Ionic Conductivity And Ultrafast Solvation Dynamics by 23o28Q1W

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									  Ionic Conductivity And
Ultrafast Solvation Dynamics




          Biman Bagchi
    Indian Institute of Science
        Bangalore, INDIA
 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)
               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.
   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 Walden’s 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.
Ultrafast solvation and ionic mobility

                       Two kinds of friction :
                       Stokes friction (0) and
                       Dielectric friction (DF)


                        0       4 R


                   How to get DF ?

                What determines DF ?
 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.
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)
Continuum Model of Solvation Dynamics
                        [BFO (1984), vdZH (1985)]




                    ( )  M (0).M (t )
                          N
                    M   i (t )
                          i 1
     ()
                    Energy    (t ).R(t )
  Polarization relaxation is single exponential.
  Debye representation
                            (0)   
             ( )    
                           1  i D
             R(t )       e  t / D
                    2   1 
                 
                   d
                               D
                    2 0  1 
                   L




For ion                            
                  ion
                           L    D
                                  0 
                   L


For water, L 500 fs
 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.
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)
                    Theoretical Approach




         E sol (t )  E sol ( )
S (t ) 
         E sol (0)  E sol ( )
                       Nandi, Roy and Bagchi, J. Chem. Phy. 102, 1390 (1995);
                       Song, Marcus & Chandler, JCP (2000).
 Mode coupling theory expression for
  solvation time correlation function
                                   

     S EE ( z )  AN  dte    zt
                                     dkk c
                                               2 2
                                                 id   (k )
                      0             0

                    Sion (k , t ) S    10
                                        solv   (k , t )
 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.
 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.
 Microscopic origin of Ultrafast solvation

                      k0
                                         k  2/




 In the bulk, the k  0 component dominates (about 75 %).
 However, this is only part of the story.
 Dynamics response comes into picture.
Effect of translational modes on ionic
conductivity and solvation dynamics.
     MCT Expression for Dielectric Friction
     including the self-motion

     ( zF ) 2          » N-E equation
0           D
       RT
     K BT               » S-E equation
D
       
   0   DF       0  4 rion

      The position dependent viscosity is given by

                                      D ( 0    )q 2 
                         (r )  0 1                   
                                        160 0 r 
                                                  2 4
                                     
                 k BT  0
                   6 2 
    DF ( z )             dte  zt  dkk 4 cid (k )
                                              2

                          0          0

                   Sion (k , t ) S solv (k , t )
                                    10




                                       Dk 2 t
Where,            Sion (k , t )  e
                        k BT
                  D
                      0   DF
                  S solv (k , t )  S   (10)
                                        solv   (k , t )
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)
 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.
 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)
 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.
 The effect of isotopic substitution on limiting
ionic conductivity in electrolyte solution.
Concentration dependence of ionic self-diffusion




                  J. –F. Dufreche et al. PRL 88, 95902 (2002).
 Velocity correlation function of Cl- for c = 0.5M and c = 1M
KCl solutions. Comparison between MCT (solid line) and Brownian
dynamics (dashed line).
  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).
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)
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)
                1:1 and (b) 2:2 electrolytes. The
                reduced viscosity ex  ion /  0
                                      *


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



• DST, CSIR
 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)
 The ratio of the microscopic polarization to the macroscopic
polarization is plotted as a function of r for water at 298K.

								
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