Molecular contour length

Figure 2.5 Critical volume fractions < i below which a solution of poly(benzyl-L-glutamate) is fully isotropic (O) and 2 above which the solution is fully liquid crystalline ( ) as functions of the number of peptide residues N in the chain. The molecular contour length is roughly 1.5N A. (From Robinson et al. 1958, reproduced by permission of The Royal Society of Chemistry.)...

The persistence length (Ip) of HEC molecule was deduced from the knowledge of molecular contour length (Ec), and Rg following Porod-Kratky formalism. Benoit and Doty [8] have shown that in the limit of degree of polymerization going to infinity, the following holds... 

In which X is the average monomer interpenetration distance, L is the contour length of interdiffused chains and n(t) is the number of chains diffused at time t. The time and molecular weight dependence of these molecular properties are given in Table 1. 

Effective molecular mass between crosslinks tvtc/kg mol 1 Tensile yield strength cry/MPa Energy release rate Gic/Jm 2 Half crack opening displacement w = 6/2 = Gic/2cry w/pm Chain contour length (Eq. 7.9) lc/nm... 

Table I. Molecular weights, contour lengths, and linear mass densities...

The doubling or amplification that is inherent in dendrimer chemistry is the dominant process that controls the dendrimer shape [1], With each generation, the number of terminal units usually doubles. Each shell (generation) enhances at approximately a constant value, whereas the total molecular mass approximately doubles with each generation as does the number of branch points. While the dendrimer mass doubles with generation, the space to fit the units increases at a much slower rate. The contour length of any chain from the core to the terminal units is proportional to the number of chemical bonds and hence the number of... 

Fig. 3. 30 Apparent tube diameters from model fits with pure reptation (filled squares) and reptation and contour-length fluctuations (open squares) as a function of molecular weight. The dotted line is a guide for the eye (Reprinted with permission from [71]. Copyright 2002 The American Physical Society)...

Staudinger showed that the intrinsic viscosity or LVN of a solution ([tj]) is related to the molecular weight of the polymer. The present form of this relationship was developed by Mark-Houwink (and is known as the Mark Houwink equation), in which the proportionality constant K is characteristic of the polymer and solvent, and the exponential a is a function of the shape of the polymer in a solution. For theta solvents, the value of a is 0.5. This value, which is actually a measure of the interaction of the solvent and polymer, increases as the coil expands, and the value is between 1.8 and 2.0 for rigid polymer chains extended to their full contour length and zero for spheres. When a is 1.0, the Mark Houwink equation (3.26) becomes the Staudinger viscosity equation. 

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