Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) ? 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.     

Evolution of an ensemble of fractal aggregates in a colloidal system

A theoretical study is presented of primary-minimum aggregation of colloidal particles, which generally leads to the formation of ramified fractal clusters. The focus is placed on the cooperative effects due to competition between aggregates for particles moving freely in the colloidal suspension. An analysis shows that the competition leads to aggregate density distributions and aggregation kinetics governed by more complicated laws as compared to those established in previous numerical and analytical studies of single-cluster growth.     

Pair correlations in magnetic nanodispersed fluids

The pair distribution function of a monodisperse magnetic fluid simulated by a liquid made of dipolar hard spheres with constant magnetic moments is calculated. The anisotropy of the pair distribution function and the related structure factor of scattering in a dc uniform magnetic field are studied. The calculation is performed by diagrammatic expansion in the volume concentration of particles and the interparticle magnetic-dipole interaction intensity using a thermodynamic perturbation theory. Limitation by three-particle diagrams makes it possible to apply the results obtained to magnetic fluids with a moderate concentration. Even for low-concentration and weakly nonideal magnetic fluids, the anisotropic interparticle magnetic-dipole correlations in a magnetic field lead to the repulsion of particles in the direction normal to the field and to the formation of particle dimers along the field.     

Bilayer-by-bilayer antiferroelectric ordering in freely suspended films of an achiral polymer-monomer liquid crystal mixture

Thin freely suspended films of a mixture of an achiral side-chain liquid crystal polymer and its monomer have been studied with depolarized reflected light microscopy. We observe that regions with an odd number of bilayers exhibit a net spontaneous polarization in the tilt plane of the molecules, while regions with an even number of bilayers have no net polarization. These odd-even effects are direct evidence that the tilted smectic bilayers are anticlinic at the polymer backbone and synclinic at bilayer interface and confirm that the phase is bilayer-by-bilayer antiferroelectric.     

Theory and simulation of anisotropic pair correlations in ferrofluids in magnetic fields

Anisotropic pair correlations in ferrofluids exposed to magnetic fields are studied using a combination of statistical-mechanical theory and computer simulations. A simple dipolar hard-sphere model of the magnetic colloidal particles is studied in detail. A virial-expansion theory is constructed for the pair distribution function (PDF) which depends not only on the length of the pair separation vector, but also on its orientation with respect to the field. A detailed comparison is made between the theoretical predictions and accurate simulation data, and it is found that the theory works well for realistic values of the dipolar coupling constant (λ = 1), volume fraction (φ ≤ 0.1), and magnetic field strength. The structure factor is computed for wavevectors either parallel or perpendicular to the field. The comparison between theory and simulation is generally very good with realistic ferrofluid parameters. For both the PDF and the structure factor, there are some deviations between theory and simulation at uncommonly high dipolar coupling constants, and with very strong magnetic fields. In particular, the theory is less successful at predicting the behavior of the structure factors at very low wavevectors, and perpendicular Gaussian density fluctuations arising from strongly correlated pairs of magnetic particles. Overall, though, the theory provides reliable predictions for the nature and degree of pair correlations in ferrofluids in magnetic fields, and hence should be of use in the design of functional magnetic materials.     

Thermodynamics of the Stockmayer fluid in an applied field

The thermodynamic properties of the Stockmayer fluid in an applied field are studied using theory and computer simulation. Theoretical expressions for the second and third virial coefficients are obtained in terms of the dipolar coupling constant (λ, measuring the strength of dipolar interactions as compared to thermal energy) and dipole–field interaction energy (α, being proportional to the applied field strength). These expressions are tested against numerical results obtained by Mayer sampling calculations. The expression for the second virial coefficient contains terms up to λ⁴, and is found to be accurate over realistic ranges of dipole moment and temperature, and over the entire range of the applied field strength (from zero to infinity). The corresponding expression for the third virial coefficient is truncated at λ³, and is not very accurate: higher order terms are very difficult to calculate. The virial coefficients are incorporated in to a thermodynamic theory based on a logarithmic representation of the Helmholtz free energy. This theory is designed to retain the input virial coefficients, and account for some higher order terms in the sense of a resummation. The compressibility factor is obtained from the theory and compared to results from molecular dynamics simulations with a typical value λ = 1. Despite the mathematical approximations of the virial coefficients, the theory captures the effects of the applied field very well. Finally, the vapour–liquid critical parameters are determined from the theory, and compared to published simulation results; the agreement between the theory and simulations is good.