D. M. A. Buzza

Monte Carlo simulation of dendrimers in variable solvent quality

We study via lattice Monte Carlo simulation and Flory theory the properties of g=1-6 dendrimers in variable solvent quality. For all the generations studied, we find that the radius of gyration R(g) collapses significantly (factor of 2) going from athermal to extreme poor solvent conditions, indicating that varying solvent quality is an effective means of controlling dendrimer size. We also find that in athermal, theta, and extreme poor solvent conditions, the radius of gyration of dendrimers scales with the total number of monomers roughly as R(g) approximately N(1/3). However, a more careful analysis shows that in athermal and theta solvents, there is, in fact, a small but systematic deviation of R(g) from R(g) approximately N(1/3) scaling and the simulation data is described better by the Flory theory prediction of R(g) approximately N(1/5)[(g+1)m](2/5) in athermal solvents and R(g) approximately N(1/4)[(g+1)m](1/4) in theta solvents. We also find for our simulation data that stronger deviations from constant density scaling are possible, with scaling behavior as shallow as R(g) approximately N(0.26) possible for solvent conditions in between theta and the completely collapsed state. It is evident therefore that dendrimers do not obey (or even approximately obey) R(g) approximately N(1/3) scaling under all solvent conditions. Under all solvent conditions, we find that the intramolecular density is dense corelike (i.e., the density maximum is in the interior of the dendrimer) and terminal groups are delocalized throughout the dendrimer.

Theory of surface light scattering from a fluid–fluid interface with adsorbed polymeric surfactants

We present a microscopic theory for the interfacial rheology of a fluid–fluid interface with adsorbed surfactant and calculate the effect of this on surface light scattering from the interface. We model the head and tail groups of the surfactant as polymer chains, a description that becomes increasingly accurate for large molecular weight surfactants, i.e., polymeric surfactants. Assuming high surface concentrations so that we have a double-sided polymer brush monolayer, we derive microscopic scaling expressions for the surface viscoelastic constants using the Alexander–deGennes model. Our results for the surface elastic constants agree with those in the literature, while the results for the viscous constants are new. We find that four elastic constants, i.e., γ (surface tension), e (dilational elasticity), κ (bending modulus), λ (coupling constant), and three viscous constants, i.e., e′,κ′,λ′ (the viscous counterparts of e, κ, and λ, respectively) are required for a general description of interfacial vis...

Micelle shape transitions in block copolymer/homopolymer blends: comparison of self-consistent field theory with experiment.

Diblock copolymers blended with homopolymer may self-assemble into spherical, cylindrical, or lamellar aggregates. Transitions between these structures may be driven by varying the homopolymer diblock molecular weight or composition. Using self-consistent field theory (SCFT), we reproduce these effects. Our results are compared to x-ray scattering and transmission electron microscopy measurements by Kinning et al. and good agreement is found, although the tendency to form cylindrical and lamellar structures is sometimes overestimated due to our neglect of edge effects due to the finite size of these aggregates. Our results demonstrate that SCFT can provide detailed information on the self-assembly of isolated block copolymer aggregates.

Determination of interaction potentials of colloidal monolayers from the inversion of pair correlation functions: a two-dimensional predictor-corrector method.

The structure and stability of colloidal monolayers depend crucially on the effective pair potential u(r) between colloidal particles. In this paper, we develop a two-dimensional (2D) predictor-corrector method for extracting u(r) from the pair correlation function g(r) of dense colloidal monolayers. The method is based on an extension of the three-dimensional scheme of Rajagopalan and Rao [Phys. Rev. E 55, 4423 (1997)] to 2D by replacing the unknown bridge function B(r) with the hard-disk bridge function B(d)(r); the unknown hard-disk diameter d is then determined using an iterative scheme. We compare the accuracy of our predictor-corrector method to the conventional one-step inversion schemes of hypernetted chain closure (HNC) and Percus-Yevick (PY) closure. Specifically we benchmark all three schemes against g(r) data generated from Monte Carlo simulation for a range of 2D potentials: exponential decay, Stillinger-Hurd, Lennard-Jones, and Derjaguin-Landau-Verwey-Overbeek. We find that for all these potentials, the predictor-corrector method is at least as good as the most accurate one-step method for any given potential, and in most cases it is significantly better. In contrast the accuracy of the HNC and PY methods relative to each other depends on the potential studied. The proposed predictor-corrector scheme is therefore a robust and more accurate alternative to these conventional one-step inversion schemes.

The structure and melting transition of two-dimensional colloidal alloys

We study theoretically the structure and melting transition of two-dimensional (2D) binary mixtures of colloidal particles interacting via a dipole–dipole potential. Using a lattice sum method, we find that at zero temperature (T = 0) the system forms a rich variety of stable crystalline phases whose structure depends on the composition and dipole moment ratio. Using Monte Carlo (MC) simulations, we also find that the melting temperature of the different T = 0 structures is a very strong and non-monotonic function of composition. For example, from a direct analysis of the radial distribution function vs.temperature, we find that the melting temperature of hexagonal AB2 and AB6 phases is three orders of magnitude higher than that of hexagonal AB5. Finally the melting transition for our binary colloidal system is found to proceed via at least two stages for hexagonal AB2 and AB6 and at least three stages for hexagonal AB5 and is thus much richer compared to the melting transition of 2D one component colloidal systems.