Figure 10. The compressibility factor for a charg and dipolar hard sphere mixture pr icted by perturbation thmiy is compared with the results of Monte Carlo simulation. Tl e elementaiy electronic charge is denoted e. |

Figure 2. Solvent-averaged potential for charged hard-sphere ions in a dipolar hard-sphere solvent. MC approximation by Patey and Valleau (16) and LHNC approximation by Levesque, Weis, and Patey (11). Also shown are the primitive model functions for solvent dielectric constants 9.6 and 6. |

Atom dynamics Group contribution and rigid bonds/angels Specific adsorption Dipolar hard sphere SPC, ST2, TIPS Polarizable H Bonds [Pg.627]

On the basis of Wertheim s solution of the MSA for dipolar hard spheres it is convenient to define a polarization parameter which is obtained directly from the relative static permittivity, that is, by solving the equation [Pg.163]

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49], [Pg.630]

Jog, P.K. and Chapman, W.G., Application of Wertheim s thermodynamic perturbation theory to dipolar hard sphere chains, Mol. Phys., 97(3), 307-319, 1999. [Pg.744]

Weis, J.J., and Levesque, D. Chain formation in low density dipolar hard spheres a Monte Carlo study. Phys. Rev. Left. 1993, 71, p. 2729-32. [Pg.177]

Agrofonov, Martinov, and Sarkisov have recently proposed another theory for dipolar hard spheres based on the HNC approximation. Their approach is similar in spirit to that followed in the usual thermodynamic perturbation theory (TPT) of dipolar fluids. It is assumed that h 2) can be expanded in the power series [Pg.244]

Again uq(R) is the hard sphere potential. This is necessary to keep the molecules from overlapping. The parameter is the dipole moment of molecule i. The factor D(i, j) is a term that depends on the orientation of the dipoles i and j and need not concern us here. We can call this potential the dipolar hard sphere potential. [Pg.555]

Another important application of perturbation theory is to molecules with anisotropic interactions. Examples are dipolar hard spheres, in which the anisotropy is due to the polarity of tlie molecule, and liquid crystals in which the anisotropy is due also to the shape of the molecules. The use of an anisotropic reference system is more natural in accounting for molecular shape, but presents difficulties. Hence, we will consider only [Pg.509]

The LHNC and QHNC approximations have not been solved analytically, but numerical solutions can be obtained by iteration. This is also true of the MSA except for the previously discussed dipolar hard-sphere system solved by Wertheim. The details of the numerical solution are described in Refs. 30, 38, 58, and 59. Essentially, (3.11) and the appropriate closure relations are written in terms of c" " and -q "" and iterated until a solution is obtained. This means that all equations defining a particular approximation are simultaneously satisfied. The present problem is very similar to that [Pg.241]

To move beyond the primitive model, we must include a molecular model of the solvent. A simple model of the solvent is the dipolar hard sphere model, Eq. (16). A mixture of dipolar and charged hard spheres has been called the civilized model of an electrolyte. This is, perhaps, an overstatement as dipolar hard spheres are only partially satisfactory as a model of most solvents, especially water still it is an improvement. [Pg.562]

The solution detennines c(r) inside the hard core from which g(r) outside this core is obtained via the Omstein-Zemike relation. For hard spheres, the approximation is identical to tire PY approximation. Analytic solutions have been obtained for hard spheres, charged hard spheres, dipolar hard spheres and for particles interacting witli the Yukawa potential. The MS approximation for point charges (charged hard spheres in the limit of zero size) yields the Debye-Fluckel limiting law distribution fiinction. [Pg.480]

Figure 2. Minimum eigenvalue of the stability matrix (see Eq. (24) in the text) and isothermal compressibility for equilibrated mixtures of charged and dipolar hard spheres. |

Two further approximations that build on the MSA solution are derived in Section II. These are the so-called LIN and L3 approximations, which have been investigated by Stell and Weis for dipolar hard spheres. Both theories substantially improve upon the MSA. [Pg.237]

The high population of ion pairs near criticality motivated Shelley and Patey [250] to compare the RPM coexistence curve with that of a dipolar fluid. It is now known that a critical point does not develop in a system of dipolar hard spheres [251]. However, ion pairs resemble dumbbell molecules comprising two hard spheres at contact with opposite charges at their centers. Shelley and Patey found that the coexistence curves of these charged dumbbells are indeed very similar in shape and location to the RPM coexistence curve, but very different from the coexistence curve of dipolar dumbbells with a point dipole at the tangency of the hard-sphere contact. [Pg.38]

The extent of the agreement of the theoretical calculations with the experiments is somewhat unexpected since MSA is an approximate theory and the underlying model is rough. In particular, water is not a system of dipolar hard spheres.281 However, the good agreement is an indication of the utility of recent advances in the application of statistical mechanics to the study of the electric dipole layer at metal electrodes. [Pg.55]

Finally, C tld /,.[ = cdd = c Jm is the Fourier transform of the replica-replica direct correlation function (blocking function), and the connected function is defined as usual by cc = cdd — cdd, and similarly for hc. Let us recall that the replicated particles are the dipolar hard spheres, i.e. the annealed fluid in the partly quenched mixture. [Pg.319]

Integral equation methods provide another approach, but their use is limited to potential models that are usually too simple for engineering use and are moreover numerically difficult to solve. They are useful in providing equations of state for certain simple reference fluids (e.g., hard spheres, dipolar hard spheres, charged hard spheres) that can then be used in the perturbation theories or density functional theories. [Pg.132]

The same approach can be applied to investigate the explosivity conditions of the H20-NaCl system. We have selected the Anderko-Pitzer (AP) equation of state,which is based on realistic physical hypotheses. It describes H20-NaCl by means of statistical thermodynamic models developed for dipolar hard spheres. This assumption is reasonable at high temperatures, where NaCl is known to form dipolar ion pairs. However, for this reason, this equation of state is only applicable above 573 K, 300°C. [Pg.301]

Mixtures of equisized charged spheres were also treated by the MSA. Such a system is then uniquely characterized by the ratio of the critical temperatures of the pure components. Harvey [235] found that a continuous critical curve from the dipolar solvent to the molten salt is maintained until the critical temperature of the ionic component exceeds that of the dipolar component by a factor of about 3.6. This ratio is much higher than theoretically predicted for nonionic model fluids. We recall that for NaCl the critical line is still continuous at a critical temperature ratio of about 5. Thus, the MSA of the charged-hard-sphere-dipolar-hard-sphere system captures, at least in part, some unusual features of real salt-water systems with regard to their critical curves. [Pg.44]

More refined continuum models—for example, the well-known Fumi-Tosi potential with a soft core and a term for attractive van der Waals interactions [172]—have received little attention in phase equilibrium calculations [51]. Refined potentials are, however, vital when specific ion-ion or ion-solvent interactions in electrolyte solutions affect the phase stability. One can retain the continuum picture in these cases by using modified solvent-averaged potentials—for example, the so-called Friedman-Gumey potentials [81, 168, 173]. Specific interactions are then represented by additional terms in (pap(r) that modify the ion distribution in the desired way. Finally, there are models that account for the discrete molecular nature of the solvent—for example, by modeling the solvent as dipolar hard spheres [174, 175]. [Pg.28]

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