Unperturbed conditions

A polystyrene sample of molecular weight 10 shows an rms end-to-end distance under unperturbed conditions equal to 735 A. In polystyrene Mq = 104 and the length of the carbon-carbon bond along the backbone is 0.154 nm. Use these data to verify the numbers given for this polymer in Table 1.6. 

It is however possible to find conditions, called unperturbed or theta conditions (because for each polymer-solvent pair they correspond to a well-defined temperature called d temperature) in which a tends to 1 and the mean-square distance reduces to Q. In 6 conditions well-separated chain segments experience neither attraction nor repulsion. In other words, there are no long-range interactions and the conformational statistics of the macromolecule may be derived from the energy of interaction between neighboring monomer units. For a high molecular weight chain in unperturbed conditions there is a simple relationship between the mean-square end-to-end distance < > and the mean-... 

The conformational properties of trimer molecules modeling PVDB (S 100) and PVDF are analyzed by the molecular mechanics method of Boyd and Kesner [J. Chem. Phys. 1980, 72, 21791, which takes into account both steric and electrostatic energy. Total conformational energies are used to calculate a set of intramolecular interaction energies that, by means of the RIS model, allowed estimation of the characteristic ratios and dipole moment ratios of PVDB and PVDF under unperturbed conditions. 

From Table 8-1 it is evident that the protein provides a catalytic effect lowering the barriers by about 10 kJ/mol with respect to the unperturbed condition. Moreover, the free-energy barriers at the two temperatures are, within the noise, almost identical suggesting low activation entropies. 

Equations (3.125) and (3.126) together with Eq. (3.120) show that the expansion factor depends significantly on two molecular parameters. The first is molecular weight. At conditions far removed from unperturbed conditions, a increases without limit as the square root of the molecular weight. The second parameter determining a is A2, which chracterizes polymer-solvent interaction. Under theta conditions at which z becomes zero, a becomes unity. Physical measurements made under these conditions will reflect the characteristics of the unperturbed molecule. The overall dimensions of such a molecule will be determined solely by bond lengths... 

The advantage of such plots is that all the members of a series (excepting, perhaps, the first few, for which /z in the unperturbed condition would not have settled down to a constant value anyway) can be included. The plot is a means of converting information which, at first sight, differs from one member to the next because the energy intervals are ever decreasing, into strictly comparable data in which the doubly-periodic (i.e. periodic in both i i and V2) nature of Rydberg states is properly displayed. 

SAXS has been used to study the morphology of polymer blends in the solid state [Khambatta, 1976 Russel, 1979 Russel and Stein, 1982, 1983]. Eor example, in the interlameUar regions of PCL/ PVC blend the system is miscible on a molecular scale. Addition of PVC impeded crystallization of PCL. At high PVC concentration PCL remained in solution. The radius of gyration was larger than that under unperturbed conditions, in spite of the fact that at the same time the second virial coefficient, A, was virtually zero. SAXS was used... 

For good solvents Xi,2 is much smaller than 0.5. For Xi,2 = 0-5 it is supposed that the attractive and repulsive forces between the polymer and the solvent are completely compensated and the polymer chains are considered to be under unperturbed conditions (ideal chains) [35]. 

The theta temperatore is a well-defined state of the polymer solution at which the excluded volume effects are eliminated and the polymCT coil is in an unperturbed condition (see Chapter 10). Above the theta tempraature, expansion of the coil takes place, caused by interactions with the solvrait, whereas below 0 the polymCT segments attract one another, the excluded volume is negative, the coils tend to collapse, and eventual phase separation occurs. 

The expansion factor, a, is used to characterize the size of polymer coils when they are not under unperturbed conditions—that is, to measure the effects of the polymer s environment on its overall dimensions. To do so, a is defined as the ratio of the root mean squared end-to-end vector relative to its value in the unperturbed state according to the following equation ... 

The use of continuous distributions of the solvent, and of its response functions, does not eliminate the fact that the solvent is made up of discrete molecules, each one composed of a given set of nuclei held together by the electrons. These molecules clearly can translate, rotate, vibrate, and are subject to changes in their electronic charge distribution. In the previous sections it has been shown that, when the solvent suffers an external field, such as that produced by a molecular solute, its unperturbed condition is troubled, and a polarization, P i.e., a dipole density, is switched on. The role of the external field which gives rise to this polarization can be summed up in three main effects ... 

The expressions (4.62) and (4.53) show that the radius of gyration of a chain subjected to the phenomenon of excluded volume is proportional to whereas that of an unperturbed chain is proportional to X. For example, the average dimension of a chain with a degree of polymerization of X = 1000 is expected to grow by a factor of 2, and its volume under unperturbed conditions is expected to increase by a factor of 2 = 8. 

Typical physical property-area correlations obtained in these studies are shown in Figs. 1 and 2. In Figure iP the distance between chain entanglements, (in terms of the number of chain atoms) is plotted as a function of area. In Figure 2p the physical property plotted is the chain stiffness factor, cr, where = f f is the ratio of the mean-square end-to-end distance of the chain in the unperturbed condition to that which the same chain would have if it were a "freely-rotating" chain. 

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