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Phillip L Geissler

Publications and source records attributed to Phillip L Geissler.

14 recordsLinked to original sources
PubMed2006

Equilibrium free energies from fast-switching trajectories with large time steps.

Jarzynski's [Phys. Rev. Lett. 78, 2690 (1997)] identity for the free-energy difference between two equilibrium states can be viewed as a special case of a more general procedure based on phase-space mappings. Solving a system's equation of motion by approximate means generates a mapping that is perfectly valid for this purpose, regardless of how closely the solution mimics true time evolution. We exploit this fact, using crudely dynamical trajectories to compute free-energy differences that are in principle exact. Numerical simulations show that Newton's equation can be discretized to low order over very large time steps (limited only by the computer's ability to represent resulting values of dynamical variables) without sacrificing thermodynamic accuracy. For computing the reversible work required to move a particle through a dense liquid, these calculations are more efficient than conventional fast-switching simulations by more than an order of magnitude. We also explore consequences of the phase-space mapping perspective for systems at equilibrium, deriving an exact expression for the statistics of energy fluctuations in simulated conservative systems.

Journal Article↗
PubMed2006

Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid.

We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically and verify this prediction numerically. In addition, we predict that the characteristic relaxation time of the model is a nonmonotonic function of attraction strength, again in agreement with numerical results.

Journal Article↗
PubMed2005

Electric field fluctuations drive vibrational dephasing in water.

We present a microscopic description of the vibrational spectroscopy of the OH stretch of HOD in liquid D(2)O. Our model predicts that OH frequency correlations decay with a sharp and rapid ( approximately 35 fs) decrease, followed by a beat at approximately 125 fs from intermolecular oxygen vibrations. On a short time scale ( approximately 200 fs), ultrafast infrared spectroscopy of the OH stretch is sensitive to localized intermolecular motions. For times longer than approximately 200 fs, cooperative molecular rearrangements drive dephasing. The interplay of electric field fluctuations, both local and cooperative, dictate vibrational frequency shifts and destroy vibrational coherence in water.

Computer Simulation↗
PubMed2005

Temperature dependence of inhomogeneous broadening: on the meaning of isosbestic points.

An isosbestic point in the temperature dependence of an absorption spectrum is commonly viewed as a sign of interconverting chemical or structural species. Here I explore an alternative microscopic origin of temperature-independent absorbance in inhomogeneously broadened spectra: While the equilibrium probability of observing a particular frequency generally changes with the magnitude of thermal fluctuations, the weight of at least one frequency is insensitive to small changes in temperature. The range of temperature accessible to aqueous solutions at ambient pressure is sufficiently small that such insensitivity would appear in experiments as an isosbestic point. This mechanism depends only on the continuity of equilibrium distributions, not on the presence of multiple components. Even the simplest model of a single solute species in a fluctuating environment exhibits isosbestic points, van't Hoff behavior, and, with appropriate dependence of transition frequency on configuration, multiple absorption peaks.

Absorption↗
PubMed2005

Unified description of temperature-dependent hydrogen-bond rearrangements in liquid water.

The unique chemical and physical properties of liquid water are a direct result of its highly directional hydrogen-bond (HB) network structure and associated dynamics. However, despite intense experimental and theoretical scrutiny spanning more than four decades, a coherent description of this HB network remains elusive. The essential question of whether continuum or multicomponent ("intact," "broken bond," etc.) models best describe the HB interactions in liquid water has engendered particularly intense discussion. Most notably, the temperature dependence of water's Raman spectrum has long been considered to be among the strongest evidence for a multicomponent distribution. Using a combined experimental and theoretical approach, we show here that many of the features of the Raman spectrum that are considered to be hallmarks of a multistate system, including the asymmetric band profile, the isosbestic (temperature invariant) point, and van't Hoff behavior, actually result from a continuous distribution. Furthermore, the excellent agreement between our newly remeasured Raman spectra and our model system further supports the locally tetrahedral description of liquid water, which has recently been called into question.

Computer Simulation↗
PubMed2005

Comparison of dynamical heterogeneity in hard-sphere and attractive glass formers.

Using molecular dynamics simulations, we have determined that the nature of dynamical heterogeneity in jammed liquids is very sensitive to short-ranged attractions. Weakly attractive systems differ little from dense hard-sphere and Lennard-Jones fluids. Particle motion is punctuated and tends to proceed in steps of roughly a single particle diameter. Both of these basic features change in the presence of appreciable short-ranged attractions. Transient periods of particle mobility and immobility cannot be discerned at intermediate attraction strength, for which structural relaxation is greatly enhanced. Strong attractions, known to dramatically inhibit relaxation, restore bimodality of particle motion. But in this regime, transiently mobile particles move in steps that are significantly more biased toward large displacements than those in the case of weak attractions. This modified feature of dynamical heterogeneity, which cannot be captured by conventional mode coupling theory, verifies recent predictions from a model of spatially correlated facilitating defects.

Journal Article↗
PubMed2005

Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods?

We have investigated the maximum computational efficiency of reversible work calculations that change control parameters in a finite amount of time. Because relevant nonequilibrium averages are slow to converge, a bias on the sampling of trajectories can be beneficial. Such a bias, however, can also be employed in conventional methods for computing reversible work, such as thermodynamic integration or umbrella sampling. We present numerical results for a simple one-dimensional model and for a Widom insertion in a soft sphere liquid, indicating that, with an appropriately chosen bias, conventional methods are in fact more efficient. We describe an analogy between nonequilibrium dynamics and mappings between equilibrium ensembles, which suggests that the practical inferiority of fast switching is quite general. Finally, we discuss the relevance of adiabatic invariants in slowly driven Hamiltonian systems for the application of Jarzynski's theorem.

