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Abdulagatov IM, Skripov PV. Thermodynamic and Transport Properties of Supercritical Fluids: Review of Thermodynamic Properties (Part 1). RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2021. [DOI: 10.1134/s1990793120070192] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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2
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Wang X, Xu C, Tao X, Yin T, Chen Z, Shen W. The heat capacities and critical behaviors of binary ionic solutions. Phys Chem Chem Phys 2018; 20:9130-9138. [PMID: 29577141 DOI: 10.1039/c7cp08604k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The heat capacities of nine binary room temperature ionic solutions {[C4mim][BF4] + 1,2-butandiol}, {[C8mim][BF4] + 1-pentanol}, {[C8mim][BF4] + 2-pentanol}, {[C8mim][BF4] + 1-hexanol}, {[C8mim][BF4] + 1-heptanol}, {[C8mim][PF6] + 1-propanol}, {[C8mim][PF6] + 1-butanol}, {[C8mim][PF6] + 2-butanol} and {[C8mim][PF6] + tert-butanol} are reported herein. The combination of the data obtained with the corresponding measured coexistence curves infers that the critical asymmetry parameter of the coexistence curves linearly varies with the molar volume ratio of the two components for each of the studied binary ionic solutions after the heat capacity contribution is considered. This indicates the importance of the heat capacity contribution to the critical asymmetry. For further analysis of the critical characteristics of the ionic solutions, a large amount of experimental data was collected and systematically discussed in detail regarding which critical character is important in the binary ionic solutions. A general increasing tendency for the RPM (restricted primitive model)-rescaled critical parameters with the relative permittivity εr,c of the solvent at the critical temperature of the corresponding system was found. This is attributed not only to the screening effect of the solvent medium, but also to solvophobic interactions, which both increase with εr,c. This study also demonstrates that the critical amplitudes increased, while the relative contribution of the heat capacity to the asymmetry of the coexistence curve decreased with an increase in εr,c.
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Affiliation(s)
- Xue Wang
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China.
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Tao X, Yin T, Shen W. Critical universality and asymmetry of ionic solution {iodobenzene + 1-decyl-3-methyl-imidazolium bis(trifluorosulfonyl)imide}. Phys Chem Chem Phys 2017; 19:22826-22835. [PMID: 28812072 DOI: 10.1039/c7cp03807k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The liquid-liquid coexistence curve, heat capacity in the critical and noncritical regions, and the turbidity in critical one-phase and two-phase regions of the binary solution {iodobenzene + 1-decyl-3-methylimidazolium bis(trifluorosulfonyl)imide ([C10mim][NTf2])} have been precisely measured. From the data collected in the critical region, the critical exponents α, β, γ and ν, as well as the universal critical amplitude ratios RB and X were obtained and were shown to agree well with their theoretical values for the 3D-Ising universality class, which further confirmed the 3D-Ising criticality of ionic solutions even in a very low relative permittivity solvent. The coulombic character of the studied system was suggested by the small values of the RPM reduced critical temperature and density. Furthermore, it was found that both the asymmetric behaviors of the diameter of the coexistence curve and the osmotic compressibility could be well described using the complete scaling theory.
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Affiliation(s)
- Xiaoyi Tao
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Tianxiang Yin
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Weiguo Shen
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China. and Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China
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Wang X, Wang M, Chen Z, Tao X, Shen W. Critical phenomena of {1-butanol + 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide} binary solution. J Mol Liq 2016. [DOI: 10.1016/j.molliq.2016.09.099] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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5
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Effect of the hockey-shaped mesogen as an additive on the critical behaviour at the smectic A to nematic phase transition. J Mol Liq 2016. [DOI: 10.1016/j.molliq.2016.04.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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6
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Sokolov AI, Nikitina MA, Kudlis A. Universal effective coupling constant ratios of 3D scalar ϕ4field theory and pseudo- ϵexpansion. EPJ WEB OF CONFERENCES 2016. [DOI: 10.1051/epjconf/201612505001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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7
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Shi S, Xu C, Yin T, Chen Z, Shen W. Critical asymmetry of liquid–liquid coexistence curve of binary mixture nitromethane+3-pentanol. J Mol Liq 2015. [DOI: 10.1016/j.molliq.2015.03.024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Yin T, Xu C, Lv H, Liu S, Wang M, Chen Z, Shen W. Asymmetric criticality of binary ionic solutions containing 1-butyl-3-methylimidazolium tetrafluoroborate and alcohol. Phys Chem Chem Phys 2014; 16:17715-23. [DOI: 10.1039/c4cp01344a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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Densities, Heat Capacities and Asymmetric Criticality of Coexistence Curves for Binary Mixtures {Dimethyl Adipate + n-Heptane or n-Octane}. J SOLUTION CHEM 2013. [DOI: 10.1007/s10953-013-0077-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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10
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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.
