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---

Lecturer : Dr M
...
Hato
Email
: Mpitloane
...
ac
...
: Office 1012, 1st Floor, N-block
Ext
...
: 4116

1

MODULE

Module Title

Physical Chemistry 3

Module code

SCHA082

No
...
Hato@ul
...
za

Telephone No
...
Magadzu@ul
...
za
reineck
...
ac
...
00

Lecture Periods

4 per week

Important Dates

Test dates

Learning Hours

20 hours

1st Test: 06/08 /2014
Semester

14/07 – 26/08=No
...
of Lectures / week: 4 x 45 minutes
Description

Tests & Assignments

Weight

60%

2

Chapter 18
Materials 1: Macromolecules and self-assembly
 Macromolecules are built from covalently
linked by smaller components called
monomers
...
Various structures:
• Random coil (structure-less), partially
structured coils, structurally precise forces
that are in polypeptides and nuclei acids
...

 Some are natural (polysaccharides,
polypeptides, etc
...

 Prepared by addition/stringed together and in
some cases cross-linked by smaller units called
monomers by a process called polymerization
...
g
...

4

 Macromolecules and aggregates give rise to
problems that need some investigation and
description of their shapes, size
determination, and so on
...
e
...
, - A – B – C and
–A–C–B
 Conformation, the spatial arrangement of the
different parts of a chain, and one
conformation can be changed into another by
rotating one part of a chain around a bond
...
1 The different structures of
Macromolecules
• Primary structure, sequence of small molecular
residues making up a polymer
...
g
...
g
...


6

Cross-linkers for polymerization of PAM
7

• They are useful in synthesis of copolymers and
biological macromolecules (e
...
polypeptides)
...
e
...

• Determination of a primary structure is quite
challenging
of
chemical
analysis
called
sequencing

8

• Secondary structure of a macromolecule is the
spatial arrangement of a chain
...


Helix

• Loss of secondary structure → denaturation,
e
...
cooking an egg – the structure denatures
into a random coil
...

• Denaturation may also occur
...

• Useful in biology, protein
haemoglobin has four sub
units working together to
take up and release O2
...
2 Random coils (RC)
• Most likely conformation of a chain of identical
units not capable of forming hydrogen bonds or
any type of specific bond is a random coil (RC)
...

e
...
simple PE
...

11

Random coils (RC)…

• We assume that residue occupy zero volume, thus
different parts of the chain can occupy the same
region of space
...
on the
next page 11
...

• Residues in 1-dimensional FJC lie in straight line
(angle θ between neighbours are either 0 or
180o)
...

13

(a) Measures of size
• Probability, P, that the ends of long 1-dimensional
FJC composed of N units of length l (total length
Nl) are a distance nl apart,
1/ 2

 2  n
P 
 e
 N 

2

2N

(18
...
18
...

• Eq
...
1 can be written as f(r)dr,
3

 a  2 a 2r 2
f r   4  1 / 2  r e
 

 3 
a
2 
 2 Nl 

1/ 2

(18
...
18
...

• Thus, we ignore that chain can’t be longer than
Nl
...
18
...

• By using Eq
...
2, we can also regard each coil in
a sample as ceaselessly writhing from one
conformation to another, then f(r)dr is the
probability that at any instant chain will be found
with separation ends between r and r + dr
...
For a polymer with N monomer
units each of length l, the Rc
Rc = Nl
(contour lenth)
(18
...

• To determine its value, the vector joining two
ends of chain is the vector sum of the vectors
joining neighbouring monomers given by
17

R

N

,
i 1 i

r where ri is end-to-end distance for
conformation i

• Rrms of the ends of the chain is;
2  R
...
r  N r 2  N r
...

• First sum is Nl2 as all bond lengths are the
identical and equal l, therefore
Rrms = N1/2l
(18
...
6)
• Rg is small because the extra dimension enables the
coil to be more compact
...

20

• e
...
, solid uniform sphere of radius R has;

21

(b) Conformational entropy (CE)
 Random coil is the least structured conformation
of a polymer chain and corresponds to the state
of greater entropy, i
...
degree of disorder
...

 Statistical entropy arising from bond
arrangement (1-dimensional chain N bonds of
length l stretched or compressed by nl) called CE
...
7)

22

 Figure 18
...

 Minimum extension corresponds
to maximum entropy
...
5 nm (n = 10 and V = 1/100)
is ∆S = -0
...

 Therefore, Sm = -0
...
42 JK-1 mol1 (use R = N k)
A
 (Check justification 18
...

