Dense Systems

This section presents a theoretical study of more concentrated deformable emulsions and microemulsions where higher order interactions become important. The purpose is to relate the microseopic droplet deformability to the structure of such systems and further to their macroscopic (thermodynamic) properties. The radial distribution function and static structure factor are calculated utilising an integral equation approach in an appropriate closure approximation. This method allows us to obtain the virial equation of state as well. A semi-empirical equation of state, based on modifying the Camahan-Starling expression, as well as comparison with Brownian dynamics simulations are also presented. 

---

In this brief review of dynamics in condensed phases, we have considered dense systems in various situations. First, we considered systems in equilibrium and gave an overview of how the space-time correlations, arising from the themial fluctuations of slowly varying physical variables like density, can be computed and experimentally probed. We also considered capillary waves in an inliomogeneous system with a planar interface for two cases an equilibrium system and a NESS system under a small temperature gradient. 

In a dense system, the acceptance rate of particle creation and deletion moves will decrease, and the number of attempts must be correspondingly increased eventually, there will come a point at which grand canonical simulations are not practicable, without some tricks to enliance the sampling. 

Due to the complexity of macromolecular materials computer simulations become increasingly important in polymer science or, better, in what is now called soft matter physics. There are several reviews available which deal with a great variety of problems and techniques [1-7]. It is the purpose of the present introduction to give a very brief overview of the different approaches, mainly for dense systems, and a few apphcations. To do so we will confine ourselves to techniques describing polymers on a molecular level. By molecular level we mean both the microscopic and the mesoscopic level of description. In the case of the microscopic description (all)... 

Intermolecular potential functions have been fitted to various experimental data, such as second virial coefficients, viscosities, and sublimation energy. The use of data from dense systems involves the additional assumption of the additivity of pair interactions. The viscosity seems to be more sensitive to the shape of the potential than the second virial coefficient hence data from that source are particularly valuable. These questions are discussed in full by Hirschfelder, Curtiss, and Bird17 whose recommended potentials based primarily on viscosity data are given in the tables of this section. 

Probe methods like particle insertion and test particle methods (29-32) are quite useful for computing chemical potentials of constituent particles in systems with low densities. Test particles are randomly inserted the average Boltzmann factor of the insertion energy yields the free energy. For dense systems these methods work poorly because of the poor statistics obtained. 

One tool for working toward this objective is molecular mechanics. In this approach, the bonds in a molecule are treated as classical objects, with continuous interaction potentials (sometimes called force fields) that can be developed empirically or calculated by quantum theory. This is a powerful method that allows the application of predictive theory to much larger systems if sufficiently accurate and robust force fields can be developed. Predicting the structures of proteins and polymers is an important objective, but at present this often requires prohibitively large calculations. Molecular mechanics with classical interaction potentials has been the principal tool in the development of molecular models of polymer dynamics. The ability to model isolated polymer molecules (in dilute solution) is well developed, but fundamental molecular mechanics models of dense systems of entangled polymers remains an important goal. 

In a hard-sphere system, the trajectories of particles are determined by momentum conserving binary collisions. The interactions between particles are assumed to be pair-wise additive and instantaneous. In the simulation, the collisions are processed one by one according to the order in which the events occur. For not too dense systems, the hard-sphere models are considerably faster than the soft-sphere models. Note that the occurrence of multiple collisions at the same instant cannot be taken into account. 

In Fig. 21, the excess compressibility is shown as a function of the solid fraction for different coefficients of normal restitution e. These results are compared with the Eq. (54), where the excess compressibility yES is taken from either the Ma-Ahmadi correlation (Ma and Ahmadi, 1986) or the Carnahan-Starling correlation. As can be seen, the excess compressibility agrees well with both correlations for a solid fraction ss up to 0.55. For extremely dense systems, i.e., es>0.55, the Ma-Ahmadi correlation presents a much better estimate of the excess compressibility, which is also the case for purely elastic particles (see Fig. 23). 

In dense systems such as encountered in solids suspension, particle-particle interaction may be important as well. Then, the closure of solid-phase stresses is an important issue for which kinetic theory models and solids phase viscosity may be instrumental (see, e.g., Curtis and Van Wachem, 2004). 

S.P. Marsh and M.E. Glicksman Kinetics of Phase Coarsening in Dense Systems. Acta Mater. 44, 3761 (1996). 

VIGNETTE V STRUCTURE AND STRUCTURAL TRANSITIONS IN DENSE SYSTEMS Single and Multiple Scattering—... 

Even the traditional methods discussed in this chapter can be used for concentrated dispersions through contrast matching. For example, silica particles coated with silane coupling agents in a refractive index-matched mixture of ethanol and toluene can be used in combination with visible probe particles to study the dynamics of particles in dense systems. In the case of microemulsions (Chapter 8), selective deuteration of a component (oil, water, or surfactant) can be used in neutron scattering experiments even to measure the curvature of the oil-water interface. 

In the dynamical approach, one attempts to solve directly the quantum-mechanical or classical equations of motion for a system, Such a direct approach is practicable, for example, for treating the binary collisions between molecules in a gas, by either classical or quantum-mechanical methods.3 However, in a dense system such as a liquid, only the classical equations are tractable,4 even with high-speed computers,... 

Content. After a brief overview of molecular collisions and interactions, dipole radiation, and instrumentation (Chapter 2), we consider examples of measured collision-induced spectra, from the simplest systems (rare gas mixtures at low density) to the more complex molecular systems. Chapter 3 reviews the measurements. It is divided into three parts translational, rototranslational and rotovibrational induced spectra. Each of these considers the binary and ternary spectra, and van der Waals molecules we also take a brief look at the spectra of dense systems (liquids and solids). Once the experimental evidence is collected and understood in terms of simple models, a more theoretical approach is chosen for the discussion of induced dipole moments (Chapter 4) and the spectra (Chapters 5 and 6). Chapters 3 through 6 are the backbone of the book. Related topics, such as redistribution of radiation, electronic collision-induced absorption and emission, etc., and applications are considered in Chapter 7. 

U. Buontempo, S. Cunsolo, P. Dore and P. Maselli, Molecular motions in liquids. In J. van Kranendonk, ed., Intermodular Spectroscopy and Dynamical Properties of Dense Systems - Proceedings of the Int. School of Physics Enrico Fermi , Course LXXV, p. 211, 1980. 

---