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, masking the components of statistical mechanics, deformation and ultrasonic spectroscopy.
Read or Download Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, DEFORMATION, ULTRASONIC SPECTROSCOPY (Advances in Polymer Science) PDF
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Extra resources for Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, DEFORMATION, ULTRASONIC SPECTROSCOPY (Advances in Polymer Science)
11), will be referred to as the assumption of equilibration in momentum space. That is, we assume that the distribution function in momentum space for a particular bead is the same as that for a bead in a system at equilibrium at the fluid temperature surrounding the bead in question. By allowing for the variation of the temperature over the full extent of a molecule, we are then in a position to study non-isothermal problems--that is, situations in which a = V In T is nonzero. We point out parenthetically that in the kinetic theory of dilute gases it is just the deviation from the Maxwellian velocity distribution that is of primary interest in the evaluation of the transport properties.
Next, we perform the integrations over all the x-variables and use the definition for the doublet distribution function given in Eq. 15) We then integrate over all momenta making use of Eq. 16) In going from Eq. 12) to this expression, all the variables have been integrated out, except for those involving two molecules; the integration over the momenta has been indicated symbolically by use of the double-bracket notation. Note that in Eq. 16), when • and ~ are the same, C~" describes interactions between beads of two different molecules of species ~.
F~. ~ZVp - V. _~. _ ~ , . - ~llv, q~, t ) a ~ a Q ~. v(r, t) = - (V. q(~)) - (V. In(*). 17) which serves to define the intramolecular potential contribution q(~) to the heat flux vector; the corresponding contribution to the stress tensor ~ ) was defined in Eq. 15). The first term after the third equals sign is zero, and the remaining term is rewritten by adding and subtracting v(r, t). '=-- v)]] ~ W~(r- ,R~, Q', t)d,dQ ~ a~'Cp d d O = I ~ j['u~ - - , ~ -r-~~. 18) The first expression is given in Table 2, and the first term in the Taylor expansion appears in Table 1.
Advances In Polymer Science Vol 125: STATISTICAL MECHANICS, DEFORMATION, ULTRASONIC SPECTROSCOPY (Advances in Polymer Science) by R.B. Bird, S.V. Bronnikov, C.F. Curtiss, S.Y. Frenkel, N. Hiramatsu, K. Matsushige, H. Okabe, V.I. Vettegren