Raj Rajagopalan

Polydispersity in colloids: implications to static structure and scattering

Abstract Theoretical and experimental analyses of the structure of colloidal dispersions have traditionally relied on model systems of monodisperse particles. However, numerous theoretical studies aimed at incorporating the effects of size-polydispersity, charge-polydispersity, and polydispersity in attractive interactions on the equilibrium structure of dispersions of spherical particles have appeared in recent years. These studies can be divided into three different groups according to the nature of the interaction forces considered, namely, dispersions of neutral hard spheres, sticky hard spheres, and charged particles. Here, we review these studies and examine the major results and conclusions. Previously unreported new results obtained by us for dispersions of charged spheres in high-ionic-strength media are also included. The theoretical techniques for computing partial structure factors and average structure factors for the above-mentioned interaction potentials are summarized, and analytical expressions are presented wherever appropriate. Representative examples of applications of each class of interaction potentials identified above are presented in order to illustrate the use of the theoretical tools in interpreting the scattering data. The common features of the average structure factors for the above model potentials are emphasized, and issues such as the importance of correctly modeling intraparticle scattering properties of the particles and transformation of observed intensities to average structure factors are illustrated. An examination of the so-called decoupling approximation (which seeks to separate the intraparticle scattering effects from interparticle interaction effects) is also presented wherever the required data are available.

Influence of the range of attractive forces on vapor/liquid phase coexistence

The influence of the range of interparticle attractions on vapor/liquid coexistence in spherically symmetric systems has been investigated by mapping the pair potential on to the adhesive‐hard‐sphere model. Comparisons of our analytical predictions with recent Gibbs‐Ensemble Monte Carlo simulations for the Yukawa potential show a very good agreement. The temperature range over which vapor/liquid coexistence is thermodynamically preferred shrinks as the range of attraction decreases, and for short ranges the coexistence curve flattens, consistent with the results of the simulations. Using the Sutherland potential model we also show that for very small ranges of attraction the liquid state is unstable down to very small temperatures and that a fluid/solid transition is preferred.

Monte Carlo simulations for sintering of particle aggregates

A new Monte Carlo simulation procedure is developed for the initial stages of sintering of randomly packed particles. This simulation takes into account the possibility of crack initiation due to the stresses generated by the sintering particles and can accommodate both localized stresses and stress propagation. This procedure is used to investigate the sintering of two-dimensional aggregates of copper particles, and the results are compared with the results of model experiments available in the literature. The two-dimensional simulations presented here lead to shrinkage in area, decreases in perimeter, and particle rearrangements that are physically consistent with the expected behavior and experimental results. The proposed procedure can be extended to accommodate more complex features of sintering and to account for the material-dependent effects of stresses. It can also be used as a probe of sintering of bulk materials with random microstructure and to identify and design model experiments.

Dynamic properties of homopolymer layers adsorbed on a solid surface

Dynamic properties of homopolymer layers adsorbed on a solid surface from a dilute solution are examined through dynamic Monte Carlo simulations over a range of surface/segment interaction energies and at different bulk concentrations. In particular, we studied the relationship between the detachment rate of adsorbed polymers and the first Rouse relaxation rate of adsorbed chains. The power‐law dependence of the detachment rate on the chain length which we have reported earlier [Phys. Rev. Lett. 74, 2503 (1995)] is seen to correspond to the power‐law dependence of the first Rouse relaxation rate of the adsorbed chains, which is also the same as the power‐law dependence of the first Rouse relaxation rate of the free chains (nonadsorbed chains). However, the detachment rate is usually much slower than the first Rouse relaxation rate of adsorbed chains. Increasing the surface/segment interaction energy (e in units of kBT) increases the difference between the two. More interestingly, when e∼1.0 or higher, the...

