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Equilibrium and Quasiequilibrium Solutions to the LG Model

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Interaction of Gases with Surfaces

Part of the book series: Lecture Notes in Physics Monographs ((LNPMGR,volume 25))

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Abstract

To find the distribution function θ 0 c (α) satisfying the conditions (8.2.24)–(8.2.27) one needs more detailed information on quantities r u , q u . This problem cannot be solved in a general form. Therefore let us consider first of all the case of structureless particles, when θ 0 c (α) should be replaced with θ0(α) and the condition (8.2.27) is absent. One can readily prove that the quasiequilibrium solution meeting (8.2.24) can be presented in the following way

$$ \begin{gathered} \theta ^0 \left( {\alpha ,t} \right) = \theta _R \left( {\alpha ,\mu _R \left( {\beta ,t} \right)} \right) = \left[ {1 + \zeta \left( {\theta _R } \right)\exp \left( {\frac{{\varepsilon \left( \alpha \right) - \mu _R \left( {\beta ,t} \right)}} {{k_B T}}} \right)} \right]^{ - 1} , \hfill \\ \zeta \left( {\theta _R } \right) = \left\{ \begin{gathered} 1, \beta = 1,2 \hfill \\ \theta _{_R }^{ - 1} (\alpha _ - ), \beta \geqslant 3 \hfill \\ \end{gathered} \right., \hfill \\ \alpha _ - = (\beta - 1,R), \alpha = (\beta ,R), \hfill \\ \end{gathered} $$
(9.1.1)

where μ R (β,t) is an arbitrary function having a sense of the chemical potential of the β-th layer, and T = Ts here and below unless otherwise specified.

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© 1995 Springer-Verlag Berlin Heidelberg

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(1995). Equilibrium and Quasiequilibrium Solutions to the LG Model. In: Interaction of Gases with Surfaces. Lecture Notes in Physics Monographs, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49107-1_9

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  • DOI: https://doi.org/10.1007/978-3-540-49107-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58802-3

  • Online ISBN: 978-3-540-49107-1

  • eBook Packages: Springer Book Archive

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