Critical crossover functions for simple fluids: non-analytical scaling determination of the ising-like crossover paramater
| Autor: | Carole Lecoutre, Samuel Marre, Yves Garrabos, Bernard LeNeindre |
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| Přispěvatelé: | Institut de Chimie de la Matière Condensée de Bordeaux (ICMCB), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université de Bordeaux (UB), Laboratoire des Sciences des Procédés et des Matériaux (LSPM), Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Cité (USPC)-Institut Galilée-Université Paris 13 (UP13) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Mathematical analysis
Crossover Critical crossover function Crossover parameter Critical isochore Xenon Thermodynamics Statistical and Nonlinear Physics [CHIM.MATE]Chemical Sciences/Material chemistry 01 natural sciences 010305 fluids & plasmas Renormalization Critical point (thermodynamics) 0103 physical sciences Compressibility Ising model Uniqueness 010306 general physics Scaling Mathematical Physics Mathematics Dimensionless quantity |
| Zdroj: | Journal of Statistical Physics Journal of Statistical Physics, Springer Verlag, 2016, 164 (3), pp.575-615. ⟨10.1007/s10955-016-1554-4⟩ |
| ISSN: | 0022-4715 1572-9613 |
| DOI: | 10.1007/s10955-016-1554-4⟩ |
| Popis: | A non-analytical scaling determination of the Ising-like crossover parameter is proposed considering the critical isochore of a simple fluid at finite distance from its critical temperature. The mean crossover functions, estimated from the bounded results of the massive renormalization scheme in field theory applied to the $$\left( \Phi ^{2}\right) _{d}^{2}\left( n\right) $$ model in three dimensions ( $$d=3$$ ) and scalar order parameter ( $$n=1$$ ), are used to formulate the corresponding scaling equations valid in two well-defined temperature ranges from the critical temperature. The validity range and the Ising-like nature of the corresponding crossover description are discussed in terms of a single Ising-like scale factor characterizing the critical isochore. The asymptotic value of this scale factor can be predicted within the Ising-like preasymptotic domain. Unfortunately, the absence of precise experimental data in such a close vicinity of the critical point leads the direct testing impossible. A contrario, from our scaling equations and the use of precise measurements performed at finite distance from the critical point, its local value can be estimated beyond the Ising-like preasymptotic domain. This non-analytical scaling determination only needs to make reference to the universal features estimated from the mean crossover functions and to introduce a single master dimensionless length common to all the simple fluids. This latter parameter guaranties the uniqueness of the physical length unit used for the theoretical crossover functions and the fluid singular properties when the generalized critical coordinates of the vapor-liquid critical point of each fluid are known. Xenon case along its critical isochore is considered as a typical example to demonstrate the singleness of the Ising-like crossover parameter. With the measurements at finite temperature range of the effective singular behaviors of the isothermal compressibility in the homogeneous domain, and the vapor-liquid coexisting densities in the non homogeneous domain, our scaling equations provide the local estimate of this crossover parameter as a function of the temperature distance from the critical temperature. Our results compare favorably with the single asymptotic value calculated only using four critical coordinates of xenon. |
| Databáze: | OpenAIRE |
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