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J. Phys. Chem. 1992,96,6762-6766
(20) hndolt-B6rnstein. Numerical Data and Functional Relationships in Science and Technology;New Series; Madelung, O., Ed.; Springer: Berlin, 1987; Vol. 22a. (21) Rcaetti, R.; Nakahara, S.;Brus, L. E. J. Chem. Phys. 1983,79,1086. (22) Venkateswaran, U.; Chandrasekhar,M.; Chandrasekhar,H. R. Phys. Rev. B 1984, 30, 3316. (23) Variano, B. F.; Schlotter, N. E.; Hwang, D. M.;Sandroff, C. J. J . Chem. Phys. 1988,88,2848. (24) Onodera, A. Rev. Phys. Chem. Jpn. 1969, 39, 65.
( 2 5 ) Murnaghan, F. D. Proc. Natl. Acad. Sci. V.S.A. 1944, 30, 244.
(26) Solliard, C.; Flueli, M. SurJ Sci. 1985, 156, 487. (27) The bulk modulus of zinc blende CIS is calculated from the linear elastic constants of Fuller and Weston (J.Appl. Phys. 1974,45, 3772) and the equation, BOE+: ( c I I+ 212)/3. The derivativeof Bo with respect to prtgsure is given by BO' = - ( c I l 1+ 6~112+ 2~,~,)/(9B,,). (28) Parameters for bulk NaCl were obtained from: Suzuki, T.; Yagi, T.; Akimoto, S.;Kawamura, T.; Toyoda, S.;Endo, S.J. Appl. Phys. 1983, 54, 748.
Importance of Orientational Rearrangement during Vitrification of Hydrocarbons: Dependence on Molecular Shapet Aparna Chakrabarti, S. Yashonath, and C. N. R. Rao* Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India (Received: January 27, 1992; In Final Form: April 20, 1992)
On the basii of Monte Carlo calculations of 2,2-dimethylpropane (neopentane), n-pentane, and 2,2ðylbutane
(neohexane) at several temperatures, thermodynamic properties and radial distribution functions as well as dimerization and bonding energy distribution functions are reported for both liquid and glassy states. Changes in the radial distribution functions on cooling depend on whether the groups are accessible (peripheral) or inaccessible. Peaks in the radial distribution functions corresponding to peripheral groups do not shift to lower distances on cooling and at times display a large increase in the intensity of the first peak. The peaks due to inaccessiblegroups, on the other hand, shift to lower distances on cooling. The magnitude of the reorientational contribution in determining the resulting structure of the glass is estimated for the different hydrocarbon molecules investigated. The reorientational contribution is highest for neopentane (26%) followed by isopentane (24%), neohexane (22%), and n-pentane (0%). It appears that molecular geometry has an important role in determining the magnitude of the reorientational contribution to the structure of the glass.
Introdwtion The difficulty in obtaining information on the structural changes accompanying the glass transition and our inadequate understanding of the nature of the glass transition are closely related.' One of the most useful techniques in the study of glasses undoubtedly is computer simulation which yields microscopic information pertaining to the structure as well as relaxation processes. During the past few years, molecular dynamics calculations by Andersen and -workers2 on monatomic glasses have shown that they possess properties quite similar to those of laboratory glasses. Thermal effects such as the dependence of the glass transition temperature on the cooling rate have been found in computer-simulated glasses. Further investigations have indicated that the structural motif that predominantly occurs in glasses compared to the liquid is the ico~ahedron.~ Unlike monatomic glasses where only translational degrees of freedom exist, in polyatomic or molecular systems, structural relaxation during the rapid oooling of the liquid involves both positional and orientational degrees of freedom. It has been suggested that the latter play an important role in the determination of the properties of the glass.4 Our earlier studies on 2-methylbutane (ipentane) indicate the orientational degrees of freedom to be of crucial importance in determining the properties of the glass5 We have now carried out detailed Monte Carlo simulations of the liquid and glassy phases of 2,2-dimethylpropane (neopentane), n-pentane, and 2,2-dimethylbutane (neohexane) with the p u v e of calculating the properties of glasses and more importantly to obtain insight into the structural changes occurring during vitrification. The results of these simulation studies have shed light on the role of reorientation in the determination of the structure of the glass and its dependence on molecular shape. Computational Details Standard geometrical parameters used for hydrocarbons are C(s$)+Lesser Blum,* and Nicole Condamines Laboratoire dElectrochimie, Tour 74, UniversitC Pierre et Marie Curie, 8 Rue Cuvier, 75005 Paris, France, Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931 -3933, and DPpartement des ProcZdPs de Retraitement. CENFAR 92, Fontenay aux Roses, France (Received: January 28, 1992; In Final Form: March 31, 1992) A free energy minimization procedure is presented for the evaluation of the association equilibrium of nonideal electrolytes in the mean spherical approximation (MSA). This model is applied to electrostatic Bjerrum association of 2-2 electrolytes
in water, to chemical association of 1-1 electrolytes in low dielectric constant media, and to weak electrolytes in water. The present model is also applicable to mixtures of associating electrolytes. 1. Introduction
The concept of ionic association is widely used in solution chemistry. There are two diffmnt mechanisms of ionic association in electrolytes. 1. The "electrostatic" Bjerrum association' in which the clustering process is due to strong Coulomb interactions. For example the 2-2 electrolytes in water or the 1-1 electrolytes in low dielectric constant solvents will cluster without real chemical bond formation. 2. The "chemical" association mechanism in which there is a true chemical bond formed, which is characterkd by a measurable molecular vibration frequency. This is the case of weak acids in water, as well as that of the formation of complexes. In the last decades the progress of statistical mechanics has opened the possibility of treating quantitativelythe effect of ionic interactions at the McMillan-Mayer level for ionic clusters.24 To whom correspondence should be addressed. Universit€ Pierre et Marie Curie. *University of Puerto Rim. SCENFAR 92.
0022-3654/92/2096-6766S03.00/0
It is possible to include the nonideal contribution in the statistical formulation of the thermodynamic properties of ionic ~ o l u t i o n s . ~ ~ This can be done by combining the concept of ionic association to the evaluation of excess thermodynamic properties. It should be noticed that a fundamental distinction exists between them: the completely dissociated reference state generally used in statistical mechanics, where the excess thermodynamic properties are evaluated taking the ideal gas of ions as the reference system (2 ions); the association model in which one postulates the existence of one given associated state (at least), with a defined chemical potential. The first one is a two-particle model (2PM) (the "free" ions) whereas the second one is a threeparticle model 3PM (two "free" ions plus the "pair"). The 2PM model is the reference state for the expression of most experimental data on electrolytes; osmotic and activity coefficients are evaluated taking as the reference state the fully dissociated electrolyte. Moreover the physical models such as the hyppernetted chains equation (HNC) for the treatment of ionic interactions use as reference state the fully dissociated gas of ionic solutes and allows for the evaluation of the nonideal properties 0 1992 American Chemical Society
