. Figure 9 shows a Cayley tree model for
a polymer that forms a connected, gel-forming cluster
without forming rings. In this tree, the functionality
or maximum number of bonds, z, that are allowed to
form at each numbered bond site is
2 = 3
Other polymers have different values for this parameter.
For example, silicic acid has a functionality of z = 4.
Four bonds may form at every site where silicon is
present.
Returning to our model with z = 3, we can define the
probability, P, of a bond forming at each site:
(9)
P = n/(Nz) (10)
number of bonds
total number of node bonds
p =
where n = number of node bonds, N = number of sites,
and z = dimensionality of the polymer. Thus, in our
simple example, shown in Figure 9
N = 43; z = 3; n = 81 (11)
This means that some bonds are counted twice. The
number of connections for each numbered node is
counted. For example (a) node 34 has one bond, (b)
node 27 has two bonds, and (c) node 1has three bonds.
Therefore, the probability for a connection for each site
in this example is
P = n/(Nz); P = 81/[(43)(3)]; P = 0.6 (12)
This example forms a gel, as we have conceptually
defined it, since the cluster is continuously connected
from one side to the other. Thus, there must be at least
two connections per node for the cluster to be a gel.
This defines the critical probability, P,, for gel forma-
tion to be
P, = 1/2 (13)
(14)
or in terms of the functionality of the polymer324
P, = l / ( z - 1)
The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, No. 1 43
a Figure 11. Bond percolation model.
b
Figure 10. Site percolation model: (a) empty grid; (b)Raman
filling of grid.
This defines then the degree of reaction at the gel
point. The distribution of molecular weights can also
be determined. However, there is a fatal flaw in this
model. Because no rings are allowed, there is an in-
creasing number of nodes as the radius of the cluster
increases.
In fact, the mass of this type of cluster increases as
the fourth power of the radius as shown by Zimm and
St~ckmayer'~~and de Gennes." In real materials the
mass must increase linearly with volume as the third
power of the radius.
However, this model is still useful in visualizing the
gelation of silica sol-gels. It yields a degree of reaction
of one-third:
P, = l / ( ~- 1) = 1/3 (15)
at the time of gelation. That means that two-thirds of
the connections are still available and play a role in
subsequent processing. This value is lower than the
experimental evidence as we shall see in the next sec-
tion. It does however represent the minimum degree
of reaction before gelation can occur as presented by
F 1 0 r y . ~ ~ ~
E. Percolation Theory
Percolation theory and its relationship to gelation has
been reviewed by ZallenlG1and Stauffer et Per-
colation allows for rings or closed loops to form, and
thus the mass of percolation models increases with the
cube of the radius.
Figure 10shows a simple percolation model. Starting
with an empty grid (Figure loa),intersections are ran-
domly filled with particles (filled circles). If two circles
or particles are adjacent, then bonding will occur
(Figure lob). Loops of various sizes may form as the
structure expands. This eliminates the fatal error of
the classical model and is called a site percolation
model.
In a manner similar to the classical model, the
probability, P, that a site may be filled is defined as
P = n / N (16)
where n = number of filled sites and N = total number
of sites.
With the simple example in Figure 10
n = 32 (17)
N = 64 (18)
P = 1/2 (19)
Thus
This simple model shows that for this value of site
filling, complete connectivity or gelation is unlikely for
the site model. Experimental results indicate that
0.6 C P, I0.84 (20)
for silica sol-gel systems, as reviewed by Zarzycki.81
Thus, this model must be modified to increase the
connectivity.
By starting with all the sites filled and randomly
adding bonds, the connectivity increases over the site
model. Figure 11 shows a bond percolation model.
Again we can define the probability of bonding as
P = n / N (21)
where n = number of bonds and N = total number of
bond sites.
In the case of the example in Figure 11we have
n = 39 (22)
N = 112 (23)
P = 0.35 (24)
where gelation appears likely.
The bond percolation model is dependent on the
lattice. Table IV shows a summary of the percolation
threshold for various lattices based on Brinker and
Scherer.'O The table also shows the volume fraction,
&, of the gel at gelation and the filling factor, u.
F. Fractal Theory
The fractal model of structures was designated as
such by M a n d e l b r ~ t l ~ ~and gives order to the many
seemingly random patterns generated by nature, such
44 Chemical Reviews, 1990, Vol. 90, No. 1 Hench and West
TABLE IV. Percolation Threshold for Various Lattices (from Brinker and Scherer'O)
dimensionality d latticea coordination z 1/(z - 1) Pc pesite filling factor u @c = up,Bibbond
I chain 2 1 1 1 1 1
1 triangular 6 0.200 0.347 0.500 0.907 0.45
2 square 4 0.333 0.500 0.593 0.785 0.47
2 kagom6 4 0.333 0.45 0.653 0.680 0.44
2 honeycomb 3 0.500 0.653 0.698 0.605 0.42
3 fcc 12 0.091 0.119 0.198 0.741 0.147
:i bcc 8 0.143 0.179 0.245 0.680 0.167
3 SC 6 0.200 0.247 0.311 0.524 0.163
3 diamond 4 0.333 0.388 0.428 0.340 0.146
:i repb -8 -0.143 -0.27 -0.637 -0.16
4 sc 8 0.143 0.160 0.197 0.308 0.061
4 fcc 24 0.043 0.098 0.617 0.060
2 SC 10 0.111 0.118 0.141 0.165 0.023
7 fcc 40 0.026 0.054 0.465 0.025
6 SC 12 0.091 0.094 0.107 0.081 0.009
fcc = face-centered cubic; bcc = body-centered cubic; sc = simple cubic; rep = random closed-packed. bLessprecise values, determined
experimentally.
tCL
xU
ul
c
a
.-
n
\ F r a i t a i
Size, R -Figure 12. Density of fractal objects.
as trees,163galaxies,164or the surface of the sun.165
Witten and S a r ~ d e r l ~ J ~ ~and Witten and Cates168have
demonstrated the fractal nature of diffusion-limited
aggregation of particles. Growth processes that are
apparently disordered also form fractal objects.168
Sol-gel particle growth has also been modeled by using
fractal c o n c e p t ~ . ~ ~ J ~ ~ J ~ ~
The nature of fractals requires that they be invariant
with scale. This is a symmetry that requires the fractal
to look similar no matter what level of detail is chosen.
For example, a tree as a whole has a very similar
structure as a small branch within that tree.
The second requirement for mass fractals is that their
density decreases with size (see Figure 12). Thus, the
fractal model overcomes the problem of increasing
density of the classical model yet retains many of its
desirable features.
Fractal objects are quantified by their fractal di-
mension, df. Figure 13 shows objects with increasing
fractal dimension.70 For linear-like structures
1 < d , < 2 (25)
(as shown in Figure 13B). Fractally rough structures
have a mass fractal dimension
2 < d , < 3 (26)
C.
't
0.
Figure 13. Fractal objects: (A) linear structures, 1< df < 1.5;
(B)fernlike structures, 1.5 <df<2; (C) fractally rough structures,
2 < df < 3; (D)solid structure, df = 3. Reprinted from ref 70;
copyright 1989 Academic Press.
TABLE V
Keefer's hydrolyzed monomer fractal dimension df
nonfractal 100% triple 3
fractal 33% double 1.8
33% triple
33% fully
fractal 50% double 1.67
50% fully
(as shown in Figure 13C). Finally, uniform nonfractal
objects have a fractal dimension
d f = 3 (27)
(as shown in Figure 13D). The mass of a fractal then
is related to the fractal dimension and its size or radius,
R, by
M a Rdi (28)
Therefore, computer models can be constructed to
generate particle growth and measure the resulting
fractal dimension.
One such fractal gelation model was developed by
Keefer.153He postulated that sol particles grow from
partially hydrolyzed TEOS (Si(OC,H,),). When fully
hydrolyzed TEOS was used in the model, a fully dense
particle was formed that had no fractal nature.
The Sol-Gel Process Chemical Reviews, 1990, Vol. 90,No. 1 45
42.5
h ( p l 1
Figure 14. Small angle X-ray scattering curves (slit smeared)
from 1 M solutions of Si(OC,H,), hydrolyzed with varying
amounts of H,O; 0.01 NHIOH was used as a catalyst. Reprinted
from ref 153; copyright 1986 John Wiley & Sons, Inc.
Table V shows selected models with varying degrees
of hydrolysis. This model yields values for dfsimilar
to those found experimentally through SAXS.
G. Small-Angle X-ray Scattering (SAXS)
Fractal particles with a radius of approximately 20
nm may be studied by SAXS. It can be shown (see ref
93 for a detailed review of this theory), that the scat-
tered intensity (0of X-rays for small angles is related
to the fractal dimension of the particle, df:
I(h) a h-df (29)
h = 4?r(sin a)/y (30)
where 2a = scattering angle and X = wavelength. Ad-
ditionally the monomer involved in the fractal particle
must be small:
R, >> h-' >> a (31)
where R, = radius of gyration and a = primary particle
radius.
The radius of gyration is basically the radius of the
scattering center derived from the number of scattering
centers, N , per unit volume, u.
This leads to the equation for the scattering intensity
known as Guinier's 1aw:145-147J69
I(h) = Npe2u2exp[-'/Rp2h2] (32)
where pe = electronic density.
Figure 14shows SAXS curves for various TEOS and
HzO sols with different R ratios, from Keefer's stud-
i e ~ . ' ~ ~As the water content increases, (increasing R),
the fractal dimension increases. That is, the particles
become more dense.
The primary particle of radius, a, is between 1and
2 nm as shown by Orcel et al.94and can be modeled by
rings and chains of three to four silica tetrahedra. The
secondary fractal particle has a radius, R,, of 5-20 nm
as seen from SAXS.lZ2
For the TMOS-based sols investigated by SAXS,
Figure 8 shown earlier, the fractal dimension, df, in-
2
a
0
-
"I, / , , , , , , , , 11.5
lo 0.1 0.3 0.5 0.7 0.9 1.1
REDUCED TIME ( t/tg)
Figure 15. Time evolution of electronic radius of gyration (Eo)
and fractal dimension (D)of a SW55 s01ution.l~~
---f---
6.0 nm
mFigure 16. Schematic representation of primary and secondary
particles in a TMOS-based alkoxide gel.
creases with time as does the Guinier radius (RJ. This
behavior is shown in Figure 15 based on the data of
Figure 8. The structure reaches a fractal dimension
around 2.3 at the gelation point. Table V summarizes
results of the structural and textural properties for two
TMOS +HzOsolutions, with and without formamide
as a DCCA.156
Near the gelation point the solsprepared from TMOS
and HzOare formed of particles of about 6.0-nm diam-
eter compared to scattering units of about 2.0-nm di-
ameter for the films.156 Dilution experiments showed
that the radius of gyration measured in the sols does
not vary with the quantity of s ~ l v e n t . ~ ~ J ~This result
indicates first that the Guinier approximation is valid
for these systems and second that the polymer is rela-
tively rigid.152 These measurements are in very good
agreement with the values obtained by the Mo acidic
test.93
These results suggest that the gel structure is formed
of different units, e.g., primary particles of about 2.0-nm
diameter that agglomerate in secondary particles of
about 6.0-nm diameter (Figure 16). On the basis of
geometric considerations, these secondary particles
contain at most 13primary particles. Gelation occurs
when the secondary particles are linked to each other,
forming a three-dimensional network across the sample.
Aggregation of particles carrying a surface charge can
be modeled by the classical Derjaguin-Landau-Ver-
wey-Overbeek (DLVO)theory."' This theory predicts
46 Chemical Reviews, 1990, Vol. 90,No. 1
that the activation barrier to aggregation increases
linearly with the size of two equal particles. Thus, the
rate of aggregation would decrease exponentially with
their size. Smaller particles however will aggregatewith
larger ones at a much higher rate. Thus, two distribu-
tions of particles are predicted, small newly formed
particles and large aggregating particles.325 This de-
scription of the structure of the sol and gel is confirmed
by another X-ray diffraction study by Himmel et al.170
They showed that gels manufactured from hydrolysis
and polycondensation of TEOS by a small amount of
acidic water are made of primary particles of about
1.0-nm diameter that associate in secondary chainlike
clusters. The size of these clusters can be approximated
as 6.0 nm in diameter, which is the average diameter
of the pores. Also, TEM experiments on silica particles
prepared by the Stober process171demonstrate that
nucleation and growth occur by a coagulative mecha-
nism, which supports the description of the gel structure
given above.
The analysis of the diffraction curves in the Porod
region leads to the computation of the fractal dimension
(df). The quantity is dependent on the shape and ge-
ometry of the diffraction centers and also indicates a
possible growth mechanism. Table I11 reports156the
value of the fractal dimension of the sols near the ge-
lation point. These values suggest a percolation cluster
(PC)or a diffusion-limited aggregation (DLA) mecha-
nism. Particles grow by addition of small polymeric
units to randomly added sites on a nucleus (PC) or
through a random walk to a seed cluster (DLA).152This
description is in good agreement with the observation
of a structure composed of agglomeration of units of
different sizes: secondary particles made of several
primary particles, which in turn agglomerate to form
a gel.
In conclusion,the Keefer fractal model yields a range
of fractal dimensions from 1.6to 2.4 depending on the
degree of hydrolysis. As the fractal dimension increases,
the pore radius of the resulting gel should decrease.
This relates well with the work of Orcel and others,
where the degree of hydrolysis and condensation (or
reaction rates) determine the pore-size distribution.
The effects of adducts such as OH, HF, ammonia, or
formamide control the rate of hydrolysis by raising the
activation energy for the removal of water in order for
condensation to occur.
Hench and West
V. Theoretical Studies
A. Hydrolysis and Condensation
Two models for the Si(OR)4hydrolysis reaction have
been proposed, one in which a trivalent'72and another
in which a penta~alentl~~transition state is formed.
