Transcript Chapter 17: Molecular Interactions
Atkins & de Paula: Atkins’ Physical Chemistry 9e
Chapter 17: Molecular Interactions
Chapter 17: Molecular Interactions ELECTRIC PROPERTIES OF MOLECULES 17.1 Electric dipole moments
electric dipole,
two electric charges +
q
electric dipole moment, μ,
and –
q
separated by a distance the vector that points from –
q
to +
q R
.
with magnitude
μ
=
qR
.
1 D = 3.33564 × 10 -30 Cm
Chapter 17: Molecular Interactions
polar molecule,
a molecule with a permanent electric dipole moment.
nonpolar molecule,
a molecule without a permanent electric dipole moment.
Chapter 17: Molecular Interactions
Resultant electric dipole moments, μ
res
2 =
μ
1 2 +
μ
2 2 + 2
μ
1
μ
2 cos
θ
.
Chapter 17: Molecular Interactions
Calculation of electric dipole moments, μ 2 =
μ
x 2 +
μ
y 2 +
μ
z 2 (
μ
i =Σq j i j )
μ
= 2.7 D
Chapter 17: Molecular Interactions
Self-test; calculation of the μ of formaldehyde
Chapter 17: Molecular Interactions 17.2 Polarizabilities
induced dipole moment, μ
*, the dipole moment induced by an applied electric field.
polarizability,
the constant of proportionality
α
in
μ
* =
α
E . (unit = C 2 m 2 J -1 ) polarizability volume, α =
α
/4π
ε
0 . (unit of
ε
0 : C 2 m -1 J -1 )
polarizability,
perturbation expression.
2
n
0
z
, 0
n E n
2
E
0 , where
z
, 0
n
: transition in the z direction
E μ n
E
0
eR
mean value
z,
0
n
E
( HOMO LUMO gap) 2
e
2
R E
2
α
≈
R
3
E
e
2 4 0
R
α increases as the molecular size increases α increases as the HOMO-LUMO gap decreases
Chapter 17: Molecular Interactions 17.3 Polarization
polarization, P , the electric dipole moment density,
P
dielectric,
a polarizable, nonconducting medium.
μ
= =
0, where no electric field is applied
μ
N .
μ z
μ z
= =
μ, where a strong electric field is applied μ 2
E /
3kT, where a weak electric field is applied dp
e
E
( ) /
kT
0
e
E
( ) /
kT
sin sin
d
d
; probabilit y of dipole orientatio
z
1 1
e xy
z
cos
dp dy
e x
e
x
L
(
x
)
x
L
(
x
) cos
dp
1 1
ye xy dy e x e x
e
x
e
x
1
x e x
0
e x
cos 0
e x
cos cos sin sin
d
d
e
x x
e x
e
x x
2 ; Langevin function
e
1 1 2 2
x
3
x
L
(
x
) 1 3
x
z
2 E 3
kT
n E
kT
, ( ) E
y
,
dy
z
1 1 1 1
e ye xy dy xy dy
Chapter 17: Molecular Interactions
orientation polarization,
the polarization arising from the permanent dipole moments; is lost at microwave frequency
distortion polarization,
the polarization arising from the distortion of the positions of the nuclei by the applied field; is lost at IR frequency
electronic polarizability,
the polarizability due to the distortion of the electron distribution; is still alive at Vis frequency
frequency dependence of polarizabilities
( ) 2
n
n
0 2
n
0
z
, 0
n
2 2 2 0
n
z
, 0
n E n
2
E
0
ħω n0 = E n
–
E
0
n
0 ( ) 2 2
n
n
0
z
, 0
n
2 ( ) 2 2
n
n
0
z
, 0
n
2 0 as
Chapter 17: Molecular Interactions 17.4 Relative permittivities
permittivity,
the quantity
relative permittivity
(dielectric constant),
ε
r
Debye equation,
(
ε
r – 1)/(
ε
r molar polarization, P m
ε
= ( in the Coulomb potential energy,
N
+ 2) =
ρP
m /
M
.
A /3
Clausius–Mossotti equation,
(
ε
r
ε
0 )(
α
+ – 1)/(
ε μ
r 2 Nonpolar molecules or high frequency of applied field /3
kT
= ).
