Handbook of Solvents - George Wypych - ChemTech - Ventech!

2.2 Molecular design of solvents 41
For any kinds of mixtures, in addition to LJ parameters for each component, combining
rule (or mixing rule) for unlike interaction should be prepared. Even for simple liquid
mixtures, conventional Lorentz-Berthelot rule is not good answer.
Once potential parameters have been determined, we can start calculation downward
following arrow in the figure. The first key quantity is radial distribution function g(r)
which can be calculated by the use of theoretical relation such as Percus-Yevick (PY) or
Hypernetted chain (HNC) integral equation. However, these equations are an approximations.
Exact values can be obtained by molecular simulation. If g(r) is obtained accurately as
functions of temperature and pressure, then all the equilibrium properties of fluids and fluid
mixtures can be calculated. Moreover, information on fluid structure is contained in g(r) itself.
On the other hand, we have, for non-equilibrium dynamic property, the time correlation
function TCF, which is dynamic counterpart to g(r). One can define various TCF’s for
each purpose. However, at the present stage, no extensive theoretical relation has been derived
between TCF and φ(r). Therefore, direct determination of self-diffusion coefficient,
viscosity coefficient by the molecular simulation gives significant contribution in dynamics
studies.
Concluding Remarks
Of presently available methods for the prediction of solvent physical properties, the solubility
parameter theory by Hildebrand 10 may still supply one of the most accurate and comprehensive
results. However, the solubility parameter used there has no purely molecular
character. Many other methods are more or less of empirical character.
We expect that the 21th century could see more computational results on solvent properties.
REFERENCES
1 N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys., 21, 1087
(1953).
2 B. J. Alder and T. E. Wainwright, J. Chem. Phys., 27, 1208 (1957).
3 (a) M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987.
(b) R. J. Sadus, Molecular Simulation of Fluids, Elsevier, Amsterdam, 1999.
4 R. C. Reid, J. M. Prausnitz and J. E. Poling, The Properties of Gases and Liquids; Their Estimation and
Prediction, 4th Ed., McGraw-Hill, New York, 1987.
5 C. R. Wilke and P. Chang, AIChE J., 1, 264 (1955).
6 K. Nakanishi, Ind. Eng. Chem. Fundam., 17, 253 (1978).
7 O. Matsuoka, E. Clementi and M. Yoshimine, J. Chem. Phys., 60, 1351 (1976).
8 S. Okazaki, K. Nakanishi and H. Touhara, J. Chem. Phys., 78, 454 (1983).
9 W. L. Jorgensen, J. Am. Chem. Soc., 103, 345 (1981).
10 J. H. Hildebrand and R. L. Scott, Solubility of Non-Electrolytes, 3rd Ed., Reinhold, New York, 1950.
APPENDIX
PREDICTIVE EQUATION FOR THE DIFFUSION COEFFICIENT IN DILUTE
SOLUTION
Experimental evidence is given in Figure 2.2.2 for the prediction based on equation [2.2.1].
The diffusion coefficient D0 of solute A in solvent B at an infinite dilution can be calculated
using the following equation:
D
0
⎛
−8
−8
997 10 240 10 ASV
= ⎜ . × . ×
+
⎜
13
[ IV]
I S V
⎝ A A
A A A
B B B
⎞
⎟ T
⎟
⎠
/ η B
[2.2.3]