Slow dynamics of supercooled hydration water in contact with lysozyme: examining the cage effect at different length scales

ABSTRACT

We study by computer simulation the dynamics of hydration water in solution with lysozyme upon approaching the glassy state of water. We calculate the self-density correlation function at different wavelengths to test the Mode Coupling Theory (MCT) of glassy dynamics at different length scales. The results show a strict and clear relation of the behaviour of the structural relaxation with the cage effect. We find a good agreement with the predictions of the MCT in the short and medium scale range, while at increasing length scales the interaction of water molecules with the protein's substrate induces deviations from the MCT behaviour, as found in previous studies. Besides at low temperatures the slow dynamics deviates from MCT due to hopping processes, similar to the bulk, as witnessed by a crossover from a fragile behaviour to a strong behaviour. We show that this deviation is evident at all length scales. Interestingly, we find that in the fragile region the confining cage decreases in radius with temperature while in the strong region it appears stable.     

Glassy dynamics of kinetically constrained models

We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying 'equilibrium glass transition'. After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and mode-coupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known results for the dynamics of KCMs both in and out of equilibrium, including topics such as relaxation time divergences and dynamical transitions, nonlinear relaxation, ageing and effective temperatures, cooperativity and dynamical heterogeneities, and finally non-equilibrium stationary states generated by external driving. We conclude with a discussion of open questions and possibilities for future work.     

Water confined in MCM-41: a mode coupling theory analysis

In this paper we analyze molecular dynamics simulation results on supercooled water in a MCM-41 pore in order to test the mode coupling theory. A layer analysis must be performed for water in the pore in order to exclude the contribution of water bound to the strongly hydrophilic surface. Upon supercooling a range of temperatures is reached where the liquid follows the mode coupling theory. From the power law behavior of the relaxation times extracted from the Kohlrausch-William-Watts fit to the self-intermediate scattering function, we obtain the crossover temperature T(C) and the γ exponent of the theory. The time-temperature superposition principle is also satisfied. A fit to the von Schweidler law yields a coefficient b from which all the other parameters of the theory have been calculated. In particular, we obtained the same value of γ as extracted from the power law fit to the relaxation times, in agreement with the requirements of the theory. For very low temperatures, the mode coupling theory no longer holds as hopping processes intervene and water turns its behavior to that of a strong liquid.     

Multi-bump, self-similar, blow-up solutions of the Ginzburg-Landau equation

For the Ginzburg-Landau equation (GL), we establish the existence and local uniqueness of two classes of multi-bump, self-similar, blow-up solutions for all dimensions 2<d<4 (under certain conditions on the coefficients in the equation). In numerical simulation and via asymptotic analysis, one class of solutions was already found; the second class of multi-bump solutions is new.In the analysis, we treat the GL as a small perturbation of the cubic nonlinear Schrödinger equation (NLS). The existence result given here is a major extension of results established previously for the NLS, since for the NLS the construction only holds for d close to the critical dimension d=2.The behaviour of the self-similar solutions is described by a nonlinear, non-autonomous ordinary differential equation (ODE). After linearisation, this ODE exhibits hyperbolic behaviour near the origin and elliptic behaviour asymptotically. We call the region where the type of behaviour changes the mid-range. All of the bumps of the solutions that we construct lie in the mid-range.For the construction, we track a manifold of solutions of the ODE that satisfy the condition at the origin forward, and a manifold of solutions that satisfy the asymptotic conditions backward, to a common point in the mid-range. Then, we show that these manifolds intersect transversely. We study the dynamics in the mid-range by using geometric singular perturbation theory, adiabatic Melnikov theory, and the Exchange Lemma.     

Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained. Received 19 December 2002 Published online 14 March 2003     

Aging in the random energy model

The random energy model (REM) has become a key reference model for glassy systems. In particular, it is expected to provide a prime example of a system whose dynamics shows aging, a universal phenomenon characterizing the dynamics of complex systems. The analysis of its activated dynamics is based on so-called trap models, introduced by Bouchaud, that are also used to mimic the dynamics of more complex disordered systems. In this Letter we report the first results that justify rigorously the trap model predictions in the REM.     

Cosmological constant and the dynamics of the Bianchi type I models with spin and torsion: A qualitative investigation

By including the cosmological term in the minimum quadratic (Poincaré) gauge theory of gravity, the basic equation set for the homogeneous anisotropic Bianchi type I spinning-fluid models are obtained. For the linear equation of state, using methods of qualitative theory of dynamical systems, we make the complete qualitative analysis of properties of every possible solution of these equations, In particular, some solutions with regular behaviour of the metric and torsion are found.     

