1
States of Matter
Gas
Random
Free space
Free movement
Far apart
Liquid
Disordered
Free movement of
particles of groups of
particles
Closer
Solid
Ordered
Fixed positions
Close distances
2
States of Matter
0.997125Liquid
3.26 10 −4400Vapor
0.91680Solid
Density, g
cm−1
Temp, oC
(press 1 bar)
Water
Gas
Liquid Molecular Crystal
3
Covalent Bond vs Intermolecular Forces
H2O 2H + O ΔH = + 920 kJ mol−1
H2O(l) H2O(g) při 100 oC ΔH = + 41.2 kJ mol−1
4
> 5London dispersion
2 – 10Dipole-dipole
10 – 50 (100)H-bond
200 – 1000Covalent
Energy, kJ mol−1Bond Type
5
Van der Waals Interactions
ion – ion Coulombic interactions
ion – dipole interactions
dipole – dipole → orientation, Keesom
dipole – induced dipole → induction, Debye
ion – induced dipole
induced dipole – induced dipole → dispersion, London
van der Waals repulsion
J. D. van der Waals
(1837- 1923)
NP in Chemistry 1910
6
7
Ion – Ion Coulombic Interactions
Coulomb’s Law
r
qq
E 21
04
1
πε
=
E = interaction energy
q = ion charge
r = interionic distance
8
Ion – Dipole Interactions
4
22
kTr
q
constE
μ
−=
E = interaction energy
q = ion charge
r = distance
μ = dipole moment
T = temp
k = Boltzmann const.
9
Hydration/Solvation of Ions
Interaction decreases with increasing ion size
[Li(H2O)4]+
[Na(H2O)x]+
K+ weak
Rb+ zero
Cs+ negative
Interaction increases with increasing ion charge
[Na(H2O)x]+ [Mg(H2O)6]2+ [Al(H2O)6]3+
Ion-dipole Polar coord. bond
Interaction decreases
Interaction increases
10
Dipole - Dipole Interactions
Keesom
6
22
kTr
constE BA μμ ×
−=
E = interaction energy
r = distance
μ = dipole moment
T = temp
k = Boltzmann const.
11
Dipole - Dipole Interactions
9.3 10 −300Dipole
moment, C m
57− 0.5Boiling point,
°C
5858Mr
AcetoneButaneCompound
12
Ion – Induced Dipole
and Dipole – Induced Dipole Interactions
4
2
r
q
constE
α
−=
μ(ind) = α E
Ion – Induced Dipole
Dipole – Induced Dipole , Debye
6
2
r
constE
αμ
−=
α = polarizability
E = electr. field intensity
α = polarizability
μ = dipole moment
E = interaction energy
q = ion charge
r = distance
13
Polarizability, α, m3
1.8
2.0
1.5
v.d.W radius,
Å
1.04
-
0.66
Atomic
Radius, r, Å
3.00S
1.80CH2
0.63O
Polarizability,
cm3 1024
Group
14
Molecule Polarizability Tboil Dipole moment
(Å3) (K) (D)
He 0.20 4.216 0
Ne 0.39 27.3 0
Ar 1.62 87.3 0
Kr 2.46 119.9 0
H2O 1.48 373.15 1.85
H2S 3.64 212.82 1.10
CCl4 10.5 349.85 0
C6H6 25.1 353.25 0
CH3OH 3.0 338 1.71
CH3F 3.84 195 1.81
CHCl3 8.50 334.85 1.01
15
Induced Dipole – Induced Dipole
Interactions
Repulsion Attraction
16
London’s Dispersion Forces
6
2
r
IE
constE
α×
×−=
IE = ionisation energy
α = polarizibility
r = distance
17
Boiling point, K Boiling point, K
F2 85.1 He 4.6
Cl2 238.6 Ne 27.3
Br2 332.0 Ar 87.5
I2 457.6 Kr 120.9
London’s Dispersion Forces
and state of halogens and
rare gases
Polarizibility increases with
molecular size
London’s Dispersion Forces and Polarizibility
Boiling point, K
18
London’s Dispersion Forces and Molecular
Shape
Same Mr
Larger contact area
19
Hydrogen Bond
O-H
O (Donorový atom)
O-H.....O
H with electronegative atoms (F, O, N, C,…)
20
Hydrogen Bond
O
H
N
O
O
o-nitrofenol
Ka = 10-7
O
H
N
O O
p-nitrofenol
Ka = 10-4
Intramolecular hydrogen bond
Lower acidity of the OH group
As a results of hydrogen bond formation
21
Hydrogen Bond
Intermolecular
22
Hydrogen Bond
Bond Distance (Å) Range (Å)
N-H...N 3.10 2.88-3.38
N-H...O
- Amide NH 2.93 2.55-3.04
- Amino NH 3.04 2.57-3.22
