Ionic Conductivity And Ultrafast Solvation Dynamics

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Ionic Conductivity And Ultrafast Solvation
Dynamics

• Biman Bagchi
• Indian Institute of Science
• Bangalore, INDIA

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? The values of the limiting ionic conductivity
(?0) of rigid, mono positive ions in water at 298
K are plotted as a function of the inverse of the
crystallography ionic radius, r-1ion.
Biswas and Bagchi J. Am. Chem. Soc. 119, 5946
(1997)
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Ionic Conductivity
What determines the conductivity of an ion in a
dilute electrolyte solution ?

• The forces acting on the ion can be divided into
  two type Short range force and the long range
  ion-dipole forces. The former can be related to
  viscosity via Stokes relation. The long range
  force part is the one which is responsible for
  the anomalous behavior of ionic conductance.
• ? Continuum models of Hubbard-Onsagar-Zwanzig
  neglected the molecularity.
• The theory of Calef and Wolynes treated the
  dipolar response as over damped, but emphasized
  the role of translational motion of the solvent
  molecules.

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Consider the mobility of an ion in a dipolar
liquid, like water or acetonitrile

• The ionic mobility is determined by diffusion
  which in turn is determined by the friction on
  the ion, via Einstein relation.
• ? ?SR ?DF
• ? The classical theory ( Hubbard-Onsagar-Zwanzig
  ) finds that the friction on the ion, and hence
  the mobility, depends inversely on the Debye
  relaxation time ?D , which is the slowest time.
• This leads to the well-known law of Waldens
  product which states that the product of the
  limiting ionic conductivity (?0) of an
  electrolyte and the viscosity (?) is inversely
  proportional to the radius (rion) of the ion.

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Ultrafast solvation and ionic mobility
Two kinds of friction Stokes friction (?0) and
Dielectric friction (?DF)
How to get ?DF ?
What determines ?DF ?
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? All the earlier theoretical studies ignored the
ultrafast response of the dipolar solvents.
(Zwanzig, Hubbard-Wolynes, Felderhof .) ?
Theory however shows that they are important, in
two ways. First, they are reduce the friction on
the ion by allowing the relaxation of the force
on the ion. Second, they make the role of the
translational modes less important. ? What is
even more important is the relative role of
various ultrafast components.
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Lots have been found about solvation dynamics of
ions in water.
Potential Energy Surfaces involved in Solvation
Dynamics
Water orientational motions along the solvation
coordinate together with instantaneous
polarization P
Pal, Peon, Bagchi and Zweail J. Phys. Chem. Phys.
B 106, 12376 (2002)
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Continuum Model of Solvation Dynamics

BFO (1984), vdZH (1985)
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? Polarization relaxation is single
exponential. ? Debye representation
For ion
For water, ?L? 500 fs
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Ultrafast solvation dynamics in water,
Acetonitrile and Methanol

• However, initial solvation dynamics in water and
  acetonitrile was found to be much faster. For
  water it is found to be less than 50 fs!!
• In addition, the ultrafast component carried
  about 60-70 of the total relaxation strength.
• Such an ultrafast component can play significant
  role in many chemical processes in water.

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Experimental (expt s(t)) and simulated (?q
c(t)) solvation response function for c343 in
water. Also shown is a simulation for a neutral
atomic solute with the Lennard-Jones parameters
of the water oxygen atom (S0).
R. Jlmenez et al. Nature 369, 471 (1994)
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Theoretical Approach
Nandi, Roy and Bagchi, J. Chem. Phy. 102, 1390
(1995) Song, Marcus Chandler, JCP (2000).
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Mode coupling theory expression for solvation
time correlation function
? Where AN is the normalization constant cid(k)
and Ssolv(k,t) are the ion-dipole DCF and the
orientational dynamic structure factor of the
pure solvent. Sion(k,t) denotes the self-dynamics
structure factor of the ion.
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? The rate of the decay of the orientational
dynamics solvent factor, S10solv(k?,t/?) as a
function of time (t), for water at two different
temperature (solid line-318K, dashed line-283K).
Note that the numerical results obtained with k?
2? and ? 1 10-12 s.
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Microscopic origin of Ultrafast solvation
k ? 0
k ? 2?/?
? In the bulk, the k component dominates
(about 75 ). ? However, this is only part of the
story. ? Dynamics response comes into picture.
? 0
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(No Transcript)
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Effect of translational modes on ionic
conductivity and solvation dynamics.
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MCT Expression for Dielectric Friction including
the self-motion
N-E equation
S-E equation
The position dependent viscosity is given by
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?
Where,
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Experimental values of the Walden product (?0?0 )
of rigid , monopositive ions in water (open
triangle), acetonitrile and fomamide (open
squares) at 298 K are plotted as a function of
the inverse of the crystallography ionic radius
(r-1ion).
Bagchi and Biswas Adv. Chem. Phys. 109, 207 (1999)
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? The values of the limiting ionic conductivity
(?0) of rigid, mono positive ions in water at 298
K are plotted as a function of the inverse of the
crystallography ionic radius, r-1ion.
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? The inverse of the calculated stokes radius
(rstokes) is plotted against the respective
crystallographic radius (rion) in acetonitrile
and water respectively.
Biswas, Roy and Bagchi, Phys. Rev. Lett. 75, 1098
(1995)
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? The effect of the sequential addition of the
ultrafast component of the solvent orientational
motion on the limiting ionic in methanol at 298
K. The curves labeled 1, 2 and 3 are the
predictions of the present molecular theory.
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? The effect of isotopic substitution on limiting
ionic conductivity in electrolyte solution.
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Concentration dependence of ionic self-diffusion
J. F. Dufreche et al. PRL 88, 95902 (2002).
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? Velocity correlation function of Cl- for c
0.5M and c 1M KCl solutions. Comparison
between MCT (solid line) and Brownian dynamics
(dashed line).
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? Time dependent self-diffusion coefficient of
Cl- for c 0.5M and c 1M KCl solutions.
Comparison between MCT (solid line) and Brownian
dynamics (dashed line).
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Mode coupling theory of ionic conductivity
The total conductance of aqueous (a) KCl (b) NaCl
solution is plotted against the square root of
ion concentration. The solid curve represents the
prediction of the theory and the square
represents the experimental results.
Chandra and Bagchi J. Phys. Chem. B 104, 9067
(2000)
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Mode coupling theory of ionic viscosity
The ionic contribution to the viscosity is
plotted against the square root of ion
concentration (in molarity) for solutions of (a)
11 and (b) 22 electrolytes. The reduced
viscosity .
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Acknowledgement

• Prof. Srabani Roy, IIT-Kharagpur
• Prof. Nilashis Nandi, BITS-Pilanyi
• Prof. A. Chandra, IIT-Kanpur
• DST, CSIR

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? The prediction from dynamic mean spherical
approximation (DMSA) for solvation time
correlation function and the comparison between
the ionic and the dipolar solvation dynamics.
Nandi, Roy and Bagchi, J. Chem. Phy. 102, 1390
(1995)
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? The ratio of the microscopic polarization to
the macroscopic polarization is plotted as a
function of r for water at 298K.