Near-dilute polymers and internal modes

Light scattering spectra of random-coil polymers differ from spectra of colloidal particles random coils have observable internal modes. At small q, polymer and colloid internal modes involve distances small relative to so internal modes do not contribute to the time dependence of 5(, t). At large 5(, t) of a rigid particle reflects only center-of-mass motion, because rigid probe particles lack observable internal motions. In contrast, for large q internal modes of flexible molecules involve motions over distances comparable to and thus contribute directly to S q,t). Except at extreme dilution, interactions between polymer chains affect both polymer center-of-mass motion and polymer internal motions. 

A basis for interpreting S(q,t) of dilute random-coil polymers was offered by Pecora( 1,2,3). His model polymer had segmental motions that could be decomposed 

Here is the low-concentration hmit of s, A2 is the second virial coefficient, and M is the polymer molecular weight. The concentration dependence of Dm is driven by the competition between an osmotic term 2A2M and a hydrodynamic term ks. Except that the concentration gradients are taken to be linear rather than sinusoidal in space, Eq. 11.6 is little different from the concentration expansions for Dm of hard spheres discussed in Chapter 10. 

We turn first to studies of the q -dependence of K1 and Dm. Han and Akcasu obtained K for six dilute polystyrenes in toluene, cyclohexane, and tetrahydrofuran(l 1). For polystyrene under Theta conditions, y of Eq. 11.3 was 2.0 for qRg 0.8, while Y 3.0wasfoundfor Rg 2. Han and Akcasu compared their measurements with two theoretical models of Benmouna and Akcasu(12,13), finding that the models 

et al extracted from the relaxation rate Ti of their faster mode an internal component AP = Pi — Dq A). At smaller q, AP is independent of q. At larger q, /ST increases as a power law in q. The power-law exponent found by Ellis, et al was 2.9 in a Theta system but 3.85 in a good solvent. They explain the difference between their good-solvent value 3.85, and the y 3 previously found experimentally for polymers in good solvents, in terms of their superior data-fitting techniques(14). In particular, Eqs. 11.2 and 11.3 do not agree except in the oo limit for finite q where they differ Eq. 11.2 should be preferred. 

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