CiteULike: dchen's theory

Diffusion-Driven Pattern Formation in Ionic Chemical Solutions

Zsanett Virányi — 2008-05-07T23:25:52-00:00

Phys. Rev. Lett. 100, 088301 (2008)

The driving force in diffusion-driven pattern formation is the difference in the diffusional flux of the key species, which in the case of ionic systems builds up a local electric field at the concentration gradients. The arising additional migrational flux not only decreases but also enhances the instability of the base state, depending on the charge distribution among the components. The opposite charges on the slower diffusing autocatalyst and its reacting counterpart favor pattern formation and shift the onset of instability to a smaller difference in the diffusion coefficients. The same charges, in addition to having the opposite effect, may even lead to the complete stabilization of planar reaction fronts unstable in the neutral system.

Theory of Superconductivity

J Bardeen — 2006-06-19T20:17:17-00:00

Physical Review, Vol. 108, No. 5. (1 December 1957), 1175.

A theory of superconductivity is presented; based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy; âÏ. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor; formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum; is lower in energy than the normal state by amount proportional to an average (âÏ) 2 ; consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about 3.5 k T c at T =0Â°K to zero at T c . Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions; useful for perturbation expansions and calculations of transition probabilities; are given.

A Topographic View of Supercooled Liquids and Glass Formation

Frank Stillinger — 2007-05-19T22:04:07-00:00

Science, Vol. 267, No. 5206. (31 March 1995), pp. 1935-1939.

Various static and dynamic phenomena displayed by glass-forming liquids, particularly those near the so-called "fragile" limit, emerge as manifestations of the multidimensional complex topography of the collective potential energy function. These include non-Arrhenius viscosity and relaxation times, bifurcation between the [agr]- and [beta]-relaxation processes, and a breakdown of the Stokes-Einstein relation for self-diffusion. This multidimensional viewpoint also produces an extension of the venerable Lindemann melting criterion and provides a critical evaluation of the popular "ideal glass state" concept. 10.1126/science.267.5206.1935

Non-Gaussian effects, space-time decoupling, and mobility bifurcation in glassy hard-sphere fluids and suspensions

Erica Saltzman — 2007-10-29T19:47:05-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 74, No. 6. (2006)

Brownian trajectory simulation methods are employed to fully establish the non-Gaussian fluctuation effects predicted by our nonlinear Langevin equation theory of single particle activated dynamics in glassy hard-sphere fluids. The consequences of stochastic mobility fluctuations associated with the space-time complexities of the transient localization and barrier hopping processes have been determined. The incoherent dynamic structure factor was computed for a range of wave vectors and becomes of an increasingly non-Gaussian form for volume fractions beyond the (naive) ideal mode coupling theory (MCT) transition. The non-Gaussian parameter (NGP) amplitude increases markedly with volume fraction and is well described by a power law in the maximum restoring force of the nonequilibrium free energy profile. The time scale associated with the NGP peak becomes much smaller than the relaxation time for systems characterized by significant entropic barriers. An alternate non-Gaussian parameter that probes the long time relaxation process displays a different shape, peak intensity, and time scale of its maximum. However, a strong correspondence between the classic and alternate NGP amplitudes is predicted which suggests a deep connection between the early and final stages of cage escape. Strong space-time decoupling emerges at high volume fractions as indicated by a nondiffusive wave vector dependence of the relaxation time and growth of the translation-relaxation decoupling parameter. Displacement distributions exhibit non-Gaussian behavior at intermediate times, evolving into a strongly bimodal form with slow and fast subpopulations at high volume fractions. Qualitative and semiquantitative comparisons of the theoretical results with colloid experiments, ideal MCT, and multiple simulation studies are presented.

Activated Hopping, Barrier Fluctuations, and Heterogeneity in Glassy Suspensions and Liquids

