Polymer segment number

Binodials calculated by Tompa are shown in Fig. 123,a for the special case of a nonsolvent [l], a solvent [2], and a polymer [3] with Vi = V2, X23 = 0, and xi2 = Xi3 = 1.5. Otherwise stated, the nonsolvent-solvent and the nonsolvent-polymer segment free energies of interaction are taken to be equal, while that for the solvent and polymer is assumed to be zero. It is permissible, then, to take Xi = X2 = l and o 3 = V3/vi. The number of parameters is thus reduced for this special case from five to two. Binodial curves are shown in Fig. 123,a for 0 3 = 10, 100, and 00 tie lines are shown for the intermediate curve only. The critical points for each curve, shown by circles, represent the points at which the tie lines vanish, i.e., where the compositions of the two phases in equilibrium become identical. 

The determined r 0-M-c equations [Eqs. (14) and (15)] are valid over a very wide concentration range, but they are restricted to samples having molar masses greater than approximately 20,000 g/mol. Viscosity data for lower molar masses show a more rapid increase in the riSp—(o [iq]) plot than the general curve, because it is assumed that the number of polymer segments is too low to form a coil. 

We have added a companion option to PBUILD, PRANDOM which eases considerably the problem of finding good conformations of a polymer segment. PRANDOM automatically selects all of the polymer backbone and/or side chain bonds and will randomly select rotations for each bond. In a few minutes, one can not only build a polymer fragment, but also set up a Monte-Carlo search of its conformational space. However, even this cannot solve the problems for large models (pentamer or larger), again due to the number of bonds to be rotated. 

For the adsorption of polymers, the number of segments per molecule n is large which allows further simplification of the relationships. If the quantity Ks(l-6) 1,... 

Some polymer molecules can be regarded to maintain their approximate solution conformation upon adsorption (19). Adsorption of a nonionic polymer would lead to a coiled adsorbed polymer configuration with a small number of polymer segments in actual contact with the surface. The number of surface sites available for surfactant adsorption would remain quite large. 

It can also be noted that all of the gels rise in enzyme activity at 30 as the number of 30 -40 cycles increases. (Compare Fig. 7 to Fig. 9 to Fig. 10) This may be due to scission of some crosslinks as the gels swell and shrink during the temperature cycling and/or to relative movements of the enzyme and polymer segments within the gel which provide more rapid access of substrate (asparagine) to the enzyme as well as more rapid diffusion of product (aspartate) away from the enzyme, with increasing number of cycles. 

Note 1 The mobility of the polymer segments surrounding the multiplets is reduced relative to that of bulk material. With increasing ion content, the number density of the ionomer multiplets increases, leading to overlapping of the restricted mobility regions around the multiplets and the formation of clusters. 

There have been many attempts to describe the process of mixing and solubility of polymer molecules in thermodynamic terms. By assuming that the sizes of polymer segments are similar to those of solvent molecules, Flory and Huggins derived an expression for the partial molar Gibbs free energy of dilution that included the dimensionless Flory Higgins interaction parameter X = ZAH/RT, where Z is the lattice coordination number. It is now... 

The degree of cross-linking can be expressed in terms of cross-links per gram or per unit volume. If C is the moles of cross-links per unit volume, n the number of network chains per unit volume, d the density of cross-linked polymer, and Me the number-average molecular weight of the polymer segments between cross-links, then... 

We begin by formulating the free energy of liquid-crystalline polymer solutions using the wormlike hard spherocylinder model, a cylinder with hemispheres at both ends. This model allows the intermolecular excluded volume to be expressed more simply than a hard cylinder. It is characterized by the length of the cylinder part Lc( 3 L - d), the Kuhn segment number N, and the hard-core diameter d. We assume that the interaction potential between them is given by... 

The Flory-Huggins theory begins with a model for the polymer solution that visualizes the solution as a three-dimensional lattice of TV sites of equal volume. Each lattice site is able to accommodate either one solvent molecule or one polymer segment since both of these are assumed to be of equal volume. The polymer chains are assumed to be monodisperse and to consist of n segments each. Thus, if the solution contains TV, solvent molecules and TV2 solute (polymer) molecules, the total number of lattice sites is given by... 

Attachment of a single segment of the polymer chain is sufficient to confine the molecule to the layer of solution adjacent to the adsorbing surface. The solid exerts very little influence on the polymer molecule as a whole in such a case. In fact, the overall spatial extension of the polymer chain is expected to be about the same as that of an isolated molecule in this situation. The polymer-solvent interaction plays a more important role than the polymer-surface interaction in determining the thickness of the adsorbed layer in this case. This is only one of the relative interaction combinations possible, but it is the one that we consider in the greatest detail. As the number of polymer segments actually attached to the surface increases, the influence of the surface causes the spatial extension of the adsorbed chains to decrease. 

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