N-H...F 2.78 2.62-3.01
N-H...Cl 3.21 2.91-3.52
O-H…N 2.80 2.62-2.93
O-H...O
- Alcohol OH 2.74 2.55-2.96
- Water OH 2.80 2.65-2.93
O-H...Cl 3.07 2.86-3.21
23
Hydrogen Bond
Boiling points, K,
Hydrides of group 14, 15 and 16
24
HF2
− Hydrogendifluoride
Strongest known H-bond
155 kJ mol−1
Symmetrical bond distances
H-F 114 pm
Bond angle
F-H-F = 180°
Autodissociation HF
2 HF ↔ H2F+ + HF2
-
F-H
F(Donorový
atom)
[F-H-F]
-
MO
3-center
4-electron bond
25
Hydrogen Bond
Crystal engineering
Self-assembly
dimer
26
Structure of HF
27
Boric Acid
28
Structure of Proteins
29
Structure of DNA
30
31
Structure of Ice
32
Equilibrium of Attractive and Repulsive Forces
Lennard-Jones Potential
Repulsive Forces (Pauli)
Repulsion of electron clouds
U = 1/ r12
Attractive Forces(v.d. Waals)
U = −1/ r6
612
11
r
B
r
AU JL −=−
A, B = constants depending on electric
properties of molecules
+
− Equilibrium
Distance
UL-J
33
Lennard-Jones Potential
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟
⎠
⎞
⎜
⎝
⎛
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=−
612
4
rr
U JL
σσ
ε
ε = depth of potential well
σ = distance where attractive and
repulsive cancel each other
rm = Equilibrium distance
UL-J
34
Van der Waals Radii, Å
Ag 1.72 Ar 1.88 As 1.85 Au 1.66
Br 1.85 C 1.70 Cd 1.58 Cl 1.75
Cu 1.40 F 1.47 Ga 1.87 H 1.20
He 1.40 Hg 1.55 I 1.98 In 1.93
K 2.75 Kr 2.02 Li 1.82 Mg 1.73
N 1.55 Na 2.27 Ne 1.54 Ni 1.63
O 1.52 P 1.80 Pb 2.02 Pd 1.63
Pt 1.72 S 1.80 Se 1.90 Si 2.10
Sn 2.17 Te 2.06 Tl 1.96 U 1.86
Xe 2.16 Zn 1.39
Atomic radius O 0.73 Å
Ionic radius O2− 1. 40 Å
35
Solids
Amorphous
Random internal order
isotropic physical properties
thermodynamically metastabile
Crystalline
Regular internal order
anisotropic physical properties = different in different
directions
(for symmetry lower than cubic)
36
Solids
Energy
r
typical neighbor
bond length
typical neighbor
bond energy
Energy
r
typical neighbor
bond length
typical neighbor
bond energy
Amorphous
Crystalline
Stabile
Metastabile
37
Crystalline Structures
• Metallic (Cu, Fe, Au, Ba, alloys CuAu)
metal atoms, metallic bond
• Ionic (NaCl, CsCl, CaF2, ... )
cations and anions, electrostatic interactions
• Covalent (C-diamond, graphite, SiO2, AlN,... )
atoms, covalent bonds
• Molecular (Ar, C60, HF, H2O, CO2, organic
compounds sloučeniny, proteins )
molecules, van der Waals and H-bonds
38
Models of Structures
P4O10
O P
O
P
O
P
O
O P
O
O
O
O
O
O O
O
O
O
O
O
O O
O
O
O
O
O
Atoms and bonds
Atoms fill
space
Coordination
polyhedra
39
Crystalline Structures
Regular internal order
40
Solidification
Boltzman distribution – kinetic energy decreases during
cooling
T1 > T2
Number
of
molecules
41
Formation of Crystallization Nuclei
cooling – nucleation = random
formation of crystallization
nucleusSolution or Melt
Crystallization nucleus
Crystal
kinetic energy decreases during cooling
42
Nucleation
Surface energy
incr. with larger
nucleus size
Volume energy
decr. with larger
nucleus size
Critical
Radius
4/3 π r 3ΔGv
4π r 2σ
ΔG = 4/3 π r 3 ΔGv + 4π r 2σ
Maximum =
critical size of
nucleus
ΔGNucleation
43
Monocrystal Synthesis
High-temperature methods
Czochralski
Medium-temperature methods
Hydrothermal method
Sublimation
Low-temperature methods
Crystallization from solution
44
Jan Czochralski
(1885–1953)
Monocrystal Synthesis
45
D = 300 mm
l = 2 m
m = 265 kg
Si Monocrystal Synthesis
46
Hydrothermal Method
