Zhong‐Ying Chen

The translational friction coefficient and time dependent cluster size distribution of three dimensional cluster–cluster aggregationa),b)

The diffusion coefficient of clusters D formed by cluster–cluster aggregation is computed according to the Kirkwood–Riseman Theory. In three dimensions one finds D proportional to sγ where s is the number of particles in the cluster and γ=−0.544±0.014. This relationship is employed to simulate the time evolution of the cluster size distribution Ns(t) which is found to exhibit simple scaling behavior Ns(t) ∼s−2g(s/tz) with z∼1.1.

Biaxial nematic phase, multiphase critical point, and reentry transition in binary liquid crystal mixtures

A model considering both short‐range and long‐range interactions for liquid crystals mixtures of rod‐like and plate‐like molecules is presented in this paper. The model is treated in the framework of a mean field, van der Waals‐type theory. The relationship of the model to a Landau‐type treatment is discussed in an Appendix. It can be shown for this model that a multiphase critical point exists between the isotropic, rod nematic, plate nematic, and biaxial nematic phases. This point can be located from a set of analytic equations. The fluctuations and the magnetically induced birefringence around this point are calculated. The model predicts the phase diagrams of binary liquid crystal mixtures both with and without reentry transition. The reentrant phase transitions from the biaxial to the uniaxial nematic phase and from the uniaxial nematic to the isotropic phase have not received prior theoretical attention but have been demonstrated in recent experiments.

Monte Carlo and mean-field studies of successive phase transitions in rod monolayers

In this paper we present a rigid‐rod model (involving a restricted set of orientations) which is solved first with mean‐field theory and then by Monte Carlo simulation. It is shown that both interparticle attractions and anisotropic adsorption energies are necessary in order for two successive fluid–fluid transitions to occur. The first is basically a gas–liquid condensation of ‘‘lying down’’ rods in the plane of the surface, and the second involves a ‘‘standing up’’ of the particles. A close qualitative correspondence is established between the results obtained in the mean‐field and Monte Carlo descriptions. The role of biaxial states, i.e., in‐plane orientational ordering, is also discussed in both contexts. To this end, we develop an analogy between our one‐component rod monolayer and a bidisperse system of interconverting isotropic particles.

Hydrodynamic radii of diffusion‐limited aggregates and bond‐percolation clusters

The hydrodynamic radii of two types of aggregates, diffusion‐limited aggregation clusters (DLA) and bond‐percolation clusters (BPC), are calculated by numerically solving the hydrodynamic interaction between different particles in the cluster. Though they have almost the same fractal dimensionality, DLA and BPC clusters exhibit different effective hydrodynamic scaling behaviors. For BPC, the ratio between the hydrodynamic radius and the radius of gyration, Rh/Rg, remains almost constant (1.14) for clusters of up to 900 particles; while for DLA the hydrodynamic radius Rh increases faster than the radius of gyration Rg, with Rh∼N0.45 for the same range of N.

Aggregation of anisotropic particles

The diffusion limited aggregation of particles with anisotropic sticking probabilities has been investigated using computer models. All of our simulations have been carried out using 2d square lattices with square ‘‘particles’’ having two more sticky and two less sticky sides with sides of different kinds adjacent to each other. In both the limits of fast and slow particle rotation the anisotropy of the particles enhances the anisotropy of the square lattice and cross‐shaped clusters (with side branches) are formed which resemble those generated by very much larger scale simulations of the regular DLA process. In the slow rotation limit a bias in the number of particles launched with sticky sides facing in the X or Y directions on the lattice leads to the formation of needle‐shaped clusters whose radius of gyration (Rg) increases with cluster mass (M) according to Rg ∼M2/3.