The model parameters of helical wormlike chains

Abstract

1613gether with the values of the parameters EkT/Vo, K and { that characterize networks A and B, respectively (see text), one may evaluate x by solution of eq A-5. Results are given in Table 11.Equation A-10 in conjunction with A-7 may be solved iteratively for u i , given the network parameters, the value of x, and the extension ratio a, relative to the system swollen to equilibrium under isotropic conditions. The reduced force that would obtain if further swelling did not occur as a result of the elongation a, may be calculated according to eq 5 and eq 1-54 of the preceding paper, with VIVO therein equated to l l v , and with AI, and A, determined by a, and VIVO according to eq 1-23. Repetition of the calculation with V'l Vo = 1 / v i , a , ' given by eq A-8, A, given by eq A-7, and All the same as above, yields the calculated reduced stress for the semiopen system at fixed length. The difference between the latter calculation and the former one gives the correction that should be subtracted from the observed reduced stress. Results shown in Figure 3 were corrected in this manner.where A 0 is defined by eq 13 and the principal axes in the order of the diagonal elements are taken parallel to O...O, perpendicular thereto in the plane defined by the Si-0 bonds, and parallel to CHg..CH3, respectively. The anisotropy tensor for the PDMS chain as a whole in any conformation is a linear combination of the group tensors so defined, additivity of these tensors for individual units being assumed. (34) Flory, P. J.; Rehner, J., Jr. , J a p a n . Received J a n u a r y 11, 1983 ABSTRACT T h e model parameters of the helical wormlike chains corresponding to various real polymer chains, both flexible and stiff, are determined from a comparison with the rotational isomeric state models or from an analysis of experimental data for equilibrium and transport properties. Then some general aspects of the behavior of the model parameters are discussed. This serves to guess their probable ranges for a given new polymer. T h e results are useful in a study of the chain dynamics recently initiated on the basis of the discrete helical wormlike chain. 1982, 15, 606.ABSTRACT: Expansion is considered for finite, regular polymethylene stars perturbed by the excluded volume effect. A rotational isomeric state model is used for the chain statistics. The number of bonds in each branch ranges u p to 10 240, and the functionality of the branch point ranges u p to 20. T h e form of the calculation employed here provides a lower bound for the expansion. If the number, n, of bonds in the polymers is held constant, expansion is found to decrease with increasing branch point functionality. Two factors dictate the manner in which finite stars approach the limiting behavior expected for very large stars. These two factors are the chain length dependence a t small n of the characteristic ratio and of (a5 -~? ) / n~/~. In very good solvents these two factors reinforce one another, but they tend to cancel in solvents in which polymer expansion is smal...

Conformation of Amylose and Excluded-Volume Effects on Its Chain Dimensions

“…Yamakawa and coworkers 26 found that the Monte Carlo data of Jordan et al 8 for the persistence vector and <R 2 ) (without excluded volume) are accurately reproduced by HW theoretical curves (for an appropriately chosen set of parameters) over the entire possible range of x ( 2) when the HW chain contour is taken along the helical sequence. The chain contour so chosen corresponds to a small length scale of one glucose residue.…”

“…The chain contour so chosen corresponds to a small length scale of one glucose residue. On the other hand, if the contour is taken along the helix axis, i.e., if a large length scale of a few glucose units (relevant to analysis of data for steady-state transport coefficients) 26 is adopted, the HW thoretical curve for <R 2 ) deviates downward from the Monte Carlo data at x smaller than 10 (see Figure 9 of ref 26). The analysis of [11] made by Nakanishi et al indeed refers to such a large length scale of two to four glucose residues.…”

Fluorescence Depolarization Study on Local Motions of Anthracene-Labeled Poly(alkyl methacrylate)s in Dilute Solutions and Evaluation of Their Chain Stiffness

“…However, it can be said that these three polymers of the adjusted racemo fractions essentially have the helical nature. The values of Ko and To for these polymers indicate that these three polymers belong to the domain I defined in ref 27.…”

“…In addition, the tendency to take the tt conformation leads to the helical nature for the syndiotactic chains. The values of Ko and To show that the syndiotactic PMMA and syndiotactic PEMA belong to the domain I defined in ref 27, which corresponds to a region for the typical HW chain. As for the racemo diad, we can see also qualitatively from the partition functions that the tendency of taking the tt conformation is slightly stronger for MMA than for EMA, i.e., Ztt,r/zgt,r(MMA) > Ztt,r/zgt,r(EMA), The relatively high probability of taking the tt conformation for the racemo diad of MMA is due to the instability of the gt state compared to the tt state, However, the reason for this is not clear at present.…”

“…The parameters for various kinds of polymers have been determined by this method. 27 Recently, an attempt of experimental determination has been done,28 and the obtained parameters are considered to be more reliable than those estimated from the comparison between the RIS and the HW theories. Indeed, the calculated characteristic ratios based on the RIS model do not always agree with the experimental data, so, we adjusted the energy parameters.…”