KS Schweizer — 2007-10-29T19:53:08-00:00

J. Phys. Chem. B, Vol. 108, No. 51. (23 December 2004), pp. 19729-19741.

Abstract: Our entropic barrier hopping theory of glassy hard sphere colloidal suspensions is extended to include heterogeneity within a simple trap model framework. The origin of local domains, their size, and the corresponding static barrier fluctuations are attributed to mesoscopic density fluctuations of an amplitude controlled by the bulk compressibility. Based on typical values of the density fluctuation correlation length in dense liquids, the domain size on which correlated hopping occurs is estimated to be 3-4 particle or molecular diameters. Consequences of barrier fluctuations include an increased average relaxation time, faster diffusion, stretched exponential relaxation, diffusion-viscosity decoupling, and a fractional Stokes-Einstein relation. The common origin of the fluctuation effects is the heterogeneity-induced component of the barrier. For colloidal suspensions in the typically studied volume fraction regime the barrier fluctuations have modest consequences, but significantly larger effects are predicted in the putative glassy regime. A statistical dynamical analysis of domain lifetime suggests that for suspensions the relaxation time of mesoscopic collective density fluctuations is at least as long as the single particle hopping time. A general, model-independent analysis of the single molecule incoherent dynamic structure factor for suspensions and thermal liquids has also been performed in the long time and intermediate wavevector regime. The coupling of single particle density and longitudinal stress fluctuations results in a wavevector-dependent apparent diffusion constant and a dynamic correlation length scale which is strongly temperature dependent and directly related to the translation-rotation decoupling factor. This dynamic length is estimated to be 10 times larger than a molecular diameter for tris-naphthyl benzene near the glass transition temperature but shrinks to a molecular size above the crossover temperature that signals the emergence of collective barriers.

Activated hopping and dynamical fluctuation effects in hard sphere suspensions and fluids

Erica Saltzman — 2007-10-29T19:49:58-00:00

The Journal of Chemical Physics, Vol. 125, No. 4. (2006)

Single particle Brownian dynamics simulation methods are employed to establish the full trajectory level predictions of our nonlinear stochastic Langevin equation theory of activated hopping dynamics in glassy hard sphere suspensions and fluids. The consequences of thermal noise driven mobility fluctuations associated with the barrier hopping process are determined for various ensemble-averaged properties and their distributions. The predicted mean square displacements show classic signatures of transient trapping and anomalous diffusion on intermediate time and length scales. A crossover to a stronger volume fraction dependence of the apparent nondiffusive exponent occurs when the entropic barrier is of order the thermal energy. The volume fraction dependences of various mean relaxation times and rates can be fitted by empirical critical power laws with parameters consistent with ideal mode-coupling theory. However, the results of our divergence-free theory are largely a consequence of activated dynamics. The experimentally measurable alpha relaxation time is found to be very similar to the theoretically defined mean reaction time for escape from the barrier-dominated regime. Various measures of decoupling have been studied. For fluid states with small or nonexistent barriers, relaxation times obey a simple log-normal distribution, while for high volume fractions the relaxation time distributions become Poissonian. The product of the self-diffusion constant and mean alpha relaxation time increases roughly as a logarithmic function of the alpha relaxation time. The cage scale incoherent dynamic structure factor exhibits nonexponential decay with a modest degree of stretching. A nearly universal collapse of the different volume fraction results occurs if time is scaled by the mean alpha relaxation time. Hence, time-volume fraction superposition holds quite well, despite the presence of stretching and volume fraction dependent decoupling associated with the stochastic barrier hopping process. The relevance of other origins of dynamic heterogeneity (e.g., mesoscopic domains), and comparison of our results with experiments, simulations, and alternative theories, is discussed. ©2006 American Institute of Physics

Statistical Mechanics of Stress Transmission in Disordered Granular Arrays

SF Edwards — 2008-04-28T13:46:02-00:00

Physical Review Letters, Vol. 82, No. 26. (28 June 1999), 5397.

Measurement of the full shear-induced self-diffusion tensor of noncolloidal suspensions

V Breedveld — 2008-04-26T00:14:23-00:00

The Journal of Chemical Physics, Vol. 116, No. 23. (2002), pp. 10529-10535.

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Strain softening, yielding, and shear thinning in glassy colloidal suspensions

Vladimir Kobelev — 2008-04-26T00:07:02-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 71, No. 2. (2005)

A microscopic theory for the dependence on external strain, stress, and shear rate of the transient localization length, elastic modulus, alpha relaxation time, shear viscosity, and other dynamic properties of glassy colloidal suspensions is formulated and numerically applied. The approach is built on entropic barrier hopping as the elementary physical process. The concept of an ideal glass transition plays no role, and dynamical slowing down is a continuous, albeit precipitous, process with increasing colloid volume fraction. The relative roles of mechanically driven motion versus thermally activated barrier hopping and transport have been studied. Various scaling behaviors are found for the relaxation time and shear viscosity in both the controlled stress and shear rate mode of rheological experiments. Apparent power law and/or exponential dependences of the elastic modulus and perturbative and absolute yield stresses on colloid volume fraction are predicted. A nonmonotonic dependence of the absolute yield strain on volume fraction is also found. Qualitative and quantitative comparisons of calculations with experiments on high volume fraction glassy colloidal suspensions show encouraging agreement, and multiple testable predictions are made. The theory is generalizable to treat nonlinear rheological phenomena in other soft glassy complex fluids including depletion gels.