 For long chain, we take groups of neighbouring
bonds, and consider direction of their resultant
...

 Expression of Rrms and Rg on long chains; must be
multiplied by the factor
F

 1 cos


 1 cos

1/ 2






(18
...
e
...

 If the chain is a rigid rod, lp = Rc
 For FJC coil, lp is the length of monomer –
monomer bond
...

 Generally, lp of a chain of identical monomers of
length l is defined as the average value of the
projection of the end to end vector on the first
bond of chain
...
R   ri
...
10)

 The ∑ ends at N-1 b/c the last atom is atom N and
the last is from atom N-1 to atom N
...
6 nm
2 nm
22 nm
...

27

From Further information 18
...
11)

 For random coil, lp = l, so Rrms = N1/2l, as we already
found
...


28

18
...

 Stress is removed, the sample
returns to its initial shape
...
e
...

29

18
...

 Hydrostatic stress is a stress applied
simultaneously in all directions as in a body
immersed in a liquid
...


30

 Thermosets have short elastic range
...
On heating to
a very high temperature they start to degrade
...

 They posses numerous cross-links (e
...
, sulphur
links in vulcanized rubber) that pull them back
into their original shape when the stress is
removed
...


31

Two types of thermoplastics
 Semi-crystalline thermoplastics
 Polymers which contain a degree of ordering in
the chains, e
...
, PP, POM, PA, etc
...

 The degree of crystallization increases as the
molecules lie close to one another
...

32

 Amorphous thermoplastics
 These polymers are usually made up of chains
with large side chains or groups
...
g
...

 Their main properties are (i) clarity, (ii)
brittleness, (iii) quick uptake of solvents in the
polymer mass and (iv) early softening upon
heating
...

 Restoring force, F, of one dimensional random coil
when stretched or compressed by nl
...
12)a

34

• When V << 1 use ln(1 + x) = x – 1/2x2

...
12)b

 The crystallinity, Xc, of synthetic polymers can be
destroyed by thermal motion at sufficienctly high
temps
...
e
...

 The melting temperature, Tm, of polymers
increases with strength and a number of
intermolecular interactions in the material
...

Nylon-66 fibres, Tm = 530 K (because of string
hydrogen bond)
...

• To visualise the glass transition, we consider what
happens to elastomer as we lower its temp
...

• Differential scanning calorimeter (DSC) →
measure glass transition and melting temp of
polymer
...

36

• Tg may also be
determined from plot
...

• α and β relaxation peaks
...
4 The electric properties of polymers
...

 Newly developed macromolecular materials have
electrical conductivities better than silicon
semiconductors and even metallic conductor
...
g
...


 The electrical conductivity of PAc increases when
it is partially oxidized by I2 and strong oxidants
...

 Further oxidation result to bipolarons (dication that moves as a unit though the chain)
...


39

18
...

 A protein is a polypeptide composed of linked αamino acids, NH2CHRCOOH, where R is one of
about 20 groups
...

40

Corey-Pauling rules
1
...

2
...

3
...

 The rules satisfied by two structures, Helix → right
or left handed screw; Sheet → form 2nd structure of
protein fibroin
...


42

 Positive angle means front atoms must be rotated
clockwise eclipsed position relative to the rear
atom
...

 Helix obtained when all ф are equal and all Ψ
equal
...

 For left handed → all angles are positive
...
13)
where A and B are constant of the order of
1 kJ/mol
43

• Only two angles (-180o or +180o) required to specify
conformation of helix
...


• The helical form of polypeptide chains formed from
the non chiral amino acid glycine (R = H), and
chiral amino acid L-alanine (R = CH3)
...

• L-alanine is unsymmetrical, with three distinct lowenergy conformations (I, II, III), with right (lower
minimum) and left helix
...

• β-sheet – form by H-bond between two extended
polypeptide chains (ф and Ψ)
...

45

 Β-parallel sheet, ф = -119o, Ψ = 113o and N-H--O
H-bond are not aligned (NH or CO bond b/n chains
are parallel)
...


46

 Proteins are relatively unstable towards chemical
and thermal denaturation (similar to melting of
synthetic polymers)
...

 Tm, is the temp at which
fraction of unfolded
polymer is 0
...


47

Example: Ribonuclease enzyme T1 has Tm = 320 K,
not far from body temp (310 K) which it has to
operate
...
0 and 298 K is
19
...


