Random coil dimensions

A RIS model with neighbor dependence is used to calculate mean-square dipole moments and their temperature coefficients for PDMS chains over a wide range of molecular weight. Chain conformational energies required in the calculations are obtained from a previous analysis of the random-coil dimensions of PDMS chains in the limit of large x (S 116). 

Dielectric constants are determined for pure liquid dimethylsiloxane oligomers. Mean-square dipole moments, calculated from the Onsager equation, are in good agreement with predicted values based on the RIS model (S 117) with neighbor dependence and chain conformational energies obtained in an independent analysis of the random-coil dimensions of such chains. In addition, the observed temperature coefficients of are in qualitative agreement with calculated results. 

The RIS model with neighbor dependence is used to calculate random-coil dimensions for the e/s-forms of PBD and PIP in the limit of large x. Comparison of calculated and experimental values of the characteristic ratio and its temperature coefficient is used to determine intramolecular energies of various conformational sequences of the chain backbone. 

The second virial coefficient A2 in the osmotic pressure equations can also be used to determine random coil dimensions (see Chap. 10). 

The systems studied by these authors are poly-L-glutamate in aqueous 0.3 ikf sodium phosphate at pH 7.85 and 37°, poly-L-lysine in aqueous 1.0 M sodium bromide at pH 4.54 and 37°, (and poly- -benzyl-E-aspartate in w-cresol at 100°). The tendency for these polypeptides to form ordered structures limits the choice of solvent systems in which random coil dimensions may be studied. These solvents, furthermore, cannot be solvents for the randomly coiled form of the polypeptides. However, if conditions are achieved (like those under which Brant and Flory carried out their investigation), such that the linear expansion of... 

Mark, J. E. Ko, J. H., Random-Coil Dimensions of Poly(methylphenylsiloxane) and Their Dependence on Stereochemical Structure. J. Polym. Sci., Part B Polym. Phys. 1975,13, 2221-2235. 

Hendra et ai. have quenched poly(oxymethylene) and polyethylene at various cooling rates quenched in liq. Nj, and from 40 to 320 K min and different melt temperatures, 650 to 430 K, and observed that the lamellae thickness varied markedly with both parameters. Since the random coil dimensions are temperature dependent, they suggest that the crystallized material retains a memory of the melt random coil dimensions. Similarly, hydrostatic pressure applied to the melt also reduced the lamellae thickness. The authors have dismissed the effect of heat losses on crystallization as irrelevant. 

The term random coil is often used to describe the unperturbed shape of the polymer chains in both dilute solutions and in the bulk amorphous state. In dilute solutions the random coil dimensions are present under Flory 0-solvent conditions, where the polymer-solvent interactions and the excluded volume terms just cancel each other. In the bulk amorphous state the mers are surrounded entirely by identical mers, and the sum of all the interactions is zero. Considering mer-mer contacts, the interaction between two distant mers on the same chain is the same as the interaction between two mers on different chains. The same is true for longer chain segments. 

The discussion above highlights the importance of the chain end-to-end distance for ring closure. Conformation of a polymer chain in space can be represented by a random coil (Scheme 2). In dilute solutions where the polymer is in a 0-solvent and in the bulk amorphous state, the polymer can be described using the random coil dimensions. The chain end-to-end distance, r, fluctuates with time but fits well to a Gaussian distribution. 

From Figure 14, it can be observed that yield stress increases with an increase in EVA concentration in the binder. One possible explanation for such a phenomenon is by assuming the formation of an immobile absorbed layer of binder molecular chains on the iron particles surface. The formation of such an interface or mesophase layer [53] would effectively increase the apparent size of the particles and in mm increase the effective solid volume fraction of the feedstock [54]. The increase in effective solid volume fraction would in mrn lead to higher suspension yield stress by the same reasoning described in the previous section [51, 52]. The thickness of this absorbed layer corresponds to the random coil dimension for the molecular chains. The chain end-to-end distance, /i, of a polymer molecular chain ranges from 20 to 100 nm and is given by the following expression [55]. 

Lindenmeyer resolves this conflict by stating that the finding by neutron scattering of random coil dimensions does not prove the existence of highly interpenetrating random coils. 

Calculations of random coil dimensions are based on mathematical chains which can achieve much denser packing near the center of gravity than that available to real chains. 

He proposes chain folding for the amorphous liquid state which will give the random coil dimensions found by neutron scattering, i.e., a radius of gyration proportional to the square root of molecular weight. 

Because of the relatively short displacement time or length scales typically probed by NMR diffusometry, it is particularly well suited to detect anomalies in the segment displacement behavior expected on a time scale shorter than the terminal relaxation time, that is for root mean squared displacements shorter than the random-coil dimension. All models discussed above unanimously predict such anomalies (see Tables 1-3). Therefore, considering exponents of anomalous mean squared displacement laws alone does not provide decisive answers. In order to obtain a consistent and objective picture, it is rather crucial to make sure that (i) the absolute values of the mean squared segment displacement or the time-dependent diffusion coefficient are compatible with the theory, (ii) the dependence on other experimental parameters such as the molecular weight are correctly rendered, and (iii) the values of the limiting time constants are not at variance with those derived from other techniques. 

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