Handbook of Solvents - George Wypych - ChemTech - Ventech!

140 Abraham Nitzan
Figure 4.3.1. The electrostatic response potential
induced by the solvent at the position of the solute ion,
as a function of the solute charge. Dashed line - the
Stockmayer-CH 3Cl model described in Section 4. Full
and dotted lines, model polyether solvents described in
the text. [From Ref. 11b].
Figure 4.3.2. The linear response relaxation function
C(t) (dashed and dotted lines] and the non-equilibrium
solvation function S(t) (solid line) computed for the
Stockmayer-CH 3Cl model described in Section 4. In
the nonequilibrium simulation the ion charge is
switched on att=0.Thedotted and dashed lines represent
C(t) obtained from equilibrium simulations with
uncharged and charged ion, respectively. [From Ref.
11a].
A typical timestep for these simulation is 3fs. In the absence of thermalization this
gives energy conservation to within 10 -4 over ~80,000 time steps. After equilibrating the
system at 240K, the equilibrium correlation function C(t) is evaluated from equilibrium trajectories
with both a charged (q = e) and an uncharged (q = 0) impurity atom. The non-equilibrium
solvation function S(t) can also be computed from trajectories that follow a step
function change in the ion charge from q=0toq=e.These calculations are done for the
CH 3Cl solvent model characterized by the above parameters and for similar models with
different parameters. In particular, results are shown below for systems characterized by
different values of the parameter 15
2
p′ = I /2Mσ
[4.3.35]
which measures the relative importance of rotational and translational solvent motions.
4.3.5 NUMERICAL SIMULATIONS OF SOLVATION IN SIMPLE POLAR
SOLVENTS: RESULTS AND DISCUSSION
The dashed line of Figure 4.3.1 shows the equilibrium solvent induced electrostatic potential
Φ at the position of the ion, as a function of the ion charge q obtained for the
Stockmayer-CH3Cl model described in Section 4. Clearly the solvent response is linear with
qallthewayuptoq=e,with slight deviations from linearity starting atq>e.Theslope (~4)
of the linear dependence of the dashed line in Figure 1 (for q < e) is considerably smaller
from that obtained from Φ=q/aε s (taking a = σA/2 gives a slope of 7.4) that is used to get
Eq. [4.3.1]. A more advanced theory of solvation based on the mean spherical approximation
predicts (using σA and σD for the diameters of the ion and the solvent, respectively) a
slope of 4.6.
The linearity of the response depends on the nature of the solvent. As examples Figure
4.3.1 also shows results obtained for models of more complex solvents, H(CH2OCH2) nCH3