Stockmayer fluids

The structure formation in an ER fluid was simulated [99]. The characteristic parameter is the ratio of the Brownian force to the dipolar force. Over a wide range of this ratio there is rapid chain formation followed by aggregation of chains into thick columns with a body-centered tetragonal structure observed. Above a threshold of the intensity of an external ahgn-ing field, condensation of the particles happens [100]. This effect has also been studied for MR fluids [101]. The rheological behavior of ER fluids [102] depends on the structure formed chainlike, shear-string, or liquid. Coexistence in dipolar fluids in a field [103], for a Stockmayer fluid in an applied field [104], and the structure of soft-sphere dipolar fluids were investigated [105], and ferroelectric phases were found [106]. An island of vapor-liquid coexistence was found for dipolar hard spherocylinders [107]. It exists between a phase where the particles form chains of dipoles in a nose-to-tail... 

PollockEL, Alder BJ, Patey GN (1981) Static dielectric properties of polarizable Stockmayer fluids. Physica A Stat Theor Phys 108(1) 14—26... 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

The GCEMC results presented in this section refer to Stockmayer fluids at a temperature T = 1.60 and dipole moment m = 2.0, which are typical for real polar molecular fluids [259]. The chemical potential is set equal to fi = —19.30, so that the bulk fluid has an average mean density of p 0.6. Keeping these parameters fixed, we investigated systems with substrate separations. s in the range 1.7 <. s < 10.0. 

Figure 6.3 GCEMC results for the disjoining pressure /(s ) [see Eq. (5.57)] for a typical polar (Stockmayer) fluid as a function of the wall separation (data have been obtained at T = 1.60, m — 2.0, and p = -19.30 corresponding to an average bulk density p 0.6). Also shown are corresponding results for an atomic LJ (12,6) fluid at the same temperature and bulk density.

Figure 6.5 Contributions to the normal stress of a Stockmayer fluid as a function of the wall separation (parameters as in Fig. 6.3). ( ) (O) ( ) r, (D)...

That this is indeed the case can be seen from Fig. 6.5 where we have plotted separately the three contributions to the normal stress of the Stockmayer fluid,... 

The hard core in Eq. (7.59) has been imposed for numerical convenience. As a consequence, it is mainly the van der Waals-like attractive (rather than the repulsive) part of the LJ (12,6) potential (oc r ) that contributes to the fluid fluid potential. The strength of the dipolar relative to the attractive LJ interactions is conveniently measured by the reduced (i.e., dimensionless) dipole moment m = fi/V a. Depending on this parameter, the Stockmayer fluid may serve as a simple model for polar molecular fluids [258, 259] (small m.) or for ferrofluids [227, 228] (large in). Here wc consider a system with dipole moment m = 2, whicli is a value typical for moderately polar molecular fluids [259] such as chloroform. For this value of m, GCEMC simulations have been presented in Section 6.4.1. 

In what follows we discuss the phase behavior of the Stockmayer fluid in the presence of disordered matrices of increasing complexity. All results are based on a variant of the HNC equation [see Eq. (7.49)], which yields very good results for bulk dipolar fluids [268, 322]. Moreover, subsequent studies of dipolar hard-sphere (DHS) fluids [defined by Eq. (7.59) with ulj = 0] in disordered matrices by Fernaud et al. [323, 324] have revealed a very good performance of the HNC closure compared with parallel computer simular tion results. The integral equations are solved numerically with an iteration procedure. To handle the multiple angle-dependence of the correlations... 

The influence of the IIS matrix on the phase behavior of an adsorbed Stockmayer fluid is checked most easily by investigation of the stability limits (spinodals) of the Isotropic high-temperature phase. Indeed, localization of true phase coexistence Hues is significantly more difficult because of the lack of a closed expression for the pressure within the replica HNC approach. 

These trends are similar to what is observed in simpler model fluids with purely spherically s3mimotric interactions [298, 313], which is to some extent expected because the gas liquid transition in Stockmayer fluids is mainly driven by the isotropic LJ (12,6) interactions underlying this model. We show in Ref. 307 that the main effects of HS matrices on the condensation can be reproduced when the dipolar model fluid is approximated by a fluid with angle-averaged dipolar interactions that are not only spherically symmetric but also short-ranged (they decay in proportion to for r — cx)). This notion is particularly important for future simulation studies on adsorbed dipolar fluids. 

At high fluid densities, bulk Stockmayer fluids exhibit an IF transition, which is signaled by a divergence of the dielectric constant eo [see Eq. (7.30)]. Results for cq are displayed in Fig. 7.3, which suggests that the IF transition... 