Drift, creep and pinning of a particle in a correlated random potential

Heinz Horner — 2008-04-26T00:04:43-00:00

Zeitschrift für Physik B Condensed Matter, Vol. 100, No. 2. (20 May 1996), pp. 243-257.

The motion of a particle in a correlated random potential under the influence of a driving force is investigated in mean field theory. The correlations of the disorder are characterized by a short distance cutoff and a power law decay with exponent$γ$ at large distances. Depending on temperature and$γ$ , drift with finite mobility, creep or pinning is found. This is in qualitative agreement with results in one dimension. This model is of interest not only in view of the motion of particles or manifolds in random media, it also improves the understanding of glassy non-equilibrium dynamics in mean field models. The results, obtained by numerical integration and analytic investigations of the various scaling regimes in this problem, are compared with previous proposals regarding the long time properties of such systems and with replica calculations.

An elastic, plastic, viscous model for slow shear of a liquid foam

P Marmottant — 2008-04-18T01:30:45-00:00

The European Physical Journal E - Soft Matter, Vol. 23, No. 4. (2007), pp. 337-347.

Abstract. We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material-specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called “quasi-static”) limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.

A Theory of Cooperative Diffusion in Dense Granular Flows

Martin Bazant — 2007-04-05T21:54:49-00:00

(8 May 2004)

Dilute granular flows are routinely described by collisional kinetic theory, but dense flows require a fundamentally different approach, due to long-lasting, many-body contacts. In the case of silo drainage, many continuum models have been developed for the mean flow, but no realistic statistical theory is available. Here, we propose that particles undergo cooperative displacements in response to diffusing “spots” of free volume. The typical spot size is several particle diameters, so cages of nearest neighbors tend to remain intact over large distances. The spot hypothesis relates diffusion and cage-breaking to volume fluctuations and spatial velocity correlations, in agreement with new experimental data. It also predicts density waves caused by weak spot interactions. Spots enable fast, multiscale simulations of dense flows, in which a small, internal relaxation enforces packing constraints during spot-induced motion. In the continuum limit of the model, tracer diffusion is described by a new stochastic differential equation, where the drift velocity and diffusion tensor are coupled non-locally to the spot density. The same mathematical formalism may also find applications to glassy relaxation, as a compelling alternative to void (or hole) random walks.

Phase Behavior and Charge Regulation of Weak Polyelectrolyte Grafted Layers

Peng Gong — 2008-03-19T17:31:41-00:00

Physical Review Letters, Vol. 98, No. 1. (2007)

The stability of weak polyelectrolytes end grafted to a planar surface has been studied with a molecular theory. The effective quality of the solvent is found to depend on the interplay between polymer grafting density, acid-base equilibrium, and salt concentration. Our results reveal that increasing salt concentration results in a thermodynamically more stable layer. This reverse salt effect is due to the competition between the solvent quality and the dual role of the ionic strength in screening the electrostatic interactions (reducing stability with increasing salt concentration), and regulating the charge on the polymer (increasing charge with increasing salt concentration). Grafted weak polyelectrolyte layers are found to be thermodynamically unstable at intermediate surface coverages. Additionally, it is established that the increased solubility of the layer at low surface coverage is due to the relatively large charge of the grafted polymers. The range of stability of the film with regard to polymer surface coverage, temperature, bulk pH and salt concentration is demonstrated.

Scaling in Ecosystems and the Linkage of Macroecological Laws

Jayanth Banavar — 2008-03-19T16:49:23-00:00

Physical Review Letters, Vol. 98, No. 6. (2007)

Scaling provides an elegant framework for understanding power-law behavior and deducing relationships between critical exponents. We demonstrate that scaling theory can be generalized to develop a framework for the analysis of diverse empirical macroecological relationships traditionally treated as independent. Our mathematical arguments predict links between the species-area relationship, the relative species abundance and community size spectra in excellent accord with empirical data.

Fluctuation-Dissipation Theorem in an Aging Colloidal Glass

Sara Farouji — 2007-11-26T20:20:36-00:00

Physical Review Letters, Vol. 98, No. 10. (2007)

We provide a direct experimental test of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this nonequilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz–10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging.