Reverse Monte Carlo procedure for cluster analysis in colloidal systems

Abstract We examine the applicability of reverse Monte Carlo (RMC) simulations for studying cluster size and bond angle distributions in dense colloidal dispersions. Forward Monte Carlo simulations are used to generate radial distribution functions for a dispersion interacting through an attractive potential. These are then used for reconstructing the microstructural details in the dispersion using RMC simulations. We find that the RMC method accurately reproduces structures that are statistically identical to the test system over a range of length scales. Both cluster size distributions and bond angle distributions are reproduced within statistical accuracy. The results demonstrate that X-ray, neutron and light scattering data on the structure of dispersions (under static or dynamic conditions) can be used for extracting microstructural information that cannot be obtained by direct means.

Effective interaction potentials in colloidal dispersions from structure data

Abstract Methods for obtaining effective pair potentials in strongly interacting colloidal dispersions and in simple fluids at liquid densities are investigated. It is shown that an inversion method based on statistical mechanical perturbation theories leads to better predictions of the pair potentials from static structure factor data than is possible through integral equation theories. The location and the shape of the hard core, the location and the magnitude of the minimum in the potential, and the attractive tail have all been obtained with very good accuracy using the perturbation theory. Inclusion of thermodynamic consistency requirements and sensitivity analyses may lead to further improvements in the procedure and the results. The predictions of the above essential features of the interaction potential can then be used for predicting equilibrium and transport properties of dense dispersions from first principles.

DEPOSITION AND RESTRUCTURING OF ADHESIVE PARTICLES IN UNIDIRECTIONAL FIELDS

The deposition of particles under the influence of gravity and adhesive interactions with the other deposited particles is examined using computer simulation. A parameter, s, that represents the probability of adhesion or sticking is used for studying the effects of variations in sticking on the resulting microstructure. A range of packing structures is generated between two limiting cases representing complete restructuring (s = 0) and no restructuring (s = 1). The bulk properties of the resulting structures, such as packing density, particle number density, and coordination number, are obtained. Structural correlations are examined through contact networks, radial and angular distribution functions, and diffraction patterns. The results show that local sticking rules have a significant influence on the long-range structure. Rhombic domains and significant long-range correlations are observed for the case of zero sticking probability. The range of correlations drops very sharply with increases in stickin...

Inversion of Structural Data for Effective Potentials in Dense Liquids and Colloids

Abstract We address the inverse problem of obtaining microscopic interaction potentials from macroscopic structure, here in the context of liquid-like systems. The proposed method uses a perturbation-theoretic formalism and requires no a priori knowledge of the form of the potential. Very stable and rapidly converging potentials are obtained for widely different classes of fluids, and the results demonstrate the feasibility of inversion. The methodology can be extended to related problems in condensed matter physics and will aid in the analyses of structural data.

Thick films of YBaCuO from precalcined powders

Preparation and some of the chemical and microstructural aspects of thick films of the YBa2Cu3O7−x superconductors (herein designated as YBaCuO) using precalcined YBaCuO powders and a colloidal method are described. Films on alumina substrates were made from calcined YBaCuO powders dispersed in hexane using a commerical dispersant which acts as a steric stabilizer and binder. The additive decomposes without residues at relatively low temperatures, and structurally stable and uniform films are obtained for proper dosage of the dispersant. Scanning electron microscopy has been used to examine the microstructure, quality and sinterability of the films. An example of the use of other additives to improve sintering and adhesion of the film to the substrate is also described. Substrate/film interaction has been studied by compositional mapping using an electron probe microanalyzer. The results show a substantial reaction layer (1−2μm) of barium aluminate and a significant diffusion distance (of several microns) of aluminum into the film.

Structural Transitions induced by Colloidal Interactions in Ceramic Dispersions

A discussion of the formation of periodic colloid structures, liquid-like ordering, and compact and fractal aggregates caused by colloidal forces in ceramic dispersions is presented. Construction of phase diagrams based on simple forms of repulsive potentials is often not adequate, and it is important to include appropriate attractive interactions in the theoretical analyses. Examples of radial distribution functions, osmotic prsueadphase diagrams are given for dispersions interacting through Derjaguin-Landau-Verwey-Overbeek potentials. Densification of colloidal aggregates dlue to positional relaxation and the effects of such densification on the structure of the aggregates are discussed.