Intermolecular Interactions

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24 Οκτ 2013 (πριν από 4 χρόνια και 2 μήνες)

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(
http://www.chem.ufl.edu/~itl/4411/lectures/lec_g.html
)

(
http://www.chem.ufl.edu/~itl/4411/lectures/lec_g.html
)

Intermolecular
interaction

Short range

Long range


< 3 Å


Repulsive



> 3 Å


Attractive


Van
der

Waals
interaction


When two non
-
bonded atoms approach each
each

other,
at some distance overlap of the occupied
orbitals

results
in electrostatic repulsion between the electrons of those
atoms.


This repulsive energy acts over a very short range, but
goes up very sharply when that range is violated.


The repulsion goes up as 1/r
12
. It is important only when
atoms are in very close proximity, but then it becomes
very important


Because this repulsive term rises so sharply as
distance decreases it is sometimes reasonable to
think of atoms as hard spheres, like small pool balls,
defined by van
der

Waals radii and surfaces.


When two atoms approach each other their van
der

Waals surfaces make contact when the distance
between them reaches the sum of their van
der

Waals radii.


Here we are assuming that bonds do not form. When
bonds form van
der

Waals radii are violated.


The smallest distance between two non
-
bonded
atoms is the sum of the van
der

Waals radii of the
two atoms.


The van
der

Waal radius of carbon is evident from
the spacing between the layers in graphite.


The distance between atoms in different layers of
graphite is never less than twice the van
der

Waals
radius of carbon (2 x 1.7 = 3.4 Å).


The atoms within a graphite layer are covalently
linked and so are in violation of the van
der

Waals
radius.

An
electric dipole

is a separation of positive and
negative charges

(
http://ww2.chemistry.gatech.edu/~lw26/structure/molecular_interactions/mol_int.html
)

(
http://hcxy.wzu.edu.cn/gdwlhx/ShowNews.aspx?ID=6845&Tid=279
)


Due to non
-
uniform distributions of positive and
negative charges on the various atoms, many
molecules have dipole moments.


Such is the case with polar compounds like water
(H
2
O), where electron density is shared unequally
between atoms.


The physical chemist Peter J. W. Debye was the first
scientist to study molecular dipoles extensively.


Dipole moment (

):





q
l







(1)

where q : charge



l

: distance of positive and negative charges


Dipole energy:

where

0

:
permittivity of vacuum (= 8.854 10
-
12

F/m)



r

: relative permittivity or dielectric constant of
the medium where the charges are located in.

(2)

For molecules there are three types of dipoles:


1.
Permanent dipoles:

These occur when two atoms in a molecule have
substantially different
electronegativity
: One atom
attracts electrons more than another, becoming
more negative, while the other atom becomes
more positive. A molecule with a permanent dipole
moment is called a polar molecule.



2.
Instantaneous dipoles:

These occur due to chance when electrons happen
to be more concentrated in one place than another
in a molecule, creating a temporary dipole.

(
http://www.chemprofessor.com/imf.htm
)

3.
Induced dipoles:

These can occur when one molecule with a
permanent dipole repels another molecule's
electrons, inducing a dipole moment in that
molecule. A molecule is polarized when it carries an
induced dipole. See induced
-
dipole attraction.

Dipole moment values of some typical gas phase in
debye

units are:

Compound

Dipole Moment (Debyes)

NaCl

9.0

(
measured in the gas phase)

CH
3
Cl

1.87

H
2
O

1.85

NH
3

1.47

CO
2

0

CCl
4

0

(
http://www.chem.purdue.edu/gchelp/liquids/iondip.html
)


A dipole that is close to a positive or negative ion will
orient itself so that the end whose partial charge is
opposite to the ion charge will point toward the ion.


This kind of interaction is very important in aqueous
solutions of ionic substances.


H
2
O is a highly polar molecule, so that in a solution of
sodium chloride, the Na
+

ions will be enveloped by a
shell of water molecules with their oxygen
-
ends
pointing toward these ions, while H
2
O molecules
surrounding the
Cl


ions will have their hydrogen ends
directed inward.

The interaction energy

can
be constructed from the
Coulomb interactions
between the bare charge
Q and the dipolar charges


q:

(3)

r
2

r
1

where



Q

: charge of ion


r

: distance between ion and dipole



0

:
permittivity of vacuum (= 8.854 10
-
12

F/m)



r

: relative permittivity or dielectric constant of the
medium where the charges are located in


l

: length of dipole moment vector




:theang汥betweenthe楰i汥浯mentvect潲
anthevect潲c潮nect楮ithe楯iw楴ithe
dipole


When

the dipole is sufficiently far away from the charge
(
r >>
l
), we can
approximate
:

The interaction energy is then

where

(4)

(1)


When deriving eq. (4) we assumed the dipole to be
sufficiently far from the charge (r >>
l
).


At about
r < 2
l
the approximation deviate more than
10% from the exact result.


Taking into account the finite size of atoms and
molecules, eq. (4) is actually an excellent
approxi
-
mation

for interactions between ions and small polar
molecules at all physically relevant distances.


