Glass-forming liquids

When liquids are cooled below their melting temperature T_m, sometimes they do not solidify immediately but remain in supercooled state up to temperatures far below the melting point. Under certain conditions, they can solidify into the form of amorphous solids without crystallizing. A supercooled liquid and a amorphous solid are metastable phases, which are not completely understood in terms of structural arrangement and thermodynamic behaviour. But by far the most interesting feature is the glass transition which is the manifestation of a true thermodynamic transition and a dynamic event since a dramatic dynamic arrest intervenes. A unified theory of supercooled liquids and glass transition does not yet exist and, more specifically, the link between the sharp increase of the relaxation time and the correlation length is a question still largely open. This article presents in the most elementary manner a brief overview of this delicate issue.     

Quantum states far from the energy eigenstates of any local Hamiltonian

What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, i.e., not a multiple of the identity, and L local, in the sense of containing interaction terms involving at most L bodies, for some fixed L. We construct quantum states psi which are "far away" from all the eigenstates E of any nontrivial L-local Hamiltonian, in the sense that ||psi-E|| is greater than some constant lower bound, independent of the form of the Hamiltonian.     

Dynamics of supercooled fluids

The dynamics of supercooled fluids is investigated. This approach is based on a static mean field theory of freezing developed by Grewe and Klein and the dynamical theory of Cahn and Hilliard. A nonlocal term is introduced to the standard Landau-Ginsburg-Wilson Hamiltonian and the resulting dynamics are explored. It is shown that for short times the supercooled liquid is unstable to density fluctuations of a nonzero wavevectork. Thek at which this instability first appears is on the order of the inverse range of the interaction potential.After Oct. 1, 1982: Institute for Basic Studies National Bureau of Standards Washington DC 20234, USASupported in part by grants from the ARO, NSF     

Theoretical approaches to the glass transition in simple liquids

Theoretical approaches to the development of an understanding of the behaviour of simple supercooled liquids near the structural glass transition are reviewed and our work on this problem, based on the density functional theory of freezing and replicated liquid state theory, are summarized in this context. A few directions for further work on this problem are suggested.     

Surface supercooling and stability of n-alkane films

The surface tension of n-octadecane was studied in the vicinity of the bulk melting point using both the maximum bubble pressure and Wilhelmy plate methods. The bubble surfaces were found to be supercooled below the surface freezing point. The onset of surface freezing is indicated by a sharp drop in surface tension at a constant temperature. This transition is accompanied by an increased film stability resulting in longer bubble lifetimes at the liquid surface. Variations in bubble lifetime reflect changes in the interfacial mechanical properties of the film from liquidlike to solidlike.     

Atomic mechanism of glass formation in supercooled monatomic liquids

Atomic mechanism of glass formation in supercooled monatomic liquids is monitored via analyzing the spatial arrangement of solid-like atoms. The supercooled states are obtained by cooling from the melt using molecular dynamics (MD) simulation. Solid-like atoms, detected via Lindemann-like freezing criterion, are found throughout the liquid. Their number increases with decreasing temperature and they form clusters. In the deeply supercooled region, all solid-like atoms form a single percolation cluster which spans throughout the system. The number of atoms in this cluster increases steeply with further cooling. Glass formation in supercooled liquids occurs when a single percolation cluster of solid-like atoms involves the majority of atoms in the system to form a relatively rigid glassy solid. By analyzing the temperature dependence of static and dynamic properties, we identify three characteristic temperatures of glass formation in supercooled liquids including the Vogel–Fulcher temperature.     

Simulations of the flipping images and microparameters of molecular orientations in liquids according to the molecule string model

The relaxation dynamics of liquids is one of the fundamental problems in liquid physics,and it is also one of the key issues to understand the glass transition mechanism.It will undoubtedly provide enlightenment on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied.In this paper,we first give five microparameters to describe the individual molecular string(MS) relaxation based on the dynamical Hamiltonian of the MS model,and then simulate the images of individual MS ensemble,and at the same time calculate the parameters of the equilibrium state.The results show that the main molecular orientation flipping image in liquids(including supercooled liquid) is similar to the random walk.In addition,two pairs of the parameters are equal,and one can be ignored compared with the other.This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of the general Glauber type,and the computer simulation time of interaction MS relaxation.Moreover,the conclusion is of reference significance for solving and simulating the multi-state MS model.     

