Statistical mechanics of helical worm-like chains. XV. Excluded-volume effects

Abstract

The expansion factors for the mean-square end-to-end distance and radius of gyration are studied for the helical worm-like (HW) chain with the excluded-volume effects incorporated in the Yamakawa–Stockmayer scheme. In this scheme, approximate closed expressions for them are expressed in terms of the excluded-volume parameter z and the first-order perturbation coefficient K(L) as a function of the total contour length L of the chain. The ring-closure probabilities necessary for the evaluation of K(L) are evaluated by a slight modification of the method previously developed for the Kratky–Porod (KP) worm-like chain. The actual evaluation is carried out for the values of the HW model parameters in their limited ranges, and also for the KP chain. It is then numerically shown that K(L) for the HW chain is approximately equal to that for the KP chain. From a simple analysis, this conclusion may be expected to be generally correct, so that the expansion factors for the HW chain may be expressed in terms of the simple K(L) for the KP chain. The derived closed expressions for them may be regarded as valid for any ordinary flexible chains of arbitrary length.

Chain Stiffness and Excluded-Volume Effects in Polyelectrolyte Solutions: Characterization of Sodium Poly(2-acrylamido-2-methylpropanesulfonate) in Aqueous Sodium Chloride

“…The differences were at most a few %; note that ½ 0 is insensitive to q (or q app ) for very short chains, for which excluded-volume effects are negligible. At 0.5 M, q app appreciably decreases only for low M and the effect on [] is insignificant throughout the entire C and the theoretical curves computed from the theory of Yoshizaki et al 23 for unperturbed wormlike touched-bead chains and the QTP theory [12][13][14] (eqs 1-6) for excluded-volume effects. For clarity, the theoretical values (discrete for low molecular weights) at the respective salt concentrations are represented by continuous solid lines and those for one and two beads are connected by dashed straight lines.…”

“…We analyze the viscosity data in Figure 6 by a combination of Yoshizaki et al's theory 23 for the intrinsic viscosity ½ 0 of an unperturbed wormlike touchedbead chain and the QTP theory [12][13][14] for the viscosity expansion factor . The former theory contains three parameters, the (total) persistence length q, the contour length L, and the bead diameter d; L is related to the molecular weight M by M=M L , with M L being the molar mass per unit contour length of the chain.…”

“…[5][6][7][8] The major problem in the estimation of q el is that excluded-volume and stiffness effects can hardly be separated for those polymers without resort to a relevant excluded-volume theory. In previous studies, [5][6][7][8][9][10][11] we utilized the quasi-two-parameter (QTP) theory (the Yamakawa-Stockmayer-Shimada theory) [12][13][14] for the wormlike chain 15 or, more generally, the helical wormlike chain 14 to estimate these effects in aqueous NaCl solutions of sodium hyaluronate and sodium poly(styrenesulfonate) (Na PSS). Except for some details, the QTP scheme satisfactorily explained the molecular weight dependence of intrinsic viscosity [] and mean-square radius of gyration hS 2 i for the two polyelectrolytes at fixed salt concentrations C s higher than 10 À2 M. On the other hand, the available polyelectrolyte theories [1][2][3][4]16 failed to describe the C s dependence of the estimated q el and excluded-volume strength, though the degree of disagreement appeared to depend on the intrinsic chain stiffness.…”

Fine characterization of oligomers and polymers in dilute solution

“…The conventional theory of the excluded-volume effect, i.e., the two-parameter (TP) theory [10] based on the Gaussian chain model, has been confirmed to be valid only in a restricted range of extremely large M where effects of chain stiffness on the excludedvolume effect is not important. On the other hand, the theory [1,[21][22][23] based on the HW model, which takes account of both effects of excluded-volume and chain stiffness, may be valid over a wide range of M including the oligomer region. Within the framework of the HW theory, all the expansion factors (intramolecular excluded-volume effect) including a S may be described by the quasi-twoparameter (QTP) theory, which claims that they are ARTICLE IN PRESS and 0 in the limits of lL !…”

Second and third virial coefficients of low-molecular-weight polystyrene with a benzyl end in toluene

“…The first term on the right-hand side of Equation (11) where K(lL) is a known function. 3,22 The second term on the right-hand side of Equation (11) may be expressed as 12 …”