1
|
Cerdeiriña CA, Orkoulas G, Fisher ME. Soluble Model Fluids with Complete Scaling and Yang-Yang Features. PHYSICAL REVIEW LETTERS 2016; 116:040601. [PMID: 26871316 DOI: 10.1103/physrevlett.116.040601] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2015] [Indexed: 06/05/2023]
Abstract
Yang-Yang (YY) and singular diameter critical anomalies arise in exactly soluble compressible cell gas (CCG) models that obey complete scaling with pressure mixing. Thus, on the critical isochore ρ=ρ(c), C(μ)≔-Td(2)μ/dT(2) diverges as |t|^(-α) when t∝T-T(c)→0^(-) while ρ(d)-ρ(c)∼|t|^(2β) where ρ(d)(T)=1/2[ρ(liq)+ρ(gas)]. When the discrete local CCG cell volumes fluctuate freely, the YY ratio R(μ)=C(μ)/C(V) may take any value -∞<R(μ)<1/2 but "anticorrelated" free volumes are needed for R(μ)>0. More general decorated CCGs, including "hydrogen bonding" water models, illuminate energy-volume coupling as relevant to R(μ).
Collapse
Affiliation(s)
- Claudio A Cerdeiriña
- Departamento de Física Aplicada, Universidad de Vigo-Campus del Agua, Ourense 32004, Spain
| | | | - Michael E Fisher
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|
2
|
Yin T, Liu S, Xie J, Shen W. Asymmetric criticality of the osmotic compressibility in binary mixtures. J Chem Phys 2013; 138:024504. [PMID: 23320701 DOI: 10.1063/1.4770750] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Heat capacities in the critical and the non-critical regions for {benzonitrile + tridecane} and {benzonitrile + pentadecane}, and light scattering for {benzonitrile + undecane}, {benzonitrile + dodecane}, {benzonitrile + tridecane}, {benzonitrile + tetradecane}, {benzonitrile + pentadecane}, and {benzonitrile + hexadecane} in the critical two-phase region were measured. Light scattering measurements confirmed the existence of the asymmetry for the osmotic compressibility while no such asymmetry was observed for the correlation length. An analysis of the osmotic compressibility asymmetry suggested the dominance of the singular term |ΔT[circumflex]|(β), which supports the complete scaling theory. The consistency of the complete scaling theory in descriptions of different asymmetry behaviors was also discussed. Moreover, it was found that the contribution of the heat capacity-related term is also important in describing the asymmetry of the osmotic compressibility as it was observed in studies of the diameters of the coexistence curves.
Collapse
Affiliation(s)
- Tianxiang Yin
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | | | | | | |
Collapse
|
3
|
Bertrand CE, Nicoll JF, Anisimov MA. Comparison of complete scaling and a field-theoretic treatment of asymmetric fluid criticality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031131. [PMID: 22587062 DOI: 10.1103/physreve.85.031131] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2012] [Indexed: 05/31/2023]
Abstract
We investigate the connection between the theory of complete scaling and a field-theoretic (FT) treatment of asymmetric fluid criticality. To facilitate the comparison, we develop an equation of state from a simplified form of the complete scaling transformations and systematically compare this equation of state with the equation of state generated by a FT treatment of an asymmetric Landau-Ginzburg-Wilson Hamiltonian. We find, with care in interpretation, that these two approaches may be read as equivalent up to terms involving an independent higher-order asymmetric correction-to-scaling exponent.
Collapse
Affiliation(s)
- C E Bertrand
- Institute for Physical Science & Technology, and Department of Chemical & Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, USA.
