Conformation and dynamics of a self‐avoiding sheet: Bond‐fluctuation computer simulation

Abstract

The conformation and dynamics of a self-avoiding sheet are analyzed by the bond-fluctuating Monte Carlo method. The mean-square displacement of the center of mass of the sheet and that of its center node R 2 n À Áshow asymptotic diffusive behavior. The segmental dynamics in short and long time regimes can be deduced from the motion of the center node described by the power law R 2 n ' C 1 t 2m þ C 2 t 2n with m^0.13 and n^½, where C 1 and C 2 are fitting constants and t is the time. The radius of gyration, R g , scales with the linear size, L s , of the sheet as R g^N g with g^½ and N ¼ L 2 s , and this is consistent with the conformational analysis of open tethered membranes with excluded-volume constraints.

Exfoliation of stacked sheets: Effects of temperature, platelet size, and quality of solvent by a Monte Carlo simulation

“…That is, the data plotted for R c 2 versus t for a free sheet should be parallel to that of a sheet (previously) in the stack. This is indeed the case for relatively small sheets, 12 2 , 16 2 , and possibly for 24 2 particularly in the long asymptotic time regime as evident in Figure 7. The differences in slopes (i.e., the speed) of a free sheet and that in a layer are however clear (Fig.…”

“…Further, the magnitudes of wrinkling and crumpling depend on the temperature and interaction (strength as well as range) as pointed out in our previous studies. 2,3 For the range of parameters explored here, the overall conformation of each sheet remains nearly flat due to entropy dissipation. The longitudinal (z, x) and transverse (y) separations between the platelets are measures of the extent of exfoliation.…”

“…We have proposed a bond-fluctuating model for the sheet on a discrete lattice to capture some of the pertinent structural details with ample degrees of freedom while accelerating segmental dynamics. 2,3 In this study, we examine the exfoliation of four bond-fluctuating sheets stacked together initially with minimal separations in an effective solvent medium. The model is presented in the next section followed by results and discussion.…”

“…2,3 In our coarse-grained model a sheet is described by a set of nodes tethered (crosslinked) together by flexible bonds in a planar structure. Such a coarse grained description is frequently used in modeling a linear polymer 4,5 including protein macromolecules 6 where nodes are tethered together in a chain with a node characterizing a unit consisting of many atoms or molecules such as an amino acid group.…”

“…Sheets with tethered nodes in a two-dimensional plane possess unique characteristics providing multiple pathways for dynamical modes to propagate and structural fluctuations, a measure of entropy, to dissipate from open edges. 2,3 Enormous efforts have been made in recent years 2,3,[5][6][7][8][9][10][11][12] to study the dynamics and morphological responses of tethered membranes and clay platelets. Using such a model for a sheet, we are focused here on the exfoliation of a layer of platelets.…”