In the case of larger molecules, where the charges
comprising the dipole may be several
ångströms

apart,
we need to exercise good
judgement

whether to use
eq. (4) or not.

(
http://2012books.lardbucket.or
g/books/general
-
chemistry
-
principles
-
patterns
-
and
-
applications
-
v1.0m/section_15_02.html
)

(
http://2012books.lardbucket.org/bo
oks/general
-
chemistry
-
principles
-
patterns
-
and
-
applications
-
v1.0m/section_15_02.html
)


As two dipoles approach each other, they will tend to
orient themselves so that their oppositely
-
charged
ends are adjacent.


Two such arrangements are possible: the dipoles can
be side by side but pointing in opposite directions, or
they can be end to end.


It can be shown that the end
-
to
-
end arrangement
gives a lower potential energy.


Dipole
-
dipole attraction is weaker than ion
-
dipole
attraction, but it can still have significant effects if the
dipole moments are large. The most important
example of dipole
-
dipole attraction is hydrogen
bonding.

(5)


1

and

2

are
the polar orientation angles of

1

and

2
,
respectively, and


楳the
az業uthal

潲entat楯渠ang汥潦

2

in reference to

1

for r > 3
l:


Dipole
-
dipole interaction is comparatively weak (for
dipole moment of 1 Debye at 0.35 nm in vacuum,
the interaction is already weaker than
kT
).


In certain molecules (small size and large dipole
moment O
-
H, N
-
H, and F
-
H), dipole
-
dipole
interaction can lead to short range association in
liquid (part of H
-
bond).


Dipole
-
dipole interaction is strongest when the two
dipoles mutually orient themselves in line.


At large separation or in a medium of high

,when
楮ieact楯渠a汬sbe汯l

,楰潬iscann潷潴ate
浯meee汹.


The angle averaged potentials are not zero because
of Boltzmann weighting factor, the energy (
Keesom

interaction or orientation interaction) becomes


(6)

for

Polarizability

(

)


Polarizability

is the ease of distortion of the electron
cloud of a molecular entity by an electric field (such as
that due to the proximity of a charged reagent).


It is experimentally measured as the ratio of induced
dipole moment (

ind
) to the field E which induces it:

(7)


Nearby ions can distort the electron clouds even in
polar molecules, thus temporarily changing their dipole
moments.


The larger ions (especially negative ones such as SO
2
2


and ClO
4
2

) are highly
polarizable
, and the dipole
moments induced in them by a
cation

can play a
dominant role in compound formation.


The most significant induced
dipole effects result from
nearby ions, particularly
cations

(positive ions).

(
http://textbook.s
-
anand.net/ncert/class
-
11/chemistry/5
-
states
-
of
-
matter
)


A permanent dipole can induce a temporary one in a
species that is normally non
-
polar, and thus produce a
net attractive force between the two particles.


This attraction is usually rather weak, but in a few cases
it can lead to the formation of loosely
-
bound
compounds.


This effect explains the otherwise surprising
observation that a wide variety of neutral molecules
such as hydrocarbons, and even some of the noble gas
elements, form stable hydrate compounds with water

(8)

(http://www.chem.ufl.edu/~itl/4411/lectures/lec_g.html)

Noble gas elements and completely non
-
polar molecules
such as H
2

and N
2

can be condensed to liquids or solids.

There must be another source of attraction between
particles that does not depend on the existence of
permanent dipole moments in either particle.


A molecule is “
nonpolar



the
time
-
averaged

dipole
moment is zero.


On a very short time scale, however, the electron must be
increasingly localized.


As a consequence, there is no guarantee that the
distribution of negative charge around the center of an atom
will be perfectly symmetrical at every instant; every atom
therefore has a weak, fluctuating dipole moment that is
continually disappearing and reappearing in another
direction.


Although these extremely short
-
lived fluctuations quickly
average out to zero, they can still induce new dipoles in a
neighboring atom or molecule, which helps sustain the
original dipole and gives rise to a weak attractive force
known as the dispersion or London force


Dispersion is applicable to all atoms or molecules
(unlike
Keesom

or Debye interaction).


It is responsible for certain phenomena in macro
-
scopic

scale (adhesion, surface tension, physical
adsorption, wetting, properties of gases and liquid,
structures of condensed macromolecules,... ).


It is a long range force that can be effective at large
distance (>10 nm) to
interatomic

spacings
.


Dispersion is non
-
additive. The dispersion of two
molecules is affected by the presence of the third
molecules


Fritz London (1937) proposed a theory based on quantum
mechanics to explain dispersion

(9)

where I is the first ionization potential I = h



Many kinds of molecules possess permanent dipole
moments, so liquids and solids composed of these
species will be held together by a combination of
dipole
-
dipole, dipole
-
induced dipole, and dispersion
forces.


These weaker forces (that is, those other than
coulombic

attractions) are known collectively as
van
der

Waals forces
.


These are short
-
ranged and weak interactions existing
between all types of atoms and molecules.


All atoms and molecules, even non
-
polar and
uncharged ones, exert attractive forces on each other.


This is a result of the atomic
polarizability


0

of
atoms.