48

(b) Nucleic acid
 Both DNA and RNA are polynucleotide → base
sugar phosphate units linked by phosphodiester
bond
...

 DNA sugar is B-ᴅ-zdeoxyribose
...


50

 At physiological pH → each phosphate group of
chain carries a negative charge and the bases are
deprotonated and become neutral
...

 Secondly → bases can interact by hydrogen
bonding
...

51

• DNA double helix polynucleotide chains are linked
together by hydrogen bonds between A-T and C-G
base pair
...

• In biological cell right-handed helix with diameter of
2
...
4 nm are formed
...

Examples: liquid crystals, DNA
...

53

18
...

 Are aggregate of atoms or molecules and optically are
microscopic (can pass through filter and detected by
light scattering)
...

 Aerosol - dispersion of liquid in a gas (fog and
many sprays) or solid in gas (smoke)
...

 Foam - dispersion of a gas in liquid
...

 A gel is a semi-rigid mass of a lyophilic sol
...

 Chemical precipitation sometimes results in a
colloid
...


56

 Emulsifying agent such as soap or surfactant or
lyophilic sol has to be added to stabilize the
product
...

 Formation of cream (droplets) on the surface of
the milk shows that casein not good emulsifier
...

 Colloids are purified by dialysis to remove the
charge materials
...

 Because of Helmholtz energy, dA, when surface
area, σ, of sample changes by dσ at constant
temperature and pressure is given by

dA  d
where the constant of proportionality, , is
interfacial surface tension (J/m-2)
Because dA < 0 if the surface decreases (dσ < 0),
 Colloids (attract each other over large distance)
have long range force that tends to condense
them into a single blob
...

 The sum of all these pairwise interactions
decreases only as approximately 1/R2 (R is the
separation of the centres of the particles)
...
next slide)
...

 Thus, the surface atoms of a Pt sol in water
react chemically and turned into -Pt(OH)3H3,
therefore, this layer encases a shell-like particle
...


61

(c) The electrical double layer (EDL)
 A major source of kinetic non lability of colloids is
the existence of an electric charge on the surface
of the particles
...

There are two regions of charge:
(i) Immobile layer of ions that adhere tightly to the
surface of the colloidal particles, e
...
, water
molecules
 The radius of sphere that captures this rigid layer
is called radius of shear and is the major factor
that determines the mobility of the particle
...

(ii) The charged unit attracts an oppositely charged
atmosphere of mobile ions
...

 The theory of the stability of the lyophobic was
develop by DLVO
...
63

• Potential energy which arises from the repulsion
of double layers on particles of radius a is given by
the relation
Aa 2 2 s rD
Vrepulsion  
e
R

(18
...
509 for aq
...


64

 Eqn 18
...

 and for thin double layer (a >> rD), therefore the
expression is replaced by



Vrepulsion  1 Aa ln 1  e
2
2

s

r
D



(18
...
91), in
which there is a competition b/n the assembling
influences of the attraction b/n opposite charges
and the disruptive effect of the thermal motion:
1

 RT 
rD  
 2 F 2 Ib o  Thickness of the EDL



2

(18
...
kg, F is
Faraday’s constant, and ɛ is permittivity, ɛ = ɛ1ɛ0)
...
17)

where B is another constant
...

66

 Coagulation occurs when the separation of the
particles is small that they enter the primary
minimum of potential energy curve and van der
Waals forces are dominant
...

 This increase is the basis of the empirical SchulzeHardy rule; hydrophobic colloids are flocculated
most efficiently by ions of opposite charge and high
charge number
...

67

 When river water containing colloidal clay flows
into the sea, the salt water induces flocculation
and coagulation which lead to silting in estuaries
...

 Colliding colloidal particles break through the
double layer and coalesce only if the collision is
sufficiently energetic to disrupt the layers of ions
and solvating molecules
...

68

18
...

Hydrophobic tail
Hydrophilic head

Schematic representation of
a micelle in aqueous solution

 In a micelle, polar or ionic heads form an outer
shell in contact with water, while non polar tails
are sequestered in the interior
...

69

 The length of the nonpolar tail, the nature and
size of the polar or ionic head, the acidity of the
solution, the temperature, and the presence of
added salts are critical in determining the kind of
the aggregate (micelle) to be formed
...

 The number of amphiphilic molecules forming the
aggregate is called aggregation number (a way to
describe the size of the micelle)
...
g
...

70

 They have an ability to dissolve and move non
polar substances through an aqueous medium, or to
carry drugs which are, often, scarcely soluble in
water
...