| | | | | |
Collapse
|
4
|
The Yang–Yang anomaly in liquid–liquid criticality: Experimental evidence from adiabatic scanning calorimetry. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2011.12.022] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
5
|
Abdulkadirova K, Peters C, Sengers J, Anisimov M. An isomorphic Peng–Robinson equation for phase-equilibria properties of hydrocarbon mixtures in the critical region. J Supercrit Fluids 2010. [DOI: 10.1016/j.supflu.2010.09.021] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
|
6
|
Pérez-Sánchez G, Losada-Pérez P, Cerdeiriña CA, Thoen J. Critical behavior of static properties for nitrobenzene-alkane mixtures. J Chem Phys 2010; 132:214503. [PMID: 20528027 DOI: 10.1063/1.3431547] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present experimental data of the isobaric heat capacity per unit volume C(p,x)V(-1) for mixtures containing nitrobenzene and an alkane (C(N)H(2N+2), with N ranging from 6 to 15) upon approaching their liquid-liquid critical points along a path of constant composition. Values for the critical amplitude A(+) have been determined. They have been combined with the previously reported ones for the leading term of the coexistence-curve width to obtain, with the aid of well-known universal relations, the critical amplitudes of the correlation length and of the osmotic susceptibility. The trends of all these critical parameters, which exhibit anomalous behavior in the low N region, are discussed in terms of particular microscopic phenomena characterizing NB-C(N)H(2N+2) mixtures. The work is completed with an analysis of the analog of the Yang-Yang anomaly in liquid-liquid criticality: the behavior of the partial molar heat capacities of the two liquid components is found to illustrate previously uncovered asymmetry effects.
Collapse
Affiliation(s)
- Germán Pérez-Sánchez
- Departamento de Física Aplicada, Universidad de Vigo, As Lagoas s/n, Ourense 32004, Spain
| | | | | | | |
Collapse
|
7
|
Abstract
Abstract
Based on the principle of isomorphic critical behavior of fluid mixtures we derive a simple equation for closed solubility loops in a temperature–concentration diagram at constant pressure. The validity of the simple equation is tested by comparisons with experimental solubility data for liquid mixtures at atmospheric pressure and at elevated pressures. We also elucidate the nature of liquid–liquid phase separation in the vicinity of a double critical point. Specifically, we show how from an expansion around the critical double point one can develop a description of solubility loops as a function of pressure.
Collapse
|
8
|
Isochoric heat capacity measurements for pure ethanol in the near-critical and supercritical regions. J Supercrit Fluids 2007. [DOI: 10.1016/j.supflu.2007.05.004] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
9
|
Wang J, Anisimov MA. Nature of vapor-liquid asymmetry in fluid criticality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051107. [PMID: 17677022 DOI: 10.1103/physreve.75.051107] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2007] [Indexed: 05/16/2023]
Abstract
We have investigated the nature and experimental consequences of vapor-liquid asymmetry in near-critical fluids within the framework of "complete scaling" [M. E. Fisher and G. Orkoulas, Phys. Rev. Lett. 85, 696 (2000); Y. C. Kim, Phys. Rev. E 67, 061506 (2003)]. We used the thermodynamic freedom for a choice of the critical-entropy value to simplify "complete scaling" to a form with only two independent parameters, responsible for two different sources of the asymmetry. We then developed a procedure to obtain these two parameters from mean-field equations of state. By combining accurate liquid-vapor coexistence and heat-capacity data, we have unambiguously separated two nonanalytic contributions from the two sources of vapor-liquid asymmetry and proved the validity of "complete scaling." Since the nonanalytic asymmetry effects in the critical region are fully determined by the Ising critical exponents for the symmetric lattice-gas model, there is no need for a special renormalization-group theoretical treatment of "non-Ising" asymmetry in fluid criticality.
Collapse
Affiliation(s)
- Jingtao Wang
- Department of Chemical and Biomolecular Engineering and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
| | | |
Collapse
|
10
|
Anisimov MA, Wang J. Nature of asymmetry in fluid criticality. PHYSICAL REVIEW LETTERS 2006; 97:025703. [PMID: 16907462 DOI: 10.1103/physrevlett.97.025703] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2006] [Indexed: 05/11/2023]
Abstract
By combining accurate liquid-vapor coexistence and heat-capacity data, we have unambiguously separated two nonanalytical contributions of liquid-gas asymmetry in fluid criticality and showed the validity of "complete scaling" [Fisher, Phys. Rev. Lett. 85, 696 (2000)10.1103/PhysRevLett.85.696; Phys. Rev. E 67, 061506 (2003)10.1103/PhysRevE.67.061506]. We have also developed a method to obtain two scaling-field coefficients, responsible for the two sources of the asymmetry, from mean-field equations of state. Since the asymmetry effects are completely determined by Ising critical exponents, there is no practical need for a special renormalization-group theoretical treatment of asymmetric fluid criticality.