Zerda and Hoang's using high-pressure Raman
spectroscopyto study the hydrolysisof TMOS indicates
that the model involving a pentavalent transition is
correct. In the case of base catalysis, eq 33, the reaction
OH- + GSCOCH, -GSi-OCli3- + Z S i - O H + OCHY (33)
AH
is caused by a hydroxyl ion. The OH- ion has high
nucleophilic power and is able to attack the silicon atom
directly. These attacks are aimed toward the silicon
atom since the Si atom carries the highest positive
charge. At acidic conditions, the proton is attracted by
the oxygen atom of the OCH, group, eq 34. This causes
I _H30+ + e S i 6 C H 3 + E S i H 3 -H
I
HZO
ESi4I-l + CH30H + H+ (34)
a shift of the electron cloud of the Si-0 bond toward
oxygen,and as a result the positive charge of the silicon
atom increases. A water molecule can now attack the
silicon atom, and a transition state is formed.174
The hydrolysis reaction is sufficiently slow that its
dynamics can be studied by using high-pressure Raman
spectroscopy, as shown by Zerda and H0a11g.l~~For the
first-order kinetics, the reaction rate constant is found
from the slope of the logarithmic plot of the concen-
tration of the reactant against time. Because the
magnitude of Raman bands is proportional to the con-
centration of the molecules in the system, the reaction
rate can be found from the time dependence of the
band intensity. The pressure dependence of the reac-
tion rate is related to the volume of a~tivation.l~~J~~At
a pH varying from 4.9 to 7.5 and at a 1:lOmolar ratio
of TMOS to water, Zerda and Hoang determined the
volume of activation, AVO,and its intrinsic, AVi,and
solvent, AV,,components. AVirepresents the change
in the volume due to changes in bond lengths and an-
gles. It is negative when a new bond is formed. AV,
represents the change in volume due to changes in
surrounding medium (electrostriction) during the ac-
tivation step. Analysis of the results174(AVO= -52 f
10, AVi= -2, AV, = -50 cm3/mol) showed that in the
transition state the silicon atom is in a pentavalent
state. This was the first experimental proof for the
pentavalent state of silicon in the transition stage of the
hydrolysis reaction. These experimental results confirm
a series of theoretical calculations.
Davis and B~rggrafl~~-"have proposed mechanisms,
based upon quantum mechanical calculations, for an-
ionic silanol polymerization in which participation of
hypervalent siliconates is important. As noted above
hypervalent silicon is an important candidate as an
intermediate in this chemistry. Strong anionic nu-
cleophiles have been shown to form pentacoordinate
complexes with silanes without activation in the gas
phase.181 Also, certain pentacoordinate siliconates are
readily stabilized in solution.182
An important key to understanding silanol polym-
erization chemistry is identifying how water is elimi-
nated as the polymerization proceeds. Davis and
Burggraf s calculation^'^^-^^ suggest that water is more
readily eliminated from hypervalent siliconates than
tetravalent silicates in hydroxide-catalyzed silanol po-
lymerization. However, accurate prediction of the entire
process of water elimination using an MNDO program
is difficult because MNDO overpredicts dissociative
activation energies and does not model hydrogen
bonding interactions.182 These faults are due to over-
estimation of core-core repulsions between atoms when
they are separated by approximately van der Waals
distances. The AM1 semiempirical program has largely
overcome this drawback; see refs 183-186 for details.
Consequently, Burggraf and Davida2have modeled
silicic acid reactions using AM1 to predict siliconate
elimination reactions as influenced by other nucleo-
The Sol-Gel Process Chemical Reviews, 1990, Vol. 90,No. 1 47
philic species that can complex to form hypervalent
intermediates. They applied semiempirical molecular
orbital calculations to examine the formation of pen-
tacoordinate silicic acid complexes with hydroxide ion
and fluoride ion, as well as neutral adducts with hy-
drogen fluoride, ammonia, and formamide. They also
have calculated reaction paths for water elimination
from silicic acid complexeswith hydroxide ion, fluoride
ion, and hydrogen fluoride. The qualitative semi-
empirical picture of the reaction surface has been
quantified by employing high-level ab initio calculations
for selected intermediates and transition-state struc-
tures. The adducts studied were chosen because of their
potential as catalystsor drying control agents in sol-gel
processing chemistry. For example,as discussed earlier,
formamide is used as a drying control additive for
sol-gel chemistry to control the ratio of rates of siloxane
hydrolysis and silanol polymerization.
The semiempirical methods used in Davis and
Burggrafs research are part of the MOPAC program
available from the Quantum Chemistry Program Ex-
change (QCPE) at the University of Indiana.lE3
Semiempirical molecular orbital calculations were
performed using MNDO6 and AM17 methods devel-
oped by Dewar and c ~ - w o r k e r s . ' ~ J ~ ~Revised silicon
parameters were used for MNDO calculations.'@ All
stationary points on the potential surfaces were fully
optimized by using procedures of the MOPAC program.
Force constant calculations and intrinsic reaction co-
ordinate calculations were performed for each station-
ary point to determine the nature and connectivity of
the potential surface.
Ab initio calculations were performed using the
GAUSSIAN86 program and basis sets it contains.'s7 All
ab initio calculations in their work were single-point
calculations at AM1 geometries. Estimates of energies
at the MP1/6-31++G(d) level'@ were calculated by
assuming correlation effects and polarization effects are
Comparisons of ab initio results and
semiempirical results are used to establish a quantita-
tive benchmark for semiempirical energies in order to
solve problems that are too large for high-level ab initio
methods.lg2
For reaction of any nucleophile with silicic acid, two
possible outcomes are (1)addition and (2) abstraction.
By studying the possible reaction paths for the removal
of water, the proton-abstracting pentacoordinated sil-
icon has no activation energy for water removal. In
contrast, the pentavalent silicon has a relatively large
activation energy for removal of water if the proton is
added and constrained to form its most stable structure
before the water is removed.
Figure 17 shows both the proton abstraction and
hydroxyl paths that include the addition of penta-
coordinated silicon as an intermediate in the conden-
sation reaction. The more favorable proton abstraction
path is one where a proton from a silanol moves toward
the hydrogen-bonded OH as the OH moves toward the
silicon. This forms a pentacoordinated silicon inter-
mediate where water easily escapes.
If, on the other hand, the OH is moved toward the
silicon to form a stable pentacoordinated structure, the
energy is much lower. From this structure, a significant
activation energy is then required to eliminate the
water.
f Condensation
.. t a Forrr Watw: 51(OH 'Kp
-50 1D r o t o n A +,( ,Addition
= -93
-103
S I ( O H ) ~
React ion Coordinat ion
Figure 17. Formation of pentacoordinate silicon.
Burggraf and Davisla2used MNDO, AM1, and ab
initio molecular orbital models to predict the proton
abstraction and resulting pentacoordinate silicon. They
constructed similar models for HF ammonia and form-
amide adducts on silicic acid. For HF they also predict
that the pentacoordinated silicon created by proton
abstraction is the more favorable path to water elimi-
nation. The difference is that water elimination from
HF adducts has a slight energy barrier. This indicates
a shift to a slower condensation rate for the HF-silanol
system over the OH-silanol system.
Ammonia and formamide adducts with silicic acid
form by hydrogen bonding. Formamide is predicted to
form a bistable bond in which one oxygen-silicon bond
is shorter than the other. The long bond oxygens
permit more favorable hydrogen-bonding interactions.
Burggraf and DavislE2also calculated the energy of
water adducts on silicic acid. They found that there
were very small energy differences between the penta-
coordinated water adducts and the corresponding hy-
drogen-bondedwater adducts. This result is important
when considering the effect of water adducts on rings
of silica tetrahedra discussed in a later section.
B. Gelation
In the previous sections, we saw that experimental
analyses of silica gelation using SAXS, Raman spec-
troscopy, and a Mo dissolution technique led to the
conclusion that a gel network is preceded by the for-
mation of very small clusters, or primary particles, of
silica tetrahedra. The primary particles are apparently
formed by polycondensation that favors nearly closed
clusters of tetrahedra rather than linear chains.
This conclusion regarding the gelation and resulting
ultrastructure of acid-catalyzed alkoxide-derived silica
gels has been tested by West et al.lg3and Davis and
Burggraflg4using semiempirical quantum calculations.
The calculations done by West et al. used an inter-
mediate neglect of differential overlap (INDO) molec-
ular orbital mode1.1g3 The INDO program was made
available by the Quantum Theory Project at the
University of F10rida.l~~The calculations done by Davis
and Burggraf used the AM1 mode1.1g4
The silica structures evaluated contain from one to
six silica tetrahedra. In each model two bridging oxy-
gens and two nonbridging oxygens are bonded to each
silicon. One hydrogen is bonded to each of the non-
bridging oxygens to terminate the structure and balance
the charge. Both ring and chain models of silica tet-
rahedra were evaluated, and their energies compared.
48 Chemical Reviews, 1990, Vol. 90, No. 1
88
9
Hench and West
-501
1 Uncorreclee for water Secondav Iparticle
Q 4
Figure 18.
TABLE VI. INDO Calculations for Silica Structures
INDO HOMO-LUMO
no. of silica energy per uv cutoff
tetrahedra struct Tetrahedra, au wavelength, nm
1 tetrahedra -73.82 87.1
2
2
3
chain
ring
chain
ring
chain
ring
chain
ring
chain
ring
-64.72
-55.82
-61.74
-55.86
-60.25
-55.80
-59.35
-rr -JJ.16
-58.55
-5,579
130.7
112.8
132.7
106.2
139.6
114.3
134.2
144.3
135.8
114.1
Figure 18shows the 2-D projections of chain and ring
structures for four silica tetrahedra that have been
geometrically optimized to minimize the molecular en-
ergy by using INDO calculations. These projections are
typical of the hydroxylated silica structures modelled
by West et al.lg3and Davis and Burggraf.lg4 The
clusters were each optimized for the minimum energy
by using a molecular mechanics (MM2)'%routine. The
molecular orbitals were determined by using geome-
trically optimized INDO calculations. The molecular
energies were evaluated and compared to establish the
relative stability of each structure. The energy gap
between the highest occupied molecular orbital
(HOMO) and the lowest unoccupied molecular orbital
(LUMO) for the single states and the corresponding UV
cutoff wavelength were determined. The calculated
optical properties are compared with experimental
values in the properties section of this review.
Table VI, summarizing the INDO calculations, is
shown to compare the relative stability of the INDO
structures. The more negative the energy, the more
stable the structure. These differences are exaggerated
because each chain structure has an extra water mole-
-65
0 2 4 6 8 1 0 1 2
Numberof SI tetrahedra
Figure 19.
TABLE VII. Cluster Sizes for Rings and Chains of
Tetrahedra
INDOno. of silica cluster size, A
tetrahedra N rings chains (chain-ring), au
2 6.6 9.1 8.9
3 7.1 12.7 5.9
4 9.3 16.3 4.4
5 11.3 19.8 3.6
6 11.9 23.4 2.8
cule when compared to the ring structure.
Figure 19 shows the INDO energy per silica tet-
rahedra for rings and chains as a function of the number
of tetrahedra. It suggests that the chain structures are
more stable than the rings for small number of silica
tetrahedra. This has been observed experimentally by
Klemperer and Ramamurthig7and Orcel and Hench1lG
using NMR spectroscopy, where a linear, as opposed
to a ring, growth model most consistently interprets the
experimental structural evidence prior to gelation.
As mentioned earlier, investigatorsg4have proposed
models for the structure of acid-catalyzed silica gels
containing two levels of structure formed before gela-
tion. These models propose the formation of primary
particles, of diameter 1-2 nm, which agglomerate to
form secondary particles of about 4-6 nm before drying.
The secondary particles give rise to the pore structure
after drying.
Table VI1 shows the differences in the INDO struc-
tural energies between chains and rings (C-R). The
relative stability of chains compared to rings decreases
as the number of silica tetrahedra increases by the
decrease in the difference between their calculated
INDO energies. The difference is estimated to reach
zero as the number of tetrahedra reaches about 10 or
12, when the driving force for rings becomes more fa-
vorable than for chains. This result is similar to the size
range where secondary particle growth stops in acidic
silica Acid catalysis ensures complete hydrolysis
of the silica tetrahedra, as used in these calculations.
The size of the INDO-calculated rings or clusters for
10-12 tetrahedra appears to fall within the range of the
radius of gyration of the primary particles calculated
from SAXS analysis of acid-catalyzed silica so1s.94J56
As gelation occurs, the cross-linking of the structure
becomes more dominant. A statistical analysis con-
ducted by Zarzyckis1 indicates that chain growth is
limited by this process and rings must be formed. The
energy differences in the ring structures in the INDO
model are very small. This indicates that a broad
distribution of ring sizesmay be possible in a gel as they
The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, No. 1 49
- 8 "
2 3 4
Number of Si tetrahedra
F i g u r e 20. AMI corrected energy difference.
TABLE VIII. AM1 Enthalpies of Rings and Chains at 25
"C (kcal/mol)
no. of silica AHf
tetrahedra N chain ring water differences
1 -296.8
2 -545.4 -458.2 -59.2 +28.0
4 -104.3 -991.7 -59.2 -4.6
3 -794.0 -727.6 -59.2 +7.2
become energetically more favorable.
Davidg4recalculated the energetics of rings and
chains using AM1. His calculations were corrected for
the extra water molecule in the chains as compared to
the rings. The AM1 energies were also corrected for
zero-point energy and converted to enthalpies at 25 "C.
These corrections moved the crossover energy from 10
to 12 tetrahedra to 3 or 4 tetrahedra (see Figure 20).
Table VI11 shows the enthalpies, AH,,in kcal/mol for
rings and chains and their differences.
Chains are still the most likely to occur in the early
stages of hydrolysis and condensation. The important
feature is that chains and rings are reversed in energy
difference when three to four tetrahedra or more are
formed. The driving force to produce chains is elimi-
nated, and therefore 4-fold rings are very likely. This
corresponds very closely to the 1-2-nm primary silica
particles that form prior to agglomeration, as shown in
Tables I11 and VII. Thus, results from quantum me-
chanical calculations compare quite favorably to ex-
perimental observations for the ultrastructure devel-
opment in alkoxide-derived s i l i ~ a s . ' ~ ~ - ~ ~ ~
VI. Aghg
When a gel is maintained in its pore liquid, its
structure and properties continue to change long after
the gel point. This process is called aging. Four pro-
cesses can occur, singly or simultaneously, during aging,
including polycondensation, synerisis, coarsening, and
phase transformation. Although there is an extensive
literature on aging by Iler,15*76J20and Scherer has made
an effort to describe agingphenomena theoretically,7°*205
there is relatively little detailed knowledge of aging
mechanisms and kinetics and even less quantitative
analysis of the effects of aging on gel structure and
properties.206
Polycondensation reactions, eqs 3 and 4, continue to
occur within the gel network as long as neighboring
silanols are close enough to react. This increases the
connectivity of the network and its fractal dimension.