+ 2) =
ε
/
ε
0
ρN
. ( A
α ε
0 /3 = vacuum permittivity)
Mε
0 .;
V
=
q
1
q
2 /4π
εr
.
no contribution from permanent dipole,
μ
Example 17.2
slope
N A
9 0
k
2
μ
ε r = C/C 0 P
m Debye eqn.
intercept
N
3
A
0
α
refractive index and relative permittivity, n r refractive index, n r = ε r 1/2 .
=
c
/
c
. c: speed of light in vacuum, c : speed of light in medium
Chapter 17: Molecular Interactions INTERACTIONS BETWEEN MOLECULES
van der Waals interaction,
an interaction between closed-shell molecules that varies with separation as 1/
r
6 .
17.5 Interactions between dipoles
multipole,
an array of point charges.
n-pole,
an array of point charges with an
n
-pole moment but no lower moment.
monopole,
a point charge.
quadrupole,
an array of point charges that has neither net charge nor dipole moment.
octupole,
an array of point charges that sum to zero and which has neither a dipole moment nor a quadrupole moment.
Chapter 17: Molecular Interactions
multipole–multipole
potential energy,
V
1/
r n
+
m
-1 .
Chapter 17: Molecular Interactions
,
17.5 (a) The potential energy of interaction
point dipole,
a dipole in which the separation between the charges is much smaller than the distance at which the dipole is being observed;
l << r
point dipole-point charge interaction
V
1
q
2 4 0
r
2
V
1 4 0
r q
1
q
2 1 2
l
r q
1
q
2 1 2
l
x
q
1
q
4 0 2
r
1 1
x
1 1
x l
r
x
1 1 1
x V
1
x
x
2
q
1
q
2 4 0
r
( 1
x
) ( 1
x
) 1 1
x
1
x
x
2 2
xq
1
q
2 4 0
r
q
1
q
4 0 2
l r
2 1
q
2 4 0
r
2
Chapter 17: Molecular Interactions
,
Calculating the interaction energy of two dipoles
V
2 1 0
r
2 3
V
1 4 0
q
1
q r
2
l
q
1
q
2
r
q
1
q
2
r
q
1
q
2
r
l l V
r
2
x
2
x
4 0 1
q
1
q
2
r
1 1
x
2 1 0
r
2 3 1
x
x
2
x
q
1
q
2 4 0
r
1 1
x
2 1 1
x
1 1
x
1
x
x
2
Self-test 17.4
Chapter 17: Molecular Interactions
,
17.5 (b) Dipole-dipole interactions
electric field
of point charge, E =
q
/4π
ε
0
r
2 .
electric field
of point dipole, E =
μ
/2π
ε
0
r
3 .
potential energy
of two parallel point dipoles
V
1 4 2 0
f r
( 3 ) [
f(θ)
= 1 – 3 cos 2
θ
] See
Further information
17.1
Chapter 17: Molecular Interactions
,
Keesom interaction,
the interaction of two freely rotating point dipoles:
first contribution to the vdW interaction
=
μ
1
μ
2
/ 4
πε 0 r
3
V
C r
6
C
; weighting factor in the averaging;
probability that a particular orientation will be adopted by a dipole f f
0 0
fpd
d
1 0
fd
1 1 0 0
fe
V
/
kT d
f
(
V
1 /
kT
)
d
0
f
( 1
V
1 0
p p
/
kT
)
d
fd
e
-V/kT
,
V
=
μ
1
μ
2
f
/4
πε 0 r
3 1-
V/kT
+ ∙∙∙, when
V
‹‹ 1 0 4 1 0 2
kTr
3
f
2
d
kT
1 0
fd
4 1 0 2
kTr
3 1 0
f
2
d
f
0 4 1 0 2
kTr
3
f
2 0 3 ( 4 2 2 1 0 ) 2 2 2
kT
, where 0 denotes an unweighted spherical average
f
0 1 0 ( 1 3 cos 2 ) sin
d
0
V
1 2 2 2
f
2 0 ( 4 0 ) 2
kTr
6
f
2 0 2 3
V
2 1 2 3 ( 4 0 ) 2 2 2
kTr
6
Chapter 17: Molecular Interactions
,
Keesom interaction,
the interaction of two rotating point dipoles:
first contribution to the vdW interaction V
C r
6
C
3 ( 4 2 2 1 0 ) 2 2 2
kT
Negative sign:
the average interaction is attractive.
V
1/r 6 :
a van der Waals interaction.