(a) Micelle formation
 Their aggregates formation can only occur when
the conc
...
called critical micelle concentration
(CMC) and above the Krafft temperature
...
of surfactant
in water slowly forming a layer
on the surface and eventually
forming micelles at or above the
CMC
...
B: The existence of micelles
does not preclude the existence
of individual surfactant
molecules in solution
...
g
...

 At CMC the physical
properties vary smoothly
but nonlinear with the
concentration
...


73

 Non-ionic surfactant molecules may cluster
together in clumps of 1000 or greater
...

 and the disruptive effect depends more on the
effective size of the head group than the charge
...

74

 Micelle population are often polydisperse
...
, and temperature
...
18)

where,
V = volume of hydrophobic surfactant tail;
A = area of hydrophilic head group and
l is maximum length of surfactant tail
...
23, page 675, Atkins & De Paula, 9th
Ed
...

 In aqueous solutions, spherical micelles can be
formed as shown in the next slide…

76

 At certain experimental conditions liposome may
form,

 Liposomes may be used to carry nonpolar drug
molecules in blood
...
soln
reduces repulsions surface heads which results to
formation of cylindrical micelles (CM)
...

77

 Reverse micelles form in nonpolar solvent, with
small surfactant head group in a micelle core and
hydrophobic heads tails extent to the organic bulk
phase
...

 Arrangements of aggregates at high surfactant
concs, other structural phases such as cubic and
hexagonal shapes may form
...

 Many ionic micelles form endothermically, with ΔH
of 10 kJ mol-1 of the surfactant
...

 The +S even though molecules are clustering
together shows that hydrophobic interaction are
important in the formation of micelles
...

 The individual molecules lie perpendicular to the
sheet with hydrophilic heads on the outside in
aqueous solution and inside in nonpolar media
...

 Bilayer shows resemblance of biological
membranes
...

 Lipids molecules forms layers instead of micelles
because of long structure
...

 The average distance the lipids travel in time t is
equal to (4Dt)1/2
...

 All lipids bilayer undergo transition from a state of
high to low chain mobility at a temperature that
depends on the structure of the lipids
...

 Phase transition is observed as melting from gel to
liquid crystals by using DSC
...

 Stabilization of gel phase in membrane of lipids
with longer chains results in relatively high melting
temp
...

 Some lipids contains unsaturated chains (C=C) form
membrane with low Tm than saturated chains (C –
C)
...

(c) Self assembled monolayer's (SAMs)
 The ordered molecular aggregates that form single
layer of material on a surface
...
Au(0)n-1 +
1/2H2
 If R is sufficiently long chain, van der Waal
interaction between adsorbed RS units lead to the
formation of a highly ordered monolayer on the
surface
...

 SAMs alter the properties of the
surface
...

 Attachment of functional groups to the expose ends
of alkyl group imparts specific chemical reactivity or
ligand-binding property to the surface, lead to
applications in chemical (or biological) sensors and
reactors
...
8 Mean Molar Masses
 A pure protein is monodisperse, has single,
definite molar mass
...

 Synthetic polymers are polydisperse,
 i
...
have mixture of molecules with various
chain lengths and molar masses
...

85

 The mean obtained from the determination of
molar mass by osmometry (5
...

_

Mn 

1
 Ni M i  M
N i

(18
...
denotes the
usual (number) average of property X
...

 Weight average molar mass is the average
calculated by weight of molar mass of the
molecules by the mass of each one present in the
_
1
sample:
M w   mi M i
(18
...

87

 Because mi = NiMi/NA
N M

N M

Mw

i

2
i

i

_

i

i



M2
M

(18
...

 Similarly, Z-average molar mass turns out to be
proportional to the mean cubic molar mass
_

Mz

N M

N M
i

3
i

i

2
i

i



M3
M2

(18
...
1 Determine the number average and
the weight average molar masses of poly (vinyl
chloride) from the following given data:
Molar mass interval/kg mol-1

5-10

10-15

15-20

20-25

25-30

30-35

Average molar mass within interval/kg
mol-1
Mass of sample within interval /g

7
...
5

17
...
5

27
...
5

9
...
7

8
...
6

3
...
7

Method: Relevant eqns
...
19 and 18
...