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Affiliation(s)
- Tianxiang Yin
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
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11
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Critical Behavior of Binary Mixtures of Nitrobenzene + n-Undecane and Nitrobenzene + n-Dodecane. J SOLUTION CHEM 2012. [DOI: 10.1007/s10953-012-9907-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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12
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A new scaled crossover parametric equation of state for water. JOURNAL OF THE IRANIAN CHEMICAL SOCIETY 2012. [DOI: 10.1007/s13738-012-0167-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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13
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Experimental study of the isochoric heat capacity of isobutanol in the critical and supercritical regions. J Supercrit Fluids 2012. [DOI: 10.1016/j.supflu.2011.11.017] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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14
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Huang M, Lei Y, Yin T, Chen Z, An X, Shen W. Heat Capacities and Asymmetric Criticality of Coexistence Curves for Benzonitrile + Alkanes and Dimethyl Carbonate + Alkanes. J Phys Chem B 2011; 115:13608-16. [DOI: 10.1021/jp206380t] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Meijun Huang
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Yuntao Lei
- Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Tianxiang Yin
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Zhiyun Chen
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Xueqin An
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Weiguo Shen
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
- Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China
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Sasaki Y, Ema K, Le KV, Takezoe H, Dhara S, Sadashiva BK. Calorimetric study of the effect of bent-shaped dopant molecules on the critical behavior at the nematic-smectic-Ad phase transition. Phys Rev E 2011; 83:061701. [PMID: 21797381 DOI: 10.1103/physreve.83.061701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Revised: 03/29/2011] [Indexed: 11/07/2022]
Abstract
We report results of calorimetric studies for the binary mixture of rodlike host n-alkyloxy-cyanobiphenyl (nOCB, n=8,9) and bent-shaped guest 1,3-phenylene-bis[4-(3-methylbenzoyloxy)]-4'-n-dodecylbiphenyl-4'-carboxylate (BC12). The effect of bent-shaped dopant molecules on the critical behavior associated with the nematic-smectic-A(d) phase transition has been studied in detail. The transition temperature for the nematic-smectic-A(d) phase sharply decreases as the increase of the mole fraction of the dopant concentration (denoted X for the BC12/9OCB mixture and Y for the BC12/8OCB mixture). The dependence of the critical exponent α on X and Y is well explained in terms of the McMillan ratio. A nearly tricritical exponent has been obtained for the X=0.01 mixture. X=0.02-0.03 mixtures, pure 8OCB, and Y=0.01-0.03 mixtures exhibit nonuniversal behaviors with effective exponents lying between the 3D-XY and tricritical exponents. The heat capacity anomaly for Y=0.05 has been well described with the 3D-XY exponent. The critical amplitude ratio A(-)/A(+) is close to 1 and insensitive to the dopant concentration. No Fisher renormalization of the critical exponent has been observed even for nearly tricritical compositions, which indicates the smallness of the concentration plays a decisive role rather than the steepness of the N-SmA(d) phase boundary.
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Affiliation(s)
- Y Sasaki
- Department of Physics, Tokyo Institute of Technology, O-okayama, Meguro, Japan
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16
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Losada-Pérez P, Tripathi CSP, Leys J, Glorieux C, Thoen J. Large heat capacity anomaly near the consolute point of the binary mixture nitromethane and 3-pentanol. J Chem Phys 2011; 134:044505. [PMID: 21280746 DOI: 10.1063/1.3535567] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The large critical anomaly in the isobaric heat capacity C(p,x)(T) of the binary mixture nitromethane + 3-pentanol is measured using high-resolution adiabatic scanning calorimetry. The unique features of this technique provided an alternative approach to the study of the critical behavior of C(p,x)(T), providing further C(p,x)(T) related quantities from which valuable information could be extracted. Our data are in full agreement with the predictions of the Modern Theory of Critical Phenomena; specifically, 3D-Ising model values for the critical exponent α and the universal amplitude ratio values of the leading critical amplitudes, as well as for the first correction-to-scaling ones, provide the optimum fits to represent the experimental data. Evidence for the need of higher-order terms, i.e., first correction-to-scaling term, is given. The large value of the coefficient E for the linear temperature dependence of the background obtained is ascribed to a possible contribution of the regular linear background term, of a higher-order asymmetry term, and of the second correction-to-scaling term. Internal consistency of C(p,x)(T) and its related quantities is successfully checked.
