Orientation averages for drawn rubber networks

Nobbs, J. H.; Bower, D. I.

doi:10.1016/0032-3861(78)90155-6

Cited by 45 publications

(20 citation statements)

References 4 publications

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“…In the case of small stretching ratios (the gaussian range), N can be decidedly replaced by Nn (the number average of N), in order to consider a distribution of segmental numbers. In the medium range of 2, the influence of a distribution of N has not yet been noticed within the model of [4]. This seems also true for a distribution of t/l-ratios in the case of the extended floating rod model.…”

Section: Introductionmentioning

confidence: 58%

“…(18). With the assumptions of Nobbs and Bower [4] the validity region of equation (5) can be extended beyond 2 = V~ by separating the fraction of fully extended chains during drawing and handle them subsequently f (2) as rigid rods (i.e. described by eq.…”

Section: Introductionmentioning

confidence: 99%

“…To get the analogue expressions for the statistical segments, it is sufficient [4] to use Treloar's approximate expression for the inverse Langevin function leading to [5] …”

Section: Introductionmentioning

confidence: 99%

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Influence of a distribution of some deformation independent parameters on the orientation coefficients of the affine model

Hennecke

1983

Colloid & Polymer Sci

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Abstract:The number N of statistical segments of a network junction and the thicknessto-length ratio (t/I) of a floating rod are deformation independent parameters which appear in approximate extensions of the affine orientation model. Within the limits of these -purely geometric -models, the influence of different distributions of N and t/l on the orientation coefficients f(2/ and J}4/is numerically calculated. In the case of a broad distribution of segment numbers, the curvature of the ]},3 vs. ;t diagrams is considerably attenuated and the ~3 values are enhanced, especially in an intermediate region of 2. A broad distribution of t/l -ratios lowers the achieved J~9 values during uniaxial stretching.

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Section: Introductionmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

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Influence of a distribution of some deformation independent parameters on the orientation coefficients of the affine model

Hennecke

1983

Colloid & Polymer Sci

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“…͑vi͒ The framework is limited to the draw ratio corresponding to bridging chains of DP 0 monomers being fully stretched. In order to predict birefringence at higher draw ratios, modifications to account for pseudoaffine deformation 16,68 are required. Care must be exercised here because our framework already considers the chains to be aligned along the stretch direction ͑i.e., they are not randomly oriented as in threedimensional networks͒.…”

Section: Discussionmentioning

confidence: 99%

“…At this elongation, the amorphous chains are fully stretched, and further elongation cannot be modeled by our current framework. Ward et al 16 and Nobbs and Bower 68 suggested a pseudoaffine deformation framework to address the deformation corresponding to amorphous chains being stretched beyond h max . In such a framework, beyond max , the deformation is only due to orientation of the chains along the stretch direction.…”

Section: A Photoelasticity Considering Strain-induced Crystallizationmentioning

confidence: 99%

Elasticity and photoelasticity relationships for polyethylene terephthalate fiber networks by molecular simulation

Nayak

Das

Nanavati

2008

The Journal of Chemical Physics

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We present a framework for the development of elasticity and photoelasticity relationships for polyethylene terephthalate fiber networks, incorporating aspects of the primary molecular structure. Semicrystalline polymeric fiber networks are modeled as sequentially arranged crystalline and amorphous regions. Rotational isomeric states-Monte Carlo simulations of amorphous chains of up to 360 bonds ͑degree of polymerization, DP= 60͒, confined between and bridging infinite impenetrable crystalline walls, have been characterized by ⍀, the probability density of the intercrystal separation h, and ⌬␤, the polarizability anisotropy. ln ⍀ and ⌬␤ have been modeled as functions of h, yielding the chain deformation relationships. The development has been extended to the fiber network to yield the photoelasticity relationships. We execute our framework by fitting to experimental stress-elongation data and employing the single fitted parameter to directly predict the birefringence-elongation behavior, without any further fitting. Incorporating the effect of strain-induced crystallization into the framework makes it physically more meaningful and yields accurate predictions of the birefringence-elongation behavior.

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Optothermal properties of fibers?20?relation between physical structure and mechanical properties of cold drawn polypropylene fibers

Fouda

1999

J. Appl. Polym. Sci.

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ABSTRACT:The structure of annealed polypropylene (PP) fibers is studied interferometrically using two-beam Pluta polarizing interference microscope connected to a device to study the draw ratio with birefringence changes dynamically. Relations of drawing changes with some optical and physical parameters are given. Evaluation of average work per chain, work per unit volume, reduction in entropy caused by elongation, and the work stored in the body as strain energy were determined. Also the resulting optical data were utilized to evaluate the orientation factor, the orientation angle, the virtual refractive index, and the number of molecules per unit volume. The value of (⌬␣/3␣ 0 ), which depends upon the molecular structure of the polymer, remains constant. Relations between the physical and optical parameters with different strains are given for these fibers. The generalized Lorentz-Lorenz equation given by de Vries is used to determine polypropylene fiber structural parameters. Comparison between Hermans optical orientation function formula and the corrected formula by de Vries are given.

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Orientation averages for drawn rubber networks

Cited by 45 publications

References 4 publications

Influence of a distribution of some deformation independent parameters on the orientation coefficients of the affine model

Influence of a distribution of some deformation independent parameters on the orientation coefficients of the affine model

Elasticity and photoelasticity relationships for polyethylene terephthalate fiber networks by molecular simulation

Optothermal properties of fibers?20?relation between physical structure and mechanical properties of cold drawn polypropylene fibers

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