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2.2 Charge-Dipole Interaction


Review (Isr2011, sec 4.1)

What is a dipole?

How are polar molecules formed?

Order of magnitude of molecular dipole
Charge-Dipole Interaction (Isr2011, sec 4.3)

In isolation

In medium
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What Is Dipole?

Dipole


Two equal charges, q, of opposite sign, separated
by a distance l, constitutes an electric dipole.
A dipole u is represented as a vector pointing
from –q to +q and has a magnitude of q l
-q
+q
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

u  q
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Two Types of Polar Molecules
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Polar molecules
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
Molecules carrying no net charge but possessing an
electric dipole
Inherent polar molecules
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E.g. in HCl, Cl atom tends to draw the hydrogen’s
electron toward itself (as indicated in the electron cloud
around the nuclei of Cl and H), forming a permanent
dipole (indicated as blue arrow)
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http://en.wikipedia.org/wiki/HCl, http://en.wikipedia.org/wiki/Water, 3/3/2009
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Two Types of Polar Molecules
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Environment-dependent polar molecules
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
contd
“The dipoles of some molecules depend on their
environment and can change substantially when they are
transferred from one medium to another, especially when
molecules become ionized in a solvent.” (Isr2011, p. 71)
E.g. glycine (amino acetic acid) in water becomes a
dipolar molecule
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Order of Magnitude of Molecular Dipoles
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Debye
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1 Debye (1 D) = 3.336 x 10-30 C-m
E.g.
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A dipole of two charges, e, separated by 1 Å
= 4.8 D
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Order of Magnitude of Molecular Dipoles
contd
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Order of Magnitude of Molecular Dipoles
contd
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Order of Magnitude of Molecular Dipoles
contd
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Use bond moments to estimate molecular
dipoles as shown in previous table
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E.g., using bond moment O-H to estimate the dipole
of H2O
Exercise. Try other molecular dipoles.
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CH3OH (methanol, 甲醇)
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CH3COOH (assuming COOH are on the same plane)
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CH3Cl
120o
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Hint:
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Order of Magnitude of Molecular Dipoles
contd
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A case where simple addition of individual bond
moments does not give right prediction
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Chloroform: CHCl3
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
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I guess the reason is the same one as that causing hydrogen
bonding in chloroform
“A hydrogen attached to carbon can also participate in
hydrogen bonding when the carbon atom is bound to
electronegative atoms, as is the case in chloroform, CHCl3”
(from wikipedia
http://en.wikipedia.org/wiki/Hydrogen_bonding, 20131022)
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Charge-Dipole Interaction in Isolation
+q
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Dipole u = ql
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Assume r >> l
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The interaction energy
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
r
+Q
-q
 
Qu cos  1
Q r u
w( r , )  

2
40 r
40 r 3
 
 E  u
(derive it)
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Charge-Dipole Interaction in Isolation
contd

Example
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
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Estimate max. interaction energy between a water
molecule and Na+
Assumptions
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Water: a spherical molecule, r = 1.4 Å, u = 1.85 D
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Na+: r = 0.95 Å (r: radius)
(Ans: 96 kJ mol-1 = 39 kBT at 300 K)
* kB: Boltzmann constant = 1.38 x 10-23 J/K
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Charge-Dipole Interaction in Medium
r = +
+Q
randomly oriented
r = finite
+Q
most likely to point
around 0o

Q. How to determine the intermolecular potential?
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If we know the probability distribution of , we can
w(r )  w(r, )

r
Q1. What is the probability distribution of ?
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To appendix
on Boltzmann
distribution 12
Charge-Dipole Interaction in Medium
contd

z dir

+Q
Boltzmann distribution theorem predicts the
probability density function p(,) using w(,r)
Prob([ ,   d), [,   d))  p(, ) dA
Boltzmann dist.theorem

 C0 e
where 1  C0 

0
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
2
0
e
 w ( r , )
k BT
2
 w ( r , )
k BT
C0 e
 w ( r , )
k BT
dA
2

  sin  dd
2

  sin  dd i.e.
2
1   p(, ) dA
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Charge-Dipole Interaction in Medium
contd

Average potential w(r) becomes
w( r )  w( r, ) r  

0
 C0 

0


2
0

2
0
w( r, ) e
2

w( r, ) p(, )   sin  d d
2
 w ( r , )
k BT
2

  sin  dd
2
For r >> 1, w(r) becomes
r>>1
2
 1  Qu 
1 2 2

 
w ( r )  w ( r , ) r 
uE 
2 
3kT  40r 
3kT
1
 4
r 
* Note this equation for charge-dipole interaction is from Atkin’s textbook on Physical
Chemistry, 7th ed. 2000. It is twice the value derived in Israelachvili 1991.
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Interaction between Charge & Dipole
in a Medium in Near Neighborhood

Consider a charge +Q is placed right inside a fluid
made of polar molecules
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Polar molecules distributed
according to Boltzmann distribution
What is free energy in this condition?
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The average free energy is still <w(r,)>
Unfortunately, because |w(r,)| << kT is no longer
valid, no simple formula as in previous case is possible.
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