Weak Forces
(Chapter 17 & 18, Atkins Physical Chem, 9th Edn)
Intermolecular Interactions
Aggregation & Self-assembly
Molecular interactions
Responsible for unique properties of substances.
Govern the structures & functions of molecular assemblies.
Interpret them in terms of electric properties of molecules
Competing influence of
nuclei with different charges
Electric dipole moment
Competition b/w the control exercised
by a nucleus & the influence of an
externally applied field
Refractive index, optical activity
Electric dipole moments
qR
Addition of dipole
moments
( 2
1
2 2
cos )1 / 2
2
1 2
Addition of dipole moments
q
x
i
x
i
qiri
i
i
( 2
x
(0.42, -2.7, 0)
2
y
2)1/ 2
z
Polarizability
It is a measure of the ability of a molecule to undergo a redistribution of charge in
response to application of an electric field (E), resulting in the induction of a dipole
moment (*).
( is the polarizability, unit: C2 m2 / J)
( = /40 is the polarizability volume, unit: m3 )
Polarizability
along with dipole moment largley determines intermoleculr
interactions in non-hydrogen bonded compounds.
increases with (a) no. of electrons, (b) as the electron less
tightly held
the polarizability volume, correlates inversely with HOMOLUMO separation.
Isotropic & anisotropic Polarizability: polarizability value
does not and does depend on orientation.
Polarization
The polarization, P, of a sample is the electric dipole moment density, the
mean electric dipole moment of the molecules <>, multiplied by the
number density N.
In absence of external field, polarization of an isotropic fluid is zero so
In presence of weak external field:
In presence of strong external field:
E
3kT
When E varies ??
Polarization
When the applied field changes direction slowly, the permanent dipole moment
has time to reorient the whole molecule rotates into a new direction following
the field.
When the frequency of the field is high the permanent dipole moment makes
NO contribution to polarization.
Loss of polarization at high frequency:
1. Orientation polarization arises due to permanent dipole moment
(>= microwave)
2. Distortion (induced) polarization due to distortion of nuclei position
by applied field (>= IR)
3. Electronic polarizability due to distortion of electron distribution by
the applied field (>= visible)
There is successive decrease in polarizability as the frequency is increased.
When the incident frequency is much higher than any excitation (vibrational,
electronic etc.) frequency, the polarizability becomes zero .
Relative permitivity
r
E0
E
is large for polar or highly polarizable molecule
r has significant effect on strength of interactions b/w
ions in solution.
Coulomb potential energy in vacuum V
q1q2
In a medium V
4 r
r is calculated from electric properties
Debye Equation:
r
r
1
2
Pm / M ;
Clausius-Mossotti Equation:
r
r
Maxwell relation:
nr
c / c'
1/ 2
r
1
2
Pm
NA
3 0
NA
3M 0
3kT
q1q2
4 0r
Interactions between
molecules
Ion dipole Interaction
1q2
dipole dipole Interaction
Static:
V
1 2
f ()
r3
0
1 2
r3
Rotating dipole-dipole Interactions:
2 2
2
C
1 2
, C
2
6
3
(
4
)
kT
r
0
Keesom Interaction
Charge arrays corresponding to electric multipoles
An n-pole is an array of point charges
with an n-pole moment but no lower
moment.
Potential energy of
interaction b/w a npole with an m-pole:
1
rn m 1
Dipole induced-dipole interactions
A polar molecule can induce a dipole in a nonpolar molecule; the laters
orientation follows the formers, so the interaction does not average to zero.
Energy of interaction b/w a polar
molecule & a polarizable molecule:
C
, C
6
r
2
1 2
4
0
The dipole-induced-dipole interaction
energy is independent of temperature
b/c thermal motion has no effect on the
averaging process.
For a molecule with dipole moment 1 D (e.g. HCl) near a molecule of
polarizability volume 10 10-30 m3, the avg. interaction energy is about -0.8
kJ/mol, when the separation is 0.3 nm.
Induced-dipole induced-dipole interactions
The interaction b/w non-polar molecules arises from the transient dipoles that
all molecules possess as a result of fluctuations in the instantaneous positions
of electrons.
An instantaneous dipole on one molecule induces a dipole on another molecule, and
then the two dipoles interact to lower the energy. This interaction is called
dispersion interaction or London interaction.
The two instantaneous dipoles are
correlated and, although they occur in
different orientations at different instants,
the interaction does not average to zero.
Approx. energy of interaction b/w two
non-polar molecules (London formula):
C
3
, C
2
r6
I1I 2
2
I1 I 2
The dispersion interaction generally dominates all the interactions b/w the
molecules other than hydrogen bonds.