Chemistry, Physical↗
PubMed2005

Short-ranged attractions in jammed liquids: how cooling can melt a glass.

We demonstrate that an extended picture of kinetic constraints in glass-forming liquids is sufficient to explain dynamic anomalies observed in dense suspensions of strongly attracting colloidal particles. We augment a simple model of heterogeneous relaxation with static attractions between facilitating excitations, in a way that mimics the structural effect of short-ranged interparticle attractions. The resulting spatial correlations among facilitated and unfacilitated regions give rise to relaxation mechanisms that account for nonmonotonic dependence of relaxation times on attraction strength as well as logarithmic decay of density correlations in time. These unusual features are a simple consequence of spatial segregation of kinetic constraints, suggesting an alternative physical perspective on attractive colloids than that suggested by mode-coupling theory. Based on the behavior of our model, we predict a crossover from super-Arrhenius to Arrhenius temperature dependence as attractions become dominant at fixed packing fraction.

Journal Article↗
PubMed2004

Solvation versus freezing in a heteropolymer globule.

We address the response of a random heteropolymer to preferential solvation of certain monomer types at the globule-solvent interface. For each set of monomers that can comprise the molecule's surface, we represent the ensemble of allowed configurations by a Gaussian distribution of energy levels, whose mean and variance depend on the set's composition. Within such a random energy model, mean surface composition is proportional to solvation strength under most conditions. The breadth of this linear response regime arises from the approximate statistical independence of surface and volume energies. Fluctuations play a crucial role in determining the excess of solvophilic monomers at the surface, and for a diverse set of monomer types can be overcome only by very strong solvent preference.

Biophysics↗
PubMed2004

Nature of slow dynamics in a minimal model of frustration-limited domains.

We present simulation results for the dynamics of a schematic model based on the frustration-limited domain picture of glass-forming liquids. These results are compared with approximate theoretical predictions analogous to those commonly used for supercooled liquid dynamics. Although model relaxation times increase by several orders of magnitude in a non-Arrhenius manner as a microphase separation transition is approached, the slow relaxation is in many ways dissimilar to that of a liquid. In particular, structural relaxation is nearly exponential in time at each wave vector, indicating that the mode-coupling effects dominating liquid relaxation are comparatively weak within this model. Relaxation properties of the model are instead well reproduced by the simplest dynamical extension of a static Hartree approximation. This approach is qualitatively accurate even for temperatures at which the mode-coupling approximation predicts loss of ergodicity. These results suggest that the thermodynamically disordered phase of such a minimal model poorly caricatures the slow dynamics of a liquid near its glass transition.

Journal Article↗
PubMed2003

Drying-mediated self-assembly of nanoparticles.

Systems far from equilibrium can exhibit complex transitory structures, even when equilibrium fluctuations are mundane. A dramatic example of this phenomenon has recently been demonstrated for thin-film solutions of passivated nanocrystals during the irreversible evaporation of the solvent. The relatively weak attractions between nanocrystals, which are efficiently screened in solution, become manifest as the solvent evaporates, initiating assembly of intricate, slowly evolving structures. Although certain aspects of this aggregation process can be explained using thermodynamic arguments alone, it is in principle a non-equilibrium process. A representation of this process as arising from the phase separation between a dense nanocrystal 'liquid' and dilute nanocrystal 'vapour' captures some of the behaviour observed in experiments, but neglects entirely the role of solvent fluctuations, which can be considerable on the nanometre length scale. Here we present a coarse-grained model of nanoparticle self-assembly that explicitly includes the dynamics of the evaporating solvent. Simulations using this model not only account for all observed spatial and temporal patterns, but also predict network structures that have yet to be explored. Two distinct mechanisms of ordering emerge, corresponding to the homogeneous and heterogeneous limits of evaporation dynamics. Our calculations show how different choices of solvent, nanoparticle size (and identity) and thermodynamic state give rise to the various morphologies of the final structures. The resulting guide for designing statistically patterned arrays of nanoparticles suggests the possibility of fabricating spontaneously organized nanoscale devices.

Journal Article↗
PubMed2002

Reversible stretching of random heteropolymers.

We analyze the equilibrium response of random heteropolymers to mechanical deformation. In contrast to homopolymer response, the stress-induced transformation of a heteropolymer from globule to coil need not be sharp. For chain lengths relevant to biological macromolecules, intermediate necklace-like structures dominate over a range of applied force. Stability of these conformations is primarily a consequence of solvation: In a typical necklace, relatively solvophilic regions of the chain are extended, while solvophobic regions remain compact. In the long-chain limit, homopolymeric behavior is recovered. Our results suggest that only select polypeptide sequences should unfold reproducibly at a specific force, explaining recent experimental observations.

Journal Article↗
PubMed2001

Transition path sampling: throwing ropes over rough mountain passes, in the dark.

This article reviews the concepts and methods of transition path sampling. These methods allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction coordinates, and transition states. Based upon a statistical mechanics of trajectory space, they provide a perspective with which time dependent phenomena, even for systems driven far from equilibrium, can be examined with the same types of importance sampling tools that in the past have been applied so successfully to static equilibrium properties.

Journal Article↗