MOLECULAR STRUCTURE AND DYNAMICS AT LIQUIDLIQUID INTERFACES

1
MOLECULAR STRUCTURE AND DYNAMICS AT LIQUID-LIQUID
INTERFACES
CHEM 2440
Submitted By Subhasis Chakrabarti
2
INTRODUCTION
Many important phenomena in chemistry and biology
involve processes that occur at the interface
between two immiscible liquids. e.g. liquid
chromatography, phase transfer catalysis,
different electrochemical processes and drug
delivery problem in farmacology. In addition to
that we need to understand the fundamental
processes such as adsorption, solvation, electron
transfer, ion transfer and proton transfer at
the interface between two immiscible liquids.
Therefore the study of the structure and the
dynamics of the neat interface is very important.
3
PROBES TO STUDY THE STRUCTURE OF THE NEAT
INTERFACE
Experimental techniques involve nonlinear
optical spectroscopies1,2 , light and neutron
scattering 3,4 and infrared spectroscopy.5
Theoretical calculations using molecular
dynamics and Monte Carlo computer simulations.
Theoretical methods are more useful than
experimental techniques! Due to the small size
of the region and the buried nature of the
interface.
4
INTERFACE WIDTH AND ROUGHNESS
The size of the interface depends on the
density profile of the two liquids and the degree
of their interpenetration. Also any thermal
fluctuations will change the position and shape
of the interface. So experimentally we need very
precise measurement to find out the actual width
of the interface.
From the surface tension value we can gain
valuable information about the interfacial charge
density which is directly related to the
interfacial thickness and density profiles of two
immiscible liquids.
5
Microscopic interpretation can be obtained from
Gibbs adsorption equation and capillary theory.
The geometry that people considered is that of
two liquids of bulk density ?1 and ?2 enclosed in
a rectangular box of cross-section s L2
The interface is flat on average and is taken to
be perpendicular to the z-axis (Fig. 1)
Benjamin, I. Annu. Rev. Phys. Chem., 1997, 48,
407.
6
Capillary wave theory gives a direct connection
between the width of the interface and its
surface tension. Considering the intrnsic
density profile ?int to be a step function we can
write
7
The mean square amplitude of the surface
fluctuation at a given temperature is the
cannonical ensemble average
After doing the calculation it can be shown that
the thickness of the interface is
Benjamin, I. Annu. Rev. Phys. Chem., 1997, 48,
407.
8
Quantitative knowledge about density variation
and fluctuation about the neat interface
obtained from molecular dynamics and Monte Carlo
method
In this method, each liquid is typically
represented by a few hundred to a thousand
molecules interacting via simple pairwise
addititive potential energy functions.
Where uij is the interactions between site i and
j, which belong to different molecules.Qi and Qj
are the charges assoiciated with each site and
eij, sij are the Lennard-Jones parameter. Also,
9
The interface width is significantly affected by
the polarity of the liquid. Increasing the dipole
moment reduces the miscibility, increases the
surface tension and give rise to sharper
interface (see figure)
Benjamin, I. Annu. Rev. Phys. Chem., 1997, 48,
407.
10
Applying statistical mechanics we can find out
the following parameters

• Molecular orientation using orientation profile.
• Pair correlation function which is proportional
  to the probability of finding an atom of type a
  at position r1 given that there is an
  atom(different) of type ß at position r2.
• 3. Hydrogen bonding energy calculation.( The
  extent of hydrogen bonding is one important
  example of pair correlation at interface.)

11
Solute transfer across the interface. The
experimental results yield the following
observations

• In most cases ion transfer is a rapid process by
  the fact that cyclic voltammograms are symmetric
  with respect to the direction of the current
  flow.
• In some cases for a series of similar ions, the
  ion transfer reaction obey a linear free energy
  relationship law.
• Dependence of the ion transfer rate on its
  diffusion constant can be studied by changing the
  viscosity of the medium.
• The rate of ion transfer from water to the
  organic phase decreases as the di-electric
  constant of the organic phase decreases.

The existance of free energy relationship
indicate that the ion transfer can be viewed as a
activated chemical reaction.
12
The following questions need to be answered
relating the microscopic aspect of the mechanism
of electron transfer

• If ion transfer is an activated process, what is
  the molecular nature of the activation barrier?Is
  ther any wee-defined activation state? Does this
  state correspond to an ionwith a mixed solvation
  shell?
• Is the process of switching the solvation shell
  an activated process?How does the external
  electric field influence it?
• Does the process of ion transfer from one phase
  to other involve significant dragging of the
  solvation shell?Is there a significant
  perturbation of the neat liquid-liquid interface
  structure?
• Are there important dielectric and ionic
  atmosphere frictional effects that can influence
  the dynamics of ion transfer?