Positive energy without supersymmetry

Witten's positive energy theorem and its generalizations can be viewed as stating that supersymmetric solutions of any supergravity theory are stable. In this paper we give a criterion to test the stability of non-supersymmetric solutions of supergravity theories and solutions of theories which cannot be embedded in a supergravity theory. Previously some of these solutions might have been considered to be unstable. In particular, we show that the non-supersymmetric stationary point of the scalar potential of the gauged N = 5 supergravity theory is stable. We also give an elegant derivation of the Breitenlohner-Freedman condition for (small fluctuation) stability.     

Relaxation phenomena at criticality

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the thermodynamic control parameters. The non-equilibrium evolution following this change displays some of the features typically observed in glassy materials, such as ageing, and it can be monitored via dynamic susceptibilities and correlation functions of the order parameter, the scaling behaviour of which is characterized by universal exponents, scaling functions, and amplitude ratios. This universality allows one to calculate these quantities in suitable simplified models and field-theoretical methods are a natural and viable approach for this analysis. In addition, if a statistical system is spatially confined, universal Casimir-like forces acting on the confining surfaces emerge and they build up in time when the temperature of the system is tuned to its critical value. We review here some of the theoretical results that have been obtained in recent years for universal quantities, such as the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the Ising model with Glauber dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting in a film is discussed within the Gaussian model.     

Non-classical configurations in Euclidean field theory as minima of constrained systems

We study a systematic method of applying the semiclassical approximation to Euclidean field theory. First, we extract generalized collective coordinates which are not in general zero modes. We then apply the semiclassical approximation to the other degrees of freedom by minimizing the action with constraints. Hence we are using configurations which are not classical solutions of the original system. After Gaussian integration we are left with a truncated system, involving only the collective coordinates, with non-trivial dynamics. In particular, this is a clear-cut way to introduce multi-instanton or meron-type configurations. The collective coordinates should be chosen such that their dynamics are a good approximation to the original system for the physical phenomenon considered; a familiar concept in other branches of physics with many degrees of freedom. The formalism leads naturally to the introduction of dynamics in an extra time evolution; in particular cases, we show that this is a very powerful tool. In this paper, we only discuss general ideas and formalisms. Specific applications are postponed to to later publications.     

Large volume behaviour of Yang-Mills propagators

We investigate finite volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. In particular, we demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. This solves an important open problem of previous studies where the infinite volume limit led to an apparent mismatch, especially of the infrared behaviour, between torus extrapolations and the existing infinite volume solutions obtained in 4-dimensional Euclidean space-time. However, the correct infinite volume limit is approached rather slowly. The typical scales necessary to see the onset of the leading infrared behaviour emerging already imply volumes of at least 10-15 fm in lengths. To reliably extract the infrared exponents of the infinite volume solutions requires even much larger ones. While the volumes in the Monte-Carlo simulations available at present are far too small to facilitate that, we obtain a good qualitative agreement of our torus solutions with recent lattice data in comparable volumes.     

Microphase separation in cross-linked polymer blends

We investigate the behaviour of randomly cross-linked (co)polymer blends using a combination of replica theory and large-scale molecular dynamics simulations. In particular, we derive the analogue of the random phase approximation for systems with quenched disorder and show how the required correlation functions can be calculated efficiently. By post-processing simulation data for homopolymer networks we are able to describe neutron scattering measurements in heterogeneous systems without resorting to microscopic detail and otherwise unphysical assumptions. We obtain structure function data which illustrate the expected microphase separation and contain system-specific information relating to the intrinsic length scales of our networks.     

Static and Time Dependent Density Functional Theory with Internal Degrees of Freedom: Merits and Limitations Demonstrated for the Potts Model

We present an extension of the density-functional theory (DFT) formalism for lattice gases to systems with internal degrees of freedom. In order to test approximations commonly used in DFT approaches, we investigate the statics and dynamics of occupation (density) profiles in the one-dimensional Potts model. In particular, by taking the exact functional for this model we can directly evaluate the quality of the local equilibrium approximation used in time-dependent density-functional theory (TDFT). Excellent agreement is found in comparison with Monte Carlo simulations. Finally, principal limitations of TDFT are demonstrated.     

