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Midya J, Egorov SA, Binder K, Nikoubashman A. Wetting transitions of polymer solutions: Effects of chain length and chain stiffness. J Chem Phys 2022; 156:044901. [DOI: 10.1063/5.0077303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Jiarul Midya
- Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation and Institute of Complex Systems, Forschungszentrum Jülich, 52425 Jülich, Germany
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Sergei A. Egorov
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, USA
| | - Kurt Binder
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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Ma Y, Ali S, Prabhu VM. Enhanced Concentration Fluctuations in Model Polyelectrolyte Coacervate Mixtures along a Salt Isopleth Phase Diagram. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c02001] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Yuanchi Ma
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Samim Ali
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Vivek M. Prabhu
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
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Llovell F, Vega LF, Anisimov MA, Sengers JV. Incorporating critical divergence of isochoric heat capacity into the soft-SAFT equation of state. AIChE J 2015. [DOI: 10.1002/aic.14911] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Fèlix Llovell
- MATGAS 2000 AIE, Campus de la UAB, Bellaterra; 08193 Barcelona Spain
| | - Lourdes F. Vega
- MATGAS 2000 AIE, Campus de la UAB, Bellaterra; 08193 Barcelona Spain
| | - Mikhail A. Anisimov
- Institute for Physical Science and Technology, University of Maryland; College Park MD 20742
- Dept. of Chemical and Biomolecular Engineering; University of Maryland; College Park MD 20742
| | - Jan V. Sengers
- Institute for Physical Science and Technology, University of Maryland; College Park MD 20742
- Dept. of Chemical and Biomolecular Engineering; University of Maryland; College Park MD 20742
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4
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The measurements of coexistence curves and critical behavior of a binary mixture with a high molecular weight polymer. J Mol Liq 2011. [DOI: 10.1016/j.molliq.2011.05.002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Mirzaev SZ, Heimburg T, Kaatze U. Critical behavior of polystyrene-cyclohexane: heat capacity and mass density. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061502. [PMID: 21230673 DOI: 10.1103/physreve.82.061502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2010] [Revised: 10/22/2010] [Indexed: 05/30/2023]
Abstract
At temperatures between 7.5 °C and 20 °C as well as 26 °C and 40 °C we have recorded the densities and specific heat at constant pressure for critical mixtures of polystyrene in cyclohexane. The degrees of polymerization were N=288 (critical temperature T(c)=9.77 °C ) and N=6242 (T(c)=27.56 °C), respectively. In the two-phase regime a series of reproducible events exists in the specific-heat traces, indicating the existence of nonequilibrium intermediate states as likely resulting from an oscillatory instability of droplet formation. In the one-phase region the critical contribution to the heat capacity follows power law with critical exponent α=0.11 compatible with Ising-like criticality. At larger N , however, the critical amplitude of the heat capacity is noticeably smaller than at lower degree of polymerization. This finding may be taken as an indication of different effects from competing mesoscale lengths: the radius of gyration of the polymer and the fluctuation correlation length of the mixture. The density traces reveal marginal deviations from simple linear temperature dependencies. If these deviations are analyzed in terms of critical contributions, different signs in the amplitude result, in conformity with the signs in the pressure dependence of the critical temperature. The absolute values of the amplitudes, however, are substantially larger than predicted from the critical amplitudes of the heat capacities.
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Affiliation(s)
- Sirojiddin Z Mirzaev
- Drittes Physikalisches Institut, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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Pérez-Sánchez G, Losada-Pérez P, Cerdeiriña CA, Sengers JV, Anisimov MA. Asymmetric criticality in weakly compressible liquid mixtures. J Chem Phys 2010; 132:154502. [PMID: 20423184 DOI: 10.1063/1.3378626] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The thermodynamics of asymmetric liquid-liquid criticality is updated by incorporating pressure effects into the complete-scaling formulation earlier developed for incompressible liquid mixtures [C. A. Cerdeirina et al., Chem. Phys. Lett. 424, 414 (2006); J. T. Wang et al., Phys. Rev. E 77, 031127 (2008)]. Specifically, we show that pressure mixing enters into weakly compressible liquid mixtures as a consequence of the pressure dependence of the critical parameters. The theory is used to analyze experimental coexistence-curve data in the mole fraction-temperature, density-temperature, and partial density-temperature planes for a large number of binary liquid mixtures. It is shown how the asymmetry coefficients in the scaling fields are related to the difference in molecular volumes of the two liquid components. The work resolves the question of the so-called "best order parameter" discussed in the literature during the past decades.
