Excluded volume effects and binary cluster integrals in dilute polymer solutions

Abstract

Recent advances in the theory of dilute polymer solutions are critically summarized. The following topics are discussed: theory of the excluded volume effect, including perturbation theory, the asymptotic solution, and approximate treatments: the second virial coefficient: the theory of intrinsic viscosity. especially perturbation theory: comparison of theory with experiment using data recently obtained for monodisperse polystyrenes: methods of determining the binary cluster integral: and simple analysis of the binary cluster integral by a cell-theory approach. INTRODUCTIONThe statistical mechanics of polymer solutions has been for many years one of the active lields of polymer science because of its close relation to molecular characterization. Specifically, since the concept of the excluded volume effect in a polymer chain was introduced by Flory"2 in 1949, there have been a number of significant advances in the study of this effect and the related equilibrium and nonequilibrium properties of dilute polymer solutions. These advances, made during the last two decades, have delineated

Solution properties of ultrahigh molecular weight polymers. 12. Systematic error sources affecting the discussion of the excluded volume effect

“…The mentioned papers showed that plasma-induced polymerization yields macromolecular compounds possessing some special properties as compared to usual length polymers, namely (a) low molecular weight and (for copolymers) compositional heterogeneity, (b) less visible and pronounced conformational changes as a function of temperature and solvent nature, (c) an increased rigidity of the macromolecular chains in dilute solution, as shown by the established relations between the radii of gyration, the second virial coefficients and/or the intrinsic viscosities and the molecular weights, and (d) for high values of the expansion factor (a: > 4 ) , from the theories permitting the discussion of the interpenetration function y ( Z ) , the experimental data are in good agreement with the KURATA-YAMAl) Part 11 : Polymer, in press KAWA theory [13] and with the new theory of DOUGLAS and FREED [14]. One has t o mention also that up to the synthesis of such ultrahigh molecular weight polymers no experimental data on synthetic polymers were available to interpret the asymptotic solution of the interpenetration function y ( Z ) for very high values of the excluded volume parameter Z .…”

“…The interpenetration function y ( Z ) can be determined from different theoretical dependences (original FLORY theory (F, o), modified FLORY theory (F, m), KURATA-YAMAKAWA theory (K-Y), renormalized group theory of DOUQLAS and FREED (RTP) [6,8,13,141) with the expansion factor a, = (S2)1/2/(So2)1/2 (where (SO2)lI2 is the unperturbed root-mean-square radius of gyration) or As mentioned, the experimental errors can be translated to different thermodynamic parameters. Starting from an error of &9% (E,) and from an error of f5.5% ((S2)1/2) errors of ill% and &33% are obtained for ag and ag3, respectively.…”

A picture of dilute solution behavior of polymers through polyelectrolyte simulation

“…This is consistent with the well-known experimental results 6,14 and also the previous finding that the values of β per repeat unit (bead in the chain) are remarkably smaller than those for the isolated monomer (bead). 15 Note also that B 0 /l for the sphere is appreciably larger than that for the cylinder with d = d b , as seen from Eqs. (27) and (30) (compare, for instance, the dotted curve with d b /l = 1 with the upper solid curve).…”

“…13 They are one or two orders of magnitude smaller than those calculated for an isolated single segment (bead) using the Debye-Hückel (DH) potential, as was shown long ago by Nagasawa and co-workers. 6,14 At about the same time, it was pointed out that a similar difference between the two values of β occurs even in the case of nonionic polymers having short-range potentials between segments, 15 and subsequently, it was explicitly shown by MC simulations. 3 Such differences may be regarded as arising from the fact that the effective segment (bead) size is in fact nearly equal to or larger than the bond length between the adjacent ones, while strictly (apart from the chain length dependence), the TP theory is valid for the limiting case in which the former is so small compared to the latter that the interaction between (effective) beads is not almost affected by their neighbors.…”

A Monte Carlo study of effects of chain stiffness and chain ends on dilute solution behavior of polymers. I. Gyration-radius expansion factor

“…This is consistent with the previous finding that the values of the binary cluster integral per repeat unit ͑monomer͒ are one order of magnitude smaller than those for the isolated monomer. 24 The value of ␤* in the chain may be considered to come close to that for an isolated single bead as n is decreased to 1. This suggests that the effects of chain ends on A 2 may probably exist even for those polymer chains which have end units almost identical with intermediate ones in chemical structure ͑without a catalyst fragment at one end͒.…”