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Affiliation(s)
- Patricia Losada-Pérez
- Laboratorium voor Akoestiek en Thermische Fysica, Departement Natuurkunde en Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
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17
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Sasaki Y, Ema K, Le KV, Takezoe H, Dhara S, Sadashiva BK. Critical behavior at transitions from uniaxial to biaxial phases in a smectic liquid-crystal mixture. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011709. [PMID: 20866637 DOI: 10.1103/physreve.82.011709] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2010] [Indexed: 05/29/2023]
Abstract
We report results of calorimetric and optical investigations of binary mixtures of rodlike and bent-shaped molecules. We find that the observed critical heat anomaly associated with the smectic-A2 to biaxial smectic-A2b transition is well described with a Fisher-renormalized form of the usual scaling expression. The effect of renormalization is large in this system in part because of the moderately steep slope of the phase boundary (dT(c)/ dX∼100 K, where X is the mole fraction of the bent-core molecules) and in part because of the proximity to the tricritical point. The magnitude of heat anomaly at the smectic-A2-smectic-A2b transition showed a drastic decrease as X becomes smaller. Moreover, the nematic-smectic-A2 transitions investigated turned out to be always first order and the transition enthalpy showed only weak dependence on the concentration X. The results imply that the energy fluctuations around the smectic-A2-smectic-A2b transition are very sensitive to the underlying ordering of the smectic-A2 background.
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Affiliation(s)
- Y Sasaki
- Department of Physics, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro, Tokyo 152-8551, Japan
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18
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Feng X, Blöte HWJ. Specific heat of the simple-cubic Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031103. [PMID: 20365693 DOI: 10.1103/physreve.81.031103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2009] [Revised: 12/09/2009] [Indexed: 05/29/2023]
Abstract
We provide an expression quantitatively describing the specific heat of the Ising model on the simple-cubic lattice in the critical region. This expression is based on finite-size scaling of numerical results obtained by means of a Monte Carlo method. It agrees satisfactorily with series expansions and with a set of experimental results. Our results include a determination of the universal amplitude ratio of the specific-heat divergences at both sides of the critical point.
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Affiliation(s)
- Xiaomei Feng
- College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, 29 Yudao St, 210016 Nanjing, People's Republic of China
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Garrabos Y, Lecoutre C, Palencia F, Le Neindre B, Erkey C. Master crossover functions for one-component fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021116. [PMID: 18351996 DOI: 10.1103/physreve.77.021116] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2007] [Revised: 10/16/2007] [Indexed: 05/26/2023]
Abstract
By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.
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Affiliation(s)
- Yves Garrabos
- Equipe du Supercritique pour l'Environnement, les Matériaux et l'Espace, Institut de Chimie de la Matière Condensée de Bordeaux, UPR 9048, Centre National de la Recherche Scientifique, Université Bordeaux I, Pessac Cedex, France
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20
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Garrabos Y, Palencia F, Lecoutre C, Broseta D, Le Neindre B. Master crossover behavior of parachor correlations for one-component fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061109. [PMID: 18233816 DOI: 10.1103/physreve.76.061109] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2007] [Indexed: 05/25/2023]
Abstract
The master asymptotic behavior of the usual parachor correlations, expressing surface tension sigma as a power law of the density difference rho(L)-rho(V) between coexisting liquid and vapor, is analyzed for a series of pure compounds close to their liquid-vapor critical point, using only four critical parameters (beta(c))-1 , alpha(c) , Z(c) , and Y(c) , for each fluid. This is accomplished by the scale dilatation method of the fluid variables where, in addition to the energy unit (beta(c))-1 and the length unit alpha(c) , the dimensionless numbers Z(c) and Y(c) are the characteristic scale factors of the ordering field along the critical isotherm and of the temperature field along the critical isochore, respectively. The scale dilatation method is then formally analogous to the basic system-dependent formulation of the renormalization theory. Accounting for the hyperscaling law delta-1/delta+1=eta-2/2d , we show that the Ising-like asymptotic value pi(a) of the parachor exponent is unequivocally linked to the critical exponents eta or delta by pi(a)/d-1=2/d-(2-eta)=delta+1/d (here d=3 is the space dimension). Such mixed hyperscaling laws combine either the exponent eta or the exponent delta , which characterizes bulk critical properties of d dimension along the critical isotherm or exactly at the critical point, with the parachor exponent pi(a) which characterizes interfacial properties of d-1 dimension in the nonhomogeneous domain. Then we show that the asymptotic (symmetric) power law [abstract; see text] is the two-dimensional critical equation of state of the liquid-gas interface between the two-phase system at constant total (critical) density rho(c) . This power law complements the asymptotic (antisymmetric) form [abstract; see text] of the three-dimensional critical equation of state for a fluid of density rho not equal to rho_(c) and pressure p not equal to p_(c) , maintained at constant (critical) temperature T=T_(c)} [mu_(rho)(mu_(rho,c)) is the specific (critical) chemical potential; p_(c) is the critical pressure; and T_(c) is the critical temperature]. We demonstrate the existence of the related universal amplitude combination [abstract; see text] = universal constant, constructed with the amplitudes D_(rho)(sigma) and D_(rho)(c) , separating then the respective contributions of each scale factor Y_(c) and Z_(c) , characteristic of each thermodynamic path, i.e., the critical isochore and the critical isotherm (or the critical point), respectively. The main consequences of these theoretical estimations are discussed in light of engineering applications and process simulations where parachor correlations constitute one of the most practical methods for estimating surface tension from density and capillary rise measurements.
