Inter And Intramolecular Correlations

At the phenomenological level, liquid solvents for polymers are divided into three classes, namely poor, theta (©) ,and good solvents. The solvent quality is directly related to the ability of the solvent molecules to mediate the attractive intrachain forces responsible for the polymer - solvent demixing. Poor solvents can scarcely impede the intrachain interactions and hence can dissolve only short chain (or low molecular weight Mw) polymers with a limited number of contacts between segments. The pairwise attractive and repulsive interactions compensate at the Flory (or ©) temperature which is defined as the upper critical solution temperature (UCST) of a polymer with infinite molecular weight Mw = oo[1]. The © condition corresponds to the threshold of unlimited polymer - solvent miscibility in the sense that polymer of arbitrary MW becomes miscible in any proportion with the solvent [4]. At T=© the radius of gyration Rg (©) of polymer chains is not perturbed by excluded volume effects and is also independent of the longrange critical concentration fluctuations. In the good solvent domain T > © repulsive forces between segments work to expand Rg above the unperturbed dimensions at © The expansion of polymer coils in semidilute solutions, i.e. solutions in which the volume fraction, ^ of the polymer is equal to or larger than the concentration ^ * at which coils begin to overlap, is expected to be smaller than in the semidilute regime due to screening of the monomer - monomer interactions (Fig. 1).

Figure 1. Generic phase diagram of polymer Figure 2. Variation of the parameter L in Eq.4 as a solutions [7,8]. function of x, the mole fraction of PDMS-h in solutions of (PDMS-h+PDMS-d) in CO2.

Figure 1. Generic phase diagram of polymer Figure 2. Variation of the parameter L in Eq.4 as a solutions [7,8]. function of x, the mole fraction of PDMS-h in solutions of (PDMS-h+PDMS-d) in CO2.

Semidilute polymer solutions are characterized by two distinct types of monomer - monomer correlations [6]. Intramolecular correlations between monomers which belong to the same coil are closely related to the conformation of the polymers in the solution and occur on length scales of the order of Rg. Intermolecular correlations are defined by fluctuations in the total concentration with a correlation length The dimension of polymer chains Rg and the correlation length in polymer solutions may be determined at different thermodynamic conditions using SANS combined with the high concentration isotope labeling method (see [2] and references therein). The coherent scattering intensity, I, from an incompressible mixture of identical protonated and deuterated polymer chains dissolved in a solvent is:

Subscripts "s" and "t" correspond to scattering from a single chain and total scattering, respectively and thus Ss(Q) is the single-chain structure factor which contains information on the intramolecular correlations. Similarly, the total scattering structure factor, St(Q) embodies information on the total (both intra- and intermolecular) correlations between monomer units, and is related to the correlation length of the concentration fluctuations, The structure factors are normalized so that Ss(Q=0) = 1 and St = Ss at infinite dilution. The scattering vector Q = 4nX -isin 9, where 29 is the scattering angle and X=4.75 Á is the neutron wavelength. Also, x is the mole fraction of protonated chains relative to all (i.e. protonated and deuterated) chains on a solvent-free basis, and n and N are the number density of the polymer molecules and the degree of polymerization, respectively. The prefactors K and L are:

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