Restructuring of force networks

The compaction of granular packings or soils is a collective process which for higher densities becomes increasingly slower reaching glassy behaviour. We present a study of this problem from various points of view, in particular we will represent the evolving force network that percolates through the system by an inverse fiber rupture model. Received 15 March 2002 and Received in final form 29 July 2002     

From a simple liquid to a polymer melt: NMR relaxometry study of polybutadiene

We utilize NMR field cycling relaxometry to study the crossover from glassy dynamics (t approximately > tau alpha) through Rouse to reptation behavior in a series of monodisperse polybutadienes with molecular weights M=355 to 817,000 g/mol. We separate characteristic polymer dynamics from the total spectrum dominated by glassy dynamics. The polymer dynamics show typical Rouse relaxation features that grow with M and saturate at high M. Comparing to Rouse theory, we determine the Rouse unit size MR approximately = 500 and entanglement weight Me approximately = 2000; the Rouse spectrum saturates at Mmax approximately = 4000. The local order parameter S approximately 0.11 is relatively large, indicating noticeable local packing already in the Rouse regime. The M dependence of the glass transition temperature Tg, obtained from dielectric relaxation spectra, shows distinctive kinks at MR and Me.     

Cosmological Dynamics of Scalar Field with Non-Minimal Kinetic Term

We investigate the dynamics of a scalar field in the framework of the scalar-tensor theory. A nontrivial behavior of the field in the vicinity of singular points of the kinetic term is observed. In particular, the singular points could serve as attractor for classical solutions.     

Anion–water interactions of weakly hydrated anions: molecular dynamics simulations of aqueous NaBF4 and NaPF6

In aqueous ionic solutions, both the structure and the dynamics of water are altered dramatically with respect to the pure solvent. The emergence of novel experimental techniques makes these changes accessible to detailed investigations. At the same time, computational studies deliver unique possibilities for the interpretation of the experimental data at the molecular level. Here, using molecular dynamics simulations, we demonstrate how competing mechanisms can explain the seemingly contradictory statements about the structure and dynamics of ion-coordinated solvent in aqueous solutions of two interesting and technologically important electrolytes, NaBF₄ and NaPF₆. While the static structural data (i.e. radial, radial-angular and spatial distribution functions, as well as hydrogen bonding statistics) unequivocally point at very weak anion–water hydrogen bonding in both salts, dynamic analyses (in particular, orientational anisotropy decay and solvent residence times) reveal quite significant retardation of water rotation and mobility due to solute coordination. Additionally, rotational immobilisation of coordinated solvent molecules is clearly unrelated to the hydrogen bond strength between them, as demonstrated by the interatomic oxygen–oxygen distance distributions for coordinated and bulk water.     

Molecular dynamic studies of the solubility of sodium chloride: fast calculations using seed crystalline cluster probe

Theoretical predictions of solubility, typically accomplished by comparing the chemical potential of pure solid and solution, currently suffer from a lack of accuracy. We suggest an alternative method for predicting solubility based on molecular dynamics simulations of the behaviour of a small seed crystalline cluster probe in solutions of varying concentrations. The size dynamics of a properly chosen seed cluster that dissolves in unsaturated solutions and grows in size in supersaturated solutions is indicative of the saturation point. This approach is illustrated by its application to NaCl in water.     

Curious behaviour of the diffusion coefficient and friction force for the strongly inhomogeneous HMF model

We present first elements of kinetic theory appropriate to the inhomogeneous phase of the Hamiltonian Mean Field (HMF) model. In particular, we investigate the case of strongly inhomogeneous distributions for T→0 and exhibit curious behaviour of the force auto-correlation function and friction coefficient. The temporal correlation function of the force has an oscillatory behaviour which averages to zero over a period. By contrast, the effects of friction accumulate with time and the friction coefficient does not satisfy the Einstein relation. On the contrary, it presents the peculiarity to increase linearly with time. Motivated by this result, we provide analytical solutions of a simplified kinetic equation with a time dependent friction. Analogies with self-gravitating systems and other systems with long-range interactions are also mentioned.     

Remarks on exact solutions

This paper first discusses the historical context of the influential “Exact Solutions” book, which was co-authored by Malcolm MacCallum. It then makes various technical points about such solutions. It is useful to characterize solutions in terms of the properties of matter they contain or the kinds of test particle motions which are possible. It is also interesting to consider which isometries are implied by particular kinds of matter behaviour. Judging the validity of an approximation by the smallness of the tensor components can be misleading. Finally, an example is given of a result which is obvious in Newtonian theory but little understood in General Relativity.