Calculate the two averages by weighting the molar
mass within each interval by the number and mass,
respectively, of molecule in each interval
...
The number weight average can be
obtained directly from the amounts in each interval
...
5

12
...
5

22
...
5

32
...
3

0
...
51

0
...
11

0
...
3  7
...
70 12
...
5117
...
92
_

n

1

0
...
5  0
...
5  0
...
5)
 13

 The weight average molar mass is calculated
directly from the data after noting that the total
mass of the sample is 37
...
6  7
...
7  12
...
9  17
...
6
5
...
5  3
...
5  1
...
5)  16

90

 The differents value of the two averages
...
2
 The ratio of Mw/Mn is called the heterogeneity
index or polydispersity index; it follows from
18
...
20b
_
M2
Mw
(18
...

91

18
...

 The procedure consists of ionizing the sample in
the gas phase and then measuring the mass to
charge ratio (m/z) of all ions
...

 Matrix assisted laser desorption/ionization (MALDI)
and electrospray ionization are used to overcome
that
...

 Macromolecules are embedded
in a sold matrix often consist
of organic materials such as
trans-3-indoleacrylic acid and
inorganic salts such as NaCl or
silver trifluoroacetate
...

93

 Macromolecules is ionized by collisions and
complexation with small cations, such as H+, Na+
and Ag+
...

 The multiple peaks in the spectrum arise from
polymers of different lengths; the intensity of each
peak is proportional to the abundance of each
polymer in sample
...

94

 It is possible to use the mass spectrum to verify
the structure of a polymer
...
The peak at 4113 g mol-1
corresponds to the polymer for which n = 20
...

95

Answer:
M(terminal groups) = M(polymer with n repeating
units) – nΔM – M(cation)
= 4113 g mol-1 – 20(200 g mol-1) – 23 g mol-1
= 90 g mol-1
 where ΔM is the molar mass difference and the
last term corresponds to the molar mass of the
cation that attaches to the macromolecule during
ionization
...

96

(b) Laser light scattering
 The intensity of light scattered from a dilute
solution excite by plane-polarized light
measurement at a distance r from the solution is
proportional to the intensity of incident light, I0,
and to (1/r2)sin2ф where r is the distance of the
detector from sample
...
22a)

 The coefficient of proportionality R(θ) (Rayleigh
ratio), depends on angle θ, and the value of R(θ) is
(with intensity θ, Φ, r)
I  ,  , r 
r2
R  
 2
(18
...

_

R   Kc p M w

(18
...

98

2 2 nr2 dnr
K
N A4 dc p

(18
...

 When size of molecule is not negligible compared
with wavelength of the incident radiation,
interference parts of the same molecule must be
taken into account
...
18
...
25)
99

 Rg is radius of geration of macromolecule
...
3
 The following data for a sample of polystyrene in
butanone were obtained at 20 oC with planepolarized light at λ = 546 nm
...
0

36
...
4

90
...
6

R(θ)/m2 19
...
8

17
...
0

14
...
42 x 10-5 mol m5 kg-2
...
Assume that
the polymer is small enough that equation 18
...
Take cp = 311 kg m-3
...
0
5
...
57

36
...
32
5
...
4
5
...
5

90
...
25
31
...
6
6
...
6

101

 The best straight line
through the data has a
slope of 0
...
07 x 10-2
...
69 x 10-8 m = 46
...


102

(c) Sedimentation
 In gravitational field, heavy particles settle towards
the foot of a column of solution by the process called
sedimentation
...

 Spherical molecules sediment faster than rods-like
and extended molecules
...

 The spread of height depends of the mass of
molecule, so equilibrium distribution is another way
of determine the molar mass
...

 Effect can be achieved in ultra-centrifuge, a
cylinder that can be rotated at high speed with
sample in cell
...

 Initially the sample is uniform, but the top
(innermost) boundary of the solute moves outwards
as sedimention proceeds
...
27)
104

 ρ is a density, vs is partial specific volume of solute
(vs =dV/dmB) with mB the total mass of solute, ρvs is
mass of solute in solvent
...

 Particle adopt a drift speed, constant speed through
medium, found by equating meffrω2 and fs
s

meff r 2
f

bmr 2

f

(18
...
29)

r 2

 because average molecular mass is related to the
_
average molar mass Mn, m  M n / N A
_

b Mn
S
fN A

(18
...
31)
106

 On substituting this expression into eqn 18
...
32)

 S may be used to
determine Mn or a, and
for non-spherical
molecules we use values
given in Table 18
...