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Affiliation(s)
- Yves Garrabos
- Equipe du Supercritique pour l'Environnement, les Matériaux et l'Espace, ICMCB-CNRS UPR 9048, Université Bordeaux I, 87 avenue du Dr. A. Schweitzer, F 33608 PESSAC Cedex France
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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]
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Utt NJ, Lehman SY, Jacobs DT. Heat capacity of the liquid-liquid mixture nitrobenzene and dodecane near the critical point. J Chem Phys 2007; 127:104505. [PMID: 17867759 DOI: 10.1063/1.2766941] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The heat capacity of the liquid-liquid mixture nitrobenzene-dodecane has been measured for the first time near its upper critical consolute point using an adiabatic calorimeter. The theoretical expression for the heat capacity near the critical point was applied to our combined data runs. The critical exponent alpha was determined to be 0.124+/-0.006, which was consistent with theoretical predictions. When alpha was fixed at its theoretical value of 0.11, our value for the amplitude ratio A(+)A(-)=0.58+/-0.02 was consistent with experimental determinations and theoretical predictions. However, the two-scale-factor universality ratio X, now consistent among experiments and theories with a value between 0.019 and 0.020, was violated in this system when using a previously published value for the correlation length.
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Affiliation(s)
- Nathan J Utt
- Physics Department, The College of Wooster, Wooster, Ohio 44691, USA
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Garrabos Y, Palencia F, Lecoutre C, Broseta D, Le Neindre B, Erkey C. Master singular behavior for the Sugden factor of one-component fluids near their gas-liquid critical point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061112. [PMID: 17677225 DOI: 10.1103/physreve.75.061112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2006] [Indexed: 05/16/2023]
Abstract
We present the master (i.e., unique) behavior of the squared capillary length-the so-called Sugden factor-as a function of the temperaturelike field along the critical isochore, asymptotically close to the gas-liquid critical point of about twenty (one-component) fluids. This master behavior is obtained using the scale dilatation of the relevant physical fields of the one-component fluids. The scale dilatation method introduces the fluid-dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the Ising-like universality class. The master behavior for the Sugden factor satisfies hyperscaling. It can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain, recently obtained from massive renormalization in field theory. In the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension, we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the Sugden factor, in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one-component fluid "subclass."
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Affiliation(s)
- Yves Garrabos
- ESEME-CNRS, ICMCB-UPR 9048, Université Bordeaux 1, 87 avenue du Docteur Albert Schweitzer, F-33608 Pessac, France.
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Garrabos Y, Bervillier C. Mean crossover functions for uniaxial three-dimensional Ising-like systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021113. [PMID: 17025399 DOI: 10.1103/physreve.74.021113] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2006] [Indexed: 05/12/2023]
Abstract
We give simple expressions for the mean of the max and min bounds of the critical-to-classical crossover functions, previously calculated [Bagnuls and Bervillier, Phys. Rev. E 65, 066132 (2002)] within the massive renormalization scheme of the Phi(d)4(n) model in three dimensions (d = 3) and scalar order parameter (n = 1) of the Ising-like universality class. The mean functions are determined relying on the properties of the theoretical functions in the two limiting three-dimensional (3D) Ising-like and mean-field-like descriptions close to the Wilson-Fisher fixed point and to the Gaussian fixed point, respectively. Such descriptions correspond to the preasymptotic domains near each fixed point where a Wegner expansion restricted to two terms (leading and first confluent terms) is valid. The Ising-like preasymptotic domain description includes the correlations between parameters due to the error-bar determination of the exponents and amplitude combinations very close to the Wilson-Fisher fixed point. Adding the equivalent description of the mean field preasymptotic domain close to the Gaussian fixed point leads to define each mean crossover function with three calculated parameters. Fixing a unique value of one parameter whatever the selected mean crossover function, we use this parameter as a relative sensor to estimate the dominant nature, either (Ising-like) critical, or (mean-field-like) classical, of the crossover behavior. Finally, we obtain an explicit criterion to measure the extension of the Ising-like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite, using a well-controlled number of system-dependent parameters (like in the subclass of one-component fluids).