Syneresis is the spontaneous shrinkage of the gel and
resulting expulsion of liquid from the pores. Coarsening
is the irreversible decrease in surface area through
dissolution and reprecipitation processes.
Disintegrated o p
F i g u r e 21. Stages in aging of gel: (A) Gel as formed and dried.
Shrinks on drying, giving small pore volume and pore diameter.
(B)Wet heat-aged-increased coalescence. Little shrinkage on
drying. Pore diameter larger than the dried sample A. (C)Further
heat aged or autoclaved. Structure-coarsened small area and large
pores but same pore volume as sample B. (D) Disintegration to
irregular round particles.
A. Polycondensation
Usually in alkoxide-basedgels the chemicalhydrolysis
reaction is very rapid and is completed in the early stage
of sol preparation, especially when the sol is acid cat-
alyzed. For silica gels synthesized in alcoholic solutions,
i.e., made by hydrolysis and condensation of alkoxides,
nuclear magnetic resonance (NMR,207p208Figure 21) and
Raman spectroscopies209show that the number of
bridging bonds increases long after gelation. The con-
densation reaction continues to occur because of the
large concentration of silanol (SiOH) groups in a newly
formed gel. As the hydroxyls are lost during aging,new
bonds are formed, creating more cross-linked structures.
29SiNMR results of Kelts et al.'07 show substantial
amounts of Q2 species at the gel point, and the pro-
portions of Q3and Q4species increase with time long
after gelation. As discussed earlier, &" represents a Si
atom bonded through a bridging oxygen to n other Si
atoms.
Since the chemical reaction is faster at higher tem-
perature, aging can be accelerated by hydrothermal
treatment,which increases the rate of the condensation
reaction.
B. Syneresis
The shrinkage of the gel and the resulting expulsion
of liquid from the pores is called syneresis.76~205*210
Syneresis in alcoholicgel systems is generally attributed
to formation of new bonds through condensation reac-
tions, which increases the bridging bonds and causes
contraction of the gel network. In aqueous gel systems,
or colloidal gels, the structure is controlled by the
balance between electrostatic repulsion and attractive
van der Waals forces. Therefore, the extent of shrink-
age is controlled by additions of electrolyte. Vysotskii
and colleagues211*212have shown that the rate of con-
traction of silica gel during syneresis has a minimum
at the isoelectric point (IEP). For silica this point is
at a pH of 2, at which the silicate species are un-
50 Chemical Reviews, 1990, Vol. 90, No. 1 Hench and West
gelation, after-treatment of the hydrogel by aging and
washing with various liquids, and drying. These influ-
ences can be qualitatively understood and predicted on
the basis of a condensation theory of aging. This theory
attributes a major role to the rate of the condensation
reaction of silicic acid in all stages during the develop-
ment of the texture.
charged.76Since the condensation is the slowest at that
point, this suggests that the shrinkage is driven by the
condensation reaction in eq 3.
that con-
traction is driven by the tendency to reduce the huge
solid-liquid interfacial area of the gel. This might be
accomplished by flexure of the solid phase, bringing
surfaces into contact, in which case it would be indis-
tinguishable from the reaction-driven mechanism. That
means the chemical potential of the gel is reduced by
both chemical reactions (since the condensation reac-
tion is exothermic) and the reduction in the solid-liquid
interfacial area. But Scherer also shows that the latter
suggestion is not supported by experimental results.83
The syneresis contraction rate increases with concen-
tration of silica in the sol and with temperature. When
organic solvents are present, they may form hydrogen
bonds with the silanol groups, which inhibit conden-
sation and slow syneresis. Vysotskii and Strazhesko
show that the rate of syneresis decreases with time.z11
This could result from the increasing stiffness of the
network as more bridging bonds are formed.
Ponomareva et al.213found that the total syneresis
strain is greater at lower temperatures, although the
contraction rate is slower. They argued that at higher
temperature the condensation reaction is faster, so the
gel becomes stiff faster and shrinkage is prevented. If
this is so, it implies that the shrinkage is not propor-
tional to the scaleof reaction. They conclude each bond
does not cause a certain amount of strain. Another
factor that may affect the rate of contraction is the
permeability of the gel to the flow of liquid in the pores.
It has also been suggested by
C. Coarsening
Another process, called "coarsening" or "Ostwald
ripening", is discussed at length by and co-work-
e r ~ . ~ ~ ~Since convex surfaces are more soluble than
concave surfaces, if a gel is immersed in a liquid in
which it is soluble, dissolved material will tend to pre-
cipitate into regions of negative curvature. That means
that necks between particles will grow and small pores
may be filled in, resulting in an increase in the average
pore size of the gel and decrease in the specific surface
area.
Since the solubility of silica increases at high pH, so
does the rate of coarsening of silicate gels. It is not
surprising that the rate of coarsening of gels is similarly
pH dependent. The pore-size distribution in a silica
xerogel increases as a result of aging in a basic solution.
At a given normality, Sheinfain et al.z15found the
effect of solution on aging to decrease in the order HC1
> H2S04> H,PO,; however, the rate of aging was in-
dependent of the type of acid if the activity of the
proton was the same in each solution. They examined
the coarsening of silica gels in concentrated mineral acid
(1< pH < 2) and showed that silica is even soluble at
very low pH. Iler76provides a number of references
concerning the change in the surface area and the pore
size during aging. The reduction in surface area is
produced by dissolution and reprecipitation. A high
pore volume results because the stiffer gel produced by
aging does not shrink as much under the influence of
capillary pressure.
Okker~e'~has shown that the texture of silica can be
affected in every stage of its preparation, including
D. Processlng Parameters That Affect Aging
Time, temperature, and pH are parameters tht can
effectively alter the aging process. Ilerlz2recognized
that once the gel structure has been formed it can be
further modified in the wet state by treatment to (1)
strengthen the structure without greatly affecting the
pore structure (sometimes referred to a gel reinforce-
ment) or (2) enlarge the pore size and reduce the surface
area by a process of dissolution and redeposition of
silica, thereby coarsening the gel texture.
Sheinfain et aL2l5recognized the first two distinct
stages in the thermal-agingprocess. The more extensive
the wet aging, the subsequently dried gel shrinks less
and the pore volume and diameter are greater, but there
is very little change in surface area. Second, upon
further aging the surface area begins to decrease while
the pore size continues to increase. However, there is
then little further change in pore volume. The expla-
nation is clear from the stages of aging shown in Figure
21. The first stage involves only an increased coales-
cence or bonding between the ultimate particles which
strengthens the gel so that it shrinks less upon drying.
Heating the gel in water until the specific surface area
has been reduced by 1040% can strengthen the weak
gel structure. Heating gel in water at 80-100 "C gen-
erally brings about reinforcement but does not modify
the pore structure. It is interesting that at 80 "C Liu
showedzo6there was no effect unless the gel had a
surface area greater than 200 mz/g.
Prolonged aging of silica gel with an initial surface
area of 920 mz/g in water at pH 6.8 at room tempera-
ture was carried out by Sheinfain et al.z15The surface
area dropped from 725 to 420 m2/g, while the pore
radius increased from 9 to 43 A. However, the porosity
also increased from 0.31 to 0.90 cm3/g. The structure
was thus strengthened so that shrinkage upon drying
was reduced. The reinforcement was striking when
samples were first washed with acetic acid and then
dried. Since the surface tension of acetic acid is only
one-third that of water, the reinforced gel had a much
higher pore volume of 2.36 cm3/g,which is a low-density
gel.
The rate of coarsening of silica increases with tem-
perature and pressure, as discussed by Iler.76 Aging in
water above 100 "C under pressure in an autoclave
brings about far greater structural changes than can be
obtained at 100 "C. Van der Grift et a1.216prepared
silica gels by neutralization of alkaline silicate solutions
and aged them in an autoclave in water at various
temperatures. When the temperature was above the
boiling point of water, the sample was exposed to steam
at high pressure, resulting in hydrothermal aging.
Washing the pore liquor out of a gel is also an "aging"
step, and the pH of the wash water is critical in the case
of gels made from acid-catalyzed silicate precursors.
The final properties of such gels depend on both the
pH at which the gel was formed and the pH in which
The Sol-Gel Process
it was washed (aged) before drying. For example, Ok-
kerse et al.217heated a series of gels for 1-4 days at 80
"C in water, acid, and potassium chloride solutions and
found that if the gel had a specific surface area greater
than about 200 m2/g, then it underwent a decrease in
surface area. There was little effect at pH 2, but in
neutral or alkaline solution, especially in the presence
of salt, the gel texture was markedly coarsened. For
example, the surface area decreased from 752 to 452
m2/g while pore radius increased from 13to 22 A,but
volume remained at 0.5 cm3/g.
Soaking a silica gel in dilute ammonium hydroxide
solution at 50-85 "C can result in drastic coarsening of
the gel texture. Girgis218reported that even soaking a
silica gel at pH 10-11 for 1day at 20 "C caused the
surface area to drop from 650 to 467 m2/g with a cor-
responding increase in pore radius. It might be thought
that since silica does not dissolve at low pH, acids would
have little effect on wet aging other than to adjust pH.
However, Sheinfain et al.215found that treating the gel
with strong acids, HC1, HNO,, or concentrated H2S04
before drying increases the pore volume of the dried gel
without lowering the surface area. This is because the
acid promotes coalescence between particles without
particle growth and coarsening of the texture. On the
other hand, 8 N HzSO4 caused a drop in surface area
from 700 to 300 m2/g and at the same time increased
the pore volume.215Thus, strong acids (pH < 2) pro-
mote the aging of silica gel but, unlike alkalis as an
aging promoter, cannot dissolve the gel if added in ex-
cess.
It is seen that aging and thermal treatments result
in a one-way process: loss of specific surface area and
an increase in pore size. The pore size can be enlarged
also by dissolution of some of the silica. Sheinfain et
al.215reported that treating a gel with 0.5 N KOH or
dilute HF can enlarge the pores from 0.7 to 3.7 nm. If
silica were dissolved away evenly from all the surface,
there should be an increase in specific surface. How-
ever, it is probable that regions of lower radius of cur-
vature will dissolve more rapidly so that the specific
area may actually decrease.
The fractal nature of a gel will also be a major in-
fluence on the gelation and aging process as discussed
earlier.219Condensation reactions between gel network
segments will be more important when the number of
interconnections is large.151
E. Properties
During aging, there are changes in most physical
properties of the gel. In the study of aging kinetics of
silica gel, the textural properties &e., pore size, porosity,
and surface area) are of great importance. With respect
to drying behavior, it is the change in mechanical
properties during aging that is most important.
Inorganic gels are viscoelastic materials responding
to a load with an instantaneous elastic strain and a
continuous viscous deformation. Since the condensa-
tion reaction creates additional bridging bonds, the
stiffness of the gel network increases, as does the elastic
modulus, the viscosity, and the modulus of rupture.
This is illustrated in Figure 22, which showsthe increase
in modulus of rupture of silica gel during aging for a gel
with a water/TMOS ratio of 16/1.220The modulus of
rupture of a gel aged at 105 "C reaches 40 Pa by 40
A
n-v)
3
0
0
a
w
K
aI-n.
3
3
a
Chemical Reviews, 1990, Vol. 90, No.
RUPTURE MODULUSABOVE 90°C
Q
I . , . , .
10 20 30
DAYS
1 51
2
Figure 22. Rupture of modulus of wet gel (made from TMOS)
versus aging time.220
days. West et al.220showed that gel strength increased
logarithmically with times ranging between 1and 32
days. The strength increased exponentially with tem-
perature between 25 and 105 "C. The strongest gels
produced had rupture moduli of approximately 400 Pa.
Similar data were obtained by Pardenek et a1.221for
polymer gels as well as for colloidal gels made from
fused silica. Dumas et followed the shear modulus
for 9 months in gels made from TEOS and found that
it continued to increase. The strength of the gel also
increased with aging. For that reason, it is advisable
to age large monolithic gels before drying to reduce the
chance of ~ r a c k i n g . ~ ~ . ~ ~The greater stiffness of the aged
gel reduces the shrinkage during drying as mentioned
before, especially if the aging treatment is performed
under hydrothermal conditions.
VII. Drying
The drying behavior of porous solids has been ex-
tensively studied by S h e r ~ o o d , ~ ~ ~ - ~ ~ ~Keey,226Mujum-
dar,227i228Moore,2mWhitaker,230Cooper,231Ford,232and
S ~ h e r e r . ~ ~ , ~ ~ - ~ y ~ ~ ~However, most of the data have been
on powder systems with relatively large pores. Even
the few quantitative studies conducted on gels by Ka-
waguchi et al.234and D ~ i v e d i ~ , ~have been on large pore
gels. Consequently, theoretical analyses of gel drying
such as by S~herer~~@-?-~~s~~~or by Zarzyckis1using Co-
oper's model for ceramic powders231have been based
upon classical concepts of drying.
It has been generally accepted since the time of
S h e r ~ o o d ~ ~ * ~ ~ ~ - ~ ~ ~that there are three stages of drying:
Stage 1: During the first stage of drying the decrease
in volume of the gel is equal to the volume of liquid lost
by evaporation. The compliant gel network is deformed
52 Chemical Reviews, 1990, Vol. 90, No. 1
by the large capillary forces, which causes shrinkage of
the object. In classical large-pore systems, this first
stage of drying is called "the constant rate period" be-
cause the evaporation rate per unit area of the drying
surface is independent of A detailed review
of the drying phenomena associated with the constant
rate period is presented in Brinker and S ~ h e r e r . ~ ~This
behavior is applicable to gels made by colloidal pre-
cipitation (method 1)or base-catalyzed alkoxide gels
(method 3) that have pores >20-nm average diameter.
However, a recent quantitative analysis by Wilson237
and Wilson and H e n ~ h ~ ~ ~ q ~ ~ ~of the drying kinetics of
acid-catalyzed alkoxide gels shows that for gels with
pores <20 nm the rate of drying in stage 1is not con-
stant but in fact decreases substantially. As discussed
below, this behavior is due to changes in pore radii
during drying, which cause substantial reductions in
vapor pressure of the liquid in the small pores. For
large or small pore gels the greatest changes in volume,
weight, density, and structure occur during stage 1
drying. Stage 1ends when shrinkage ceases.
Stage 1 ends and stage 2 begins when the "critical
point" is reached; classical drying theory calls this the
"leatherhard point".232-236-240The critical point occurs
when the strength of the network has increased, due to
the greater packing density of the solid phase, sufficient
to resist further shrinkage. As the network resistance
increases, the radius of the meniscus is reduced.