107

 Measurements for macromolecules has to be
carried out at series of concentrations and
extrapolated to zero concentration to avoid
complications (that may arise from bulk molecules)
Example 18
...
The initial
location of the solute surface was at 5
...
p
...
it receded as follows:
t/s

0

500 1000 2000 3000 4000 5000

r/cm 5
...
55 5
...
70

5
...
91 6
...
18
...

The integrated expression, an expression for r as a
function of t, will suggest how to plot the data and
obtain from it the sedimentation constant
...
18
...
Use ω = π2v, where v is
in cycles per second and draw up the following
Table:
t/s
102
ln(r/ro)

0
0

500
0
...
80

2000
3
...
31

4000
7
...
87

 The straight line graph has a
slope of 1
...
78
x 10-5 s-1
...
95 x 103 s-1, it
follows that S = 5
...

The unit 10-13 s is sometimes
called a ‘svedberg’ and denoted
Sv; therefore, S = 5
...

110

 Sedimentation does not give reliable results, that
can be avoided by allowing the system to reach
equilibrium, for property D no longer relevant
...
33)

 An alternative treatment of data leads to Zaverage molar mass
...


(d) Viscosity
 The average molar mass can be determine from
measurement of viscosity of solutions of
macromolecules
...
g
...

 Macromolecule solute increases the viscosity of
solution
...

'

18
...

 Suitable in determination of [η], ratio
of the sample and pure solvent is
proportional to drainage time t after
collection from difference ρ and ρo
...
35

113

 t 
 
 o to  o

18
...
18
...


 Rotating rheometer – the toque on
the inner cylinder is monitored
while the outer one is rotated
...

114

 Complications in interpretation of viscosity
...

 Some regularities are observed that help in
determination, e
...
, some molecules fit the
Mark-Kuhn-Houwink-Sakuranda equation:
_

   KM va

18
...
4), M v viscosity average molar mass
...
38

116

Example 18
...
dm-3)
0
η/(10-4 kg
...
58

2
6
...
74

6
8
10
7
...
98 8
...
37
with K = 3
...
g and a = 0
...


 Method The intrinsic viscosity is defined in eqn
18
...
= 0
...
mol 1  in eqn 18
...
dm-3)
0
η/ηo
1
100[η/ηo-1]/c/g dm3

2
4
6
1
...
208 1
...
11
5
...
28

8
10
1
...
549
5
...
49
118

 Extrapolated intercept at
c = 0 is 0
...
0504 dm3 g-1
 Therefore;
_

   KM va
   
M v     9
...
mol 1
K
1

a

119

 In some cases, the flow is non-Newtonian in
the sense that the viscosity of the solution
changes as the rate of flow increases
...

 Rarely, stress set up by flow are greater that
long molecules are broken up, with further
consequences for the viscosity
...
8
...

 Stress is the applied force divided by the area to
which it is applied
...

121

 The general field of the relations between
stress and strain is called rheology
...

 Hydrostatic stress is a stress applied
simultaneously in all directions, e
...
, a body
immersed in a liquid
...
A
sample subjected to a small stress typically
undergoes elastic deformation
...

 For low stresses, the strain is linearly
proportional to the stress
...

 above a threshold, the strain becomes plastic
such that non-recovery occurs upon removal
of the stress
...
For pure metals, plastic deformation
occurs due to dislocations
...
9
...


 There are two types of solid
 which depend on the temperature their
electrical conductivity

1
...

2
...
e
...
g
...

(a) The formation of bands (Self-Study!)
 Distribution of electrons of the solid material
determines their electrical properties
...

131

 Two models are known for such distribution
...
Free-electron approximation
 The VE are assumed to be trapped in a box
with a periodic potential, with low energy
corresponding to the locations of cations
...
Tight-binding approximation
 The VE are assumed to occupy the molecular
orbitals delocalized throughout the solid
...
g
...

(b) The occupation of orbitals (self-study!)
(c) Insulators and semiconductors (self-study!)
133

19
...
IMPACT ON NANOSCIENCE
 Nanowires
 Synthesis of nanowires (nanometer-sized)
atomic assemblies that conduct electricity is a
major step in the preparation of of
nanodevices, e
...
CNTs, graphite, etc
...

 The research indicated a correlation btn
structure and conductivity of SWCNTs in
which graphite doesn’t show
...

 SWCNT has E that is approx
...
375 x larger
than that of steel
...


135



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Title: micromolecules and assembly with properties of solid
Description: The notes is for Advance physical chemistry for fourth year student doing honours in chemistry. The topic covered in this notes are micromolecules and assembly focusing more on polymers and their measurements as well as introduction of physical properties of solid.

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