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Affiliation(s)
- Yves Garrabos
- Equipe du Supercritique pour l'Environnement, les Matériaux et l'Espace, Institut de Chimie de la Matière Condensée de Bordeaux, ICMCB-CNRS, UPR 9048, Université Bordeaux I - 87, avenue du Docteur Schweitzer, F 33608 PESSAC Cedex, France
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Garrabos Y. Universality and quantum effects in one-component critical fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056110. [PMID: 16803001 DOI: 10.1103/physreve.73.056110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2006] [Indexed: 05/10/2023]
Abstract
Nonuniversal scale transformations of the physical fields are extended to pure quantum fluids and used to calculate the susceptibility, the specific heat, and the order parameter density along the critical isochore of near its liquid-vapor critical point. Within the so-called preasymptotic domain, where the Wegner expansion restricted to the first term of confluent corrections to scaling is expected to be valid, the results are in agreement with the experimental measurements and recent predictions, either based on the minimal-substraction renormalization and the massive renormalization schemes within phi (4)(d = 3) (n = 1)the model, or based on the crossover parametric equation of state for Ising-like systems.
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Affiliation(s)
- Yves Garrabos
- Equipe du Supercritique pour l'Environnement, les Matériaux et l'Espace - Institut de Chimie de la Matière Condensée de Bordeaux - Centre National de la Recherche Scientifique - Université Bordeaux I - 87, PESSAC, France.
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26
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Mirzaev SZ, Behrends R, Heimburg T, Haller J, Kaatze U. Critical behavior of 2,6-dimethylpyridine-water: Measurements of specific heat, dynamic light scattering, and shear viscosity. J Chem Phys 2006; 124:144517. [PMID: 16626224 DOI: 10.1063/1.2188396] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The specific heat C(p) at constant pressure, the shear viscosity eta(s), and the mutual diffusion coefficient D of the 2,6-dimethylpyridine-water mixture of critical composition have been measured in the homogeneous phase at various temperatures near the lower critical demixing temperature T(c). The amplitude of the fluctuation correlation length xi(0)=(0.198+/-0.004) nm has been derived from a combined evaluation of the eta(s) and D data. This value is in reasonable agreement with the one obtained from the amplitude A(+)=(0.26+/-0.01) J(g K) of the critical term in the specific heat, using the two-scale-factor universality relation. Within the limits of error the relaxation rate Gamma of order parameter fluctuations follows power law with the theoretical universal exponent and with the amplitude Gamma=(25+/-1)x10(9) s(-1). No indications of interferences of the critical fluctuations with other elementary chemical reactions have been found. A noteworthy result is the agreement of the background viscosity eta(b), resulting from the treatment of eta(s) and D data, with the viscosity eta(s)(nu=0) extrapolated from high-frequency viscosity data. The latter have been measured in the frequency range of 5-130 MHz using a novel shear impedance spectrometer.
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Affiliation(s)
- S Z Mirzaev
- Drittes Physikalisches Institut, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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27
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Garrabos Y, Palencia F, Lecoutre C, Erkey C, Le Neindre B. Master singular behavior from correlation length measurements for seven one-component fluids near their gas-liquid critical point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:026125. [PMID: 16605416 DOI: 10.1103/physreve.73.026125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2005] [Indexed: 05/08/2023]
Abstract
We present the master (i.e., unique) behavior of the correlation length, as a function of the thermal field along the critical isochore, asymptotically close to the gas-liquid critical point of xenon, krypton, argon, helium-3, sulfur hexafluoride, carbon dioxide, and heavy water. It is remarkable that this unicity extends to the correction-to-scaling terms. The critical parameter set, which contains all the needed information to reveal the master behavior, is composed of four thermodynamic coordinates of the critical point and one adjustable parameter which accounts for quantum effects in the helium-3 case. We use a scale dilatation method applied to the relevant physical variables of the one-component fluid subclass, in analogy with the basic hypothesis of the renormalization theory. This master behavior for the correlation length satisfies hyperscaling. We finally estimate the thermal field extent where the critical crossover of the singular thermodynamic and correlation functions deviates from the theoretical crossover function obtained from field theory.
