Conformation and Dynamics of a Sheet

In addition to excluded volume, the conformation and dynamics of a sheet can be controlled by introducing (intrasheet) interactions among its particles as well as interactions and constraints with other constituents in the host matrix. The physical properties of the sheet (clay platelet or tethered membrane) depend on the type of interaction with the underlying matrix (e.g., solvent), concentration, temperature, and a host of external and internal parameters. 

In a simple model [33,40], one can use empty lattice sites to represent an effective solvent medium in which a particle can exchange its position with the solvent sites. The interaction energy of a particle can be described by 

Wrinkles are caused by the local movements of particles and propagate along their cormected pathways of the membrane. How the global dynamics emerge from the interplay between the competition and cooperation of these local dynamical modes is one of the fundamental questions to be addressed. 

The collective dynamics of the sheet can be examined by tracking the motion (rms displacement) of its center of mass. It is often diffusive in simple (unconstrained) systems in the asymptotic time regime. The dynamics of the center of mass, however, does not elucidate the effect of internal structure succinctly due to mode averaging. Such details can be captured by monitoring the motion of an interior partide, say, the center one. 

In order to cover the fidl range of multiscale dynamics, one needs a relatively large dimension of the sheet in our bond fluctuation top-down) approach as in studying the multiscale dynamics of polymer chains. As mentioned above, a composite consists of a number of components represented by particles, chains, and sheets. Multiscale characteristics of each component, for example, particles, chains, and sheets, are further modified when a large number of these constituents are placed in a simulation box, that is, by their concentrations (volume fractions). Interaction and physical constraints at higher concentrations introduce multiple relaxation times for composites to reach equilibrium or steady state. In order to carry out a systematic investigation and draw meaningful conclusions, we restrict ourselves to constituents 

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