CHEM 2060 Lecture 11: Polarizability L11-1

Polarizability and Electronegativity • Polarizability increases with volume…larger species are more polarizable. • Polarizability also depends on electronegativity.

Electronegative atoms are not very polarizable.

Monopole - Induced Dipole

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E =-Q12α22r4

(~ 5 kJ mol-1)

Permanent Dipole - Induced Dipole

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E = -µ12α2r6 (~ 0.05 kJ mol-1)

Induced Dipole - Induced Dipole

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E =-32

I1I2I1 + I2

"

# $

%

& ' α1α2r6

(~ 0.5 kJ mol-1)

I = ionization energy

CHEM 2060 Lecture 11: Polarizability L11-2

The physical phase (solid, liquid, gas, etc.) in which a species exists under STP conditions is primarily a function of the type of bonding/interactions that can occur between atoms/molecules/polymeric units/etc. For species that do not have permanent dipoles (and have filled octets, so are not good candidates for participating in covalent bonding) the solid is held together by weak forces. (e.g., solids of Xe, Kr, He, H2, O2, N2 etc…) These weak forces are called van der Waals forces. van der Waals forces

There are 2 principal v.d.W. forces: attractive and repulsive. Attractive – Induced dipole; also called London (dispersion) forces Repulsive - Repulsion between electrons on neighboring atoms

CHEM 2060 Lecture 11: Polarizability L11-3

van der Waals forces - Attractive Part – London dispersion forces

Attractive (Potential) Energies have a dependence on

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1r6

Any attractive interaction that has this energy dependence as a function of distance is lumped under the general term “van der Waals Forces”. In 1930, Fritz London derived the quantum mechanical theory for this attractive force based on the fluctuation of electron density about atoms. Source: DeKock & Gray

The electron densities are constantly fluctuating, but the net effect is an extremely small but important attraction between atoms.

CHEM 2060 Lecture 11: Polarizability L11-4

van der Waals forces - Repulsive Part There must also be a repulsion… …or everything would collapse into itself! Repulsion Energy has dependence on

e-r The electron “clouds” repel each other at very small distances. This can be understood as a simple Coulomb-like repulsion between negatively charged species… The repulsive energy has an exponential dependence on distance due to the exponential nature of radial wave functions (see Part 4).

CHEM 2060 Lecture 11: Polarizability L11-5

van der Waals force – net effect Everything balances out. The total potential energy of van der Waals interactions is the sum of the attractive and repulsive energies.

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PE = be−arrepulsive

extremely short range

−dr6

attractiveshort range

Note: a, b, and d are constants.

Another (simplified, less accurate) way of writing this is the Lennard-Jones 6-12 potential.

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E = C 1r12

repulsive

- 1r6

attractive

"

#

$ $ $ $

%

&

' ' ' ' where C is a constant

CHEM 2060 Lecture 11: Polarizability L11-6

Pictorially, the PE as a function of inter-atomic distance looks like this…

DAB = BOND

ENERGY • Actually, the well depth for a crystal refers to the enthalpy of sublimation.

solid → gas

CHEM 2060 Lecture 11: Polarizability L11-7

Short & Long Range “Forces” Potential Energy 12

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

12r1 Shortest Range

6 ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

6r1

4 ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

4r1

2 ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

2r1 Longest Range

Distance

12642

CHEM 2060 Lecture 11: Polarizability L11-8

van der Waals Radii • The size of molecule (or atom) revealed by LJ potential is actually much

larger than that revealed by other measures of atomic size (see Part 3) such as covalent radius or ionic radius.

• …because electron clouds stop interpenetration for a non-bonding interaction

(or no electron sharing). • Covalent and Ionic Bonding will be discussed later Parts 3, 4 and 5.