V
1/T :
the greater thermal motion overcomes the dipole interactions at higher temperatures.
V
1/r 6 :
arises from
V
1
/
r
3
weighted by the energy in the Boltzmann term
(
1
/
r
3 )
Chapter 17: Molecular Interactions
,
17.5 (c) Dipole-induced-dipole interactions
V C
C r
6 2 4 1 0 2
Independent on the temperature
; thermal motion has no effect on the averaging process
Chapter 17: Molecular Interactions
,
17.5 (d) Induced-dipole-induced-dipole interactions
dispersion interaction
(London interaction)
London formula
V
C r
6
C
3 2 1 2
I
1
I
1
I
2
I
2
Chapter 17: Molecular Interactions
,
17.5 (e) Hydrogen bonding
hydrogen bond,
an attractive interaction between two species that arises from a link of the form A–H∙∙∙B, where A and B are highly electronegative elements (N, O, or F) and B possesses a lone pair of electrons.
= c 1 A + c 2 H + c 3 B Net effect: lowering of energy
anti-bonding nonbonding bonding
Chapter 17: Molecular Interactions
,
17.5 (f) The hydrophobic interaction
hydrophobic,
water-repelling; possessing a positive Gibbs energy of transfer from a nonpolar to a polar solvent. Δ transfer G > 0, Δ transfer H < 0, Δ transfer S < 0 hydrophobicity constant, π = log(
S
/
S
0 )
S
: ratio of the molar solubility of R-A in octanol to that in water
S
0 : ratio of the molar solubility of H-A in octanol to that in water
hydrophobic interaction,
an effective interaction that is due to the increase in entropy of the surrounding solvent.
A hydrocarbon molecule in a water cage
Chapter 17: Molecular Interactions
,
17.5 (g) The total attractive interaction
total attractive interaction between rotating molecules;
dipole-dipole, dipole-induced dipole, and dispersion interactions.
V = –C
6
/r 6 limitation of V = –C
6
/r 6 ;
consider only dipolar interactions, assume freely rotating molecules, and consider only the interactions of pairs of molecules
Axilrod–Teller formula,
total dispersion energy of three closed-shell molecules
V
C
6 6
r
AB
C
6 6
r
BC
C
6 6
r
CA
C
r r r
AB BC CA 3
C
=
a
(3 cos
θ
A cos
θ
B cos
θ
C + 1), where
a
≈ 3 / 4
α
C 6
Chapter 17: Molecular Interactions Interactions between dipoles; impact on medicine (molecular recognition & drug design). See I17.1
Chapter 17: Molecular Interactions
,
17.6 Repulsive and total interactions
hard-sphere potential, V = for
r
d
;
V
= 0 for
r
>
d
.
Mie potential, V =
C n
/
r n
–
C m
/
r m
.
Lennard-Jones potential, V = 4
ε
{(
r
0 /
r
) 12 exp–6 potential, V = 4ε{e –
r
/
r
0 – (
r
0 /
r
) 6 }.
ε:depth of the well, r
0
:seperation where V=0
– (
r
0 /
r
) 6 }.; better than L-J(12,6) potential
Chapter 17: Molecular Interactions GASES AND LIQUIDS 17.7 Molecular interactions in gases
molecular beam,
a collimated, narrow stream of molecules travelling though an evacuated vessel.
hydrodynamic flow,
net flow arising from intermolecular collisions.
molecular flow,
collision-free flow.
Chapter 17: Molecular Interactions
Chapter 17: Molecular Interactions
supersonic,
a stream of molecules in which the average speed of the molecules is much greater than the speed of sound for the molecules that are not part of the stream.
supersonic beam,
a beam obtained when the region of hydrodynamic flow is skimmed from a supersonic jet and the excess gas pumped away.
crossed beam technique,
a technique in which two molecular beams are incident at right angles.
Low translational T
Chapter 17: Molecular Interactions
differential scattering cross-section, σ , the constant of proportionality between the change in intensity (d
I
) and the intensity of the incident beam (
I
), the number density of target molecules (
N)
, and the infinitesimal path length d
x
through the sample: d
I
=
σIN
d
x
.
impact parameter, b , the initial perpendicular separation of the paths of the colliding molecules.
