Isolated polymer coils

A typical excluded volume effect is the occurence of nontrivial power laws. As a first (jx miple lei us consider the average size of an isolated polymer coil consisting of n segments. We assume e rch segment to consist of several monomtirs, so that any bond constraints among the directions of sub-... 

Ensemble Average Conformation of Isolated Polymer Coils in Solid Blends... 

Due to the sensitivity of electronic excitation transport to the separation and orientation of chromophores, techniques which monitor the rate of excitation transport among chromophores on polymer chains are direct probes of the ensemble average conformation (S). It is straightforward to understand qualitatively the relationship between excitation transport dynamics and the size of an isolated polymer coil which is randomly tagged in low concentration with chromophores. An ensemble of tagged coils in a polymer blend will have some ensemble averaged root-mean-squared radius of gyration,... 

Even in dilute solutions, molecular interference is likely to occur, and is extrapolated to zero concentration to obtain a measure of the influence of an isolated polymer coil. This is accomplished in either of two ways T sp can be expressed as a reduced quantity (tlsp/c) and extrapolated to c = 0 according to the relation... 

There is another bunch of problems that we still need to tackle when portraying an isolated polymer coil. We might as well start with a very simple question What does it mean to say that a coil size is proportional to the square root of the chain length, i.e. or Can the chain, acciden-... 

As we discussed in Section 4.6, isolated polymer coils are typical for dilute solutions, where the volumes taken up by the coils do not overlap (Figure 4.7 a). Things change when the polymer concentration exceeds the threshold value c (which is defined by Equation (6.14) for an ideal polymer). In this case we have a semi-dilute solution (Figure 4.7 c). Although the fraction of the volume taken up by the polymer is still rather small, the coils are already highly intermingled. Can we work out what the excluded volume effect does to the coils in this case (i.e., when the polymer concentration c c ) ... 

The extrapolation to zero concentration is performed to eliminate the effects of molecular interferences likely to occur even in dilute solutions and obtain the influence of an isolated polymer coil on the viscosity of the solution. Only T and T <, have the dimensions of viscosity (Poise or Pa. s). Specific viscosity and relative viscosity are dimensionless. Intrinsic viscosity, reduced viscosity, and inherent viscosity all have the dimension of inverse concentration. The nomenclature of viscosity parameters is given in Table 7. 

The transition from dilute solution behaviour (isolated polymer coils) to semi-dilute (interpenetration of coils, uniform polymer segment density) usually occurs over a narrow range of concentration, and a critical concentration c identified. This c will, however, depend to some extent upon the particular experiment performed, e.g., solution viscosity, diffusion (cf., e.g., ref. 99) ... 

Munk has treated the statistical thermodynamics of isolated polymer coils (see Chapter 9) in some detail covering the number of conformations, number of intramolecular contacts and the difficulty of excluding self-intersecting conformations. He introduces a description of the polymer coil in terms of a conformational distribution function which includes only plausible conformations but whose analytical form is left unspecified. He concludes that some of the interesting features of the distribution function, and hence partition function derived therefrom, can be inferred from suitable experimental data. 

The central idea of this approach is the treatment of a swollen isolated polymer coil - surrounded by a sea of pure solvent - as a sort of microphase and applying the usual equilibrium condition to such a system. In a thought experiment, one can insert a single totally collapsed polymer molecule into pure solvent and let it swell... 

This relation contains four adjustable parameters even if they are molecularly justified these are too many for practical purposes. For this reason, it would be helpful to be able to calculate at least one of them independently. The most obvious candidate for that purpose is 2 (17) because it refers to the spatial extension of isolated polymer coils. Radii of gyration would be most qualified for calculation of the required volume fractions of segments, inside the microphase formed by isolated polymer molecules. Unfortunately, however, it is hard to find tabulated values for different polymer/solvent systems in the literature. For this reason, we use information provided by the specific hydrodynamic volume of the polymers at infinite dilution, i.e., to intrinsic viscosities [r/]. The volume of the segments is... 

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