Abstract. A system of identical disks is confined to a narrow channel, closed off at one end by a stopper and at the other end by a piston. All surfaces are hard and frictionless. A uniform gravitational field is directed parallel to the plane of the disks and perpendicular to the axis of the channel. We employ a method of configurational statistics that interprets jammed states as configurations of floating particles with structure. The particles interlink according to set rules. The two jammed microstates with smallest volume act as pseudo-vacuum. The placement of particles is subject to a generalized Pauli principle. Jammed macrostates are generated by random agitations and specified by two control variables. They are inferred from measures for expansion work against the piston, gravitational potential energy, and intensity of random agitations. In this two-dimensional space of variables there exists a critical point. The jammed macrostate realized at the critical point depends on the path of approach. We describe all jammed macrostates by volume and entropy. Both are functions of the average population densities of particles. Approaching the critical point in an extended space of control variables generates two types of jammed macrostates: states with random heterogeneities in mass density and states with domains of uniform mass density. Criticality is shown to be robust against some effects of friction.
The properties of rubber are strongly influenced by the distribution of filler within the polymer matrix. Here, we introduce a Monte Carlo-based morphology generator. The basic elements of our model are cubic cells, which, in the current version, can be either silica filler particles or rubber volume elements in adjustable proportion. The model allows the assignment of surface free energies to the particles according to whether a surface represents, for instance, ‘naked’ silica or silanised silica. The amount of silanisation is variable. We use a nearest-neighbour site-exchange Monte Carlo algorithm to generate filler morphologies, mimicking flocculation. Transmission electron micrographs (TEM) as well as small angle scattering (SAS) intensities can be calculated along the Monte Carlo trajectory. In this work, we demonstrate the application of our morphology generator in terms of selected examples. We illustrate its potential as a tool for screening studies, relating interface tensions between the components to filler network structure as characterised by TEM and SAS.
This work introduces a methodology for the statistical mechanical analysis of polymeric chains under tension controlled by optical or magnetic tweezers at thermal equilibrium with an embedding fluid medium. The response of single bonds between monomers or of entire groups of monomers to tension is governed by the activation of statistically interacting particles representing quanta of extension or contraction. This method of analysis is capable of describing thermal unbending of the freely-jointed or worm-like chain kind, linear or nonlinear contour elasticity, and structural transformations including effects of cooperativity. The versatility of this approach is demonstrated in an application to double-stranded DNA undergoing torsionally unconstrained stretching across three regimes of mechanical response including an overstretching transition. The three-regime forceextension characteristic, derived from a single free-energy expression, accurately matches empirical evidence. (c) J τ J J (b) (d) (a) FIG. 1: (Color online) Schematic representations for a chain of N = 7 monomers of (a) the reference state, (b) a state under tension with extension particles activated, (c) a state under tension and torque with twist-contraction particles activated, and (d) a state under tension with extension particles and contact particles activated.
The properties of rubber are strongly influenced by the distribution of filler within the polymer matrix. Here we introduce a Monte Carlo-based morphology generator. The basic elements of our model are cubic cells, which, in the current version, can be either silica filler particles or rubber volume elements in adjustable proportion. The model allows the assignment of surface free energies to the particles according to whether a surface represents, for instance, 'naked' silica or silanised silica. The amount of silanisation is variable. We use a nearest-neighbour site-exchange Monte Carlo algorithm to generate filler morphologies, mimicking flocculation. Transmission electron micrographs (TEM) as well as small angle scattering (SAS) intensities can be calculated along the Monte Carlo trajectory. In this work we demonstrate the application of our morphology generator in terms of selected examples. We illustrate its potential as a tool for screening studies, relating interface tensions between the components to filler network structure as characterized by TEM and SAS.
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