Chapter 17: Molecular Interactions
Scattering patterns depend on the impact parameter (b) for the impact of two hard spheres
Chapter 17: Molecular Interactions
for real molecules;
scattering patterns depend on the intermolecular potential, molecular shape, and relative speed of approach as well as the impact parameter.
repulsive core long range attractive potential
Chapter 17: Molecular Interactions
quantum oscillation,
the modification of the scattering in the forward direction by interference between the wavefunctions of a particle along two different paths.
rainbow scattering,
strongly enhanced scattering in a nonforward direction.
rainbow angle, θ r , the angle for which d
θ
/d
b
= 0 and the scattering is strong.
van der Waals molecules,
complexes of the form AB in which A and B are held together by van der Waals forces or hydrogen bonds.
Chapter 17: Molecular Interactions 17.8 The liquid–vapour interface 17.8 (a) surface tension
surface tension, γ , the constant of proportionality between the increase in surface area of a liquid and the work needed to create the increase: d
w
=
γ
d
σ
(=d
A
, where constant T).
dA < 0 (dσ < 0)
; spontaneous process: surfaces have a natural tendency to contract.
Example17.4
dw =2γlh
Chapter 17: Molecular Interactions 17.8 (b) curved surfaces
bubble,
a region in which a vapour is trapped by a thin film.
cavity,
a vapour-filled hole in a liquid.
droplet,
a small volume of liquid Laplace equation, p
in = p out + 2γ/r
.
outward force; pressure × area
= 4πr 2 p in
inward force; force from
p out
force from
p out
; pressure × & surface tension area
= 4πr 2 p out
force from surface tension; d
σ = 4π(r+dr) 2 8πγr - 4πr 2 = 8πrdr
d
w
=
8πγr
d
r 4πr 2 p in = 4πr 2 p out + 8πγr
p in = p out + 2γ/r
Chapter 17: Molecular Interactions 17.8 (c) capillary action
capillary action,
the tendency of liquids to rise up capillary tubes.
capillary rise
and surface tension,
γ = (ρ
β –ρ α
)ghr/2
Same pressure at same height in a same phase P 1 =P 6 , P 2 =P 5 , P 2 =P 3 Curved surface: P 4 < P 5 P 5 =P 3 =P 3 P 4 < P 3
;capillary rise
At equilibrium P 1 =P 6 , P 2 =P 3 P 8 =P 5 , P 3 =P 4 P 8 -P 3 = P 5 -P 4 P 8 -P 2 = P 5 -P 4 P 8 -P 2 = (P 5 -P 7 )+(P 7 -P 4 ) P 8 -P 2 =-
ρ α gh
, P 7 -P 4 =-
ρ β gh
, P 5 -P 7 =2
γ
/
r
(θ c =0) -
ρ α gh
= 2
γ
/
r
-
ρ β gh γ =
(
ρ β –ρ α
)
ghr/2
Chapter 17: Molecular Interactions
nonzero angle between the edge of meniscus and the wall contact angle
and interfacial tension, cos
θ
c superficial work of adhesion, w
cos θ c = w ad /γ lg – 1
ad =
γ
sg +
γ
lg
criterion for surface wetting,
1<
w
ad /
γ
lg < 2.
= (
γ
sg –
γ
sl
criterion for non-surface wetting,
0<
w
ad /
γ
lg < 1.
–
γ
sl )/
γ
lg .
;
γ
sg =
γ
sl +
γ
lg cos
θ
c (work of adhesion/area of contact)
Chapter 17: Molecular Interactions 17.9 Surface films; will be covered in Chap. 18 17.10 Condensation
Kelvin equation
for the vapour pressure of droplets,
p
supersaturated
=
p*
e 2
γVm/rRT
phase, a phase that is thermodynamically unstable with respect to the liquid.
spontaneous nucleation centre,
a location at which a sufficiently large number of molecules congregate into a droplet.
nucleate,
provide surfaces to which molecules can attach and thereby induce condensation.
superheated,
a liquid that has not boiled but is above its boiling temperature.
supercooled,
a liquid that has not frozen but is below its freezing temperature.
Chapter 17: Molecular Interactions Impact on nanotechnology
Spontaneous Assembly of a Monolayer of Charged Gold Nanocrystals at the Water/Oil Interface Directing Self-Assembly of Nanoparticles at Water/Oil Interfaces
Angew. Chem. Int. Ed
.
2004
,
43
, 458.
Angew. Chem. Int. Ed
.
2004
,
43
, 5639.