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Affiliation(s)
- Yves Garrabos
- ESEME-CNRS, ICMCB-UPR 9048, Université Bordeaux 1, 87 avenue du Docteur Albert Schweitzer, F-33608 Pessac France.
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28
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Zhong F, Barmatz M. Comparison of theoretical models of crossover behavior near the 3He liquid-vapor critical point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066105. [PMID: 15697432 DOI: 10.1103/physreve.70.066105] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2004] [Indexed: 05/24/2023]
Abstract
Parametric expressions, based on three different theoretical models, are used to calculate the isothermal susceptibility, specific heat, and order parameter along the critical isochore and coexistence curve from the asymptotic region to the crossover region. These models are (i) the minimal-subtraction renormalization scheme, (ii) the massive renormalization scheme within the phi(4) model, and (iii) the crossover parametric model based on the crossover Landau model. We fit these theories globally to experimental measurements of the isothermal susceptibility and specific heat along the critical isochore and coexistence curve, and to the coexistence curve of 3He near its liquid-vapor critical point. All of the theories provide good agreement with the experimental measurements within the reduced temperature range |t| < or =2 x 10(-2) . The differences in the fits between the theories and the correlations between the adjustable model parameters are discussed.
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Affiliation(s)
- Fang Zhong
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, USA
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29
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Usatenko Z, Hu CK. Crossover between special and ordinary transitions in random semi-infinite Ising-like systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066115. [PMID: 14754277 DOI: 10.1103/physreve.68.066115] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2003] [Indexed: 05/24/2023]
Abstract
We consider the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent Phi, the critical exponents of the layer alpha(1), and local specific heats alpha(11) by applying the field theoretic approach directly in three spatial dimensions (d=3) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Padé and Padé-Borel resummation techniques. We find that Phi, alpha(1), alpha(11) obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results support the idea that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.
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Affiliation(s)
- Z Usatenko
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
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30
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Kiselev SB, Ely JF. Generalized corresponding states model for bulk and interfacial properties in pure fluids and fluid mixtures. J Chem Phys 2003. [DOI: 10.1063/1.1605375] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Bonetti M, Calmettes P, Bervillier C. Study of supercritical krypton by small-angle neutron scattering: Analysis of the cross-over region. J Chem Phys 2003. [DOI: 10.1063/1.1612472] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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32
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Hernández MP, Ortega F, Rubio RG. Crossover critical phenomena in an aqueous electrolyte solution: Light scattering, density and viscosity of the 3-methylpyridine+water+NaBr system. J Chem Phys 2003. [DOI: 10.1063/1.1594179] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Strösser M, Dohm V. Minimal renormalization without epsilon expansion: four-loop free energy in three dimensions for general n above and below Tc. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:056115. [PMID: 12786228 DOI: 10.1103/physreve.67.056115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2002] [Indexed: 05/24/2023]
Abstract
We present an analytic four-loop calculation of the free energy in three dimensions within the O(n) symmetric phi(4) theory at infinite cutoff for general n above and below T(c). It is shown that Goldstone singularities arising at intermediate stages of the calculation cancel among themselves. The correlation length above T(c) and an appropriately defined pseudocorrelation length below T(c) are calculated analytically up to four-loop order for general n. The method of minimal renormalization at fixed dimension d=3 is used to determine the analytic expressions for the four-loop series of the amplitude functions of the free energy, correlation length, and specific heat above and below T(c) in terms of the renormalized coupling. These expressions provide the basis for future accurate Borel resummations of universal amplitude ratios characterizing the asymptotic critical behavior and of crossover functions describing the nonasymptotic critical behavior. A brief application is given by a variational calculation of the universal specific-heat amplitude ratios A+/A- and P=alpha(-1)(1-A+/A-) and of the universal quantity R+(xi)=xi+0(A+)(1/d) for general n.
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Affiliation(s)
- M Strösser
- Institut für Theoretische Physik, Technische Hochschule Aachen, D-52056 Aachen, Germany
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34
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Braganza CI, Jacobs DT. Turbidity of the liquid–liquid mixture perfluoroheptane and 2,2,4-trimethylpentane near the critical point. J Chem Phys 2002. [DOI: 10.1063/1.1518009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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35
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Martín-Mayor V, Pelissetto A, Vicari E. Critical structure factor in using systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:026112. [PMID: 12241242 DOI: 10.1103/physreve.66.026112] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2002] [Indexed: 05/23/2023]
Abstract
We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L(3) with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernike expression of Puglielli and Ford.