Simulations of the flipping images and microparameters of molecular orientations in liquids according to molecule string model

The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly give enlightenments on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied. In this paper, we first give five microparameters to describe the individual molecular string (MS) relaxation based on the dynamical Hamiltonian of the MS model, and then simulate the images of individual MS ensemble, at the same time calculate the parameters of the equilibrium state. The results show that the main molecular orientation flipping image in liquids (including supercooled liquid) is similar to the random walk. In addition, two pairs of the parameters are equal, and one can be ignored compared with the other. This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of general Glauber type, and the computer simulation time of interaction MS relaxation. Moreover, the conclusion has no doubt of the reference significance for solving and simulating the multi-state MS model.     

Melting, freezing and nucleation in nanoclusters of potassium chloride

Molecular dynamics simulations of the melting, freezing and nucleation are presented for unconstrained nanoclusters of KCl with a number of ions between 512 and 10648. The maximum extent of the probed liquid supercooling is analysed to the light of theoretical predictions and compared with experimental data. The fraction of the solid-like ions in the supercooled liquid is used as an indicator of heterogeneities within the liquid. Induced nucleation by seeding the supercooled liquid indicates that solid-liquid coexistence is stable, and sustained during the lifetime of the clusters, relatively to the supercooled liquid. A phenomenological analysis on the relaxation times of the crystal growth process is made. Critical nuclei sizes computed from the effectiveness of the seeds in the heterogeneous nucleation of the supercooled liquid, and from the residual crystallites in clusters not totally melted, are presented as a function of the temperature. The behavior of the systems is followed through various properties such as liquid and solid molar fractions, enthalpies of melting, heat capacities, self-diffusion coefficients and relaxation times related to the freezing process. The consistency of the simulation results for the heterogeneous nucleation is assessed by means of a classical nucleation model, from which an estimate of the interfacial surface tension is also worked out and compared with experimental data.     

The exciton many-body theory extended to any kind of composite bosons

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between N excitons can be treated exactly through a set of dimensionless “Pauli scatterings” between two excitons. Many-body effects with free excitons turn out to be rather simple because these excitons are the exact one-pair eigenstates of the semiconductor Hamiltonian, in the absence of localized traps. They consequently form a complete orthogonal basis for one-pair states. As essentially all quantum particles known as bosons are composite bosons, it is highly desirable to extend this free exciton many-body theory to other kinds of “cobosons” — a contraction for composite bosons — the physically relevant ones being possibly not the exact one-pair eigenstates of the system Hamiltonian. The purpose of this paper is to derive the “Pauli scatterings” and the “interaction scatterings” of these cobosons in terms of their wave functions and the interactions which exist between the fermions from which they are constructed. It is also explained how to calculate many-body effects in such a very general composite boson system.     

Skyrme liquid versus Skyrme solid

Based on generic sum rules for two-dimensional, isotropic electron quantum liquids in the lowest Landau level, we propose analytic pair distribution functions for spin-polarized and spin-unpolarized liquid phases at filling factors . From the pair distribution functions we calculate the energy of such liquid phases and compare with the energy of the solid phase. The comparison suggests that the quantum melting phase transition to the Skyrme solid may lie much closer to ν=1 than ever expected.     

