Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energies for the fluid and solid phases. Cloud and shadow curves are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or reentrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus be defined only for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find, in addition, that coexistence of several solids with a fluid phase is also possible.     

Freezing of Classical Fluids in a Quenched Random Potential

The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.     

Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

The phase diagram of a polydisperse mixture of uniaxial rodlike and platelike hard parallelepipeds is determined for aspect ratios kappa=5 and 15. All particles have equal volume, and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for kappa=15, but to be unstable against demixing into two uniaxial nematics for kappa=5. The phase diagram for kappa=15 is qualitatively similar to that of the binary mixture, regardless of the amount of polydispersity, while for kappa=5 a sufficient amount of polydispersity stabilizes the biaxial phase. This provides clues for designing an experiment to observe this long searched biaxial phase.     

Phase instabilities in small particles

In this review we consider the existing theories for the structure of small particles and the nature of morphological instabilities as the size is reduced. The various electron microscopic observations confirming the stability of a new phase, the so called ‘Multiply twinned structure’, in small particles is discussed. A theoretical model is presented to calculate the free energy surfaces for a series of asymmetric and single crystal structures using a modified Curie-Wulff construction for the surface energy, and a disclination model for the elastic strain energy. Depending on the activation barrier heights and the Boltzmann occupancy factors for the various local minima on the energy surface, the idea of ‘quasi-melting’ is introduced and compared with the structural instabilities in molecular clusters seen recently by various authors using computer simulations. A phase diagram for small particles as a function of size and temperature is presented and the effect of statistical fluctuations on stability is discussed. Finally a phenomenological discussion relating the phase instabilities to various melting and related phase transitions is given.     

Influence of polydispersity on the phase behavior of statistical multiblock copolymers with Schultz-Zimm block molecular weight distributions

In this paper we investigate in a systematic way the influence of polydispersity in the block lengths on the phase behavior of AB-multiblock copolymer melts. As model system we take a polydisperse multiblock copolymer for which both the A-blocks and the B-blocks satisfy a Schultz-Zimm distribution. In the limit of low polydispersity the expressions for the vertex functions are clarified by using simple physical arguments. For various values of the polydispersity the phase diagram is presented, which shows that the region of stability of the bcc phase increases considerably with increasing polydispersity. The strong dependence of the periodicity of the microstructure on the polydispersity and on the interaction strength is presented. Received 2 July 1998     

Evidence for the strain critical point in high Tc superconductors

We report experimental evidence for the phase diagram of doped cuprate superconductors as a function of the micro-strain of the planar Cu-O bond length, measured by Cu K-edge EXAFS, and hole doping . The local lattice distortions are measured by EXAFS and the charge ordering is measured by synchrotron radiation diffuse X-ray diffraction. This phase diagram shows a QCP at P() where for charge-orbital-spin stripes and free carriers co-exist. The superconducting phase occurs in the region of critical fluctuations around this QCP. The function of two variables shows its maximum at the strain QCP. The critical fluctuations near this strain QCP give the self-organization of a metallic superlattice of quantum wires “superstripes" that favors the amplification of the critical temperature. Received 25 September 2000     

Phase diagram of a polydisperse soft-spheres model for liquids and colloids

The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.     

Precursor state of skyrmions in MnSi: a heat capacity study

The magnetic phase diagram of MnSi based on the detailed magneto‐heat capacity study is presented. It shows the A‐phase, a precursor to the formation of stable skyrmion lattice, along with the intermediate, helical, conical, ferromagnetic and paramagnetic phases. The field isotherms of specific heat in and around the transition temperature reveal the different magnetic modulations. The local minima represent the relatively low entropy state due to the formation of A‐phase as a precursor to the stable skyrmion lattice. The field‐induced second‐order phase transition is observed by melting the intermediate phase. The region of existence of first‐order phase transition is found to be, effectively, from helical to the intermediate phase. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polydispersity stabilizes biaxial nematic liquid crystals

Inspired by the observations of a remarkably stable biaxial nematic phase [van?den?Pol et?al., Phys. Rev. Lett. 103, 258301 (2009)], we investigate the effect of size polydispersity on the phase behavior of a suspension of boardlike particles. By means of Onsager theory within the restricted orientation (Zwanzig) model we show that polydispersity induces a novel topology in the phase diagram, with two Landau tetracritical points in between which oblate uniaxial nematic order is favored over the expected prolate order. Additionally, this phenomenon causes the opening of a huge stable biaxiality regime in between uniaxial nematic and smectic states.     

