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Journal ArticleDOI

A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers

01 Jul 1953-Journal of Chemical Physics (American Institute of Physics)-Vol. 21, Iss: 7, pp 1272-1280
TL;DR: In this paper, the necessary coordination of the motions of different parts of a polymer molecule is made the basis of a theory of the linear viscoelastic properties of dilute solutions of coiling polymers.
Abstract: The necessary coordination of the motions of different parts of a polymer molecule is made the basis of a theory of the linear viscoelastic properties of dilute solutions of coiling polymers. This is accomplished by use of the concept of the submolecule, a portion of polymer chain long enough for the separation of its ends to approximate a Gaussian probability distribution. The configuration of a submolecule is specified in terms of the vector which corresponds to its end‐to‐end separation. The configuration of a molecule which contains N submolecules is described by the corresponding set of N vectors. The action of a velocity gradient disturbs the distribution of configurations of the polymer molecules away from its equilibrium form, storing free energy in the system. The coordinated thermal motions of the segments cause the configurations to drift toward their equilibrium distribution. The coordination is taken into account by the mathematical requirement that motions of the atom which joins two submolecules change the configurations of both submolecules. By means of an orthogonal transformation of coordinates, the coordination of all the motions of the parts of a molecule is resolved into a series of modes. Each mode has a characteristic relaxation time. The theory produces equations by means of which the relaxation times, the components of the complex viscosity, and the components of the complex rigidity can be calculated from the steady flowviscosities of the solution and the solvent, the molecular weight and concentration of the polymer, and the absolute temperature. Limitations of the theory may arise from the exclusion from consideration of (1) very rapid relaxation processes involving segments shorter than the submolecule and (2) the obstruction of the motion of a segment by other segments with which it happens to be in contact. Another possible cause of disagreement between the theory and experimental data is the polydispersity of any actual polymer; this factor is important because the calculated relaxation times increase rapidly with increasing molecular weight.

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Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors studied possible motions for one polymer molecule P performing wormlike displacements inside a strongly cross-linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: the only motions allowed for the chain are associated with the displacement of certain "defects" along the chain.
Abstract: We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: The only motions allowed for the chain are associated with the displacement of certain “defects” along the chain. The main conclusions derived from this model are the following:(a) There are two characteristic times for the chain motion: One of them (Td) is the equilibration time for the defect concentration, and is proportional to M2. The other time (Tr) is the time required for complete renewal of the chain conformation, and is proportional to M3.(b) The over‐all mobility and diffusion coefficients of the chain P are proportional to M−2.(c) At times t < Tr the mean square displacement of one monomer of P increases only like 〈(rt − r0)2〉 = const t1/4.These results may also turn out to be useful for the (more difficult) problem of entangle...

3,467 citations

Journal ArticleDOI
TL;DR: In this article, an extensive molecular-dynamics simulation for a bead spring model of a melt of linear polymers is presented, where the number of monomers N covers the range from N=5 to N=400.
Abstract: We present an extensive molecular‐dynamics simulation for a bead spring model of a melt of linear polymers. The number of monomers N covers the range from N=5 to N=400. Since the entanglement length Ne is found to be approximately 35, our chains cover the crossover from the nonentangled to the entangled regime. The Rouse model provides an excellent description for short chains N

3,232 citations

Book
01 Jan 1971
TL;DR: A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations can be found in this article, which provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers and other fields.
Abstract: A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations. This updated edition provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers, breaking phenomena, and other fields.

2,335 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the problem of diffusing a chain molecule diffusing in a viscous fluid under the influence of external forces or currents, and calculated the viscosity, birefringence of flow, and dielectric and tensile relaxation behavior explicitly.
Abstract: The problem of the motions of a chain molecule diffusing in a viscous fluid under the influence of external forces or currents is considered for a particular model. This model is a chain of beads connected by ideal springs. Hydrodynamic interaction between the beads is introduced in the approximate form due to Kirkwood and Riseman. It is possible to solve this problem exactly with the use of a transformation to a set of normal coordinates. The viscosity, birefringence of flow, and dielectric and tensile relaxation behavior are calculated explicitly. The intrinsic viscosity in steady flow is somewhat different from the Kirkwood‐Riseman result, and there is no change of viscosity with shear rate. The spectrum of relaxation times is similar to that found by Rouse and by F. Bueche, but has its maximum at a lower frequency than those obtained by Kuhn and Kuhn and by Kirkwood and Fuoss in other ways.

2,110 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce a picture of a boson superfluid and show how superfluidity and Bose condensation manifest themselves, showing the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution.
Abstract: One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

1,908 citations

References
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Book
01 Jan 1951

1,320 citations

Journal ArticleDOI
TL;DR: Piezoelectric crystals and their application to ultrasonics were discussed in this paper, where the authors proposed a method for the extraction of the ultrasonic properties of these crystals.
Abstract: Piezoelectric crystals and their application to ultrasonics , Piezoelectric crystals and their application to ultrasonics , دانشگاه تهران

1,057 citations

Book
01 Jan 1943

913 citations