Temperature gradient
47
Van Arkelova Method
W-wire (T2 = 1500 K)
Ti-powder (T1 = 800 K)
I2
Ti-crystals
Ti + 2I2 = TiI4 ΔH = -376 kJ mol-1
exothermal: transport from cold to hot end
48
KDP crystals
(KH2PO4)
Supersaturated
solution
Nucleation with
crystals
Slow cooling
Crystallization from Solution
49
Structure of Metals
• Cubic Close Packing = Face Centered Cubic
• Hexagonal Close Packing
• Body Centered Cubic
50
Cubic Close Packing = Face Centered Cubic
Hexagonal Close Packing
Body Centered Cubic
51
Electron Gas
Electrical conductivity:
Electrons move freely in positive
charge field of nuclei
Electrical resistance of metals
increases with temperature –
larger atom vibrations
Electrical resistance of metals
increases with impurity
concentration – hinder electron
movement
Thermal conductivity :
Transfer of energy by
electrons
52
Electrical Conductivity S and Resistance R
A
l
R ρ=
Σ
=
1
Rσ, S cm
108
104
10−8
10−4
R = electrical resistance , Ω
ρ = specific resistivity , Ω m
L = conductor length, m
A = conductor cross area, m2
σ
ρ
1
=
53
Metallic Bond
54
Band Theory
Antibonding orbitals = conduction band
Bonding orbitals = valence band
MO for 2, 3, 4,....NA atoms
Many closely
spaced
energy levels
overlap and
form a band
55
Band Theory
3d
4
s
4p
1 atom NA atoms
Electron energies quantized = only some energies allowed, can
occupy only allowed levels, forbidden bands = band gap
56
Filling Bands with Electrons
N atoms, each with 1 electron
N levels in a band
Occupied by pairs of electrons
N/2 levels filled
N/2 levels empty
57
Atomic Radii of TM, pm
3d
4d
5d
Small incr of atom
size down from 4th to
5th period – filled forbitals
of lanthanides
screen poorly nuclear
charge
58
Molar Volume of TM
1 2 3 4 5 6 7 8 9 10
6
8
10
12
14
16
18
20 Molární objem
3d
4d
5d
Vm
[cm
3
/mol]
n
Molar Volume
59
Density of TM
1 2 3 4 5 6 7 8 9 10
2
4
6
8
10
12
14
16
18
20
22
24
Hustota3d
4d
5d
ρ[g/cm
3
]
n
Os 22.5 g cm−3
Ir 22.4 g cm−3
Density
60
Melting Points of TM
0 1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
3000
3500
3d
4d
5d
pře chodné kovy
teploty tání
n
Tt
[°C]
Melting Point = Strength of Metallic bond
61
Melting Points of TM
Filling of bonding
orbitals t2g (bands)
Filling of antibonding
orbitals eg (bands)
62
Liquid Hg
2.3−395d10 6s2Hg
12.810645d10 6s1Au
ΔHmelt, kJ mol −1Tmelt,°CEl. conf.Metal
Lanthanide contraction, decr energy of 6s band, 6s
further from 6p band.
6s2 inert pair
63
Graphite Bands
Graphite is a electrical conductor
Conductivity in layers
64
Diamond Bands
65
Fermi Level
Ef – Probability of occupation is ½
Levels
E < Ef occupied
E > Ef empty
Fermi
Level
Above Fermi Level empty
Below Fermi Level
occupied
66
Metals, Semiconductors, Insulators
Valence
band
Conduction
band
Metal
Semiconductor
Insulator
Metal
Fermi Level
67
Doped Semiconductors
Silicon semiconductors type n and p
Electrons in
conduction bandu
Electron holes in
valence bandDonor levels
e.g. P (1 electron)
Acceptor levels
e.g. B (free orbital)
68
Alloys
Substitutional Interstitial
Solid solution
Similar atom size
Filling voids with small atoms
(C, N, H)
Interstitial compound (Fe3C)
Constant ratio metal/nonmetal
69
Coordination Number
Coordination Number = number of closest neighbors
70
Size of Atoms and Ions
Metallic
Covalent
Ionic
r(O) = 140 pm
71
Ionic Radius
Ionic radius increases with coordination number
Coordination number
72
Electron
density