Molecular Theory of Physical Aging in Polymer Glasses

Kang Chen — 2008-03-18T23:12:48-00:00

Physical Review Letters, Vol. 98, No. 16. (2007)

A molecular level theory for the physical aging of polymer glasses is proposed. The nonequilibrium time evolution of the amplitude of long wavelength density fluctuations, and its influence on activated barrier hopping, plays an essential role. The theory predicts temperature-dependent apparent power-law aging of the segmental relaxation time and logarithmic aging of thermodynamiclike properties, in good accord with experiments. A physical origin for the quantitative nonuniversal aspects based on the amplitude of quenched density fluctuations is suggested.

Density-Functional Theory for Polymer Fluids with Molecular Weight Polydispersity

Clifford Woodward — 2008-03-17T22:37:46-00:00

Physical Review Letters, Vol. 100, No. 9. (2008)

We develop a density-functional theory for polydisperse polymer fluids satisfying the Schulz-Flory distribution. The resulting equations are remarkably simple and quickly solved, the computational effort scaling with the polydispersity index, rather than the average molecular weight. Equilibrium, or “living”, polymers enter naturally as very polydisperse samples. We illustrate the importance of polydispersity on colloid stability by investigating interactions between adsorbing and nonadsorbing surfaces. Significant free energy barriers are present in monodisperse samples, but these diminish as the degree of polydispersity increases.

Chemical Theory and Computation Special Feature: Molecular dynamics studies of heterogeneous dynamics and dynamic crossover in supercooled atomic liquids

Hans Andersen — 2007-04-27T09:47:54-00:00

PNAS, Vol. 102, No. 19. (10 May 2005), pp. 6686-6691.

Supercooled liquids near the glass transition exhibit the phenomenon of heterogeneous relaxation; at any specific time, a nominally homogeneous equilibrium fluid undergoes dynamic fluctuations in its structure on a molecular distance scale with rates that are very different in different regions of the sample. Several theoretical and simulation studies have suggested a change in the nature of the dynamics of fluids as they are supercooled, leading to the concept of a dynamic crossover that is often associated with mode coupling theory. Here, we will review the use of molecular dynamics computer simulation methods to investigate heterogeneous dynamics and dynamic crossovers in models of atomic liquids. 10.1073/pnas.0500946102

Entropic barriers, activated hopping, and the glass transition in colloidal suspensions

Kenneth Schweizer — 2007-10-29T19:56:08-00:00

The Journal of Chemical Physics, Vol. 119, No. 2. (2003), pp. 1181-1196.

A microscopic kinetic description of single-particle transient localization and activated transport in glassy fluids is developed which combines elements of idealized mode-coupling theory, density functional theory, and activated rate theory. Thermal fluctuations are included via a random force which destroys the idealized glass transition and restores ergodicity through activated barrier hopping. The approach is predictive, containing no adjustable parameters or postulated underlying dynamic or thermodynamic divergences. Detailed application to hard-sphere colloidal suspensions reveals good agreement with experiment for the location of the kinetic glass transition volume fraction, the dynamic incoherent scattering relaxation time, apparent localization length, and length scale of maximum nongaussian behavior. Multiple connections are predicted between thermodynamics, short-time dynamics in the nearly localized state, and long-time relaxation by entropic barrier crossing. A critical comparison of the fluid volume fraction dependence of the hopping time with fit formulas which contain ideal divergences has been performed. Application of the derivative Stickel analysis suggests that the fit functions do not provide an accurate description over a wide range of volume fractions. Generalization to treat the kinetic vitrification of more complex colloidal and nanoparticle suspensions, and thermal glass-forming liquids, is possible. ©2003 American Institute of Physics.

Dynamical density functional theory for glassy behaviour

Kazuhiro Fuchizaki — 2008-03-01T21:07:23-00:00

Journal of Physics: Condensed Matter, Vol. 14, No. 46. (2002), pp. 12203-12222.

Glassy dynamics of fluid particles in a supercooled liquid is discussed on the basis of the time-evolution equation obtained through the dynamical density functional theory (DDFT). The advantage, brought about by the coarse-grained nature of the formalism, in treating such strongly correlated motion over other approaches, such as the mode-coupling theories and direct computer simulations, is emphasized. A direction in which the DDFT should prove its worth on examining the phenomena is suggested.

Ten questions on glassformers, and a real space `excitations' model with some answers on fragility and phase transitions

CA Angell — 2008-03-01T20:23:55-00:00

Journal of Physics: Condensed Matter, Vol. 12, No. 29. (2000), pp. 6463-6475.