Collapse
Affiliation(s)
- Mikhail A Anisimov
- Department of Chemical and Biomolecular Engineering and Institute for Physical Science and Technology, University of Maryland, College Park, 20742, USA.
| | | |
Collapse
|
11
|
Cerdeiriña CA, Anisimov MA, Sengers JV. The nature of singular coexistence-curve diameters of liquid–liquid phase equilibria. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.04.044] [Citation(s) in RCA: 78] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
12
|
Kim YC. Yang-Yang anomalies and coexistence diameters: simulation of asymmetric fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:051501. [PMID: 16089536 DOI: 10.1103/physreve.71.051501] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2005] [Indexed: 05/03/2023]
Abstract
A general method for estimating the Yang-Yang ratio, R(mu) , of a model fluid via Monte Carlo simulations is presented on the basis of data for a hard-core square-well (HCSW) fluid and the restricted primitive model (RPM) electrolyte. The isothermal minima of Q(L)(triple bond)<m(2)>2L/<m(4)>L scaling are evaluated at T(c) in an LxLxL box where m=rho-<rho>L is the density fluctuation. The "complete" finite-size scaling theory for the Q(+/-)(min) (T(c);L) incorporates pressure mixing in the scaling fields, thereby allowing for a Yang-Yang anomaly. It yields a dominant term in the asymmetry, Q(+)(min)-Q(-)(min) , varying as L(-beta/nu) with an amplitude proportional to the crucial pressure-mixing coefficient, j(2) . The reliably known critical order-parameter distribution for (d=3) Ising systems then enables one to estimate j(2) , thereby yielding R(mu) , from the Q minima together with information on the nonuniversal amplitudes for the order parameter and the susceptibility. The detailed analysis needed to estimate j(2) for an HCSW fluid and the RPM is presented. Furthermore, the Q-minima below T(c) can also provide the coexistence-curve diameters, rho(diam) (T) (triple bond)1/2 (rho(+) + rho(-)) , very close to T(c) for both models: here rho +/-(T) are the densities of the coexisting liquid and gas phases. The recently developed recursive scaling algorithm for Deltarho(infinity) (T) (triple bond)rho(+)-rho(-) is adapted to investigate the corresponding universal scaling functions. The two extremal forms of these scaling functions are computed with the aid of the exactly soluble decorated lattice-gas model. The critical densities for the RPM and HCSW fluid found via this route are consistent with previous estimates obtained from the data above T(c) ; the magnitudes of the |T- T(c)|(2beta) and |T- T(c)|(1-alpha) corrections to rho(diam)(T) are estimated.
Collapse
Affiliation(s)
- Young C Kim
- Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
| |
Collapse
|
13
|
Kim YC, Fisher ME. Fluid Critical Points from Simulations: The Bruce−Wilding Method and Yang−Yang Anomalies. J Phys Chem B 2004. [DOI: 10.1021/jp037071f] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Young C. Kim
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
| | - Michael E. Fisher
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
| |
Collapse
|
14
|
Kim YC, Fisher ME, Orkoulas G. Asymmetric fluid criticality. I. Scaling with pressure mixing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:061506. [PMID: 16241232 DOI: 10.1103/physreve.67.061506] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2002] [Indexed: 05/04/2023]
Abstract
The thermodynamic behavior of a fluid near a vapor-liquid and, hence, asymmetric critical point is discussed within a general "complete" scaling theory incorporating pressure mixing in the nonlinear scaling fields as well as corrections to scaling. This theory allows for a Yang-Yang anomaly in which mu(")(sigma)(T), the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when T-->T(c); it also generates a leading singular term, /t/(2beta), in the coexistence curve diameter, where t[triple bond](T-T(c))/T(c). The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which chi((k))[triple bond]chi(rho,T)/rho(k) (with chi=rho(2)k(B)TK(T)) and C((k))(V)[triple bond]C(V)(rho,T)/rho(k) are maximal at fixed T, is carefully elucidated. These results are useful for analyzing simulations and experiments, since particular, nonuniversal values of k specify loci that approach the critical density most rapidly and reflect the pressure-mixing coefficient. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte. For comparison, a discussion of the classical (or Landau) theory is presented briefly and various interesting loci are determined explicitly and illustrated quantitatively for a van der Waals fluid.
Collapse
Affiliation(s)
- Young C Kim
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | | | | |
Collapse
|