Core-softened potentials,multiple liquid–liquid critical points,and density anomaly regions: An exact solution

The pressure versus temperature phase diagram of a system of particles interacting through a multiscale shoulder-like potential is exactly computed in one dimension. The N-shoulder potential exhibits N density anomaly regions in the phase diagram if the length scales can be connected by a convex curve. The result is analyzed in terms of the convexity of the Gibbs free energy.     

The 2D Alternative Binary L—J System：Solid—Liquid Phase Diagram

The Lennard-Jones potential is introduced into the Collins model and is generalized to the two-dimensional alternative binary system.The Gibbs free energy of the binary system is calculated.According to the thermodynamic conditions of solid-liquid equilibrium,the “cigar-type ” phase diagram and the phase diagram with a minimum are obtained.The results are quite analogous to the behavior of three-dimensional substances.     

On phase equilibrium of Fe-Ni films

A phase equilibrium diagram of Fe-Ni films with Ni content from 0% to 30% and the thickness up to 1000 within the 0–850 °C temperature interval is proposed. The study of phase equilibrium was conducted by the method of electron-diffraction analysis of free films. The results obtained show some difference from the phase diagram of bulk alloys and film data published before.     

Influence of the polydispersity of side chains on the phase behavior of multigraft copolymers

Weak segregation theory is applied to studying the phase behavior of a melt of a binary multigraft copolymer with polydisperse side chains regularly spaced along the backbone. The resulting phase diagrams of the melt show an increase of the temperature of transition to an ordered state with increasing coefficient of polydispersity of side chains. The effects of the average length of the side chains and the distance between the points of their grafting on the phase diagram of the melt are examined.     

Quarksonic matter at high isospin density

Analogous to the quarkyonic matter at high baryon density in which the quark Fermi seas and the baryonic excitations coexist,it is argued that a "quarksonic matter" phase appears at high isospin density where the quark(antiquark) Fermi seas and the mesonic excitations coexist.We explore this phase in detail in both large Nc and asymptotically free limits.In the large Nc limit,we sketch a phase diagram for the quarksonic matter.In the asymptotically free limit,we study the pion superfluidity and thermodynamics of the quarksonic matter by using both perturbative calculations and an effective model.     

一维强相互作用极化费米子的相图

文章首先简要评述了目前强相互作用的极化冷费米原子体系的研究现状.在三维,人们对该体系基态存在着不同认识.为对这个问题有进一步了解,文章探讨了一维强相互作用极化费米气体.在均匀情况下,这是一个可积系统,可以得到该体系的一个严格相图.作者发现了一种非均匀的超流相在相空间占主导地位.在有外加束缚势的实验情况下,通过局域密度泛函近似,作者发现了两种新颖的相分离相.     

Flowing crystals: nonequilibrium structure of foam

Bubbles pushed through a quasi-two-dimensional channel self-organize into a variety of periodic lattices. The structures of these lattices correspond to local minima of the interfacial energy. The "flowing crystals" are long-lived metastable states, a small subset of possible local minima of confined quasi-two-dimensional foams [P. Garstecki and G. M. Whitesides, Phys. Rev. E 73, 031603 (2006)10.1103/PhysRevE.73.031603]. Experimental results suggest that the choice of the structures that we observe is dictated by the dynamic stability of the cyclic processes of their formation. Thus, the dynamic system that we report provides a unique example of nonequilibrium self-organization that results in structures that correspond to local minima of the relevant energy functional.     

Critical voltages and blocking stresses in nematic gels

We present a model of the dynamics of director rotation in nematic gels under combined electro-mechanical loading. Focusing on a model specimen, we describe the critical voltages that must be exceeded to achieve director reorientation, and the blocking stresses that prevent alignment of the nematic director with the applied electric field. The corresponding phase diagram shows that the dynamic thresholds defined above are different from those predicted on the sole basis of energetics. Multistep loading programs are used to explore the energy landscape of our model specimen, showing the existence of multiple local minima under the same voltage and applied stress. This leads us to conclude that hysteresis should be expected in the electro-mechanical response of nematic gels.     

Enhancement of Nematic Order and Global Phase Diagram of a Lattice Model for Coupled Nematic Systems

We use an infinite-range Maier–Saupe model, with two sets of local quadrupolar variables and restricted orientations, to investigate the global phase diagram of a coupled system of two nematic subsystems. The free energy and the equations of state are exactly calculated by standard techniques of statistical mechanics. The nematic–isotropic transition temperature of system A increases with both the interaction energy among mesogens of system B, and the two-subsystem coupling J. This enhancement of the nematic phase is manifested in a global phase diagram in terms of the interaction parameters and the temperature T. We make some comments on the connections of these results with experimental findings for a system of diluted ferroelectric nanoparticles embedded in a nematic liquid-crystalline environment.