New criterion in predicting glass forming ability of various glass-forming systems

It has been confirmed that glass-forming ability （GFA） of supercooled liquids is related to not only liquid phase stability but also the crystallization resistance. In this paper, it is found that the liquid region interval （T1 - Tg） characterized by the normalized parameter of Tg/T1 could reflect the stability of glass-forming liquids at the equilibrium state, whilst the normalization of supercooled liquid region △Tx=（Tx - Tg）, i.e. △Tx/Tx （wherein T1 is the liquidus temperature, Tg the glass transition temperature, and Tx the onset crystallization temperature） could indicate the crystallization resistance during glass formation. Thus, a new parameter, defined as ζ = Tg/T1＋△Tx/Tx is established to predict the GFA of supercooled liquids. In comparison with other commonly used criteria, this parameter demonstrates a better statistical correlation with the GFA for various glass-forming systems including metallic glasses, oxide glasses and cryoprotectants.     

New criterion in predicting glass forming ability of various glass-forming systems

It has been confirmed that glass-forming ability (GFA) of supercooled liquids is related to not only liquid phase stability but also the crystallization resistance. In this paper, it is found that the liquid region interval ($T_{\rm l}-T_{\rm g})$ characterized by the normalized parameter of $T_{\rm g}$/$T_{\rm l}$ could reflect the stability of glass-forming liquids at the equilibrium state, whilst the normalization of supercooled liquid region $\Delta T_{\rm x}$=($T_{\rm x}-T_{\rm g})$, i.e. $\Delta T_{\rm x}$/$T_{\rm x}$ (wherein $T_{\rm l}$ is the liquidus temperature, $T_{\rm g}$ the glass transition temperature, and $T_{\rm x}$ the onset crystallization temperature) could indicate the crystallization resistance during glass formation. Thus, a new parameter, defined as $\xi =T_{\rm g}$/$T_{\rm l}+\Delta T_{\rm x}$/$T_{\rm x}$ is established to predict the GFA of supercooled liquids. In comparison with other commonly used criteria, this parameter demonstrates a better statistical correlation with the GFA for various glass-forming systems including metallic glasses, oxide glasses and cryoprotectants.     

Amorphous solidification in polymer-platelet nanocomposites

Computer simulations are used to understand the molecular basis of the rheology changes in polymer melts when loaded with platelet filler particles, specifically when the polymer and nanofiller interact attractively. With decreasing temperature, there is increasing aggregation between chains and filler and an increase in the polymer matrix structural relaxation time. These lifetimes are predicted to diverge at an extrapolated temperature, which we identify with the emergence of an amorphous solid state. Our findings suggest that filled polymers are phenomenologically similar to solutions of associating polymers and to supercooled liquids near their glass transition.     

Many-Body Localization Transition in the Heisenberg Ising Chain

In this paper, we use exact matrix diagonalization to explore the many-body localization (MBL) transition of the Heisenberg Ising spin-1/2 chain with nearest neighbor couplings and disordered external fields. It demonstrates that the fidelity, magnetization and spin-spin space correlation can be used to characterize the many-body localization transition in this closed spin system which is also in agreement with previous analytical and numerical results. We test the properties for the middle third many-body eigenstates. It shows that for this model with random-field, the excited-state fidelity exhibits a pronounced drop at the transition and then gradually tends to be stable in the localized phase, the critical point and the final value of averaged fidelity are all size dependent. It demonstrates that disordered external fields drive the occurrence of the MBL transition. Moreover, we investigate the magnetization and spin-spin space correlation in this model to verify the conclusion we got and further explore the properties of ergodic phase and localized phase.

     

Quantitative theory of thermal fluctuations and disorder in the vortex matter

A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zero temperature liquid state therefore serves as a (pseudo) ‘fixed point’ controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order-disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.     

Exchange frequencies in the 2D Wigner crystal

Using path integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2D Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2D (3)He. Using the resulting multispin exchange model we find the spin Hamiltonian for r(s) < or = 175 +/- 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.     

Spin-Dependent Bohmian Electronic Trajectories for Helium

We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable, we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of one-particle hydrogenic eigenstates. First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory quantum mechanics textbook. For example, the trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical. We then examine higher-dimensional approximations, i.e., eigenstates Ψ _α of the Hamiltonian in this truncated basis, and show that ∇ _i S _α =0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the same, regardless of the accuracy of the eigenfunction approximation. The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii) execute circular orbits around the z-axis with constant velocity.