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Affiliation(s)
- G Pérez-Sánchez
- Departamento de Física Aplicada, Universidad de Vigo, As Lagoas s/n, Ourense 32004, Spain
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Pradeep UK. Critical behavior on approaching a special critical point in a complex fluid. J Chem Phys 2008; 129:204903. [PMID: 19045877 DOI: 10.1063/1.3013540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The critical behavior of osmotic susceptibility is investigated in the re-entrant complex mixture 1-propanol (P)+water (W)+potassium chloride (KCl) through light-scattering measurements. The measurements are performed on approaching a special critical point [i.e., the double critical point (DCP)] in this mixture, along the line of upper critical solution temperatures (T(U)'s), by varying t from the high temperature one-phase region. The light-scattering data analysis emphasizes the need for corrections to the asymptotic Ising behavior and yields very large magnitudes for the correction-to-scaling amplitudes A(1) and A(2), with the first-correction amplitude A(1) being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the T(U) closest to the DCP, the effective susceptibility exponent gamma(eff) displays a nonmonotonic crossover from its nearly doubled three dimensional (3D)-Ising value toward its nearly double mean-field value with an increase in t. While for that far away from the DCP, it displays a nonmonotonic crossover from its single-limit Ising value toward a value slightly lower than its mean-field value of 1 with an increase in t. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic high t region. The renormalized Ising regime extends over a larger t range for the sample (or T(U)) closest to the DCP when compared to that far away from it. The in-between T(U)'s display a trend toward shrinkage in the renormalized Ising regime as T(U) shifts away from the DCP. Nevertheless, the crossover to the mean-field behavior is completed only beyond t>10(-2) for the T(U)'s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover behavior is discussed in terms of the varying influence of the DCP on the critical behavior along the T(U) line. The crossover behavior for the T(U)'s is pronounced and more sharp compared to the T(L)'s (lower critical solution temperatures) [U. K. Pradeep, J. Chem. Phys. 129, 134506 (2008)] in this mixture, although there exists no difference in the growth of the mesoscale clusters in the lower and upper one-phase regions in this mixture. Our observations suggest the need to look at the crossover behavior probably from two perspectives, namely, the dielectric effect and the clustering effect. The effective susceptibility exponent as a function of the field variable t(UL), instead of the conventional variable t, displays a sharp nonmonotonic crossover from its asymptotic 3D-Ising value ( approximately 1.24) toward a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis for the T(U) far away from the influence of the DCP.
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Affiliation(s)
- U K Pradeep
- Department of Physics, Indian Institute of Science, Bangalore, India.
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Pradeep UK. Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point. J Chem Phys 2008; 129:134506. [DOI: 10.1063/1.2987344] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Douglas JF, Dudowicz J, Freed KF. Lattice model of equilibrium polymerization. VI. Measures of fluid “complexity” and search for generalized corresponding states. J Chem Phys 2007; 127:224901. [DOI: 10.1063/1.2785187] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Vogel T, Bachmann M, Janke W. Freezing and collapse of flexible polymers on regular lattices in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061803. [PMID: 18233861 DOI: 10.1103/physreve.76.061803] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2007] [Indexed: 05/25/2023]
Abstract
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple-cubic and face-centered-cubic lattices by means of sophisticated chain-growth methods. In contrast to the bond-fluctuation polymer model in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.
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Affiliation(s)
- Thomas Vogel
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany.
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11
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Jacobs DT, Braganza CI, Brinck AP, Cohen AB, Lightfoot MA, Locke CJ, Suddendorf SJ, Timmers HR, Triplett AL, Venkataraman NL, Wellons MT. Universality in eight-arm star polystyrene and methylcyclohexane mixtures near the critical point. J Chem Phys 2007; 127:124905. [PMID: 17902935 DOI: 10.1063/1.2771161] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Measurements of the coexistence curve and turbidity were made on different molecular mass samples of the branched polymer-solvent system eight-arm star polystyrene in methylcyclohexane near its critical point. We confirmed that these systems belong in the Ising universality class. The location of the critical temperature and composition as well as the correlation length, susceptibility, and coexistence curve amplitudes were found to depend on molecular mass and the degree of branching. The coexistence curve diameter had an asymmetry that followed a "complete scaling" approach. All the coexistence curve data could be scaled onto a common curve with one adjustable parameter. We found the coexistence curve amplitude to be about 12% larger for branched than linear polystyrenes of the same molecular mass in either solvent cyclohexane or methylcyclohexane. The two-scale-factor universality ratio R was found to be independent of molecular mass or degree of branching.
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Affiliation(s)
- D T Jacobs
- Physics Department, The College of Wooster, Wooster, Ohio 44691, USA.
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Kostko AF, Anisimov MA, Sengers JV. Dynamics of critical fluctuations in polymer solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021804. [PMID: 17930058 DOI: 10.1103/physreve.76.021804] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2007] [Indexed: 05/25/2023]
Abstract
Using dynamic light scattering we have investigated the time dependence of fluctuations near the critical point of phase separation in solutions of polystyrene in cyclohexane with polymer molecular weights ranging from 196,000 to 11.4 x 10(6) g mol(-1). At the lowest polymer molecular weight the dynamic correlation function follows a single-exponential decay with a decay rate that can be represented by the mode-coupling theory of critical dynamics but with a mesoscopic viscosity that characterizes the hydrodynamic environment of the polymers in the solution. At all higher polymer molecular weights two distinct dynamic modes are observed, a slow and a fast mode, that originate from a coupling of the critical concentration fluctuations with viscoelastic relaxation of the polymer chain in solutions. This coupling causes an additional slowing down of the fluctuations on top of the well-known critical slowing down expected in the absence of a coupling between the two modes. From an analysis of the time dependence of the experimental dynamic correlation functions in terms of a theory of coupling of dynamic modes we are able to determine the viscoelastic properties of the polymers in the solution. These viscoelastic properties diverge in the theta-point limit of infinite polymer molecular weight.
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Affiliation(s)
- A F Kostko
- Chemical and Life Sciences Engineering, School of Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, USA
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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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Anisimov MA, Kostko AF, Sengers JV, Yudin IK. Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions. J Chem Phys 2005; 123:164901. [PMID: 16268722 DOI: 10.1063/1.2056543] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.
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Affiliation(s)
- M A Anisimov
- Department of Chemical and Biomolecular Engineering and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
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