Measures of Polymer Conformations

When a polymer is dispersed in a solvent, there are generally three kinds of pairwise interactions at the local level monomer-monomer, monomer-solvent, 

We shall now define some quantifies, which are either measured experimentally or computed theoretically, to describe polymer conformations. These definitions are general, independent of the particular conformations taken by the polymer. As an example, consider a specified conformation of a polyethylene 

Radius of gyration, Rgi This is defined as the root mean square radius of gyration, where the mean square radius of gyration is given by 

This quantity is measured in static scattering techniques using light, x-rays, and neutrons. 

This quantity is measured in dynamic light-scattering technique, and its origin lies in the hydrodynamic interactions in the solution. 

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There are no closed-form expressions (Muthukumar and Nickel 1987, des Cloizeaux and Jannink 1990) for other measures of polymer conformations of a swollen chain, such as the form factor and monomer density profiles. Nevertheless, the general laws discussed in Section 2.2 for statistical fractals are valid, with the approximate value of 5/3 for df. The monomer density decays with the radial distance r as... 

We introduced several measures of polymer conformations, the most important being the radius of gyration Rg of the chain. It depends on the number of monomers N in the chain, according to a power law. 

The interaction between the water and the polymer occurs in the vicinity of the polymer chains, and only the water molecules situated in this interface are affected by the interaction. The space fractal dimension da is now the dimension of the macromolecule chain. If a polymer chain is stretched as a line, then its dimension is 1. In any other conformation, the wrinkled polymer chain has a larger space fractal dimension, which falls into the interval 1 < d( < 2. Thus, it is possible to argue that the value of the fractal dimension is a measure of polymer chain meandering. Straighter (probably more rigid) polymer chains have da values close to 1. More wrinkled polymer (probably more flexible) chains have da values close to 2 (see Table III). 

Some measure of polymer size is obtained from molecular weight, but what is the actual length of the molecule and what is its shape Before trying to answer these questions we should first consider a simple molecule such as butane and examine the behavior when the molecule is rotated about the bond joining two adjacent carbons. This rotation produces different conformational states of the molecule. 

Another measure of the conformational flexibility of substituted polythiophenes is found in the determination of colligative properties of solutions of such polymers. Experimental studies have demonstrated poly(3-octylthiophene) in solutions to follow the... 

We have discussed the occurrence of hydrophobic collapse in the folding of proteins. This is a general phenomenon and was treated quite early by Flory in his well-known study of polymer conformations across theta temperatures in polymer solutions. When a polymer chain is dissolved in water or the temperature of the polymer solution is lowered, it often undergoes a transition from extended state to collapsed state. This is reflected in the sharp decrease in the size of the polymer, measured by its radius of gyration. This phenomenon is known as collapse transition. Though the collapse transition is primarily initiated by the change of temperature, it may also be introduced by a change in the quality of the... 

This series of calculations [20][21][6] on the conformational dependence of chemical shifts Illustrates the need of a continuously more precise determination of the conformation of the mononucleotides and of the contribution of the "rearrangement effect" to the polymerization shift, 1f one wants to be able to fully Interpret the NMR measurements of polymers In solution. 

The literature outlines the considerable efforts dedicated to the measurement of chain conformation in polymer nanocomposites, sometimes yielding contradicting results depending on the chemical system, size ratio between polymer and filler, and filler concentration (Jouault et al. 2010a, 2010b Crawford et al. 2013 Tung et al. 2013). 

Jouault Nicolas, Dalmas Florent, Said Sylvbre, et al. Direct measurement of polymer chain conformation in well-controlled model nanocomposites by combining SANS and SAXS. Macromolecules. 43 no. 23 (2010a) 9881-9891. 

Another measure of polymer chain size is the end-to-end length, the length of the vector pointing through space from one end of the chain to the other, when the chain is in a given conformation (see Figure 32.1(b)). The end-to-end length varies from one chain conformation to the next. The end-to-end vector r is the vector sum over the bonds Sj for bonds i = 1,2,3,...,N ... 

While there have been numerous measurements of polymer fast relaxation rates which can be attributed to conformational transitions, few have contributed directly to a determination of the transition mechanism. Let us cite several of the results which do provide some indirect evidence. 

Vibrational spectroscopy potentially has sufficient sensitivity and specificity to detect chain conformations in solid polymer samples. An analogy can be drawn between the compos ite infrared spectrum arising from n-compound mixtures of simple organic solvents and the composite spectrum due to differii chain conformations in amorphous polymer glasses. Each mixture spectrum is a linear combination of a set of spectra assignable individually to the components of the mixture. In our study of polymer conformations, we will need techniques to analyze sets of mixture spectra for the number of basic spectra (e. g. number of conformations) and to derive the individual component spectra themselves. Furthermore, a method of internal calibration of the component spectra is necessary for measuring amounts of polymer confor-... 

In our previous discussion of the lattice model of adsorption, we have already made use of the components of the radius of gyration as excellent measures for the globular compactness of polymer conformations parallel [see Figs. 13.9(a,b)] and perpendicular [Figs. 13.9(c,d)] to the surface, respectively. These components are particularly helpful for the identification of structural changes induced by the presence of an attractive substrate. 

It is indispensable to know the responsive rate, when constructing photore-sponsive devices using the photoresponsive polymers described in the foregoing. The most convenient way to find the response time is to measure the conformational change of the polymer chain in solution. Direct measurement of the conformational change was carried out using a flash photolysis method... 

The measurement of molecular weight and RMS radius provides the means to examine the conformational characteristics of a polymer using the relationship... 

Entropy is a measure of disorder in materials. Relaxed polymer chains with a random conformation (shape in space), like cooked spaghetti or a box of fishing worms, have a high degree of entropy, which is favored by Mother Nature. If the chains are stretched out (stressed), the number of conformations the chains can have in space is limited, and the entropy is reduced (see Figure B). The ratio of final length to initial length is denoted a. 

Another largely unexplored area is the change of dynamics due to the influence of the surface. The dynamic behavior of a latex suspension as a model system for Brownian particles is determined by photon correlation spectroscopy in evanescent wave geometry [130] and reported to differ strongly from the bulk. Little information is available on surface motion and relaxation phenomena of polymers [10, 131]. The softening at the surface of polymer thin films is measured by a mechanical nano-indentation technique [132], where the applied force and the path during the penetration of a thin needle into the surface is carefully determined. Thus the structure, conformation and dynamics of polymer molecules at the free surface is still very much unexplored and only few specific examples have been reported in the literature. 

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