Sheet self-avoiding

Further improvements in modeling flexible sheet polymers must take into account the molecular connectivity within the membrane. To analyze the shapes of these structures, one discards elasticity theory and finds a more appropriate context in statistical mechanics of random surfaces. A number of approaches have been proposed. For example, the membrane may be (a) represented as a self-avoiding surface,"i2.i99 and its shape characterized by asphericity and radius of gyration,"i2.i99 or (b) viewed as a tethered surface with fixed internal connectivity.200-203 in case (b), nuclei are regarded as hard spheres tethered together by elastic or fluid strings, forming a net with a specified architecture. 

Flexible, solid membranes, are also of interest. However, they are experimentally much less prevalent and are somewhat more complicated to treat since in addition to the membrane shape one must include the effects of shear. Their curvature energy is discussed in the problems at the end of this chapter. Another type of system that has received much theoretical attention is that of a tethered membrane which may describe polymerized, but not crystalline sheets. While a single fluid membrane that is unconstrained by walls or other membranes is strongly affected by thermal fluctuations ( crumpled ), solid membranes, particularly if self-avoidance of the membrane is included, tend to be more weakly affected by fluctuations and are hence flattef . 

Pandey, R. B., Anderson, K. L., Heinz, H., and Farmer, B. L. 2005. Conformation and dynamics of a self-avoiding sheet Bond-fluctuation computer simulation. Journal of Polymer Science B 43 1041-1046. 

If a straight line is one dimensional and a flat sheet is 2D, how can we describe the dimensionality of a coastline or the shape of a polymer molecule In these cases, 2D or 3D space is being partially filled by a ID object. Figure 1.13 illustrates this concept the coiled up self-avoiding polymer wraps around on itself to partially fill the illustrated 2D space. 

The excluded volume, self-avoiding sheet (SAS) deforms and wrinkles propagate as its particles execute their stochastic motion. The conformation and dynamics of the sheet can be studied by keeping track of the rms displacement of the center of mass of the sheet and that of its center (interior) particle, radius of gyration, as a function of molecular weight and rigidity of the covalent bonds. Effects of the quality of the solvent and entanglement barriers (e.g., polymer chains matrix) can be incorporated (see below). A few observations from our computer simulations are briefly discussed in the next section. 

Uses Self-crosslinking emulsions, heat-curing coatings, silk grafting, crosslinked acrylic sheets, thermosetting paints Properties Pt-Co 100 max. colorless clear to yish. liq. faintly ester-like odor misc. with water m.w. 115.1 sp.gr. 1.1 b.p. 100 C solid, pt. -37 C flash pt. none pH 7 1 40 1.5% water Toxicology LD50 (oral, rat) 1815 mg/kg avoid contact with skin, eyes, mucous membranes TSCA listed... 

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