Über die Gestalt fadenförmiger Moleküle in Lösungen
TL;DR: In this paper, the authors describe a kleinen Abanderungen der vorkommenden Konstanten auch fur den Fall beschrankter Drehbarkeit and fest vorgegebener bis ganz „regelloser Valenzwinkelung.
Abstract: Es werden statistische Betrachtungen angestellt betreffend die Form, welche kettenformig gebaute Molekule, welche in einer Losung (oder im Gasraum) suspendiert sind, infolge der Valenzwinkelung und der freien Drehbarkeit annehmen konnen. Die erhaltenen Beziehungen gelten mit kleinen Abanderungen der vorkommenden Konstanten auch fur den Fall beschrankter Drehbarkeit und fest vorgegebener bis ganz „regelloser“ Valenzwinkelung. Eine besonders wahrscheinliche ausere Begrenzung des „regellos“ geknauelten Fadenmolekuls ist die eines stark verbogenen Ellipsoids, dessen Achsen sich ungefahr wie 6∶2,3∶1 verhalten. Wenn beim Aufbau des Knauels das Eigenvolumen der einzelnen Teile des Fadens vernachlassigt wird, ergibt sich ein Knauelvolumen, welches proportional √Z (Z=Zahl der Kettenglieder) zunimmt, und damit eine spezifische Viskositat, welche ebenfalls proportional √Z anwachsen wurde. Die Berucksichtigung des von den einzelnen Teilen des Fadens beanspruchten Volumens ergibt aber eine Aufweitung des Knauels, welche das lineare Anwachsen der Viskositat mit der Gliederzahl Z wenigstens teilweise, vielleicht sogar ganz erklart. Versuche uber die Bildungsgeschwindigkeit von Ringen mit hoher Gliederzahl sprechen ebenfalls fur eine bedeutende Aufweitung der Knauel, verbunden mit verminderter Diffusionsgeschwindigkeit der im Innern des Knauels enthaltenen Knauelbestandteile gegeneinander. Es wird gezeigt, das die geknauelten Fadenmolekule zu einer Eigendoppelbrechung Anlas geben, in solcher Weise, das diese bei niedrigmolekularen Produkten merklich, bei hochmolekularen Produkten verschwindend klein wird.
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TL;DR: A review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena as mentioned in this paper.
Abstract: Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.
4,044 citations
Cites methods from "Über die Gestalt fadenförmiger Mole..."
...The simplest model system Kuhn, 1934 treats a polymer as a dumbbell with two beads each of hydrodynamic resistance connected by a Hookean entropic spring of stiffness kH....
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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
TL;DR: In this paper, a model for the structure of a cross-linked network, such as exists in a vulcanized rubber, which is amenable to statistical treatment, is proposed, and expressions for the structural entropy of the network, and for the entropy change on deformation.
Abstract: A model is proposed for the structure of a cross‐linked network, such as exists in a vulcanized rubber, which is amenable to statistical treatment. Expressions are derived for the structural entropy of the network, and for the entropy change on deformation. The latter is in agreement with the relationship derived by Wall and others by a different treatment.
1,963 citations
TL;DR: In this paper, the mean square radii of various branched and ringed polymer molecules were derived under the usual assumptions regarding the statistics of chain configuration, and it was shown that the number of branches or rings can be determined from light scattering measurements.
Abstract: Formulas for the mean square radii of various branched and ringed polymer molecules are developed under the usual assumptions regarding the statistics of chain configuration. For branched molecules, the mean square radii vary less rapidly with molecular weight than for strictly linear molecules, while for systems containing only rings and unbranched chains the variation is more rapid than for the linear case. These results show that in principle the quantity of branches or of rings can be determined from light‐scattering measurements.
1,466 citations
TL;DR: In this paper, the behavior of chains of very many molecules is investigated by solving a restricted random walk problem on a cubic lattice in three dimensions and a square lattice, subject to the restrictions of no crossing or doubling back.
Abstract: The behavior of chains of very many molecules is investigated by solving a restricted random walk problem on a cubic lattice in three dimensions and a square lattice in two dimensions. In the Monte Carlo calculation a large number of chains are generated at random, subject to the restrictions of no crossing or doubling back, to give the average extension of the chain 〈R2〉Av as a function of N, the number of links in the chain. A system of weights is used in order that all possible allowed chains are counted equally. Results for the true random walk problem without weights are obtained also.
938 citations