Eventually, at the critical point, the contact angle ap-
proaches zero and the radius of the meniscus equals the
radius of the pore. This condition creates the highest
capillary pressure, and unable to compress the gel any
further, the pores begin to empty, which is the start of
stage 2. In stage 2 liquid transport occurs by flow
through the surface films that cover partially empty
pores. The liquid flows to the surface where evapora-
tion takes place. The flow is driven by the gradient in
capillary stress, as described by Whitaker.241Because
the rate of evaporation decreases in stage 2, classically
this is termed "the first falling rate period".242-244
Stage 3: The third stage of drying is reached when
the pores have substantially emptied and surface films
along the pores cannot be sustained. The remaining
liquid can escape only by evaporation from within the
pores and diffusion of vapor to the surface. During this
stage, called the "second falling rate period",225there
are no further dimensional changes but just a slow
progressive loss of weight until equilibrium is reached,
determined by the ambient temperature and partial
pressure of water. Whitaker230.241has developed a
theoretical analysis of the second falling rate period.
Brinker and Scherer70review the factors in this stage
that are relevant to the drying of gels.
A comparison of Dwivedi's results235on the drying of
an alumina gel with those of Wilson and H e n ~ h ~ ~ ~ * ~ ~ ~
for an acid-catalyzed alkoxide silica gel illustrates the
importance of pore size in gel drying behavior. Dwivedi
prepared the alumina gels using the Y01das~~method,
which yields gels with pores >>20 nm. Samples up to
3 mm thick were weighed at periodic intervals during
drying at 80 "C. Figure 23, from D~ivedi,2~~shows that
the rate of water loss was constant from his gels during
stage 1 (within the range of the considerable experi-
mental error caused by removing the sample from the
oven for weighing). He showed that the rate was similar
.-
c
`E 0.20
N
60) 0.15
v
u)
u)
0
- 0.10
(L,
m
L
u
3
0.05
0,
m
CI:
-
Hench and West
- Evaporation
rate of--- --------
- `7 T distiled water
ILL`
-- L
Second Stage- First Stage
4 P
-
I I
The Sol-Gel Process Chemical Reviews. 1990, Vol. 90, No. 1 53
0 25 50 71 IW I75 150 (75
Time lhourr)
Figure24. Time dependenceof (A) temperature and weifhG (B)
absolute loss rate; (C) loss rate per unit area for gel A. 37
atmosphere after casting. It also is consistent with the
fact that traditional porous ceramic bodies are much
more crack resistant during drying. Since the perme-
ability of a 50% porous body with 1-pm pores has a
value of D i; cm2,the stress will be lo4 smaller
than in a gel drying at the same rate.
When the pores in a gel are <5 nm, characteristic of
acid-catalyzed alkoxide gels, the analysis of drying
stresses is complicated by the fact that stage 1is not
a constant-rate period of drying. This is in dramatic
contrast to all classicaldrying experiments. As shown
in Figure 24, from Wilson and Hench,239the evaporation
rate from the gel during stage 1dropped from a max-
imum of 0.034 to 0.013 g/(h cm*)at the critical point,
even though the meniscus remained at the surface
throughout this stage, as required by the definition of
stage 1. These data were taken by use of a specially
designed drying apparatus developed by Wilsonu7that
permitted simultaneous monitoring of sample dimen-
sions, weight, and optical properties at constant tem-
perature and atmosphere without removing the samples
from the drying chamber?% Consequently, high accu-
racy was obtained. Wilson and Henchm show the time
dependence of weight and dimensions of a representa-
tive silica gel monolith in Figure 25. The relationship
between relative weight (W/Wo)and relative volume
(V/Vo)of the gel during the various stages of drying is
shown in Figure 26. The change between stage 1and
stage 2 is very clear.
The reason for the decrease in drying rate in stage
1 for these gels is associated with the effect of pore
0 ii) 2n 10 40 IO fa 70 so 90 I W
wlwo c.
Figure 26. WJW,percent vs VIVOpercent for gel B."
radius on evaporation rate. Recall that acid-catalyzed
alkoxide gels have very small pores, <5 nm. The
evaporation rate from the gel is dictated by the dif-
ference between the vapor pressure at the evaporating
surface, Ps,and the vapor pressure of the ambient at-
mosphere, Pw Evaporation continues as long as P. >
Pawith a rate (VJ:
v,= u p ,- Pa) (36)
where Ke is a constant.
The vapor pressure of a surface comprised of a large
number of very small pores, Pv,will be influenced by
the radii of the pores, as described hy the Gibbs-Kelvin
equation
(37)
54 Chemical Reviews, 1990, Vol. 90, No. 1
x
< 1
$ 2 -
I -
.
n -
1.0
I
C 26
BID0
* I 9
BSW 0650
_.__.____________.__..---
m = ..-Y
*BW *6iD i I W
, , ' . ' '
Hench and West
0a
.e"
0 1 2 3 4 5 6 7 8 9 10
Meniscus radius (nm)
Figure 27. Reduction of vapor pressure with decreasin meniscus
radius as predicted by the Gibbs-Kelvin equation.23f
i n
5
3.
-.1
I I
0.9 1
0.8
0.7
0.6
0.5 -
WPo no Round wstpr layer
0.0
1 ' 1 ' 1 ' 1 ~ 1 ' 1 '
2.0 2.5 3.0 3.5 4.0 4.5 5.0
Pore/ meniscusradius (nm)
Figure 28. Comparison of observed evaporation rate (VJ Vo)to
that predicted by the Gibbs-Kelvin equation.
where P, is the vapor pressure over the meniscus of the
pore, Pois the vapor pressure over a flat surface (760
Torr), B is the molar volume of the liquid (0.18g/cm3),
R is the gas constant (8.314 X Tis temperature
(kelvin), rm the radius of curvature of the meniscus
(meters),and y the difference in the solid-vapor and
liquid-vapor interfacial energies (y = 0.072 J/m2).
Figure 27 plots the dependence of vapor pressure on the
pore radius, using the values above in the Gibbs-Kelvin
equation, from Wilson and H e n ~ h . ~ ~ ~
The average pore radius of the acid-catalyzed alk-
oxide silica gels when dry is 2.3 nm. The structural
density can be assumed to remain constant during
drying. Therefore, the decrease in dimension during
drying (Figure 25) should also be indicative of the de-
crease in pore radius during shrinkage of the gel. This
assumption yields an average pore radius of the wet gel
to be -4.1 nm. Thus, the change in the ratio of
evaporation rate between a free surface (Vo)and the gel
surface (VJ Vo)during stage 1should be comparable
to the drop in vapor pressure (P,/Po)predicted by the
Gibbs-Kelvin equation as the gel shrinks.239Figure 28
-RbfromDSC
e-' ---e--h b S l r o m D S C 1
I0.04 i
0 1 1 6 n
\?erago Pore Radius R [nm]
Figure 29. Dependence of the bound water thickness on the
average pore
*-- DRS Samples
1 c1s
compares the measured ratio of evaporation rates
(V,/ V,) for the gel in stage 1as a function of the pore
radii in the gel. The ratio of evaporation rates predicted
by the Gibbs-Kelvin equation is also plotted in Figure
28. The Gibbs-Kelvin equation predicts higher evap-
oration rates than are observed.
An important contribution to the depressed evapo-
ration rate from the small pore gel is the presence of
a bound layer of water on the pore surfaces. The bound
water layer has a structure that is substantially more
ordered than free water and possesses properties, such
as melting point, that are markedly different than bulk
water. Wallace and H e n ~ h ~ ~ " ~ ~ ~used dielectric relax-
ation spectroscopy (DRS) and differential scanning
colorimetry (DSC) to analyze the properties and cal-
culate the thickness of the bound water layer in acid-
catalyzed alkoxide silica gel monoliths with porosity
nearly identical with those used in the Wilson and
H e n ~ h ~ ~ ~ - ~ ~ ~drying experiments.
A fundamental assumption made in relating the DRS
and DSC studies to drying kinetics is that the structure
of water adsorbed into the pore network of a dried gel,
the starting condition for the Wallace and H e n ~ h ~ ~ ~
study, is nearly equivalent to the structure in the gel
during stage 1drying. This appears to be a reasonable
assumption since Wallace and H e n ~ h ~ ~ ~show that
bound water thickness appears to be dependent upon
pore radius and temperature (Figure 29). This result
is valid for two different models: a bound cylindrical
layer and a bound statistical layer of water. The pore
radius is also independent of surface silanol concen-
tration (Figure 30).
When H20is adsorbed onto the surface of silica, the
first H20molecules form H bonds with, on average,two
The Sol-Gel Process
z 5 -
Y 4 -
z 3 -
LL
>
W
3 '
II
Chemical Reviews, 1990, Vol. 90, No. 1 55
nm (sampleC75)while keeping [SiOHls = 4.9 OH/nm2.
The ratio of 1F/lv for free H20 is 0.148. If it is as-
sumed that all the adsorbed H20vaporized, then lv is
a measure of the saturated H20 content, We Therefore
the ratio of lF/lV for the adsorbed H20divided by 0.148
equals the fraction of free H20,FF, in the pores. The
flat and cylindrical thicknesses of the bound and free
pore H20can then be calculated from fractions FF and
FB as discussed below.
The pore volume, V (cm3/g),and surface area, S
(m2/g), were measured by using N2 adsorption iso-
therms, and R (nanometers) = 2000V/S. The [SiOHls
values were assumed for the stabilization temperature
of each sample by using data taken from Z h u r a ~ l e v . ~ ~ ~
The shape of the pores in gels is difficult to charac-
terize, due to their size and complex fractal nature, as
discussed earlier. For the same reason talking about
the "true"thickness of a bound H20layer in micropores
is meaningless due to these geometric considerations
and the dynamic properties of H bonding. (See the
following sections for a discussion of the quantum ef-
fects at the SO2-H20 interface.) For this reason as-
sumptions about the shape of the pores must be made
before any conclusions about the uthickness" can be
reached.
Considering the result of Vasconcelos topological
model of gel and Wallace's analysis of water
ad~orption,2~~the porosity can be considered as one long
cylinder whose length decreases during sintering while
R is constant. Consequently, a cylindrical "thickness"
can be calculated for the bound and free H20fractions
adsorbed on the cylindrical pores. This is done by
calculating the radius, RF &e., "thickness" for a cylin-
drical geometry), of the cylindrical core of free H20
occupyingthe same fraction of area of the circular cross
section (radius Rc) of a pore as FF.Therefore the free
H20 cylindrical thickness RF = RcFF1l2. The bound
cylindrical thickness RB = Rc - RFfor FB (see Wallace
and H e n ~ h ) . ~ ~ ~
The dielectric relaxation that DRS is measuring is a
space charge polarization at the measuring electrodes
due to H+hopping, and the change from a logarithmic
to a linear dependence of Fdlon W at WBis related to
the completion of the bound H20layer. Consequently,
the fraction of free (FF= WF/W~)and bound (FB =
W,/WS) H20 can then be calculated from the DRS
results. The logarithmic dependence of Fdlon the
statistical H20 thickness W/S, which makes no as-
sumptions about the pore geometry, is presented in
Figure 31 for sample series B. It shows that the bound
H20statistical thickness WB/S increases slightly as the
processing temperature of the gel, Ts,increases. It also
shows that for a given value of W / S ,Fsl decreases as
the bulk density, DB, increases. All the structural re-
sults are listed in Wallace.252
Figure 32 shows some of the experimental DSC
curves for the same Wallace and Hench sample^.^' The
increase in the relative ratios of freezing point, lF, to
boiling point, lv, is clearly visible as R increases. Both
freezing point suppression and boiling point rise occur
for increased pore radius. The dependency of the
bound H20thickness on [SiOHls,calculated for flat and
cylindrical geometries from the DRS and DSC data, is
shown in Figure 33. The bound H20thickness does
not change significantly with [SiOHIs (if anything it
? 1 -
W
I I '
- 67 I
0 0
0 E180
A 8650
8800
1ccorr
Figure31. Logarithmic dependence of the relaxation frequency
on W/S.246
surface silanols. Before a complete monolayer is
formed, clusters of H-bonded H20 molecules start
forming around the ~ilanols,~~*followed by multilayer
condensation. A portion of the H20adsorbed directly
adjacent to the surface, called the bound H20fraction,
FB, does not show a freezing or melting transition in a
DSC, while remaining diffusionally mobile as shown by
G ~ e r i n . ~ ~ ~The exact state of this bound layer of H20
is not well understood. The remaining free H20frac-
tion, FF, adsorbed in silica gel pores exhibits a sup-
pressed melting point, TIM.The questions especially
relevant to drying of gels are (1)Does the structure of
the pore water change as the pores shrink? (2) What
causes the changes? (3) What is the extent or thickness
of the bound surface H20?
Differential scanning calorimetry (DSC) and dielec-
tric relaxation spectroscopy (DRS) were used to de-
termine the effect of pore texture and structure on the
statistical thickness of the adsorbed H20.2461247Three
sets of monolithic gels were investigated. Series A and
B had a constant pore radii but were heat treated to
decrease the surface silanol concentration, [SiOHIs.
Series C had a constant [SiOHIs = 4.9 OH/nm2,based
on Zhurvalev's analysis,250but increasing pore radii.
These variables relate directly to the structure of H20
in drying gels as both the average pore radius, R, and
the surface silanol concentration change during drying.
The dependence of the frequency, FJ1,of the maxi-
mum of the dielectric loss tangent spectra of the gel,
tan 6, was measured by using DRS on series B gels as
a function of the H20content, W[grams of H20/grams
of Si02]by Wallace and H e n ~ h . ~ ~ > ~ ~ ~The dependence
of FJ1on W changed from a lograithmic to a linear
dependence at the bound H2O content, W, (Figure 31).
This change in dependence at WB is related to the
change from bound to free H20, where WB is a statis-
tically averaged measurement due to the dynamic na-
ture of the system on the time scale being measured.
The DRS spectra were measured as a function of W,
up to the saturated pore H20 content, Ws,on three
cylindrical SiOzgels (series B) heat treated at 180,650,
and 800 "C in order to decrease [SiOHls.
