Colloids computer simulations

The entropically driven disorder-order transition in hard-sphere fluids was originally discovered in computer simulations [58, 59]. The development of colloidal suspensions behaving as hard spheres (i.e., having negligible Hamaker constants, see Section VI-3) provided the means to experimentally verify the transition. Experimental data on the nucleation of hard-sphere colloidal crystals [60] allows one to extract the hard-sphere solid-liquid interfacial tension, 7 = 0.55 0.02k T/o, where a is the hard-sphere diameter [61]. This value agrees well with that found from density functional theory, 7 = 0.6 0.02k r/a 2 [21] (Section IX-2A). 

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

Our main focus in this chapter has been on the applications of the replica Ornstein-Zernike equations designed by Given and Stell [17-19] for quenched-annealed systems. This theory has been shown to yield interesting results for adsorption of a hard sphere fluid mimicking colloidal suspension, for a system of multiple permeable membranes and for a hard sphere fluid in a matrix of chain molecules. Much room remains to explore even simple quenched-annealed models either in the framework of theoretical approaches or by computer simulation. 

We have reviewed the basics of computer simulations with colloidal particles and with the physics of colloids. We could only touch on the most basic concepts, that do not lead to highly optimized, rapid code but, nevertheless, lead to working programs. 

So far we have considered computer simulations as a tool to investigate the physics of colloids. In this section we mention work that, besides its physical content, is important because of this tool has been sharpened by the invention of new techniques. 

The world of colloidal particles is large and fasdnating. Basic simulation techniques rapidly lead to challenging questions and new things to be discovered. Computer simulations are close enough to experiments to allow intellectual inspiration as well as a quantitative comparison of the results. We have reviewed the basic simulation techniques and their principal implementation but could only briefly mention advanced techniques and results. A survey of the recent literature shows the variety of physical effects present in colloidal systems and accessible to computer simulations. 

The reviews collected in this book convey some of the themes recurrent in nano-colloid science self-assembly, constraction of supramolecular architecture, nanoconfmement and compartmentalization, measurement and control of interfacial forces, novel synthetic materials, and computer simulation. They also reveal the interaction of a spectrum of disciplines in which physics, chemistry, biology, and materials science intersect. Not only is the vast range of industrial and technological applications depicted, but it is also shown how this new way of thinking has generated exciting developments in fundamental science. Some of the chapters also skirt the frontiers, where there are still unanswered questions. 

M. Hecht, J. Harting, M. Bier, J. Reinshagen, and H. J. Herrmann, Shear viscosity of claylike colloids in computer simulations and experiments, Phys. Rev. E 74, 021403 (2006). 

Y. Sakazaki, S. Masuda, J. Onishi, Y. Chen, and H. Ohashi, The modeling of colloidal fluids by the real-coded lattice gas, Math. Comput. Simulation 72, 184 (2006). 

Meijer, E. J. Azhar, F. El, Novel procedure to determine coexistence lines by computer simulation, application to hard-core Yukawa model for charge-stabilized colloids, J. Chem. Phys. 1997,106, 4678-4683... 

An analogy may be drawn between the phase behavior of weakly attractive monodisperse dispersions and that of conventional molecular systems provided coalescence and Ostwald ripening do not occur. The similarity arises from the common form of the pair potential, whose dominant feature in both cases is the presence of a shallow minimum. The equilibrium statistical mechanics of such systems have been extensively explored. As previously explained, the primary difficulty in predicting equilibrium phase behavior lies in the many-body interactions intrinsic to any condensed phase. Fortunately, the synthesis of several methods (integral equation approaches, perturbation theories, virial expansions, and computer simulations) now provides accurate predictions of thermodynamic properties and phase behavior of dense molecular fluids or colloidal fluids [1]. 

Chronopotentiometry, galvanostatic transients, 1411 as analytical technique, 1411 activation overpotential, 1411 Clavilier, and single crystals, 1095 Cluster formation energy of, 1304 and Frumkin isotherm, 1197 Cobalt-nickel plating, 1375 Cold combustion, definition, 1041 Cole-Cole plot, impedance, 1129, 1135 Colloidal particles, 880, 882 and differential capacity, 880 Complex impedance, 1135 Computer simulation, 1160 of adsorption processes, 965 and overall reaction, 1259 and rate determining step, 1260... 

Theories or computer simulations used to calculate the potential of mean force W(r) are typically based on numerous simplifying assumptions and approximations (de Kruif, 1999 Bratko et al., 2002 Prausnitz, 2003 de Kruif and Tuinier, 2005 Home et al., 2007 Jonsson et al., 2007). Therefore they can provide only a qualitative or, at best, semi-quantitative description of the potential of mean force. Such calculations are nevertheless useful because they can serve as a guide for trends in the factors determining the interactions of both biopolymers and colloidal particles. Thus, an increase in the absolute value of the calculated negative depth of W(r) may be attributed to a predominant type of molecular feature favouring aggregation or self-association. To assist with such a theoretical analysis, expressions for some of the mean force potentials will be presented here in the discussion of specific kinds of interactions occurring between pairs of colloidal particles covered by biopolymers in food colloids. 

FIG. 13.4 Stereo pairs of colloidal dispersions generated using computer simulations, (a) Polystyrene latex particles at a volume fraction of 0.13 with a surface potential of 50 mV. The 1 1 electrolyte concentration is 10 7 mol/cm3. The structure shown is near crystallization. (The solid-black and solid-gray particles are in the back and in the front, respectively, in the three-dimensional view.) (b) A small increase in the surface potential changes the structure to face-centered cubic crystals. (Redrawn with permission from Hunter 1989.)... 

Computer simulations of V4+ signals were also very useful for the determination of the EPR parameters, and they confirmed the interpretation of the experimental spectra as it had been done in [145-149] for vanadium doped Ti02 colloid powders and bulk samples. The EPR parameters of V4+ ions in Ti02 lattices (rutile, anatase and brookite) are summarized in Table 8.6 for nano-, polycrystalline and single crystal samples (NC, PC, SC). 

Barker, G. C., and Grimson, M. J. (1991). Computer simulations of the flow of deformable particles. In Food Polymers, Cels and Colloids, Dickinson, E. (Ed.), pp. 262-271. Royal Chem. Soc., London. 

The radial distribution function plays an important role in the study of liquid systems. In the first place, g(r) is a physical quantity that can be determined experimentally by a number of techniques, for instance X-ray and neutron scattering (for atomic and molecular fluids), light scattering and imaging techniques (in the case of colloidal liquids and other complex fluids). Second, g(r) can also be determined from theoretical approximations and from computer simulations if the pair interparticle potential is known. Third, from the knowledge of g(r) and of the interparticle interactions, the thermodynamic properties of the system can be obtained. These three aspects are discussed in more detail in the following sections. In addition, let us mention that the static structure is also important in determining physical quantities such as the dynamic an other transport properties. Some theoretical approaches for those quantities use as an input precisely this structural information of the system [15-17,30,31]. 

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

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