Entanglement and reversible gelation for polymers of different architectures

Abstract

Entanglement has been studied in the past mainly with flexible linear chains. Early predictions were based upon scaling theory which gave only data on exponents of power laws but no prefactors. Tests were strongly inhibited by ambiguities in the definition of the overlap concentration c*. The present study uses the thermodynamically well-defined scaling parameter X = A ₂ M _wc. Recent renormalization group theories succeeded in the derivation of an analytic expression for the osmotic modulus in terms of X. The osmotic modulus was measured by static light scattering at the scattering angle zero. Experimental data from polystyrene chains of different molecular weights and from many other linear polymers demonstrate a good agreement with theory up to values of X = 3–5. Beyond that point the osmotic modulus increases stronger than predicted. The final exponent is 1.40 ± 0.03 instead of the predicted. 1.25. Good agreement with the theoretical prediction by Carnahan and Starling is also found for impenetrable particles (spheres). As a third architecture the experimental curve for stiff chain molecules is shown for which no theory is available to date. The results can, however, be interpreted qualitatively in a consistent manner.

Many polymers show at moderately high concentrations pronounced deviations from the pure entanglement behavior. Three effects are observed: 1) a strong low-angle excess scattering is found; 2) the osmotic modulus shows a turnover and decreases again; and 3) a pronounced slow mode of motion becomes apparent. The three effects increase strongly with concentration. Finally, behavior is observed which indicates reversible gelation.