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Affiliation(s)
- Victor Martín-Mayor
- Dipartimento di Fisica dell'Università di Roma La Sapienza and INFN, I-00185 Roma, Italy.
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36
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Campostrini M, Pelissetto A, Rossi P, Vicari E. 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:066127. [PMID: 12188803 DOI: 10.1103/physreve.65.066127] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2002] [Indexed: 05/23/2023]
Abstract
25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining gamma=1.2373(2), nu=0.63012(16), alpha=0.1096(5), eta=0.036 39(15), beta=0.326 53(10), and delta=4.78 93(8). Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate Delta=0.52(3) for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.
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Affiliation(s)
- Massimo Campostrini
- Dipartimento di Fisica dell'Università di Pisa and INFN, I-00185 Rome, Italy.
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37
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Bagnuls C, Bervillier C. Classical-to-critical crossovers from field theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:066132. [PMID: 12188808 DOI: 10.1103/physreve.65.066132] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2002] [Indexed: 05/23/2023]
Abstract
We extend our previous determinations of nonasymptotic critical behavior of Phys. Rev. B 32, 7209 (1985) and 35, 3585 (1987) to accurate expressions of the complete classical-to-critical crossover (in three-dimensional field theory) in terms of the temperaturelike scaling field (i.e., along the critical isochore) for (1) the correlation length, the susceptibility, and the specific heat in the homogeneous phase for the n-vector model (n=1 to 3) and (2) the spontaneous magnetization (coexistence curve), the susceptibility, and the specific heat in the inhomogeneous phase for the Ising model (n=1). The present calculations include the seventh-loop order of Murray and Nickel and closely account for the up-to-date estimates of universal asymptotic critical quantities (exponents and amplitude combinations) provided by Guida and Zinn-Justin [J. Phys. A 31, 8103 (1998)].
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Affiliation(s)
- C Bagnuls
- Service de Physique de l'Etat Condensé, CEA/DSM/SPEC, CEA/Saclay, 91191 Gif-sur-Yvette cédex, France.
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38
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Abdulkadirova KS, Wyczalkowska AK, Anisimov MA, Sengers JV. Thermodynamic properties of mixtures of H2O and D2O in the critical region. J Chem Phys 2002. [DOI: 10.1063/1.1450125] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Caerels J, Glorieux C, Thoen J. Photopyroelectric ac calorimetric study of the nematic-smectic-A phase-transition line in binary liquid crystal mixtures with injected smectic-A phases. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:031704. [PMID: 11909078 DOI: 10.1103/physreve.65.031704] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2001] [Indexed: 05/23/2023]
Abstract
Using a recently developed photopyroelectric ac calorimetric technique we investigate two binary liquid crystal mixtures with so-called injected smectic-A phases. Characteristic of these systems is the occurrence of nematic-to-smectic-A transition lines in the phase diagram of mixtures of pure compounds having only a nematic phase. The two binary systems are pentylcyanobiphenyl with either 4-n-propylcyclohexyl-carboxylate or 4-n-pentylphenyl 4(')-n-pentyloxybenzoate. Both these systems have domelike smectic-A ranges with narrow nematic ranges at the top. Near the top the N-SmA transitions are of first order and are crossing over to second order at a tricritical point on either side of the top with the increasing width of the nematic range. The obtained critical exponents are almost completely Fisher renormalized because of the strong concentration dependence of the nematic-to-smectic-A transition temperatures.
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Affiliation(s)
- J Caerels
- Laboratorium voor Akoestiek en Thermische Fysica, Department Natuurkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, 3001 Leuven, Belgium
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40
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Caracciolo S, Causo MS, Pelissetto A, Rossi P, Vicari E. Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:046130. [PMID: 11690113 DOI: 10.1103/physreve.64.046130] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2001] [Indexed: 05/23/2023]
Abstract
We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, which corresponds to the limit N-->0 of an N-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed by using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions for the critical crossover functions, finding good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal crossover behavior of our data for any finite range.
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Affiliation(s)
- S Caracciolo
- Scuola Normale Superiore, INFN and INFM, I-56100 Pisa, Italy.
