Polymers molecular size

Chain and step polymerizations differ in several features, but the most important difference is in the identities of the species that can react with each other. Another difference is the manner in which polymer molecular size depends on the extent of conversion. 

For branched polymers, molecular size is crucial because the material eluting at any value of Vr consists of a mixture of species having different molecular weights and degrees of branching but constant hydrodynamic volume. 

Gold, L. Statistics of polymer molecular size distribution for an invariant number of propagating chains. J. Chem. Phys. 28, 91 (1958). 

Colloidal systems are generally of a polydispersed nature - i.e. the molecules or particles in a particular sample vary in size. By virtue of their stepwise build-up, colloidal particle and polymer molecular sizes tend to have skew distributions, as illustrated in Figure 1.2, for which the Poisson distribution often offers a good approximation. Very often, detailed determination of relative molecular mass or particle size distribution is impracticable and less perfect experimental methods, which yield average values, must be accepted. The significance of the word average depends on the relative contributions of the various molecules or particles to the property of the system which is being measured. 

Several size parameters can be used to describe the dimensions of polymer molecules radius of gyration, end-to-end distance, mean external length, and so forth. In the case of SEC analysis, it must be considered that the polymer molecular size is influenced by the interactions of chain segments with the solvent. As a consequence, polymer molecules in solution can be represented as equivalent hydrodynamic spheres [1], to which the Einstein equation for viscosity may be applied ... 

When polymer molecular sizes are larger than some pores in a porous medium, the polymer molecules cannot flow through those pores. The volume of those pores that cannot be accessed by polymer molecules is called inaccessible pore volume (IPV). In an aqueous polymer solution with tracer, the polymer molecules will run faster than the tracer because they flow only through the pores that are larger than their sizes. This results in earlier polymer breakthrough in the effluent end. On the other hand, because of polymer retention, the polymer breakthrough is delayed. In other words, if only polymer retention is considered, the polymer will arrive in the effluent later than the tracer. 

The polymer molecular size is described by its molecular weight. If a hydrogen atom is given a weight of one, carbon, which is approxi-... 

Qualitatively, a sharp crossover to mean-field behavior has been reported earlier for metal-ammonia solutions [50, 51]. Crossover between Ising-like asymptotic behavior and mean-field classical behavior has also been reported for polymer blends [42-46] and for a microemulsion system [52]. Solutions of polymers in low-molecular-weight solvents exhibit sharp nonmonotonic crossover behavior when the correlation length of the critical fluctuations and the polymer molecular size, as specified by the radius of gyration, are of the same order [24]. Hence, a description of this crossover phenomenon requires two independent parameters associated, respectively, with intramolecular and intermolecular correlations [53]. It has been demonstrated that the two-term crossover Landau model is indeed... 

The specific surface area of the surfactant- and polymer-templated gels, that is, the ambient pressure aerogels, is nearly the same as that of the aerogels prepared by the supercritical extraction of CO2. Also, the pore size and the pore volume, that is, the porosity, are larger (twice or more) than those of the xerogels, but smaller than those of the super-critically extracted aerogels, estimated to be ca. 55%. The pore size and pore volume depended on the properties of surfactants and polymers, molecular size, and micelle- or aggregate shape. Also, the concentration of polymers in the immersion solutions, as well as the kind of template materials, affected the pore size and pore volume (Table 7.2). 

Polymer Molecular Size, Structure and Chemical Composition... 

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