Multiscale Approaches and Perspectives to Modeling Aqueous Electrolytes and Polyelectrolytes - Multiscale Molecular Methods in Applied Chemistry - page 266

thermodynamic changes and formation of CIPs, SIPs, and 2SIPs can be examined
in a relatively straightforward manner. To see this, we express these derivatives in
terms of excess coordination numbers by means of the Kirkwood-Buff theory of
solution [ 76 , 77 ]:

@ log a s

@ log r s

1

p;T ¼

(2)

1 þ D N SS D N WS

where a s ¼ g s r s the salt activity, g s denotes the molar scale salt activity coefficient,

and D N ss and D N ws denote the salt-salt and water-salt excess coordination numbers

defined as

ð 1

r 2 d r

D N ij ¼ r j 4 p g ij ð r Þ 1 : (3)

0

N ws within a Hofmeister series result from short-range
contributions to this integral. If we assume that contributions to the integral in
equation (3) vanish beyond distance R,

Differences in D N ss D

N ij can be interpreted as the change in the
average number of particles of type j in a spherical region of radius R caused by
placing a particle of type i at the center of the region. Hence,

D

N ij is a measure of
the affinity between particle types i and j . Molecular simulations of alkali chlorides
and alkali acetates showed that (at 1 M salt) ion specificity, as expressed by the
denominator on the right hand side of equation (2), arises from the interactions
between oppositely charged ions. We therefore replace the denominator 1

D

þ D N ss

D N ws with 1 þ D N :

@ log a s 1

p;T

:

(4)

@ log r s 1 þ D N

This equation relates thermodynamic changes to a measure of affinity, deter-
mined by the local electrolyte structure. We can furthermore write

D N ¼ D N CIP þ D N SIP þ D N 2SIP þ C (5)

with N CIP denoting the excess number of CIPs, obtained by integration over the

first peak of g ( r ;

D

N SIP denoting the excess number of SIPs, obtained by
integration over the second peak, etc. Equations (4) and (5) provide a route to link
thermodynamics to structure by means of integrals over peaks of the pair correla-
tion function corresponding to CIPs, SIPs, and 2SIPs. All ion-specificity for the
systems in Fig. 5 was observed in the three excess coordination numbers

r s ), D

D N CIP , D N SIP ,

and N 2SIP ,whiletheconstant C in equation (5), corresponding to the contribution

from distances larger than approximately 0.8 nm, was the same for all cations with-
in the alkali ion series investigated [ 70 ]. It was found [ 70 ] that the series shown in
Fig. 5a (alkali bromides) can be explained with the observed changes in

D

D N CIP ,in