Hydrogen bonding
A hydrogen bond is an attractive interaction b/w two species that arise from a link of
the form A HB, where A and B are highly electronegative elements and B
possesses a lone pair.
It is virtually a contact type
interaction
Strength of H-bond ~ 20 kJ/mol
It dominates the other intermolecular
interactions.
May be symmetric or unsymmetric
Evidence
A A
H H
B B
The hydrophobic interaction
Consider a nonpolar molecule in polar solvent
- Strong solute-solvent interaction not possible
- Each solute molecule is surrounded by solvent cage
Consider the thermodynamics of transfer of a non-polar
hydrocarbon from nonpolar to polar solvent:
G 0, H 0;
S 0
HYDROPHOBIC
S
S
0
Where, S and S0 are ratios of the molar solubility of the compounds R A and
H A in octanol to water, respectively.
Hydrophobicity constant:
0; Hydrophobic
0; Hydrophilic
log
The total attractive interaction
Vd
2 2 2
1 2
3(4
) 2 kT r 6
0
Vd
id
2
1 2
4
r6
0
att
VTotal
Vd
Vdis
Vd
id
C
3
, C
2
r6
Vdis ??
Axilrod Teller formula:
C6 C6 C6
C
V
6
6
6
rAB
rBC
rCA
(rAB rBC rCA )3
3
C
C6 (3 cos A cos B cos C 1)
4
I1I 2
2
I1 I 2
Total Interaction Potential
Mie Potential:
Cn
rn
Cm
; n m
m
r
Lennard-Jones Potential:
r0
r
12
r0
r
Gases & Liquids
Molecular interactions in gases
Can be studied using molecular beam technique, which is a collimeted narrow
stream of molecules travelling through an evacuated vessel.
Fraction of molecule in the incident beam:
: differential collision cross section
I intensity of beam
N: no. density of targeted molecules
Dx: path length
depends on the impact parameter b
and the details of intermolecular potential.
dI
INdx
Scattering of Hard Spheres
Scattering in real molecules
The scattering pattern of real molecules,
depends on:
Intermolecular potential
Relative speed of approach
Outcome of collision is determined by quantum
& not classical mechanics.
Quantum oscillation:
b/c of interference the intensity is
Modified.
Rainbow scattering
The liquid-vapour interface
Liquids tend to adopt shape that minimize their surface area; so maximum
no. of molecules are in bulk & hence surrounded by and interacting with
neighbours.
This results in formation of bubbles, cavities, and droplets.
The liquid-vapour interface
The work needed to change the surface area of a sample by an
infinitimal amount
dw
d ,
At const. T & V, dw = dA , thus
: surface tension
dA
Because dA < 0, if the surface area decreases
(d < 0), surfaces have a natural tendency to
contract.
The liquid-vapour interface: Curved surfaces
The minimization of the surface area of a liquid may
result in the formation of a curved surface.
Pressure on the concave side of an
interface (Pin) is always greater than
the pressure on the convex side (Pout),
and is related by Laplace equation:
Pin Pout
2
r
Difference in pressure decreases to
zero as the radius tends to infinity.
A bubble (cavity) of radius 0.1mm in
champagne implies a pressure
difference of 1.5 kPa, which is enough
to sustain a column of water of height
15 cm.
Capillary action
The tendency of liquids to rise up capillary tube (capillary action) is a
consequence of surface tension.
When a glass capillary tube is immersed in
water, a thin film covers as much of the glass
as possible (to minimize energy). As this film
creeps up the inside wall, it has the effect of
curving the surface of liquid inside the tube.
2
gr
Reasonably
accurate way of
measuring
surface tension
of liquid.
2
r
Capillary action: Angle of contact
When there is a non-zero angle (c) b/w the
edge of the meniscus and the wall, then h
From the vertical forces balance:
sg
Work of adhesion of the liquid to solid:
cos
wad
c
sl
wad
lg
cos
sg
2
cos
c
gr
lg
sl
lg
The liquid wets (spread over) the surface
1
corresponds to 0 < c < 90
wad
lg
The liquid do not wets (spread over) the
surface corresponds to 90 < c < 180
wad
lg
For Hg in contact with glass, c =143, adhesive
force is weaker than cohesive force.
Surface films: Surface pressure
Surface film balance
The surfactant is spread on
the surface of the liquid in
the trough, and then
compressed horizontally by
moving the compression
barrier towards the mica
float. The latter is
connected to a torsion
wire, so the difference in
force either side of the float
can be monitored.
Surface films: Surface pressure
Collapse pressures are indicated by arrows