The constant motion of electrons in atoms results in
the fact that at any given instant in time, any atom
actually has a finite electric dipole moment.


Despite the quantum
-
mechanical uncertainty of
position, even particles as light as electrons have to
occupy some region of space at a given time.



In the absence of an external influence, the average
dipole moment of an atom is zero.

In general, the van
der

Waals forces arise from three
different contributions:

(1)
orientation or
Keesom interaction;

(2)
induction or Debye interaction; and

(3)
dispersion or London interaction

Thus, in general the total van
der

Waals energy is given by

(10)


The

dispersion term is the most important of the
three contributions, as it is always present, regardless
whether permanent dipoles take part in the
interaction or not.


Moreover, usually the dispersion term is also the
strongest, contributing around 80
-

100% to the total
van
der

Waals interaction energy.


A notable exception to this is water, where in fact the
Keesom

interaction dominates (about 70% of the
total
interaction energy)

Summary

Intermolecular forces are responsible most properties
of all the phases:

1.
Gas: Vapor pressure, critical point, and boiling point

2.
Liquid: viscosity, diffusion, and surface tension.

3.
Solid: melting and sublimation.


The calculation of the potential energy involves
assumptions concerning the nature of attraction
and repulsion between molecules.


Intermolecular interaction is the result of both
short
-

and long
-
range effects.


Electrostatic, induction, and dispersion effects
are examples of long range interactions.


In these cases, the energy of interaction is
proportional to some inverse power of
intermolecular separation. Electrostatic
interactions result from the static charge
distribution between molecules.


The effect can be either attractive or repulsive
and it is exclusively
pairwise

additive.


Induction effects are always attractive, resulting
from the distortions caused by the molecular
fields of
neighbouring

molecules


The specification of intermolecular potential,
representing interaction between molecules, is a
critical step in Molecular Dynamics simulations.


Generally, a two
-
body potential of the form U(
r
ij
) is
used, where
r
ij

is the distance between the centers of
molecules
i

and j.


This form neglects
multibody

interactions.


Once the potential is prescribed, the intermolecular
force is obtained from
F
ij

=
-
dU
(
r
ij
)/
dr
ij
.


In the following, we will discuss intermolecular
potential models.

In this model, the molecules move freely and do not
interact with one another except when they collide.
The intermolecular potential is
given by

(11)

Here (σ) is the diameter of the molecule.

Thus the molecules exert force on one another only
when they
collide

Intermolecular potential for the hard
-
sphere model

www.uic.edu/eng/ems/MEng/ChEME494/pdf/
L8pt1
.pdf


The square
-
well potential is the simplest inter
-
molecular potential that is capable of representing the
properties of liquids

(12)

where


iss潭浵mti灬p潦t桥桡
-
s灨ee摩浥te
a湤


isa浥as畲u潦t桥attactivei湴eacti潮⸠

The square
-
well potential represents a mathematically
idealised

model of molecular interactions.

U(r)

Square well potential model

The square
-
well potential can be made more realistic by
changing the variation of attractive interactions. There have
been many such variations of which the Yukawa potential is
an important example.

(13)

where


i猠an⁡ttactivetem⡤epth映tential睥ll⤬)


i猠
theha
-
獰heeiametean


i猠an⁡橵獴ablepaamete.

heinve獥p睥epenence映thi猠ptentialmean猠that
itcanbeapplietinicsy獴em献

Hard
-
core Yukawa potential with various interaction ranges

(
Naresh

and Singh, 2000)

The
Lennard
-
Jones potential (also referred to as the L
-
J
potential, 6
-
12 potential, or 12
-
6 potential) is a
mathematically simple model that approximates the
interaction between a pair of neutral atoms or molecules.

(14)

where


i猠theepth映ptential睥llⰠ


i猠theha
-
獰hee
iamete
the晩nitei獴anceat⁷ichtheinte
-
paticle
potential is zero), and

r is the distance between the
particles
.

http://what
-
when
-
how.com/molecular
-
biology/van
-
der
-
waals
-
interactions
-
molecular
-
biology/

Lennard
-
Jones potential

www.uic.edu/eng/ems/MEng/ChEME494/pdf/
L8pt1
.pdf



The parameter σ is the zero energy separation
distance, and defines a molecular length scale related
to the particle diameter, while ε is the minimum
energy and controls the strength of the interaction.


As an example, σ= 0.41 nm, and ε/
k
B

=
221K for
xenon
,
where
k
B

is the Boltzmann's constant.


For a pure substance, σ equals the particle diameter.


The parameter σ is also related to the critical volume
of the fluid, while ε to its critical temperature.


This dependence is particularly strong for small
molecules.

For simulations involving two fluids, σ and ε are
expressed using the Lorentz
-
Berthelot mixing rules
(Allen and
Tildesley
, 1984), as:

(15)

(16)

The force between the two L
-
J molecules is given by

(17)

By convention, repulsive (short
-
range) forces are
positive while attractive (long
-
range) forces are
negative. i.e.,

(18)

Lennard
-
Jones intermolecular force

www.uic.edu/eng/ems/MEng/ChEME494/pdf/
L8pt1
.pdf