We formulate ten questions, covering outstanding aspects of the phenomenology of glassforming liquids, which we believe must be properly answered by any successful theory of structural glassformers. The questions range across thermodynamic, mass transport and vibrational dynamics phenomena. While these questions will only be addressed properly by a collective variables approach (many aspects of which are reported in these proceedings) a number of them can be dealt with by use of simple physical models of appropriate form. Here we discuss one such model in which the existence of elementary configurational excitations of the amorphous quasilattice is proposed. These states, which may range from broken bonds to packing defects, can be excited independently in the majority of cases, or cooperatively in others. We summarize essential results of this model. These suggest that the source of the different fragilities in liquids (and the reason that structural glasses, alone among `glassy' systems, have marked heat capacity jumps at Tg) may lie largely in the way these configurational excitations couple to the vibrational modes of the system. The generation of low frequency modes in the density of vibrational states, as a direct consequence of the excitation of configurational states, explains why the quasi-elastic scattering from fragile liquids is so much stronger near and above Tg than in the case of strong liquids, and why the normal glass transition can be detected in picosecond time scale experiments. Interactions among the `excitations', or `defects', are taken into account using the one component system equivalent of the binary system `regular solution' model (which keeps only the first order term of the free energy of mixing expansion). We show that a liquid-liquid first order transition must occur at sufficiently strong defect-defect interactions. The highly overconstrained amorphous silicon quasilattice is a strong candidate for such a transition. We identify the `first order melting' of amorphous silicon, and the sudden, reproducible, termination of supercooling in experimental liquid silicon and germanium, with the phase transition predicted by the model. Many more cases of this phase transition may be anticipated, and a corresponding range of glasses with low residual entropies - approaching the `perfect' glass state - are predicted.

Connection between Adam-Gibbs Theory and Spatially Heterogeneous Dynamics

Nicolas Giovambattista — 2008-03-01T18:18:24-00:00

Physical Review Letters, Vol. 90, No. 8. (28 February 2003), 085506.

We investigate the spatially heterogeneous dynamics in the extended simple point charge model of water using molecular dynamics simulations. We relate the average mass n * of mobile particle clusters to the diffusion constant and the configurational entropy. Hence; n * can be interpreted as the mass of the “cooperatively rearranging regions” that form the basis of the Adam-Gibbs theory of the dynamics of supercooled liquids. We also examine the time and temperature dependence of these transient clusters.

Heterogeneity at the glass transition: a review

Hans Sillescu — 2007-11-28T00:10:01-00:00

Journal of Non-Crystalline Solids, Vol. 243, No. 2-3. (February 1999), pp. 81-108.

Theoretical concepts and experimental evidence of heterogeneity in glass-forming liquids and polymers are reviewed. The main purpose is to provide an introduction to theoretical developments and recent experiments which have led to rapidly increasing knowledge. Realizing that there is no consensus in regard to the various scenarios of the glass transition starting from rather different assumptions we try to give a balanced overview although we also compare and interrelate some of the approaches. The experimental part describes recent nuclear magnetic resonance, dielectric, and optical experiments from which dynamically distinguishable subensembles can be selected thus proving the existence of a well defined dynamical heterogeneity.

How does a system respond when driven away from thermal equilibrium?

C Jarzynski — 2006-08-07T18:54:14-00:00

PNAS, Vol. 98, No. 7. (27 March 2001), pp. 3636-3638.

10.1073/pnas.081074598

Dynamics of supercooled liquids and the glass transition

U Bengtzelius — 2006-07-27T15:35:26-00:00

Journal of Physics C: Solid State Physics, Vol. 17, No. 33. (1984), pp. 5915-5934.

Closed nonlinear equations are derived for a self-consistent treatment of density propagation, self-diffusion and current relaxation in a classical monatomic fluid. The solution for a hard-sphere model system brings out a phase transition to a glass at the packing fraction 0.516. Approaching the transition from the glass side the particle mean-square displacement increases to a finite value. A simplified model is analysed in detail. Approaching the transition from the liquid side the diffusivity is predicted to decrease to zero with a power law with exponent 1.76 which the authors find to agree well with some experimental data. The low-frequency density spectrum is found to consist of two contributions; one is an elastic line of the frozen structure on the glass side, which then decays to a narrow diffusion broadened quasielastic peak on the fluid side; the other part is described by a dynamical scaling law and it yields in particular a spectrum diverging at the glass point with certain exponents.

Mode-coupling theory

David Reichman — 2006-07-27T15:15:31-00:00

In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori–Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory.