Phase Transition

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David Andelman - One of the best experts on this subject based on the ideXlab platform.

  • ion induced lamellar lamellar Phase Transition in charged surfactant systems
    Journal of Chemical Physics, 2006
    Co-Authors: Daniel Harries, Rudi Podgornik, Adrian V Parsegian, Etay Maror, David Andelman
    Abstract:

    We propose a model for the liquid-liquid (L(alpha)-->L(alpha(') )) Phase Transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological nonelectrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae and the Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid Phase Transition when the Poisson-Boltzmann theory is self-consistently augmented by the Langmuir-Frumkin-Davies adsorption. This Phase Transition depends on the area per amphiphilic head group, as well as on nonelectrostatic interactions of the counterions with the lamellae and interactions between counterion-bound and counterion-dissociated surfactants. Coupling the lateral Phase Transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the L(alpha)-->L(alpha(') ) Phase Transition of didodecyldimethylammonium bromide (DDABr), but the Transition's apparent absence for the chloride and the iodide homologs. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.

  • ion induced lamellar lamellar Phase Transition in charged surfactant systems
    arXiv: Soft Condensed Matter, 2005
    Co-Authors: Daniel Harries, Rudi Podgornik, Adrian V Parsegian, Etay Maror, David Andelman
    Abstract:

    We propose a model for the liquid-liquid Phase Transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological non-electrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae, and Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid Phase Transition when Poisson-Boltzmann theory is self-consistently augmented by Langmuir-Frumkin-Davies adsorption. This Phase Transition depends on the area per amphiphilic headgroup, as well as on non-electrostatic interactions of the counterions with the lamellae, and interactions between counterion-bound and counterion-dissociated surfactants. Coupling lateral Phase Transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the Phase-Transition of DDABr (didodecyldimethylammonium bromide), but its apparent absence for the chloride and the iodide homologues. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.

Dan Vilenchik - One of the best experts on this subject based on the ideXlab platform.

  • The Condensation Phase Transition in Random Graph Coloring
    Communications in Mathematical Physics, 2016
    Co-Authors: Victor Bapst, Amin Coja-oghlan, Samuel Hetterich, Felicia Raßmann, Dan Vilenchik
    Abstract:

    Based on a non-rigorous formalism called the “cavity method”, physicists have put forward intriguing predictions on Phase Transitions in diluted mean-field models, in which the geometry of interactions is induced by a sparse random graph or hypergraph. One example of such a model is the graph coloring problem on the Erdős–Renyi random graph G ( n , d / n ), which can be viewed as the zero temperature case of the Potts antiferromagnet. The cavity method predicts that in addition to the k -colorability Phase Transition studied intensively in combinatorics, there exists a second Phase Transition called the condensation Phase Transition (Krzakala et al. in Proc Natl Acad Sci 104:10318–10323, 2007 ). In fact, there is a conjecture as to the precise location of this Phase Transition in terms of a certain distributional fixed point problem. In this paper we prove this conjecture for k exceeding a certain constant k _0.

  • the condensation Phase Transition in random graph coloring
    International Workshop and International Workshop on Approximation Randomization and Combinatorial Optimization. Algorithms and Techniques, 2014
    Co-Authors: Victor Bapst, Samuel Hetterich, Amin Cojaoghlan, Felicia Rasmann, Dan Vilenchik
    Abstract:

    Based on a non-rigorous formalism called the "cavity method", physicists have put forward intriguing predictions on Phase Transitions in discrete structures. One of the most remarkable ones is that in problems such as random k-SAT or random graph k-coloring, very shortly before the threshold for the existence of solutions there occurs another Phase Transition called condensation [Krzakala et al., PNAS 2007]. The existence of this Phase Transition appears to be intimately related to the difficulty of proving precise results on, e.g., the k-colorability threshold as well as to the performance of message passing algorithms. In random graph k-coloring, there is a precise conjecture as to the location of the condensation Phase Transition in terms of a distributional fixed point problem. In this paper we prove this conjecture for k exceeding a certain constant k0.

Prabir K. Mukherjee - One of the best experts on this subject based on the ideXlab platform.

  • isotropic to smectic c Phase Transition in liquid crystalline elastomers
    Journal of Chemical Physics, 2012
    Co-Authors: Prabir K. Mukherjee
    Abstract:

    A phenomenological model is developed to describe the isotropic-smectic-C Phase Transition in liquid-crystalline side-chain elastomers. We analyze the influence of external mechanical stress on the isotropic-smectic-C Phase Transition. While this Phase Transition is first order in low-molecular-weight materials, we show here that the order of this Transition does not change in liquid-crystalline elastomers. The temperature dependence of the heat capacity and the nonlinear dielectric effect in the isotropic Phase above the isotropic-smectic-C Phase Transition in liquid crystalline elastomers are calculated. The theoretical results are found to be in good agreement with experiment.

  • landau model of the smectic c isotropic Phase Transition
    Journal of Chemical Physics, 2002
    Co-Authors: Prabir K. Mukherjee, Harald Pleiner, Helmut R. Brand
    Abstract:

    We propose a Landau model to describe the smectic C–isotropic Phase Transition. A general Landau theory for the coupled orientational and translational order parameters and including the tilt angle is developed. The conditions for the smectic C–isotropic Phase Transition and the stability conditions of the smectic C Phase are calculated. On the basis of this model it is argued that the smectic C–isotropic Phase Transition is always first order. We present a detailed analysis of the question under which conditions a direct smectic C–isotropic Phase Transition prevails in comparison to smectic A–isotropic and nematic–isotropic Transitions. The theoretical results are found to be in qualitative agreement with all published experimental results.

  • simple landau model of the smectic a isotropic Phase Transition
    European Physical Journal E, 2001
    Co-Authors: Prabir K. Mukherjee, Harald Pleiner, Helmut R. Brand
    Abstract:

    A simple Landau-type free energy function is presented to describe the smectic-A-isotropic Phase Transition. Varying the coupling between orientational and positional order parameters, a smectic-A-isotropic or a nematic-isotropic Phase Transition occurs. Within this model the smectic-A-isotropic Phase Transition is found to be always more strongly first order than the nematic-isotropic Phase Transition. The theoretical results are found to be in good agreement with all published experimental results.

Daniel Harries - One of the best experts on this subject based on the ideXlab platform.

  • ion induced lamellar lamellar Phase Transition in charged surfactant systems
    Journal of Chemical Physics, 2006
    Co-Authors: Daniel Harries, Rudi Podgornik, Adrian V Parsegian, Etay Maror, David Andelman
    Abstract:

    We propose a model for the liquid-liquid (L(alpha)-->L(alpha(') )) Phase Transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological nonelectrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae and the Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid Phase Transition when the Poisson-Boltzmann theory is self-consistently augmented by the Langmuir-Frumkin-Davies adsorption. This Phase Transition depends on the area per amphiphilic head group, as well as on nonelectrostatic interactions of the counterions with the lamellae and interactions between counterion-bound and counterion-dissociated surfactants. Coupling the lateral Phase Transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the L(alpha)-->L(alpha(') ) Phase Transition of didodecyldimethylammonium bromide (DDABr), but the Transition's apparent absence for the chloride and the iodide homologs. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.

  • ion induced lamellar lamellar Phase Transition in charged surfactant systems
    arXiv: Soft Condensed Matter, 2005
    Co-Authors: Daniel Harries, Rudi Podgornik, Adrian V Parsegian, Etay Maror, David Andelman
    Abstract:

    We propose a model for the liquid-liquid Phase Transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological non-electrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae, and Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid Phase Transition when Poisson-Boltzmann theory is self-consistently augmented by Langmuir-Frumkin-Davies adsorption. This Phase Transition depends on the area per amphiphilic headgroup, as well as on non-electrostatic interactions of the counterions with the lamellae, and interactions between counterion-bound and counterion-dissociated surfactants. Coupling lateral Phase Transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the Phase-Transition of DDABr (didodecyldimethylammonium bromide), but its apparent absence for the chloride and the iodide homologues. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.

R Wada - One of the best experts on this subject based on the ideXlab platform.

  • nuclear liquid gas Phase Transition with machine learning
    Physical Review Research, 2020
    Co-Authors: R Wada, Rui Wang, Y G, Liewen Chen, Huanling Liu, Kaijia Sun
    Abstract:

    Machine-learning techniques have shown their capability for studying Phase Transitions in condensed matter physics. Here, we employ machine-learning techniques to study the nuclear liquid-gas Phase Transition. We adopt an unsupervised learning and classify the liquid and gas Phases of nuclei directly from the final-state raw experimental data of heavy-ion reactions. Based on a confusion scheme which combines the supervised and unsupervised learning, we obtain the limiting temperature of the nuclear liquid-gas Phase Transition. Its value 9.24±0.04MeV is consistent with that obtained by the traditional caloric curve method. Our study explores the paradigm of combining machine-learning techniques with heavy-ion experimental data, and it is also instructive for studying the Phase Transition of other uncontrollable systems, such as QCD matter.

  • nuclear liquid gas Phase Transition with machine learning
    arXiv: Nuclear Theory, 2020
    Co-Authors: R Wada, Rui Wang, Y G, Liewen Chen, Huanling Liu, Kaijia Sun
    Abstract:

    The machine-learning techniques have shown their capability for studying Phase Transitions in condensed matter physics. Here, we employ the machine-learning techniques to study the nuclear liquid-gas Phase Transition. We adopt an unsupervised learning and classify the liquid and gas Phases of nuclei directly from the final state raw experimental data of heavy-ion reactions. Based on a confusion scheme which combines the supervised and unsupervised learning, we obtain the limiting temperature of the nuclear liquid-gas Phase Transition. Its value $9.24\pm0.04~\rm MeV$ is consistent with that obtained by the traditional caloric curve method. Our study explores the paradigm of combining the machine-learning techniques with heavy-ion experimental data, and it is also instructive for studying the Phase Transition of other uncontrollable systems, like QCD matter.

  • quantum nature of a nuclear Phase Transition
    Physical Review Letters, 2008
    Co-Authors: A Bonasera, Zhichu Chen, R Wada, K Hagel, J B Natowitz, P K Sahu, L Qin, S Kowalski, Thomas Keutgen, T Materna
    Abstract:

    At finite temperatures and low densities, nuclei may undergo a Phase change similar to a classical liquid-gas Phase Transition. Temperature is the control parameter while density and pressure are the conjugate variables. In the nucleus the difference between the proton and neutron concentrations acts as an additional order parameter, for which the symmetry potential is the conjugate variable. We present experimental results which reveal the N/Z dependence of the Phase Transition and discuss possible implications of these observations in terms of the Landau free energy description of critical phenomena.