In addition, the latent heat of fusion, lF (J/g), and
latent heat of vaporization, lv, of the H20adsorbed in
powdered Si02gel monoliths were measured by using
DSC247with a heating rate of 10 "C/min. In sample
series A, [SiOHJswas decreased by a factor of 7 (the
same as for series B) while keeping R = 1.2 nm. In
series C, R was increased from 1.2 (sample A180) to 7.45
56 Chemical Reviews, 1990, VOI. 90, NO. 1
2 , I
Hench and West
endothermic ---c45
' I ---Pure
-14
-16
-100 -50 0 50 100 150 200 250
Temperature T ["C]
Figure 32. Experimental DSC spectra.?"
surraceSihnol cmcm,rntm ISIOHI, Imwnm~ll
Figure 33. Dependence of the hound water thickness on the
silanol c~ncentration?'~
increases as [SiOH], decreases) but increases with R.
The bound water thickness is plotted as a function of
R in Figure 29, showing that thickness approximately
doubles. For constant R, the fraction of bound HzO,
FB.the associated bound statistical thickness, WB/S,
and the bound cylindrical thickness, RB,values appear
to increase slightly with bulk density, when the asso-
ciated [SiOHls decreases by a factor of 7. The DSC
data therefore imply that the "thickness" of the ad-
sorbed HzO layer depends not on [SiOH], but rather
on R. The DRS data appear to confirm the DSC con-
clusions, with the "thickness" of the bound HzOlayer
decreasing slightly with increasing [SiOHIs, but the
influence of the measurement temperature on the
bound H 0 layer thickness must also be c o n ~ i d e r e d . ~ ~
GuerinL9used H+NMR to investigate the tempera-
ture dependence of the statistical thickness WB/S of
bound H20on two amorphous silicapowders, Spherosil
XOR 75 and Aerosil200. SpherosilXOR 75is a porous
silica gel powder, S = 200 m2/g, with S due to the in-
ternal concave pores, as in the Wallace and Hench
study. Aerosil200 is a nonporous submicrometer silica
powder, S = 85 mz/g, with all S due to the external
convex surface. Guerin showed that for the assumed
flat geometry, WB/S is thicker in the concave pores of
Spherosil than on the convex Aerosil particles at a
specifictemperature, T.She also showed that for either
sample WB/Sapproximatelydoubled when Tincreased
from 220 to 260 K. This means that both pore geom-
etry and temperature influence WB/S. In the Wallace
and Hench studyz4'TMincreased from 221to 266 K in
silica gel series C as R increased from 1.2 to 7.45 nm.
FBand therefore WB/Sand Rs are calculated at TMfor
each sample. The doubling in WB/S and RBseen in
series C could therefore be due to the increase in the
I I I I
I I I I Told SiOI~ipai9%
I I I I
rots,po.e*na=Pl%
I I I I
I I 10 l i 20 *5 30
S n l e . . a m ~ m
Figure 34. Schematic representation of gel surface at the be-
ginning of stage
measuring temperature, Le., TM,and/or the increase in
R.
These studies show that adsorption behavior of HzO
on SiOzgels is largely govemed by pore geometry rather
than surface chemistry, as well as temperature. This
is in agreement with the fractal dependence of S, of a
mesoporous SiOz gel, on the size of the molecular
yardstick used in sorption is~therms.l~~+'~~S depends
entirely on the size of the adsorption molecule and not
on its adsorbent-adsorbate physisorption interac-
tions?s4 The increases in FBobserved, for constant R,
with the increase in bulk density are probably related
to the associated increases in helium pycnometry
structural density from 2.11 to 2.30 g/cm3 for these
acid-catalyzed gels. This is also discussed in detail by
Wallacezs2and summarized in section VI11 on stabili-
zation in this review.
The inference with regard to drying gels is that as
pores shrink the "thickness" of the bound surface HzO
layer decreases slightly, while increasing drying tem-
perature tends to increase the "thickness". This implies
that the ratio of the free to bound HzO fractions de-
creases during drying and is not influenced by [SiOH],.
A. Stage I: Drying
Combining the drying analysis of Wilsonz3' and the
pore analysis of Wallacezszyields a schematic of the gel
surface at the beginning of stage 1drying (Figure 34).
The surfacearea is initially largely freewater, separated
by a relatively small areal fraction of gel network with
a transition zone of bound water. As the free water
evaporates, the solid network is drawn together by the
capillary stresses which decreases the areal fraction of
free water and increases the areal fraction of solid. At
the critical point, the end of stage 1, the structural
schematic is as depicted in Figure 35. The decreasing
rate of evaporation throughout stage 1is a consequence
The Sol-Gel Process
1 1 1 1
I
I I IO ,I la 25 I
Su,tuuamra
Figure35. Schematicrepresentation of gel surface at the end
of stage 1 (criticalpoint). Drawn to the same relative scale as
Figure 34.237
of the effective pore radius decreasing from 3.2 to 1.3
nm. The bound water is apparently not removed until
much higher temperatures in the stabilization regime.
This analysis of effects of pore radius on stage 1
evaporation also explains why DwivediB5and Kawag-
u c h P observed a classical constant rate period during
the drying of their gels. The magnitude of vapor
pressure reduction required to produce a noticeable
decrease in evaporation rate during stage 1 does not
occur until menisci of r, <10nm are formed. Menisci
of this radius cannot form in pores of the dimensions
reported for their gels, and no significant change in the
evaporation rate was seen.
B. Stage 2 The Opaque Stage
The second stage startsat the critical (or leatherhard)
point. At this point the meniscus radius is equal to the
pore radius and is able to penetrate the bulk. The loss
rate of the acid-catalyzedalkoxide silicagelsm steadies
at a constant, low value of -0.008 g/(h cm?. This stage
is consistent with the stage Scherer'O terms the "first
falling rate period". Liquid is driven to the surface by
gradients in capillary pressure, where it evaporates due
to the ambient vapor pressure being lower than inside
the pores.
Shortly after entering the second stage,the gel is seen
to turn opaque, starting at the edges and progressing
linearly toward the center. There are several possible
causes of this phenomena, including phase separation
of the pore liquid or exsolution of gas from the liquid.
The most plausible explanation is that put forward by
Shaw,2&who suggests that this phenomenon is caused
by light scattering from isolated pores (or groups of
pores) in the process of emptying, of such a dimension
that they are able to scatter light. The data obtained
during stage 2 indicate an increase in open porosity
from -0.012 to -0.364 cm3/g during the opaque
transition, which started at -16% (&1.5%)moisture
and ended at 6% (f1.5%)for both samples in Wilson
Chemical Reviews. 1990, Vol. 90. No. 1 57
and Hench's e~periment;'~'seeFigure 24.
C. Stage 3
After transparency is regained, Figure 2j shows that
the loss rate of the acid-catalyzed alkoxide silica gel
monolith gradually falls to a value of -0.001 g/(h cm')
until no further weight changes occur. The transition
to stage 3 is the hardest to identify, and its start is
probably best defined as the end of the opaque stage.
Scherer'O describes stage 3 as the "second falling rate
period", where the temperature of the body is not as
strongly suppressed as when evaporation rates were
higher. The remaining liquid evaporates within the
pores and is removed by diffusion of its vapor to the
surface. It is unaffected by local changes in tempera-
ture, ambient vapor pressure, flow rate, etc., as dem-
onstrated for gel B in Wilson and Hench's study.wg By
the start of stage 3 the gel is to all intents and purposes
dry. It can be removed from the drying chamber and
dehydrated under much more severeconditions (180 "C
at 0.1Torr) without risk of cracking. Stress birefrigence
measurements during drying indicate a gradual reduc-
tion in residual stress during stage 3 and the end of
stage 2, because of the reduction in number of bire-
frigent lines and eventual elimination of the isogyres
caused by biaxial strain.23'
D. Cooling
During the cooling period (which can be rapid) the
samples gained weight as shown in Figure 24. On
cooling, gel B gained almost all of the weight lost during
stage 3. As the chamber cools, the vapor pressure in
the chamber rises until Pa>P. and condensationoccurs
within the pores.
E. Drying Failure
The drying times reported in Wilson and Hench's
study" arethe experimentally determined minimum
for gels of 2-4-cm diameter without cracking. When
samples fail, they do so at distinct points within the
drying sequence. Cracking during stage 1 is rare but
can occur when the gel has had insufficient aging and
strength (see S ~ h e r e r ' ~ * ~ - ~ )and therefore does not
possess the dimensional stability to withstand the in-
creasing compressive stress. If the loss rate is increased
(by lowering the vapor pressure of the ambient atmo-
sphere or increasing the draft rate), there comes a point
where it exceeds the maximum rate of shrinkage. If this
occurs, localized pore emptying results and surface
cracks develop.
Most failure occurs during the early part of stage 2,
the point at which the gel stops shrinking. This is the
point at which the meniscus falls below the surface. A
distribution of pore sizes exists in these materials, and
some pores must empty before others. At the start of
stage 2 the modulus of the gel is very high and the
compressive stress is in the order of -100 MPa. The
pores that empty first (at the larger end of the distri-
bution) stop shrinkingat the point of emptying and can
only passively shrink under the influence of nearby
saturated pores. The possibility of cracking at this
point is great due to the high stresses and low strain
tolerance of the material. Cracking during stage 3does
not occur, in the experience of Wil~on.~'The moisture
58 Chemical Reviews. 1990. Vol. 90. NO. 1
level and thus the stress is considerably diminished by
this point, and cracking generally will not occur even
under fairlyextreme dehydration conditions unless very
large defects are present. Hench et al. have discussed
the types of defects that can be introduced during gel
processing and their effects on strain ~oncentration.5~
Successfuldrying of large gel monoliths requires control
of the drying rate through the opaque stage and elim-
ination of processing defects during mixing, casting, and
gelation.
VIII. Stabilization
A. Introduction
Optically transparent dried silicagel monoliths have
been made by Hench et al."$ of over 80-mm diameter.
This new type of optical material is termed type VI
and its physical characteristics are described in
the properties section of this review. A critical step in
preparing type VI gelsilica is stabilizationof the porous
structure as indicated in Figure 3. Both thermal and
chemical stabilization is required for the material to be
used in an ambient environment. The reason for the
stabilization treatment is the very large concentration
of silanols on the surface of the pores of these large
surface area (>400 m2/g) materials.
Chemical stabilization involves removing the con-
centration of surface silanols below a critical level so
that the surfacedoes not rehydroxylate in use. Thermal
stabilization involves reducing the surface area suffi-
cient to enable the material to be used at a given tem-
perature without reversible structural changes. The
mechanisms of thermal and chemical stabilization are
interrelated because of the extreme effects that surface
silanols and chemisorbed water have on structural
changes. In fact, full densification of the silica gels,
transforming them to a glass, is nearly impossible
without dehydration of the surface prior to pore closure.
Dehydration, dilation, and contraction of the silica
network with adsorption and desorption of water are
equally important in forming a stable porous gel mon-
olith (typeVI) or a fully dense gel3lass monolith (type
B. Dehydration
A major problem in producing gel-silica optics is
removal of gel surface hydroxyl groups and hydrogen-
bonded pore water, which give rise to atomic vibrational
energy absorption in almost the entire range of ultra-
violet to infrared wavelengths (16C-4500 nm) and de-
creases the optical applications of silica-gel monoliths.
Consequently, to achieve the theoretical optical per-
formance of silica, complete dehydration is imperative.
Many chlorine compounds-some of these include
methylated chlorosilanes,such as CISi(CH,),, C12Si(C-
H3)2,Cl3Si(CH3),silica tetrachloride (SiC14),chlorine
(C12),and carbon tetrachloride (CC14)-can completely
react with surfacehydroxyl groups to form hydrochloric
a ~ i d , 2 ~ - ~ ~ ~which then desorbs from the gel body at a
temperature range (400-800 "C) where the pores are
still interconnected. In a study by Wang and
Hench,52wmcarbon tetrachloride was used successfully
to achieve complete dehydration of ultrapure gelsilica
monoliths.
V),52,53,256
Hench and West
Y H ti
\Reversible
(25°C <-----> 170°C)
Figure 36. Physical water decreasesand silanol~oupscondense
in the range of room temperatureand 170 O C . 6o
To achieve dehydration it is necessary to recognize
that "water" is present in two forms: free water within
the ultraporous gel structure (i.e., physisorbed water)
and hydroxyl groups associatedwith the gel surface (i.e.,
chemisorbedwater). The amount of physisorbed water
adsorbed to the silicaparticles is directly related to the
number of hydroxyl groups existing on the surface of
silica. During the 1950s and 19605, researchers
YoungY61Benesi and Jones,"2 Hockey and PethicaYm
Kiselev,% and McDonaldB5contributed much infor-
mation regarding the hydration/dehydration charac-
teristics of the silica gel/water system, as summarized
below: (1) The physisorbed water can be eliminated,
and surfacesilanol (Si-O-H) groups condensed starting
at about 170 "C, as shown in Figure 36.260
(2) The dehydration is completely reversible, up to
about 400 "C, as shown in Figure 37.260 Decomposition
of organic residuals, up to 400 "C, was also confirmed
by using DSC and TGA for TMOS-derived silica gels,
as discussed by Wang.2"
(3) Above 400 "C, the dehydration process is irre-
versible as a result of shrinkage and sintering across
pores, as shown in Figure 38.2@' Thus, the amount of
existinghydroxyl groups on the gel surfaceis an inverse
function of the temperature of densification. UV-vis-
NIR absorption data also show that the reduction of
surface hydroxyl groups occurs above 400 "C.
(4) Viscous flow occurs above 850 "C with the exact
temperature dependingon the pore sizeof a specific gel.
The isolated hydroxyl groups on the gel surface react
with each other, bringing particles together, thereby
eliminating voids within the gel. If surface water is
unable to be desorbed prior to pore closure, it is trapped
inside the densified gel.
The Sol-Gel Process
H
Figure 37. Surface silanol groups are reversible in the range
17C-400 'Cm
H
Figure 38. Irreversible eliminationofadjacent hydroxyl
Young, in his early work,261found that the decrease
in surface area of silica gel at high temperatures is a
function of the time and temperature of the heat
treatment. This supports the concept that the sintering
mechanism is essentially the result of viscous flow,
Chemical Reviews. 1990. VOI. 90. No. 1 59
Tkl- H
H
u@16 88 nm
Figure 39. Reabsorption of physical water below 400 O C W
rather than surface diffusion. Impurities (i.e., surface
water) effectively lower surface energy and thereby
decrease the sintering temperature, presumably by fa-
cilitatingviscousflow;Phalippou et dmconfirmed this
point.
