Influence of bond angle restrictions on polymer elasticity

Flory, Paul J.; Hoeve, C. A. J.; Ciferri, A.

doi:10.1002/pol.1959.1203412726

Cited by 182 publications

(40 citation statements)

References 17 publications

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“…At higher concentrations of the adsorbed substance 2 in the melt the chemical potential of mixing (39) would appear in the denominator of (53) as reduced quantity as does in (41). There follows from (53) for a sufficiently great c*…”

Section: The Lamella As a Growth Shape Caused By Activated Sorptionmentioning

confidence: 89%

Crystallization of low and high molecular materials

Kanig

1983

Colloid & Polymer Sci

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Section: The Lamella As a Growth Shape Caused By Activated Sorptionmentioning

confidence: 89%

Crystallization of low and high molecular materials

Kanig

1983

Colloid & Polymer Sci

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“…∆f e /f ∼ -0.07 (18) can be easily corrected, either with eq 17 if the thermal expansion coefficient is known or with eq 18 if not. The molecular interpretation of f e /f, based on the Gaussian network model, was made possible by the demonstration that the force-deformation relationship for random coils is universal.…”

Section: Discussionmentioning

confidence: 99%

“…The molecular interpretation of f e /f, based on the Gaussian network model, was made possible by the demonstration that the force-deformation relationship for random coils is universal. 17,18 For a Gaussian network, the force-temperature relationship at constant volume can be expressed as where 〈R 2 〉 0 is the mean-square end-to-end distance for unperturbed free chains of the network species at the test temperature. Thus, assuming no other contribution to the restoring force, eq 3 leads immediately to the result 18,19 Accordingly, the correction from values of κ obtained with eq 8 to those corresponding to the more nearly correct eq 14 is or with the typical polymeric liquids value, R ) 6 × 10 -4 K -1 , Some comparisons of κ obtained from f e /f data with those obtained from size vs temperature data from small-angle neutron scattering are shown in Table 4.…”

Section: Discussionmentioning

confidence: 99%

Thermoelasticity of Polymer Networks

Graessley

Fetters

2001

Macromolecules

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The thermoelastic properties of polymer networks are of interest owing to the information they provide on κ ) d ln〈R 2 〉0/dT, the temperature coefficient of chain dimensions of the network species. Stress-strain measurements at constant volume provide that information directly, through a determination of the energetic fraction of the restoring force fe/f. Almost always, however, the measurements are conducted under constant-pressure conditions, and a correction is applied to account for the effect of volume change. The correction formula commonly used is known to be inaccurate, and here we present a new one that predicts the volume change and κ quite satisfactorily. Some comparisons of κ obtained from thermoelastic measurements, from small-angle neutron scattering, and from intrinsic viscosity data in athermal solvents are given.

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“…Here ν is the number of chains in the network of volume V , f is the functionality of the cross-links, and k is Boltzmann's constant. Using somewhat convoluted reasoning, [16,17] the ratio r 2 i / r 2 0 was inserted into the theoretical Young's modulus in the 1950s. The numerator in this expression is the value of the mean-square end-to-end distance of the average network chain in a reference state and the denominator is the similar quantity for the free unperturbed chain at temperature T .…”

mentioning

confidence: 99%

Rubber elasticity: Solution of the James-Guth model

Eichinger

2015

Phys. Rev. E

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The solution of the many-body statistical mechanical theory of elasticity formulated by James and Guth in the 1940s is presented. The remarkable aspect of the solution is that it gives an elastic free energy that is essentially equivalent to that developed by Flory over a period of several decades. IntroductionRubber elasticity is the first bulk property of polymers that yielded to theoretical analysis. The identification of the relation between the Gaussian distribution of the end-to-end distance of a random walk with the quadratic strain dependence of phenomenological stress-strain theory was key to this success. Of course, the underlying physics that makes this connection inevitable and viable is that a polymer chain in the bulk amorphous melt phase is unperturbed by intermolecular interactions.[1] This fact allows one to realize the force that a chain delivers to the cross-links that terminate it, and which tie it to other chains in the three-dimensional space filling random network, is determined solely by the chain's intramolecular potential. While high elasticity theory was the first to successfully predict bulk polymeric materials behavior, it remains one of the few, and perhaps the only, analytical theory of polymers to do so, computer simulations notwithstanding. This is reason enough to justify efforts to improve upon the theory. Given the history of the subject, rubber elasticity is one of the first soft materials to admit an atom-based theoretical analysis.The extent to which the elastic equation of state is determined by the interaction between network connectivity and chain statistics has been a point of contention from the earliest days of polymer theory. The theory initiated by Kuhn,[2] elaborated by Wall [3,4]and Flory and Rehner, [5,6] and discussed extensively in treatises, [1,7,8,9,10] is constructed by adding together the contributions to the stress from independent chains. This requires the so-called affine assumptionthe displacement of the ends of an average network chain is congruent to the macroscopic strain.This theory is relatively easy to execute, but by treating the chains as independent it incurred the criticism of James and Guth. [11,12,13] In their many-body theory the individual chains obey Gaussian statistics, just as in the independent chain theory, but James and Guth emphasized the fact that in tying the chains together with cross-links they become an indissoluble whole that must be treated as a single entity. This insight carried a heavy price -their many-body formulation was too difficult to be convincingly solved. To make progress, James and Guth [11] introduced the

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Influence of bond angle restrictions on polymer elasticity

Cited by 182 publications

References 17 publications

Crystallization of low and high molecular materials

Crystallization of low and high molecular materials

Thermoelasticity of Polymer Networks

Rubber elasticity: Solution of the James-Guth model

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