Figure 7.3 Dielectric constant ep versus (inverse) temperature for Stockmayer fluids at fixed fluid density p = 0.7. Curves aie labeled according to values of the matrix density.

Figure 7,4 Top Replica HNC predictions for the stability limits of the homogeneous isotropic phase of Stockmayer fluids adsorbed to disordered DHS matrices of density p,n = 0.1. Curves are labeled according to the reduced matrix dipole moment fJ m/ sTocr (the pure HS matrix corresponds to = 0). Bottom Dielectric constant of a dense adsorbed fluid as a function of the matrix dipole moment T = 0.5, f) = 0.7, Pm = 0.1). The inset shows the integrated blocking part of the dipole dipole correlation function.

The analytic solution of the SSOZ-MSA equation for polar hard dumbbells came before any serious consideration was given to calculating the dielectric constants of such systems by computer simulation. At the time, there was considerable controversy about the simulation methods used to calculate the dielectric constant, and for the model systems then in vogue (dipolar hard spheres and the Stockmayer fluid) there was also debate about the correct value of the dielectric constant. Today, this problem is becoming better understood in particular, the quality of the simulation work has improved greatly, and this has allowed meaningful conclusions to be drawn about the relative merits of simulation methods. 

QHNC and Ewald results for Stockmayer fluids have been compared by Pollock and Alder (Figs. 11 and 12), and Adams has made similar comparisons for dipolar hard spheres (Figs. 9 and 10). We know from the work... 

Fig. 17. The dielectric constant of Stockmayer fluids at p 0.8 and 7 = 1.35. The solid and dashed curves are the QHNC and LHNC approximations, respectively. The dots are the Ewald (A —256) results of Pollock and Alder.

The results of Pollock and Alder for Stockmayer fluids are compared with the QHNC theory in Figs. 18 and 19. It can be seen that at =0.741... 

Fig. 18. Values of g(k) for a Stockmayer fluid at p 0.8, r = 1.35, and —0.741. The curve is the QHNC theory, and the solid and open circles are the Ewald results of Pollock and Alder for A—256 and 500, respectively. The open square is the Ewald (A — 500) result for the Kirkwood g-factor.

Fig. 22. Comparison with the dielectric constant of real liquids LHNC results for dipolar hard spheres at p 0.8 (solid curve), Stockmayer fluids at p — 0.8, 7 —1.35 (dashed curve) ONS Onsager. The dots are the experimental results for the following Uquids (1) CH3I, (2) CHjCl. (3) NHj, (4) CHj— C—CH3, (5) CH3F, (6) CH3— C—H, (7) QHjNOj, (8)...

We shall be concerned with fluids in the liquid rather than gaseous state and with their classical rather than quantum-mechanical description. Our detailed illustrative examples will be further restricted to a few sample model potentials, although our ultimate goal includes the treatment of polyatomic molecules, real electrolytes, and fused salts as well as the sorts of models—the Lennard-Jones and Stockmayer fluids and the primitive-model ionic solution—that have already been treated accurately by the techniques herein. Recent theoretical developments that promise to transform our goal from a vision into a well-defined research program lie beyond the rather narrow sights... 

The simplest simulated system is a Stockmayer fluid structureless particles characterized by dipole-dipole and Lennard-Jones interactions, moving in a box (size L) with periodic botmdary conditions. The results described below were obtained using 400 such particles and in addition a solute atom A which can become an ion of charge q embedded in this solvent. The long range nature of the electrostatic interactions is handled within the effective dielectric environment seheme. In this approach the simulated system is taken to be surrounded by a continuum dielectric environment whose dielectric constant e is to be chosen self consistently with that eomputed from the simulation. Accordingly, the electrostatic potential between any two partieles is supplemented by the image interaction associated with a spherical dielectric boundary of radius (taken equal to L/2) placed so that one of these... 

Numerical simulations of solvation dynamics in polar molecular solvents have been carried out on many models of molecular systems during the last decade. The study described in sections 4.3.4-4.3.5 focused on a generic model for a simple polar solvent, a structureless Stockmayer fluid. It is found that solvation dynamics in this model solvent is qualitatively similar to that observed in more realistic models of more structured simple solvents, including solvents like water whose energetics is strongly influenced by the H-bond network. In particular, the bimodal nature of the dynamics and the existing of a prominent fast Gaussian relaxation component are common to all models studied. 

---