Revealing and resolving degeneracies in stretching exponents in temporally heterogeneous environments.

Supercooled liquids are proposed to be dynamically heterogeneous, with regions exhibiting relaxation time scales that vary in space and time. Measurement of the distribution of such time scales could be an important test of various proposed theories of vitrification. Single molecule fluorescence experiments attempt to uncover this distribution, typically by embedding single molecule probes into these systems and monitoring their individual rotational relaxations from a computed autocorrelation function (ACF). These ACFs may exhibit stretched exponential decays, with the value of the stretching exponent assumed to report the set of dynamical environments explored by the probe. Here, we use simulated trajectories of rotation to investigate how the time scale of dynamic exchange relative to underlying relaxation time scales in the system affects probe ability to report the distribution relaxation of time scales present. We find that dynamically heterogeneous regions must persist for approximately 50 times the median relaxation time scale for a single molecule to accurately report the full distribution of time scales it has experienced. In systems with faster dynamic exchange, single molecule ACFs average over successive environments, limiting the reported heterogeneity of the system. This leads to degeneracies in stretching exponent for systems with different underlying relaxation time distributions. We show that monitoring single molecule median stretching exponent as a function of trajectory length or simultaneously measuring median stretching exponent and measured relaxation time distribution at a given trajectory length can resolve these degeneracies, revealing the underlying set of relaxation times as well as median exchange time.

Effect of pressure on the anomalous response functions of a confined water monolayer at low temperature.

We study a coarse-grained model for a water monolayer that cannot crystallize due to the presence of confining interfaces, such as protein powders or inorganic surfaces. Using both Monte Carlo simulations and mean field calculations, we calculate three response functions: the isobaric specific heat C(P), the isothermal compressibility K(T), and the isobaric thermal expansivity α(P). At low temperature T, we find two distinct maxima in C(P), K(T), and ∣α(P)∣, all converging toward a liquid-liquid critical point (LLCP) with increasing pressure P. We show that the maximum in C(P) at higher T is due to the fluctuations of hydrogen (H) bond formation and that the second maximum at lower T is due to the cooperativity among the H bonds. We discuss a similar effect in K(T) and ∣α(P)∣. If this cooperativity were not taken into account, both the lower-T maximum and the LLCP would disappear. However, comparison with recent experiments on water hydrating protein powders provides evidence for the existence of the lower-T maximum, supporting the hypothesized LLCP at positive P and finite T. The model also predicts that when P moves closer to the critical P the C(P) maxima move closer in T until they merge at the LLCP. Considering that other scenarios for water are thermodynamically possible, we discuss how an experimental measurement of the changing separation in T between the two maxima of C(P) as P increases could determine the best scenario for describing water.

More than one dynamic crossover in protein hydration water.

Studies of liquid water in its supercooled region have helped us better understand the structure and behavior of water. Bulk water freezes at its homogeneous nucleation temperature (approximately 235 K), but protein hydration water avoids this crystallization because each water molecule binds to a protein. Here, we study the dynamics of the hydrogen bond (HB) network of a percolating layer of water molecules and compare the measurements of a hydrated globular protein with the results of a coarse-grained model that successfully reproduces the properties of hydration water. Using dielectric spectroscopy, we measure the temperature dependence of the relaxation time of proton charge fluctuations. These fluctuations are associated with the dynamics of the HB network of water molecules adsorbed on the protein surface. Using Monte Carlo simulations and mean-field calculations, we study the dynamics and thermodynamics of the model. Both experimental and model analyses are consistent with the interesting possibility of two dynamic crossovers, (i) at approximately 252 K and (ii) at approximately 181 K. Because the experiments agree with the model, we can relate the two crossovers to the presence at ambient pressure of two specific heat maxima. The first is caused by fluctuations in the HB formation, and the second, at a lower temperature, is due to the cooperative reordering of the HB network.

Effect of hydrogen bond cooperativity on the behavior of water.

Four scenarios have been proposed for the low-temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism that leads to each is debated. Moreover, it is still unclear which of the scenarios best describes water, because there is no definitive experimental test. Here we address both open issues within the framework of a microscopic cell model by performing a study combining mean-field calculations and Monte Carlo simulations. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. We argue that our conclusions are model independent. Using estimates from experimental data for H-bond properties the model predicts that the low-temperature phase diagram of water exhibits a liquid-liquid critical point at positive pressure.