By R.B. Bird, S.V. Bronnikov, C.F. Curtiss, S.Y. Frenkel, N. Hiramatsu, K. Matsushige, H. Okabe, V.I. Vettegren

This article examines advances in polymer technological know-how, overlaying the components of statistical mechanics, deformation and ultrasonic spectroscopy.

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Extra resources for Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, DEFORMATION, ULTRASONIC SPECTROSCOPY (Advances in Polymer Science)

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6): F~. • 6(r - r:)J(p "~ - p:) ~Ju F,. 4) When this is inserted into the previous equation, we finally get the equation for the time evolution of the distribution function in the one-molecule phase space: Integration over all momenta p~, and use of the definitions in Eq. F. B. Bird and, when Eq. 13) is used, we get the equation for Wat(r~, Qat, t): -d Wat(~, Qat, t ) = - ( ~ r ~ . 7, The [[ ]]~ quantities in these last two equations have the same arguments as the distribution functions with which they are associated.

12). F. B. Bird heat-flux vector, which is: q(e) = R ' F (e)'- [[/'~ -- v i i " W,(r -- CR~, Q , t)dCdQ" = ~ j~D~F(e) --~-v ~. "~ - v]]" qJ,(r, Q ' , t)dQ ~ + ... 14) The first line of Eq. 14) is included in Table 2, and the first term of the second line in Table 1. The term q(e), when dotted into n and multiplied by dS, is the rate of work that is done as the beads diffuse under the external force that is acting on the beads. N o t e that in this term, the unit normal vector is dotted into the position vector rather than into the relative velocity vector.

10) must be carefully preserved. Formally one can include all the terms in the expansion in Eq. 11) 0 as described in Sect. 2 of DPL. 11) are the main results of this subsection; they are used repeatedly in subsequent sections. The higher terms in the Taylor series in Eq. 11) may be needed for the description of nonhomogeneous systems and wall effects. 3 A v e r a g e s Involving Functions in the Phase Space o f T w o M o l e c u l e s Only Another relevant set of average quantities involves interactions between pairs of beads belonging to different molecules.

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