13
Quantitative model for ion transfer( where the
cylindrical symmetry of the planer interface
between two immiscible liquids suggests that the
free energy profile is only a function of the
distance along the interface normal z)
The model is continuum electrostatic model of
solvation where the two liquids are considered as
structureless dielectric media with a fixed
dielectric constant upto a discontinuous jump at
the interface.
Where E is the electric field and D is the
induction vector
The free energy of transfer from liquid I to II
is given by
Which gives a reasonable qualitative idea about
the driving force for ion transfer!!
Benjamin, I. Annu. Rev. Phys. Chem., 1997, 48,
407.
14
Free energy profiles for the series of neutral
solutes across the water-hexane and water
membrane interface has been calculated
In this method,the solvation free energy is given
by the following expression
Where Ui(i1, 2) is the potential energy of
interaction between the solute and the solvent
and is determined by a random insertion of the
solute at any position within a narrow slab
centered at the position Z.
Benjamin, I. Annu. Rev. Phys. Chem., 1997, 48,
407.
15
The following graphs show the results of the free
energy profile for ion transfer in two different
systems (Figure 3)
The calculated value of the free energy
transfer (15 kcal/mol) is in reasonable agreement
with the experimental value of 12.4 kcal/mole
Benjamin, I. Annu. Rev. Phys. Chem., 1997, 48,
407.
16
Electron transfer at the Electrochemical
liquid-liquid interface
Thoretical considerations Continuum model
Marcus theory can be applied to the interfacial
case with some modifications. The main
differences are

• The geometrical constraints imposed by the
  interface, especially if some of the reactants or
  products are insoluble in one of the liquid.
• The influence of the internal elctric field in
  the electric double layer
• The different dielectric behaviour of the two
  phases

17
The ET reaction can be described as a sequence of
the following steps

• The donor and acceptor diffuse to the interface,
  where they form the precursor ion-pair.
• Solvent reorganization due to thermal
  fluctuations brings the system to the transition
  state.
• The actual change in the quantam states occur
• Solvent relaxation and diffusion of the products
  away from the interface complete the reaction.

18
The net effect can be summerized by the following
equations
The rate constant for the interfacial ET reaction
has been given by Marcus
Where k is the quantum transmission factor that
depends on the electronic coupling between the
two states and ? is a nuclear frequncy factor.
19
Reaction volume ( which is a geometrical measure
for all the possible configurations of the
reactant pairs per unit area of the interface)
For two spherical reactants of diameter d1 and d2
which are approaching each other from the two
sides of a mathematically sharp interface, Marcus
derives the following approximate expression
dR is the thickness of the region where the
elctronic coupling between the two states is
substantial (around 1Å) also the activation
energy is given by
20
A schematic reprentation of the free energy
functions for electron transfer reaction in a
polar medium
? is the medium reorganization free energy, which
is reversible work required to change the solvent
nuclear polarization from its reactants
equilibrium value to products equilibrium value.
Kharkats Volkov and later Marcus have
represented a continuum electrostatic expression
for the reorganization free energy and the work
terms appropriate to the liquid-liquid interface
?q is the magnitude of the charge transfer, R is
the distance between the reactants in precursor
pair.
21
Conclusions
The interface between two liquids is a unique
environment that is characterized by electrical,
structural and dynamical properties that are just
now beginning to be explored in detail. New
experimental techniques and theoretical advances
provide nuch more needed insight into the
properties of the neat interface. Experimental
studies of time-resolved phenomena, which have
contributed immensely to our understanding of
solution phase chemical dynamics, are also needed
( with close collaboration with theory) at the
interface between two liquids.
22
References

• Eisenthal. K. B. Annu. Rev. Phys. Chem., 1992,
  43, 627.
• Corn, R. M. Chem. Rev., 1994, 94, 107.
• Pershan, P. S. Faraday Discuss. Chem. Soc., 1990,
  89, 231.
• Lee, L. T. Langevin, D. Mann, E. K. Farnoux,
  B. Physica B., 1994, 198, 83.
• Sperline, R. P. Freiser, H. Langmuir, 1990, 6,
  344.