Hair (see p 87 in ref 268) also proved that heating
silica gel in the 170-400 "C range causes reversible
dehydration via elimination of surface water and the
formation of both singleand adjacent surface hydroxyl
groups, as illustrated in Figure 37. Hair found that at
400 "C, no more than half of the surface hydroxyl
groups had been desorbed and that most of the re-
maining surface hydroxyl groups were adjacent to each
other and therefore situated for preferential water ad-
sorption (Figure 39). He stated that heating the gel
above 400 "C causes a drastic, irreversible elimination
of adjacent hydroxyl groups, as shown in Figure 38,
until at about 800 "C, only single hydroxyl groups re-
main (Figure40). As the temperature increases, single
hydroxyl groups depart from the gel surface until the
gel is densified; this occurs in the 850-1000 "C range.
However, some single hydroxyl groups are still unable
to escape from the gel surface and therefore can con-
tribute to foaming of the gel as the temperature in-
creases.
More importantly, Hair describes2@that when the
silica gel has been completely dehydrated, there are no
surface hydroxyl groups to adsorb the free water; in
other words, the surface is essentially hydrophobic.
Clearly, it is the realization of this critical point that
is the focus for making stable monolithic gels.
The vibrational overtones and combinations of hy-
droxyl groups and their associated molecular water,
occurringin the 1251F3000-nm range, have been studied
60 Chemical Reviews. 1990, VoI. 90, No. 1 Hench and West
2" c
ti
t
u,= 2668.80 nm
4Figure 40. On1 single hydroxyl groups remain at temperatures
above 8M) "C.2 2
by Anderson and Wi~kersheim.2~~Evaluation of a
partially dehydrated (800 "C) silica gel shows an ab-
sorption peak at u1 = 2668.80 nm (seeFigure 40),surely
due to the fundamental stretching vibration of hydroxyl
groups on the gel surface. These singular, or free, hy-
droxyl groups are also referred to as "isolated silanol
groups". The symmetry of this peak indicates that
these singularhydroxyl groups have no interaction with
water molecules. The band at 1366.12 nm ( 2 4 is the
first overtone of the adjacent silanol group vibration v2
= 2732.24 nm (see Figure 37). The 1366.12-nm peak
becomes less intense as the gel is heated and disappears
with complete dehydration. The combination peak at
2207.51 nm (u2 +uoH(bend))is the result of the hydroxyl
ion's stretching and bending vibrations. Perino suggests
that this comhination band is due to the Si-0-H
stretching vibration and an out-of-plane 0-H dis-
placement (bending) vibration. This type of hydroxyl
group is labeled an OH(2) group.
The adjacent hydroxyl groups also interact with free
water (us,Figure 39) to form hydrogen bonds; this effect
causes a change in both the fundamental stretching
vibration and its associated overtones and combina-
tions. Therefore, the hydroxyl groups associated with
water show a new combination peak at 2262.44 nm (us
+ voH(bend));this kind of hydroxyl group is called
OH(3). The energy calculations by Benesi and Jonesm
predict that the fundamental stretching vibration of
OH(3)at u3 = 2816.88 nm is a value shifted ahout 148.08
nm from the vibration of the free hydroxyl group at u1
= 2668.80 nm (OH(1)). From actual absorption data,
McDonaldm observed a peak at 2816.88 nm, indicating
a strong interaction between free pore water and surface
hydroxyl groups.
When a dehydrated silica gel is exposed to a slightly
humid air atmosphere, sharp peaks appear at 2816.88
(us), 2732.24 (uz), 1890.35 (v3 + 2voH(bend)),1459.85
1 2
0 m 4w Bw 8W 1wo 12
Temperature ("c)
Figure 41. Density measurementsat varioustemperaturesfor
samples with or without CCl, treatment.m0
(2v4),and 1408.44nm ( 2 ~ ~ ) .Hair (see p 89 in ref 268)
believes that the intensity changes associated with ad-
sorption of water indicate that all these bands are
connected with the hydroxyl group which is associated
with physical pore water. Further hydration resnlts in
a broadened band at about v4 = 2919.70 nm (Figure39),
characteristic of bulk water.
Cant and Littlen'*272and Hair and Chapmann3 tend
to agree that for silica gel a sharp and slightly asym-
metrical peak on the high-wavelength side, at 2668.80
nm (I+),together with a distinct band at 2732.24 nm (uZ),
can be attributed to freely vibrating surface silanol
groups and to hydrogen-bonded adjacent silanolgroups,
respectively. In addition, a broad band at 2919.70 nm
(u4) is due to the stretching of molecular water. Elmer
et aLn4in their study of rehydrated porous silica showed
that the intensity of the peak at 2668.80 nm increases
during rehydration. They also indicated that physical
water prefers to adsorb on adjacent hydroxyl groups
rather than on the singular hydroxyl groups. Studies
of optical fibers by Keck, Maurer, and SchultP found
that the extrinsic hydroxyl groups alsogive rise to some
noticeable overtones and combinations occurring
roughly at 725, 880, 950, 1125, 1230, and 1370 nm.
These absorptions stronglydegrade the performance of.. -
optical fibers.
Most of the silica glasses manufactured by melt or
svnthetic methods result in imwrities (e.e.. water. Y l
and/or metallic elements)?' Three significant absorp-
tion peaks at 2732.24 (v2), 2207.51 (u2+uoH(bend)),and
1366.12nm ( 2 4 are found to be the unique stretching
vibration of adjacent silanol groups and their overtones
and combinations in alkoxide-derived silica gel mono-
liths, discussed by Wanpa66 and Hench and No
singular silanol group (ul) was found by using a high-
resolution UV-vis-NIR spectrophotometer.
The bulk density measurements at various sintering
temperatures for alkoxide-derived silica gel monoliths
with and without chlorination treatment for dehydra-
tion are shown in Figure 41. The density of the
water-rich (without chlorination) gel sample reaches a
maximum ( ~ 2 . 2g/cm3) at a temperature of about 860
"C, and the density of the water-free (with chlorination)
gel sample has its maximum ( ~ 2 . 2g/cm3)at a relatively
The Sol-Gel Process Chemical Reviews, 1990,Vol. 90,No. 1 61
TABLE IX. Absorption Peaks of the Pore Water and the
Surface Hydroxyl Groups of Gel-Silica Monolithsz6'
wave-
length,
nm identificationa observation
2919.70 * * * * * ~ 4 broad peak on a broad band
2816.88 * * * * ~ 3 tiny peak on a broad band
2732.24 ***p2 joint of two small peaks at
2768.90 and 2698.90 nm
2668.80 **Y very sharp sym peak
2262.48 ~3 + *YOH broad band, no peak
2207.51 ~2 + YOH high broad asym peak
1890.35 Y3 + 2VOH high broad asym peak
1459.85 2u4 tiny peak on a broad band
1408.44 2 ~ 3 small peak on a broad band
1366.12 2 ~ 2 very sharp sym peak
1237.85 ([2u3+ vOH] + small peak
1131.21 2Y3 + 2b'OH tiny peak
938.95 3U3 + 2YOH small peak
843.88 3 ~ 3+ YOH no peak obsd
704.22 4 ~ 3 tiny peak
[2u2 + vOHll/2
a *u0+ an out of plane bending vibration of Si-0-H bond. **q:
stretching vibration of an isolated Si-0-H bond. ***uZ: stretching
vibration of an adjacent Si-0 bond. ****u3: stretching vibration of
a Si-0-H bond which is hydrogen bonded to water. *****u4:
stretching vibration of adsorbed water.
2.00
1.60
1.20
L
$0.80
3
0.40
0.00 I I I I I I 1 I I I
200 800 1400 2000 2600 3200
Wavelength (nm)
curve a is the spectrum01 150°C sample
curve b is the spectrum of 750% sample
curvec is the spectrum of 800°C sample
curved is the spectrum of 850°C sample
Figure 42. Absorption curves of partially densified gels in air.260
higher temperature of about 1100 "C. This indicates
that the hydroxyl groups significantly decrease the
sintering temperature by lowering the surface energy
of silica.
The important absorption peaks and bands found in
Wang's dehydration studyzffiare summarized in Table
IX. These peaks and bands found in the preparation
of alkoxide-derived silica gel monoliths are identical
with those discovered by previous researchers reviewed
above on studies of silica gel powders.
Curves a-d in Figure 42 show the UV-vis-NIR
spectra of silica gel monoliths heated in ambient air at
various temperatures up to about 850 0C.260Overtone
and combination vibrational peaks are observed at
704.22, 938.95, 1131.21, 1237.85, 1366.12, 1408.44,
1459.85,1890.35,and 2207.51nm. A very strong, broad
absorption band occurs between 2400 and 3200 nm.
None of these peaks have been eliminated by heating;
instead they have only decreased in intensity with in-
creasing temperatures. Clearly, the gel is not com-
2884.3 nm
1897.6 nm -0.20
0.00 ~
200 800 1400 2000 2600 3200
Wavelength (nm)
Figure 43. Absorption curve of gel partially densified in con-
trolled CC14 atmosphere for a 950 OC sample of 3.8-mm thick-
ness.26o
(a) 105OOCsample
:: 1
0.20 1
8 0.00
B
a
c 200 800 1400 2M)O 2600 3200
Wavelength (nm)
;0.40
(b) 1150°C sample
0.00
200 800 1400 2000 2600 3200
Wavelength (nm)
Figure 44. Absorption curves of gels partially densified in
controlled CCll atmosphere for a 1050 OC sample of 3.6-mm
thickness and a 1150 O C sample of 3.4-mm thickness.2B0
pletely dehydrated, even when heated to the point of
full densification; further heating results in a foaming
problem.
Data obtained in Wang's work260p266show that a
combination vibrational mode is identified at 2207.5
nm, resulting from the adjacent silanol stretching vi-
bration at 2732.24 nm (v2)and the out-of-planehydroxyl
ion deformation vibration at 11494.25nm (voH(bend)).
The peak at 1890.35nm is a combination vibration of
2816.88 nm (v3) plus 2 times the bending frequency
(2voH(bend)). The peak at 1459.85 nm (2v4)seems to
be the first overtone of the 2919.70-nm (v4) peak. The
peak at 1408.44nm (2v3) observed is the first overtone
at 2816.88 nm (v3), whereas the 1366.12-nm ( 2 4 peak
is from the first overtone of the fundamental hydroxyl
stretching vibration observed at 2732.24 nm (v2).
The peak observed at 1237.85nm is presumed to be
an overlap from the contribution of two types of modes,
which are 1221.00(2v2+voH(bend))and 1254.70 nm (2v3
+ voH(bend)). A tiny peak at 1131.21 nm is believed
to be 2v3+2voH(bend),and a small peak at 938.95 nm
is presumed to be a second overtone of 2816.88 nm (3v3).
There is a very tiny peak at 704.22 nm, which is a third
overtone of 2816.88 nm ( 4 ~ ~ )as shown in Figure 42,
curve d.
These results show that for critical optical applica-
tions where complete transmission over a broad range
of wavelength is important, densification in an air at-
mosphere is obviously a failure. The resulting quality
of this gel cannot compete with that of fused silica,52
and it will never reach the point of complete dehydra-
tion.
62 Chemical Reviews, 1990, Vol. 90,No. 1
UV TRANSMISSION
Hench and West
to be rate-determined by a diffusion process that is
probably governed by the adsorption and desorption
of chlorine atoms. Susa et a1.256indicate that reducing
the surface area by a presintering process is useful for
reducing both the hydroxyl and chlorine content in the
densified silica glass.
C. Structural Characterization
The structure of alkoxide-derived silica gels has been
examined in some detail, by using Raman spectroscopy,
from the dry gel through to the fully dense amorphous
Si02.326-330Gottardi et al.326report the Raman spectra
of a silica gel heated from 140 to 800 "C,showing the
interrelated changes in intensity of the SiOH peaks at
980 and 3750 cm-', the cyclotrisiloxane D2and cyclo-
tetrasiloxane D, "defect'! peaks, at 495 and 605 cm-l,
respectively, and the main Si02structural vibrations
at 440, 800, 1060, and 1195 cm-l. These results were
reproduced by Krol et a1.,3271328confirming the D1and
D2peak assignments to be four- and three-membered
siloxane rings respectively, and the formation of large
concentrations of cyclotrisiloxane D2rings on the in-
ternal pore surface as the hydroxyl concentration and
the internal pore surface area decrease with increasing
temperature. The three-membered D2 rings are
strained in comparison to the four-membered D, rings
and consequently can form only above 250 "C on the
surface of the gels via the condensation of adjacent
isolated surface silanols. In contrast the four-membered
D, rings form initially in the sol stage and are retained
until the gel is dense.282
The existence of another peak has been postulated
by Mulder et al.329to explain the behavior of the peak
at 490 cm-' between 100and 800 "C. He proposes that
the symmetric stretch vibration of network oxygen at-
oms coupled to a network-terminating SiOH group gives
rise to a strongly polarized Raman peak at 490 cm-',
which he called the Dopeak and which is transformed
to the D, peak as the condensation reaction goes to
completion. However, Brinker et a1.282dispute this
interpretation of the 495-cm-' peak behavior with tem-
perature.
Recent analysis of the structure of silica gels using
low-frequency (0-200 cm-l) Raman scattering has been
interpreted by assuming that the gels are fractal. This
infers that the scattering was characteristic of the
scattering from fractons,m,331where fractons are defined
as phonons with vibrational modes localized by the
fractal nature of the structure. Most of this work has
been done on hypercritically dried aerogels. Raman
scattering from gels involves a large contribution due
to the tail of the Rayleigh scattering peak. The inten-
sity of this peak is proportional to the heterogeneous
density fluctuations, and therefore in porous gels it can
be up to 8 orders of magnitude more intense than the
Raman peaks. Consequently, this tail is removed by
thermal reduction using Bose-Einstein statistics, and
the reduced Raman spectra is then analyzed.330Con-
sequently, the reduced data must be interpreted cau-
tiously due to the magnitude of the thermal correction.
