Ronald Dickman

High density Monte Carlo simulations of chain molecules: Bulk equation of state and density profile near walls

We introduce a new Monte Carlo method suitable for simulations of chain molecules over a wide range of densities. Results for the equation of state of chains composed of 4, 8, and 16 freely joined hard spheres are compared with the predictions of several theories. The density profile of the fluid in the vicinity of the wall, and the scaling of the pressure with chain length are also discussed.

Entropic Forces in Binary Hard Sphere Mixtures: Theory and Simulation

We perform extensive Monte Carlo simulations of binary hard-sphere mixtures (with diameter ratios of 5 and 10), to determine the entropic force between (1) a macrosphere and a hard wall, and (2) a pair of macrospheres. The microsphere background fluid (at volume fractions ranging from 0.1 to 0.34) induces an entropic force on the macrosphere(s); the latter component is at infinite dilution. We find good overall agreement, in both cases, with the predictions of a hypernetted chain-based theory for the entropic force. Our results also argue for the validity of the Derjaguin approximation relating the force between convex bodies to that between planar surfaces. The earlier Asakura-Oosawa theory, based on a simple geometric argument, is only accurate in the low-density limit.

Self-organized criticality as an absorbing-state phase transition

We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving field h - are set to their critical values. The critical values of epsilon and h are both equal to zero. The first is due to the absence of saturation (no bound on energy) in the sandpile model, while the second result is common to other absorbing-state transitions. The original definition of the sandpile model places it at the point (epsilon=0, h=0+): it is critical by definition. We argue power-law avalanche distributions are a general feature of models with infinitely many absorbing configurations, when they are subject to slow driving at the critical point. Our assertions are supported by simulations of the sandpile at epsilon=h=0 and fixed energy density (no drive, periodic boundaries), and of the slowly-driven pair contact process. We formulate a field theory for the sandpile model, in which the order parameter is coupled to a conserved energy density, which plays the role of an effective creation rate.

Random sequential adsorption: Series and virial expansions

We introduce an operator formalism for random sequential adsorption on lattices and in continuous space. This provides a convenient framework for deriving series expansions for the deposition rate dθ/dt in powers of t. Several specific examples—the square lattice with nearest‐neighbor exclusion, and with exclusion extended to next‐nearest neighbors, and disks and oriented squares on the plane—are considered in detail. Precise estimates for θ(t) and the jamming coverage are obtained via Pade approximant analysis. These are found to be in excellent agreement with simulation results. A diagrammatic expansion for dθ/dt is derived, and its relation to the equilibrium Mayer series is elucidated.

Interaction between colloids in solutions containing dissolved polymer

Abstract The effective interaction between colloids in solutions containing dissolved polymer is investigated using integral equations. The colloidal particles are modeled as hard spheres, the polymer molecules are modeled as freely jointed hard chains, and the solvent is treated as a continuum that doesnt interact with either the colloidal particles or the polymer molecules. The model therefore concentrates on excluded volume effects in these systems. It is found that at low polymer volume fractions, the effective intermolecular potential (or potential of mean force) between the colloidal particles is attractive, thus facilitating a phase separation or precipitation of the colloids. As the polymer volume fraction is increased, the strength of this attraction increases; but a repulsive interaction appears at larger separations, which resembles the double-layer repulsion between charged colloidal particles in an aqueous solution. The effects of varying polymer chain length, colloid particle size, and polymer volume fraction on the effective potential are also studied.

Perturbation density functional theory and Monte Carlo simulations for the structure of hard triatomic fluids in slitlike pores

A model fluid composed of semiflexible tangent hard sphere trimers is investigated using Monte Carlo simulations and perturbation density functional theory (PDFT), focusing on the density profile and conformational properties in the vicinity of a hard wall. The surface density is reduced (enhanced) at low (high) densities. We also observe preferential end absorption. Both features arise from competition between chain conformational entropy and packing constraints. Molecules adjacent to the wall tend to lie flat against it, particularly at high density and/or stiffness. But the bond angle distribution is only weakly affected by the presence of the wall. For rigid molecules, the density profiles depend strongly on the value of the bond angle. PDFT is in excellent agreement with simulation, and promises to be a successful means of elucidating the interfacial structure of complex fluids.

CRITICAL DYNAMICS OF THE CONTACT PROCESS WITH QUENCHED DISORDER

We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical pointc is characterized by the critical exponents of directed percolation: in 2+1 dimensions, � = 0.46, � = 0.214, and z = 1.13. Disorder causes a dramatic change in the critical exponents, to � ≃ 0.60, � ≃ −0.42, and z ≃ 0.24. These exponents govern spreading following a long crossover period. The usual hyperscaling relation, 4� + 2� = dz, is violated. Our results support the conjecture by Bramson, Durrett, and Schonmann (Ann. Prob. 19, 960 (1991)), that in two or more dimensions the disordered CP has only a single phase transition.

Polymer‐induced forces between colloidal particles. A Monte Carlo simulation

Monte Carlo simulations of the fluctuating bond lattice model are used to determine the force between colloidal particles immersed in a nonadsorbing polymeric fluid. Monodisperse systems with chain lengths of 20 to 100 segments are studied at occupation fractions ranging from 0.1 to 0.6, covering the semidilute and dense regimes. The variation of the force with concentration, particle diameter, and interparticle separation is in qualitative agreement with predictions of scaling theory and of integral equations for the colloid–polymer system. In semidilute solutions the force is purely attractive and displays an approximately linear dependence upon separation for small colloid separations. At higher concentrations the force is repulsive, for certain separations.

Nonequilibrium critical poisoning in a single-species model

Abstract A simple model is introduced, which exhibits a poisining transition similar to that observed in studies of catalyc surface reactions. Steady-state behavior and critical exponents are determined via series expansion and Monte Carlo simulations. The relation between catalytic surface models and reggeon field theory is examined.

New simulation method for the equation of state of lattice chains

A new method for determining the pressure in Monte Carlo simulations of lattice chains is described, and preliminary results are presented. The method, in which the pressure is related to the density of segments at a repulsive wall, is applicable over a wide range of densities and chain lengths. Flory–Huggins theory is in good agreement with simulation results at high densities.