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41
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Bonetti M, Calmettes P, Bervillier C. Small-angle neutron scattering from supercritical heavy water at off-critical densities. J Chem Phys 2001. [DOI: 10.1063/1.1392362] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Agayan VA, Anisimov MA, Sengers JV. Crossover parametric equation of state for Ising-like systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:026125. [PMID: 11497669 DOI: 10.1103/physreve.64.026125] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2001] [Indexed: 05/23/2023]
Abstract
We present a parametric equation for the thermodynamic properties in the critical region of three-dimensional Ising-like systems which include fluids and fluid mixtures. The equation of state incorporates a crossover from singular Ising behavior asymptotically close to the critical point to classical (mean-field) behavior further away from the critical point, characterized by two physical crossover parameters: a coupling constant related to the strength and range of molecular interactions and a "cutoff" wave number for the critical fluctuations. In the asymptotic Ising limit, the crossover equation reproduces the most recent theoretical estimates for the universal ratios of the leading and correction-to-scaling critical amplitudes. The equation has been tested by comparing it with recent experimental thermodynamic-property data for 3He near its vapor-liquid critical point.
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Affiliation(s)
- V A Agayan
- Institute for Physical Science and Technnology and Department of Chemical Engineering, University of Maryland, College Park 20742, USA
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43
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Brognara A, Parola A, Reatto L. Construction of an effective Hamiltonian for a three-dimensional Ising universality class. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:026122. [PMID: 11497666 DOI: 10.1103/physreve.64.026122] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2000] [Indexed: 05/23/2023]
Abstract
The asymptotic and preasymptotic critical behavior in fluids, mixtures, and uniaxial magnets is believed to be described by an effective straight phi(4) scalar field theory with suitable, nonuniversal, coupling constants. The critical parameters as well as the extent of crossovers and corrections to the leading critical behavior in physical systems, crucially depends on the choice of these couplings. Here we propose a new method for deriving the effective scalar field theory appropriate to a microscopic model in this universality class. Use is made of the hierarchical reference theory, which implements the basic ideas of Wilson momentum space renormalization group to microscopic Hamiltonians. The effective low-energy field theory is then analyzed by the minimal subtraction scheme of Schloms and Dohm. We discuss the application of this method to the three-dimensional Ising model and to the liquid-vapor phase transition. We make comparison with high-temperature expansion results and with experimental data for rare gas.
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Affiliation(s)
- A Brognara
- Università di Milano, Via Celoria 16, Italy
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44
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Kleinert H, Van den Bossche B. Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:056113. [PMID: 11414967 DOI: 10.1103/physreve.63.056113] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2000] [Indexed: 05/23/2023]
Abstract
We use variational perturbation theory to calculate various universal amplitude ratios above and below Tc in minimally subtracted straight phi4 theory with N components in three dimensions. In order to best exhibit the method as a powerful alternative to Borel resummation techniques, we consider only two- and three-loops expressions where our results are analytic expressions. For the critical exponents, we also extend existing analytic expressions for two loops to three loops.
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Affiliation(s)
- H Kleinert
- Institut für Theoretische Physik, Arnimallee 14 D-14195 Berlin, Germany
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45
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Oby ER, Jacobs DT. Heat capacity of the liquid–liquid mixture perfluoroheptane and 2,2,4-trimethylpentane near the critical point. J Chem Phys 2001. [DOI: 10.1063/1.1350661] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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47
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Nowicki AW, Ghosh M, McClellan SM, Jacobs DT. Heat capacity and turbidity near the critical point of succinonitrile–water. J Chem Phys 2001. [DOI: 10.1063/1.1344613] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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48
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Kiselev SB, Ely JF, Belyakov MY. Adsorption of critical and supercritical fluids. J Chem Phys 2000. [DOI: 10.1063/1.480919] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Ema K, Kanai M, Yao H, Takanishi Y, Takezoe H. Effect of optical purity on the critical heat capacity at the smectic-A-(chiral)-smectic-C transition in an antiferroelectric liquid crystal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:1585-92. [PMID: 11046441 DOI: 10.1103/physreve.61.1585] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/1999] [Revised: 10/19/1999] [Indexed: 04/15/2023]
Abstract
High resolution ac calorimetric measurements have been carried out near the smectic-A-chiral-smectic-C phase transition in the antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4(')-octyloxybiphenyl-4-carboxylate (MHPOBC). Data on samples with different optical purities have been analyzed in detail using a renormalization-group expression with corrections-to-scaling terms. The chiral-smectic-C(alpha)-chiral-smectic-C phase transition is first order, while the smectic-A-chiral-smectic-C(alpha) phase transition is second order. A direct smectic-A-chiral-smectic-C phase transition, which occurs in near-racemic mixtures, was found to be quasitricritical and weakly first order. This implies that the smectic-A-smectic-C transition in the racemate locates at a special point where four critical lines intersect.
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Affiliation(s)
- K Ema
- Department of Physics, Faculty of Science, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro, Tokyo 152-8551, Japan
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50
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