D. Stralned Defects
Brinker et a1.279-283have used solid-state 29Simagic-
angle spinning NMR, XPS, 'H cross-polarizationMASS
NMR, and Raman spectroscopy to investigate the local
100 7. , GELSIL
7 5 % -
50% -
0 INCREASING
OH CONCENTRATION
794a
CORNING
DYNASIL
WAVELENGTH
OUANNM BASED QUANTUMBASED
THEORETICAL RING OF FIVE 6 MOLE % OH
SlUCA TETRAHEDRA IN SIUCA
Figure 45. Improvements in UV transmission of alkoxide gel-
silicas with time compared with quantum mechanics predictions
of UV cutoff ~ a v e l e n g t h . ~ ~
Carbon tetrachloride treated samples were prepared
at 850,950, 1050,and 1150 "C,and their characteristic
UV-vis-NIR absorption spectra compared, as shown
in Figures 43 and 44 (from refs 260 and 266). Absorp-
tion peaks were visible at 2890.1, 2768.9,2698.9,2668.8,
2207.5, and 1897.6 nm for the 850 "C sample and at
2884.3, 2765.4, 2698.3,2669.4,2207.5,and 1897.6nm for
the 950 "C sample.
Stretching vibrations of the adsorbed physical water
gives rise to typical broad absorption peaks at 2890.1
and 2884.3 nm, which are shifted from 2919.70 nm (YJ
within a broad range from 2700 to 3200 nm. Absorption
peaks at 2698.3 and 2698.9 nm are suggested260p266to be
the result of the stretching vibrations of hydrogen-
oxygen bonds of adjacent silanol groups. The 2768.9
and 2765.4-nm peaks are proposedmsm to be the result
of stretching of the hydrogen bonds to the neighboring
silanol oxygens,as shown in Figure 37. These two kinds
of absorption peaks in general cannot be distinguished
and thus form the combined broad peak at 2732.24 nm,
which is observed by many r e ~ e a r ~ h e r ~ . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~The
sharp peaks at 2668.8 and 2669.4 nm are identified to
be caused by vibrating surface isolated silanol groups
(Le., free hydroxyl groups).
The intensity of all absorption peaks decreases as the
temperature increases. The spectrum from the 1050 "C
sample shows only one peak, as shown in Figure 44,260
occurring at 2668.8 nm (vJ, which is caused by isolated
hydroxyl groups. The sample heated to 1150 "C has
a spectrum in which the water peaks have been elimi-
nated, as shown in Figures 44 and 45 (from ref 260 and
53). The absorption loss due to water approaches zero
as no water or hydroxyl absorption peaks are present
at any wavelength. The quality of optical transmittance
of this sample is significantly higher than that of tra-
ditional fused silica glass and equivalent to that of op-
tical fibers used in communication systems.
One of the complications associated with use of
chlorine compounds in the dehydration of silica gels is
the incorporation of chlorine ions in the densified
gel-glass structure. Susa et al.256describe a dechlori-
nation treatment using an oxygen atmosphere at
1000-1100 "C after chlorination at 800 "C to remove
the hydroxyl ions. The dechlorination reaction seems
The Sol-Gel Process
800 7
600 -
400 -h
' 2 0 0 -
0
- 0 -
\
-200-
_I
___
-4---
- I
-R.1.21 NM
-Rz4.18NM
-R=8.98NM
2.15
R = HYDRAULIC PORE RADIUS
2.10
-."" .
2 0 0 400 600 8 0 0 1000 1 2 0 0
TEMPERATURE ["C] (HELD FOR 12 HRS)
Figure 46. Dependence of the structural density ps (g/cm3) of
alkoxide-derived porous silica gels, as a function of sintering
temperature, for three different average hydraulic pore radii, R
(nanometers).
silicon environment and siloxane ring vibrations in
amorphous alkoxide (TEOS) derived silica gels. Their
results relate the 608-cm-' Raman "defect" mode in
amorphous Si02with reduced Si-0-Si bond angles in-
dicative of strained three-membered rings of silicate
tetrahedra.282g283They showB3that dehydroxylation of
the silica surface results in cyclotrisiloxane species that
have altered acid-base characteristics due to the
strained bonds. Their XPS experimentsm indicate that
the expected 0.35-eV shifts in silicon and 2p oxygen 1s
binding energies which are due to the reduced bond
angles are hidden within broad peaks due to the re-
maining hydroxyls. Brinker et al. also observe addi-
tional silicon 2p oxygen 1s and carbon peaks which are
postulated to result from preferential absorption of
extrinsic 1s carbon-containing species on sites with
enhanced acid-base properties. Molecular orbital
calculations by O'Keefe and Gibbs2%have established
that the optimized geometry of the cyclic trisiloxane
molecule, H6Si303,is planar with D3hsymmetry with
a bond angle 4 = 136.7", which is 10" less than the 147"
angle characteristic of traditional vitreous silica.
Spectroscopic investigations of isolated model molecules
by Galeener285show that the symmetric oxygen ring
breathing vibration occurs at 586 cm-l, which is close
to the D2Raman bond observed for gels and glasses.286
The change in structural density of alkoxide-derived
silica gels during thermal processing is apparently
caused by at least four interrelated mechanisms. These
mechanisms include the elimination of metastable
three-membered rings (see above),the loss of hydroxyls,
the loss of organicgroups, and the relaxation of the Si02
structure. Figure 46, from Wallace and H e n ~ h , ~ ~shows
the structural density ps (g/cm3)of a series of silica gel
powders, held for 12 h at each temperature with average
hydraulic pore radii R of 1.21, 4.18, and 8.98 nm. The
true or structural density was measured by using He
pycnometry. The structural density ps starts out below
that for amorphous silica (p, = 2.20 g/cm3) and goes
through a maximum of about 2.30 g/cm3 before
equilibrating at full densification at about 2.22 g/cm3.
The average standard deviation of the measurements
is about 0.004 g/cm3. The observed variation of ps with
temperature is potentially due to a number of effects,
including reducing the surface alkoxide and hydroxyl
0
rw -400
n
-800-600 I0 200 400 600
Temperature ("C)
Figure 47. Expansion and contraction of 950 "C stabilized
gel-silica cycled to 600 0C.278
-5001 I - I I 9 I -
0 100 200 300 400 500
TEMPERATURE("C)
Figure 48. Repeated cycling of gel-silica above 250 0C,278
concentration, formation and elimination the metasta-
ble three- and four-membered siloxane ring surface
defects (D2and D1,respectively, in the Raman spec-
troscopy nomenclature), structural relaxation, comple-
tion of condensation reactions, and viscous flow. Con-
siderable additional research is required to isolate each
of these contributions to the observed changes in
structural density of the gels.
E. Dilation of Sol-Gel Silica Monolithswith
Adsorbed Water
The expansion of porous gel-silica monoliths has been
studied by using a dual pushrod Theta dilatometer.27s
The expansion and contraction showed a hysteresis with
heating and cooling. Figure 47 shows this hysteresis for
a sample stabilized to 950 "C. As long as the sample
was cycled below approximately 500 "C, there was no
hysteresis and the monolith appeared to be thermally
stable.278
If thermal cycling is performed on the gel monolith,
the hysteresis is reduced significantly. Figure 48 shows
the thermal cycles performed on a porous gel monolith
between 250 and 400 "C before cooling to room tem-
perature. The material shrinks a lot initially, but during
thermal cycling the expansion behavior is totally re-
versible. It is postulated that the expansion of porous
gel-silica upon cooling below 250 "C was due to ab-
sorption of water onto the pore walls of the material.
This was tested by running diatometry and thermo-
gravimetric analysis (TGA) under an ambient atmo-
sphere.278Figure 49 shows expansion in the dilatometer
over 23 h at 23 "Cdue to water absorption onto the pore
surfaces of the gel. Thus, adsorption of water into the
64 Chemical Reviews, 1990, Vol. 90, No. 1 Hench and West
TABLE X. Silica Dilation
diagonals
Si-Si dist, A av neighbor water av expansionINDO
4 fold ring energy, au (1)-(14) (6)-(7) Si-Si dist, 8, content, wt Yo UIL,PPm
without H,O -223.4 4.6 4.5 3.2 0 0
with H,O -241.4 5.2 4.0
35c r--
-50 C - r - 7 ~- ~-T - - T 7 - - - - T -1
0 4 0 12 16 2C 24
-IME (hours)
Figure 49. Expansion of porous gel-silica at room temperature
over 24-h in ambient air.
porous sol-gel silica appears to dilate the gel structure.
F. Quantum Calculationsof Water Adsorption
onto Sol-Gel Silica
The INDO models presented earlierlg39lg4attempted
to show the energetics of rings and chains of silica
tetrahedra during the sol to gel transition. After con-
densation is complete and thermal processing has oc-
curred, the sol-gel silica monoliths should be primarily
made up of rings. There is roughly an equal distribu-
tion of 4-fold, 5-fold, 6-fold, and 7-fold rings of silica
tetrahedra in vitreous silica and equivalent structures
are believed to be present in silica gels (Klemperer et
aLg7). The 4-fold ring shown in Figure 50 shows the
structure selected by West et a1.288to study the theo-
retical effect of water on silica rings. The water was
hydrogen bonded to the silica cluster as predicted by
T a k a h a ~ h i . ~ ~ ~Intermediate neglect of differential
overlap (INDO) molecular orbital theory developed by
Zerner et was used to optimize the structure in
Figure 50. The 4-fold ring was geometricallyoptimized
with and without the adsorbed water molecule.
Table X shows the results of the calculations for the
dilation of the 4-fold silica ring. The distances between
the diagonal silicon atoms are shown. The ring without
water is uniform. However, the ring with the water
adsorbed is elongated along the axis with the water.
Also, the averagesilicon-silicon distance for neighboring
atoms increases.
In an amorphous structurethere should generally be
a random orientation of the structural elongation. Some
orientation can be imposed on an amorphous material
through fiber drawing or spin casting. In gel monoliths
with random structures some of the water-induced ex-
pansion will occur in regions of the glass where con-
traction of the rings can compensate, thereby inducing
strain. However, on the average there is predicted to
be a small expansion when the water is bonded to the
structure.
ci ( 2 7 )
Water
H (26:
Figure 50. The 4-fold silica structure with one absorbed water
molecule.251
TABLE XI
water water
content. wt 70 ALIL,rmm content, wt % U J L ,ppm
5.8 836 0.725 104
2.9 418 0.36 52
1.45 209
The average bond length between neighboring silicon
atoms increases with the bonding of water. This in-
crease can be used to estimate the expansion and con-
traction ( U / L )of porous sol-gel silica associated with
adsorption and desorption of water. When the porous
material is heated, there are two competing contribu-
tions to the observed thermal dilation: (1) the uniform
increase in dimension due to thermal expansion of the
silica structure; (2) a decrease in dimension due to
contraction resulting from desorption of water from the
surface of the pores. Upon cooling, the reverse occurs,
i.e., there is an intrinsic contraction of the structural
network and an extrinsic expansion as water is adsorbed
(Figure 49). If the effect is linear, then the calculated
expansion is shown in Table XI.
For the observed expansion, we have
( u / L ) o b s = (AL/L)H,O + ( u / L ) i n t r j n s i c (38)
then, solving for the extrinsic effect of water on heating
the sample:
(BL/L)H,O = ( u / L ) o b s - ( u / L ) i n t r i n s i c (39)
where the thermal expansion of the material can be
calculated from Figure 47, shown earlier. Thus
( u / L ) i n t r i n s i c = 60 P P ~ (40)
with
( U / L ) O , S = 200 PPm (41)
Then
(WL)I-I,O = 140 PPm (42)
The Sol-Gel Process Chemical Reviews, 1990, Vol. 90.No. 1 65
with approximately 1.0% water loss. This compares
remarkably well with the calculated extrinsic expansion
or contraction shown in Table XI, e.g.
(U/L),,, = 150 P P ~ (43)
for a dilation or contraction caused by -1.0% water
absorption or desorption.
IX. Densification
Densification is the last treatment process of gels. As
illustrated in Figure 3, densification of a gel network
occurs between 1000and 1700"C depending upon the
radii of the pores and the surface area. Controlling the
gel-glass transition is a difficult problem if one wants
to retain the initial shape of the starting material. It
is essential to eliminate volatile species prior to pore
closure and to eliminate density gradients due to non-
uniform thermal or atmosphere gradients.
Initially gel-derived glasses were made by melting.261
The interesting feature of the sol-gel process that was
exploited in this early work was the molecular scale
homogeneity of the gels, which helped prepare glasses
that ordinarily devitrify at low temperatures. The use
of hot pressing of gels by a number of investigators
resulted in densification at lower temperature and
produced a number of glassesthat otherwisewould have
~rystallized.'~~-'~~With successful stabilization treat-
ments it is possible to manufacture monolithic dense
gel-derived glasses by using furnaces, and sometimes
vacuum, without applying pressure or heating to tem-
peratures above the melting point.52~53J40~256~297-302
The amount of water in the gel has a major impor-
tance in the sintering behavior. The viscosity is strongly
affected by the concentration of water,303which in turn
determines the temperature of the beginning of den-
sification. For example, a gel prepared in acidic con-
ditions has a higher surface area and water content than
a gel prepared in basic conditions and starts to densify
about 200 "C sooner than the base-catalyzed gel, as
shown by Nogami and Moriya.lM Simultaneously with
the removal of water, the structure and texture of the
gel evolves. Gels have higher free energy than glasses
mainly because of their very high specific surface area.
During sintering the driving force is a reduction in
surface area.184 Most authors report a diminution of
the specific surface area when the densification tem-
perature increases.110J42~304-3ffiHowever, it was shown
that certain samples display first an increase of surface
area until a temperature between 300 and 400 "C, and
then the specific surface area decreases with a further
increase of t e m p e r a t ~ r e . ~ ~ ~ ~ ~ ~ ~The increase in surface
area was attributed to the removal of water and or-
ganics.
The structural evolution during the gel to glass con-
version is difficult to quantify in absolute terms because
there is no definitive structure of a gel. However, it is
possible to compare physical properties at different
stages between gels and between gel and glass. Some
work shows that the small pores close first for some
gels308~309because they have a higher "solubility" in the
gel or glass matrix due to their small radii of curvature.
The major conclusion of several studies is that despite
the complex manner in which the gel evolves toward a
glass, once the gel has been densified and heated above
the glass transition temperature, its structure and
properties become indistinguishable from those of a
melt-derived glass.49J19.310-313
There are at least four mechanisms responsible for
the shrinkage and densification of gels (seeBrinker and
Scherer70 for details): (1)capillary contraction; (2)
condensation; (3) structural relaxation; (4)viscous sin-
tering. It is possible that several mechanisms operate
at the same time (e.g., condensation and viscous sin-
tering). Using three different models, one can describe
the sintering behavior of a gel. Frenkel's theory,314
which is derived for spheres, is valid for the early stages
of sintering, because of the geometrical assumptions.
