Chain four-bead

Let us describe the results for the case of a matrix made of chains with four beads, i.e., m = M = 4. We observe that both the PY and the HNC approximation quite accurately describe the adsorption isotherms in matrices of different microporosity (Fig. 5). However, a discrepancy between the HNC results and simulation data increases with increasing chemical potential, especially at higher matrix densities. The structural... 

FiG. 7 The same as in Fig. 6, for the matrix made of chains with four beads (m = Af = 4) at packing fraction 0.126. The nomenclature of lines and symbols and their location are similar to those of Fig. 6. 

In principle, another type of collapse, of intermolecular rather than intramolecular origin, might occur whenever four beads (two from one chain, and two from another chain) describe a regular tetrahedron, with side L, on the... 

Here s the kind of problem we want to solve. Example 8.2 (page 13.5) describes a two-dimensional model of a four-bead polymer chain that has four open conformations and one compact conformation. In that example, we com-... 

Figure 10.1 The five conformations of the four-bead chain in Example 8.2 (page 1 35) are grouped on an energy ladder. Conformations with one bead-bead contact, /ic = 1, are taken to have energy e = 0. The other four conformations have no bead-bead contacts so f = fo. where fo is a constant. The number 1 next to the first bead indicates that the chain has a head and a tail otherwise the counting of conformations is a little different.

So it is often useful to switch your attention from microstates to macrostates. For example, for the four-bead polymer, each configuration shown in Figure 10.1 is one microstate. But a typical experiment might only tell you whether the chain is open (four microstates) or compact (one microstate). Then the terms open and compact define macrostates. The density of states W (E) is the number of microstates in a given macrostate. When W > 1, an energy level is called degenerate. 

For the four-bead chain, there is one compact conformation and four open conformations (see Figure 10.1), so the density of states is W(0) = 1 and W(fo) = 4. Since W is the number of microstates per level, the partition function can be expressed as a sum over the two levels (open and compact, in this case), rather than over the five microstates,... 

EXAMPLE 10.3 The collapse distribution for the four-bead polymer chain. 

Figure 3.5. Schematic drawing of the complete Nafion copolymer, which is composed of apolar beads (blue) and charged beads (yellow), and also a part of the atomistic level configuration of a Nafion chain. Four-monomer unit (—(CF2CF2)4—) is represented by one blue bead as the hydrophobic backbone, while the side chain (-0-CF2CF(CF3)—O—CF2CF2—SO3H) with the sulfonic acid group is expressed as one yellow bead with hydrophilic property.

We would like to discuss consistently the results obtained in the theory and simulations for a hard sphere fluid adsorbed in a matrix of chains with four, eight, and sixteen monomer beads (m = M = 4 8 16). 

FIGURE 3.5 A molecular shuttle. The "bead", consisting of a macrocycle containing four pyridine rings and two benzene rings, moves back and forth between the two "stations", which are benzene rings. The "stoppers" prevent the bead from falling off the chain.1,5... 

Most of the resins used in batch synthesis are derivatives of 1% crosslinked copoly-(styrene-divinylbenzene) resin in the form of beads 50 to 100 p in diameter. These beads swell four to six times their dry volume in the solvents used in peptide assembly and during the chain elongation process the resin again may double its swollen volume. In batch synthesis, provided the proper size vessel is chosen, the increase in swollen volume is not a major concern. 

In general, polymers can be divided into four major categories, depending on their physical behavior thermoplastics, fibers, elastomers, and thermosetting resins. Thermoplastics are the polymers most people think of when the word plastic is mentioned. These polymers have a high T, and are therefore hard at room temperature, but they become soft, and viscous when heated. As a result, they can be molded into toys, beads, telephone housings, or into any of a thousand other items. Because thermoplastics have little or no cross-linking, the individual chains can slip past one... 

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