J . S o p o u š e k ú l o h a
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1.a-c
1.a. Determination of viscosity-average molar mass of polymer
The dynamic viscosity η of the liquid can be measured by capillary U-tube type
Ubbelohde viscometer (FIGURE 1). At this instrumental setup, the following formula
is valid:
η ρ= ⋅ ⋅C t (1.1.)
where C is constant of the viscometer (given by manufacturer), ρ is density of the
liquid to be examined, and t is flow time between upper Z1
and lower Z2
level (FIGURE 1).
At low concentrations, we can approximate the solution density with the density of pure
solvent. Strictly isothermal conditions are important for an exact viscosity measurement.
The dynamic viscosity of the solutions can be compared with dynamic viscosity of the
pure solvent ηo
. Thus we obtain relative viscosity:
00/ ttrel == ηηη (1.2.)
where t and 𝑡𝑡0 are the flow times for solution and solvent.
Specific viscosity η𝑠𝑠𝑠𝑠
is given by
0
0
0
0
1
t
tt
relsp
−
=−=
−
= η
η
ηη
η (1.3.)
Reduced viscosity can be calculated as
0
0
ct
tt
c
sp
red
−
==
η
η (1.4.)
At low solute concentration 𝑐𝑐, the reduced viscosity η𝑟𝑟𝑟𝑟𝑟𝑟
become important mainly for
macromolecules because an extrapolation η𝑟𝑟𝑟𝑟𝑟𝑟
to zero concentration c gives intrinsic
viscosity. It is found that some solutions of macromolecules often fit the Mark-KuhnHouwing-Sakurada
(MKHS) relationship:
a
MK ⋅= *
*
η
η (linear form: MaK ln)ln()ln( *
*
+= η
η ) (1.5.)
where *
η
K and 𝑎𝑎 are constant that depend on temperature, the solvent type, and type
of macromolecule. 𝑀𝑀 is the viscosity-average molar mass of macromolecule. The linear
form (1.5.) enables the determination of the MKHS constants using fit of the
experimental intrinsic viscosity dependence on known molar mass of monodisperse
homologous polymers. The knowledge of MKHS constants *
η
K and 𝑎𝑎 allows for an
easy determination of the viscosity-average molar mass of a polymer by measuring the
intrinsic viscosity η∗
.
The good method for the extrapolation of the intrinsic viscosity η𝑟𝑟𝑟𝑟𝑟𝑟
to 𝑐𝑐 = 0 is to use
empirical equations:
( ) ck
c
sp 2*
1
*
ηη
η
+= (1.6.)
( ) ( ) ck
c
2*
2
*0/ln
ηη
ηη
−= (1.7.)

J . S o p o u š e k ú l o h a
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1.a-c
The intercept and the slope of the each equation we obtain using linear least square
regression. The intercepts on y axis are equal to intrinsic viscosity in both equations.
The slopes are different but the sum of the constants 𝑘𝑘1 and 𝑘𝑘2 gives ½.
TASK: Determine viscosity-average molar mass of polyethylene glycol (PEG)
using Ubbelohde viscometer. Find intrinsic viscosity η∗
using eqns (1.6.) and (1.7.)
and verify empirical relation: 𝑘𝑘1 + 𝑘𝑘2 = 0,5. MKHS constants of PEG are *
η
K =
1,05 10−4
dm3
g−1
, a = 0,570 at 25-30ºC.
LABORATORY AIDS AND CHEMICALS: Ubbelohde viscometer (FIGURE 1), thermostatic
bath, thermometer, stopwatch, funnel, 2 beakers (50 ml), 2 divided pipettes
(10 ml), 1 divided pipettes (5 ml), syringe with thin hosepipe, small stopper, 6 volumetric
flasks (50 ml), PEG solution 50 g/dm3
.
INSTRUCTIONS: Become familiar with the
function of the viscometer and
thermostatic bath (set temperature to 25°C).
Refill and flush the viscometer`s tubes and
reservoirs (FIGURE 1) by pure water three
times at least by means of syringe with thin
hosepipe.
Fill the sample reservoir of the viscometer by
pure solvent (water) through filling tube 1 to
level L0. Close tube 3 with a stopper. Connect
tube 2 with syringe. Adjust liquid using syringe
to a point about 10mm above level Lu.
Remove syringe and stopper. Measure the
flow time taken for the bottom of the meniscus
to fall from the upper level mark Lu to the
lower level mark LL. Repeat the measurement
of the solvent until the difference between the
flow times less than 0,25 s.
Prepare water solutions with PEG
concentrations: 5, 10, 15, 20, 25 and 30
g /dm3
in volumetric flasks (note: this sample
preparation may start within tempering of the
viscometer). Fill viscometer with first sample 5
g /dm3
. Measure the flow time of the sample
three times. Apply the same procedure for
more concentrated sample. Cleaning by
flushing with water is not necessary with
exception for final cleaning.
REPORT: TABLE 1: solute concentrations c, flow times t (three per solvent as well
as for each solution), average flow times, values: ηrel ,ηsp , ηred , and
( )ln η η0
c
.
COMMON GRAPH 1: two dependences: ηred and
( )ln /η η0
c
on c (including regression
?


FIGURE 1: Ubbelohde viscometer: S …
sample reservoir, X ... timing bulb, C
…capillary, LU and LL … markers of
upper and lower level, 1… filling tube,
2…capillary tube, 3 … venting tube.

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1.a-c
lines). NEXT: intrinsic viscosity *
η [dm3
g­1
], molar mass of PEG in g mol­1
and number
of ethylene glycol units. Apply slopes of regression lines, eqn (1.6.), and eqn (1.7.) to
verify relation 𝑘𝑘1 + 𝑘𝑘2 = 0,5.