It is based on the fact that the energy dissipated during
viscous flow is provided by the reduction in surface area.
Scherer315developed a model for describing the early
stage as well as the intermediate stage of sintering. It
is assumed that the microstructure consists of cylinders
intersecting in a cubic array. To reduce their surface
area, the cylinders become shorter and thicker.315The
last stage of densification is represented by the Mack-
enzie-Shuttleworth model, which is applicable only to
systems with a closed porosity.316 This set of models
predicts reasonably well the behavior of gels upon
heating, although more work needs to be done to rec-
ognize the contribution of each mechanism to the sin-
tering process.317
V a s c o n ~ e l o s ~ ~ ~and Vasconcelos et al.89 have at-
tempted to understand the structural evolution of the
gel-glass transition using topological concepts. As in-
dicated above, densification is the increase in bulk
density that occurs in a material as a result of the de-
crease in volume fraction of pores. Consequently the
parameter volume fraction (V,) has been traditionally
used to characterize a structure during sintering.
Rhines318added to the metric parameters the topolog-
ical concepts that provide complementary information
about the sintering process.230-319*321~322In topological
terms the densificationprocess can be divided intothree
stages, according to the genus3I8(which is defined as
the maximum number of non-self-reentrant closed
curves that may be constructed on the surface without
dividing it into two separate parts):321
First stage: growth of weld necks while the genus
remains constant.
Second stage: the genus decreases to zero as the
pores become isolated.
Third stage: the genus remains constant at zero while
the number of pores goes to zero.
The introduction of topological parameters to the
structural characterization of a material yields infor-
mation that is not visible by considering metric pa-
rameters only. One important application of topological
characterization is the characterization of intercon-
nected pore structures suitable for diffusion, doping,
catalysis, and impregnation procedures. In those cases,
knowledge about the volume or surface area of pores
is not enough to characterize the structure, because one
has to know the extent of interconnection of the
structure. The first topological model developed by
Vasconcelos et aLE9assumes a prismatic geometry in
which the pores are tetrahedra connected by triangular
prisms (Figure 51). The second model uses a cylin-
drical geometry (Figure 52). Correlating the volume
of pores (V,),the surface area of pores (S,),the average
branch size (L),and the average pore diameter (D)to
66 Chemical Reviews. 1990, Vof. 90,No. 1 Hench and West
Figure 51. Tetragonal geometric model.
4(1.V")
L = -sv
Bv = sv3
1GrVv(1-Vu)
Nv =E"
2
Gv = BY Nv+l
Figure 52. Cylindrical geometricm0del.4~~
a particular geometry, one obtains a unique set of so-
lutions that yield the number of branches (BJ,number
of nodes (N"),the genus (GJ, and the coordination
number of pores (CN),as shown in Figures 51and 52."
The average pore size (D)reported for the cylindrical
model is the mean lineal intercept of the pore
D = 4V,/Sv (44)
The prismatic model associates a volume to both the
nodes and the branches of the pores, while the cylin-
drical model considersthat all the volume is associated
with the branches that form the p0rosity.2~~
As shown in Figure 53," the models assume 4 as the
averagecoordinationnumber of pores (CN) in the dried
stage. That initial stage usually corresponds to a
maximum number of branches, nodes, and genus. In
a sol-gel processed material the interconnected struc-
ture is developed during gelation, aging, and drying, as
discussed in previous sections. In topological terms
these processes correspond to the first stage of densi-
fication. During the second stage of densification, the
genus decreases, but the number of nodes remains
constant and the number of branches decreases. The
pyramidal model (Figure 53a) assumes that when CN
reaches 2, further elimination of branches leads to
disappearame of nodes, and therefore both B, and N,
decrease, keeping CN constant at 2 during the third
stage of densification. At this stage of densification G,
is equal to 1 and it is kept constant during the third
stage. The cylindrical model assumes a constant num-
her of nodes for the entire process, and the coordination
number varies from 4 to 0, as shown in Figure 53b.
Both models can be incorporated in a generalized
modeP considering the zeroth Betti number (number
of separate parts, P,) in the expression G, = B, - N,
+ P,. During the third stage of densification, as the
number of nodes and branches decrease, CN actually
goes to zero. The temperatures indicated in Figure 53a
correspond to the processing temperatures of the sili-
ca-gel monoliths.
The temperature dependence of the structural evo-
lution of alkoxide silica gel monoliths as described by
Figure 53. (a)Variation of the numberof branches (BJ,number
of nodes (Nv),and genus (GJ, as a function of the coordination
number (CN). (b) Schematicof the evolutionof the pore coor-
dination number.='
0 200 400 600 800 1000 1200
TEMPERATURE (C)
Figure 54. Variation of the number of branches (B,),number
of nodes (NJ,and genus (GJ as a function of temperature of an
organometallic silica-gel monolith.2s1
both models is shown in Figure 54. The genus de-
creases along with the number of pores at increasingly
higher sintering temperatures. The models indicate the
temperature for the beginning of the third stage of
densificationto he in the range lOo(t1150 O C for these
acid-catalyzed alkoxide silica gels. Despite differences
in the numerical values of N,,G,, and B, associated
with the pyramidal and cylindrical models, they de-
scribe the structure in a very similar way, which is
consistent with a topological description.
Because the number of nodes is constant during the
second stage of densification and the genus is constant
during the third stage of densification, the number of
branches is a useful parameter to follow the evoluation
of the structure. To make it numerically easier to
compare the different topological states, a topological
index (fraction of removed branches) has been defined
by Vas~oncelos~~~as follows:
(45)
where Bvocorrespondsto the number of branches of an
arbitrary reference state. If the dried state is chosen
asreference, 0for the dried sample iszeroand ,9 for the
fully dense material is equal to 1. Thus the topological
index p can be associated with the densificationprocess
changing from 0 to 1with time. The rate of topological
change will therefore be d@/dt.
The choice of the initial coordination number (CNO)
does not affect the evaluation of B,, but it influences
the numerical values of N, and G,. For the beginning
B = 1- (B,/B,")
The SOl-Gel Rocess
0
0 200 400 600 800 1000 1200
TEMPERATURE (C)
Figure55. Variation of the numberof branches(B.) BS a function
of temperaturefor structures of 24- and 64-Apore diameter."'
of the third stage of densification Vasconcelos shows
that @ is given by
B(G,=O) = 1 - (2/CN0) (46)
Application of the cylindrical topological model to
structures of different pore sizes (24-and 64-.&average
diameter) isshown in Figure 55. While B, for the 24-.&
structures decreases sharply after about 800"C,B, for
the 64-A structure remains roughly the same (in fact
it increases slightly) over a much broader temperature
range. An explanation for the apparently largerthermal
stability of the large pore size structure is the smaller
driving force for sintering associated with the smaller
pore-solid surface area present in the large-pore
structure.
such asthose
studied by Rhines and DeHoff:Ism show similar paths
of topological evolution during densification (particu-
larly a decrease in G. as V, decreases), indicating the
broad spectrum of applications of the topological con-
cepts. The path of microstructural evolution described
for silica gel monoliths is similar to the path associated
with the sintering of larger ~tructures.2~'
Thus, application of topological modeling to the
densification of sol-gel-derived nanometer-scale struc-
tures reveals the same principles as determined for the
sintering of micrometer to millimeter scale powder
structures. As shown in the next section,the topological
evolutionof the gel structure can be related to physical
properties and presents potentially useful information
that is complementaryto traditional metric parameters.
X. Physical Propertes
There are relatively few papers .describingthe ther-
mal, mechanical, and optical properties of gel-derived
monoliths. This isbecause of the difficultyof producing
large stable structures, as reviewed in the previous
sections. During 1988-89, processingoptimization has
been achieved for the production of gel-derived silica
optical components. Hench et al?2.53described the
processing and properties of these new materials,
termed type V (fully dense) gel-silica and type VI
(opticallytransparent porous gel-silica). The properties
of types V and VI are compared with commercial fused
quartz optics (types I and 11) and synthetic fused silica
optics (types 111and IV)?2
T y p V gelsilica has excellenttransmission from 160
to 4200 nm with no OH absorption peaks. As shown
in Figure 45, the UV cutoff is shifted to lower wave-
numbers by removal of OH from the gel glass. Also,
Much larger structures (G,= 106
Figure 56. Sol-gel silica monoliths in the (A) dry state, (B)
stabilized state (poroustype VI),and (C)fully dense state (type
w . 5 3
quantum calculations, discussed earlier, predict this
effect.lq3
Other physical properties and structural character-
isticsof type V gel-silica are similar to high-grade fused
silica but offer the advantages of near net-shape casting,
including internal cavities, and a lower coefficient of
thermal expansion of 0.2 X lo6 cm/cm compared with
0.55 X lo6 Optically transparent porous
gel silica (type VI) has a UV cutoff ranging from 250
to 300 nm. Type VI gel-silica optics has a density as
low as 60%of types I-V silica and can be impregnated
with up to 30-4070 by volume of a second-phase opti-
cally active organic or inorganic compound. Photo-
graphs of a dried alkoxide silica gel monolith, a type VI
porous Gelsil sample and a fully dense type V Geld
sample are shown in Figure 56.
Shoup and Hagy has shown that the colloidal method
of making reflective silica opticsm(method 1) yields a
different thermal expansion behavior than types 1-111
vitreous silica, presumably due to the rapid quenching
of the gel-glasses from 1720 oC."2
Bachman et aLS3 describe the use of centrifugal de-
position of 12-40-nm colloidalsilica powders to produce
synthetic silicatube used in the manufacture of optical
telecommunication fibers. They report optical losses
of a13w= 0.97 dB/km and d5%= 0.77 dB/km for o p
tical fibers made by using the tubes. A Rayleigh
scattering coefficient of aR = 1.1 dB/(km pm') was
measured for the bulk sintered tubes, equivalent to that
of the single-mode fibers. One of the main advantages
of the sol-gel technique was very high accuracies
(*0.05%) for the diameter, cross-sectional area, and
wall thickness of the tubes.
Mechanical properties of the type VI porousgel-silica
monoliths have been determined by Vasconcelos et
al.8q.251and related to the topological and metric fea-
tures. The variation of flexural strength as a function
of V,shows relatively scattered data (Figure57a). The
flexural strength correlates better with @, as shown in
Figure 57b. for the topological cylindrical model dis-
cussed in the Densification section. The points in
Figure 57 represent an average; the total number of
mechanical testsperformed is27. The true density data
are incorporated into the topological modeling. The
true density of some selected samples (of 24-.&pore
diameter) is as follows: dried, 2.10 g/cm3; 800 O C , 2.31
g/cm3; 1150 "C, 2.20 g/cm3.
Additional details of ultrastructure-poroperty cor-
relations of various gelsilica monoliths are to be pub-
68 Chemical Reviews, 1990, Vol. 90,No. 1 Hench and West
n
5.
EazW
[I:
c
v)
-I
[I:
3
x
W
A
U.
a
0 4 0 0 42 0 44 0 46 0.48 0 50
v v
60
5 0
4 0
30
20
i n
fl
Figure 57. Variation of the flexural strength (a) as a function
of the volume fraction of pores (V,) and (b) as a function of the
topological index p.251
lished later by Hench and Vascon~elos.~~~
X I . Conclusions
The goal of sol-gel processing is to control the
structure of a material on a nanometer scale from the
earliest stages of processing. For pure silica powders,
fibers, and even monoliths this goal has been achieved.
The potential of improved properties due to ultra-
structural processing, control of higher purity, and
greater homogeneity has been realized. Other engi-
neering advantages of the lower temperature chemically
based sol-gel processing such as net-shape casting, fiber
pulling, and film coating have also reached economic
potential.
Advances in understanding the science of sol-gel
processing are less conclusive. General aspects of the
chemistry of each of the seven sol-gel process steps are
established. However, understanding of the molecular
reaction mechanisms and the thermodynamics and
kinetics of sol-gel systems is meager. Many studies
involve model systems that yield self-consistent data
but may not necessarily apply to processing formulas
that yield useful materials. Only a few studies use
multiple experimental methods to confirm reaction
mechanisms or determine kinetics. Likewise,there are
few investigations of the interrelationships between the
seven processing steps. For example, many investiga-
tors have shown that base catalysis yields gels with a
coarser texture than acid catalysis. However, there is
little understanding as to how the differences in gel
texture influences aging, drying, stabilization, or den-
sification of the gels. Systematic studies on multicom-
ponent gel systems are especially rare.
A major difficulty in developing molecular level un-
derstanding of the sol-gel processing is the extremely
small scale of the structures involved. After gelation
occurs, and often even at t > 0.3-0.5tg, the substance
usually must be treated analytically as a solid. Since
the solid phase at t, can be as little as 1-1070 of the
mass of the object, a cross section of the solid web is
only a few molecules wide, but the length of the mo-
lecular chains extend throughout the object with an
enormous number and complexity of interconnections.
The molecular structure of the liquid phase in these gels
is as important as the structure of the solid phase.
However, the liquid characteristics deviate from clas-
sical liquids in many ways. The concept of phase
boundary is stretched to the quantum mechanical limit.
Consequently, it is quite likely that quantum mechan-
ical based models are much more likely to yield the next
level of understanding of sol-gel processes rather than
a macroscopic fractal approach.
In some ways it may be useful to think of sol-gel
science in terms of a few fundamental questions, i.e.,
How does the gel structure form? How does the
structure evolve? How does it interact with its envi-
ronment? How does it collapse? These questions
parallel the fundamental questions in the biological
sciences. It is fitting that they do, for silicon is the fiith
most abundant element in the biosphere, and life forms
with hydrated silicon exoskeletons, diatoms, are re-
sponsible for more than half of the carbon and nitrogen
biochemical fixation that occurs annually on the
earth.334The biologicalsilicon-based structures of both
plants and animals form at low temperatures and with
elegant highly repetitive ultrastructures. The various
theories regarding formation of biological silicon-based
the metabolic pathways for the
role of silicon in 0steogenesis,3~~atheroscler~sis,~~and
even biogenesis337are of considerable current interest
and debate. Thus, our quest for the answers to the
fundamental questions of sol-gel science may also offer
advances in the understanding of biological science and
perhaps even of the origins of life and preservation of
health. In our opinion, these answers are most likely
to come from the exploration of molecular order and
disorder at the interface of nanometer-scale structures.
Acknowledgments. We gratefully acknowledge the
support of the Air Force Office of Scientific Research
under Contract No. F49620-88-C-0073during the course
of this work.
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