Charusita Chakravarty

Entropy, diffusivity, and structural order in liquids with waterlike anomalies

The excess entropy, defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is studied as a function of density and temperature for liquid silica and a two-scale ramp potential, both of which are known to possess waterlike liquid state anomalies. The excess entropy for both systems is evaluated using a fairly accurate pair correlation approximation. The connection between the excess entropy and the density and diffusional anomalies is demonstrated. Using the pair correlation approximation to the excess entropy, it can be shown that if the energetically favorable local geometries in the low and high density limits have different symmetries, then a structurally anomalous regime can be defined in terms of orientational and translational order parameters, as in the case of silica and the two-scale ramp system but not for the one-scale ramp liquid. Within the category of liquids with waterlike anomalies, we show that the relationship between the macroscopic entropy and internal energy is sufficient to distinguish between those with local anisotropy and consequent open packings at low densities and those with isotropic interactions but multiple length scales. Since it is straightforward to evaluate the pair correlation entropy and internal energy from simulations or experimental data, such plots should provide a convenient means to diagnose the existence as well as type of anomalous behavior in a range of liquids, including ionic and intermetallic melts and complex fluids with ultrasoft repulsions.

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

Excess entropy scaling of transport properties of Lennard-Jones chains

Excess-entropy scaling relationships for diffusivity and viscosity of Lennard-Jones chain fluids are tested using molecular dynamics simulations for chain sizes that are sufficiently small that chain entanglement effects are insignificant. The thermodynamic excess entropy S(e) is estimated using self-associating fluid theory (SAFT). A structural measure of the entropy S(2) is also computed from the monomer-monomer pair correlation function, g(m)(r). The thermodynamic and structural estimators for the excess entropy are shown to be very strongly correlated. The dimensionless center-of-mass diffusivities, D(cm) (*), obtained by dividing the diffusivities by suitable macroscopic reduction parameters, are shown to conform to the excess entropy scaling relationship, D(cm) (*)=A(n) exp(alpha(n)S(e)), where the scaling parameters depend on the chain length n. The exponential parameter alpha(n) varies as -(1n) while A(n) varies approximately as n(-0.5). The scaled viscosities obey a similar relationship with scaling parameters B(n) and beta(n) where beta(n) varies as 1n and B(n) shows an approximate n(0.6) dependence. In accordance with the Stokes-Einstein law, for a given chain length, alpha(n)=-beta(n) within statistical error. The excess entropy scaling parameters associated with the transport properties therefore display a simple dependence on chain length.

Stimulated emission pumping of van der Waals vibrations in the ground electronic state of OHAr

Stimulated emission spectroscopy is used to measure the frequencies of the van der Waals bending and stretching modes in the ground electronic state of the OHAr complex correlating with OH(X 2Π) + Ar(1S0). The results are compared with those predicted using an ab initio potential energy surface. Encouraging agreement between experiment and theory is obtained, particularly for the van der Waals bending modes.

Relationship between structure, entropy, and diffusivity in water and water-like liquids.

Anomalous behavior of the excess entropy (S(e)) and the associated scaling relationship with diffusivity are compared in liquids with very different underlying interactions but similar water-like anomalies: water (SPC/E and TIP3P models), tetrahedral ionic melts (SiO(2) and BeF(2)), and a fluid with core-softened, two-scale ramp (2SRP) interactions. We demonstrate the presence of an excess entropy anomaly in the two water models. Using length and energy scales appropriate for onset of anomalous behavior, we show the density range of the excess entropy anomaly to be much narrower in water than in ionic melts or the 2SRP fluid. While the reduced diffusivities (D*) conform to the excess-entropy-scaling relation, D* = A exp(alphaS(e)) for all the systems (Rosenfeld, Y. Phys. Rev. A 1977, 15, 2545), the exponential scaling parameter, alpha, shows a small isochore dependence in the case of water. Replacing S(e) by pair correlation-based approximants accentuates the isochore dependence of the diffusivity scaling. Isochores with similar diffusivity-scaling parameters are shown to have the temperature dependence of the corresponding entropic contribution. The relationship between diffusivity, excess entropy, and pair correlation approximants to the excess entropy are very similar in all the tetrahedral liquids.

Thermodynamic, Diffusional, and Structural Anomalies in Rigid-Body Water Models

Structural, density, entropy, and diffusivity anomalies of the TIP4P/2005 model of water are mapped out over a wide range of densities and temperatures. The locus of temperatures of maximum density (TMD) for this model is very close to the experimental TMD locus for temperatures between 250 and 275 K. Four different water models (mTIP3P, TIP4P, TIP5P, and SPC/E) are compared with the TIP4P/2005 model in terms of their anomalous behavior. For all the water models, the density regimes for anomalous behavior are bounded by a low-density limit at around 0.85-0.90 g cm(-3) and a high-density limit at about 1.10-1.15 g cm(-3). The onset temperatures of the density anomaly in the various models show a much greater variation, ranging from 202 K for mTIP3P to 289 K for TIP5P. The order maps for the various water models are qualitatively very similar with the structurally anomalous regions almost superimposable in the q(tet)-τ plane. Comparison of the phase diagrams of water models with the region of liquid-state anomalies shows that the crystalline phases are much more sensitive to the choice of water models than the liquid state anomalies; for example, SPC/E and TIP4P/2005 show qualitatively similar liquid state anomalies but very different phase diagrams. The anomalies in the liquid in all the models occur at much lower pressures than those at which the melting line changes from negative to positive slope. The results in this study demonstrate several aspects of structure-entropy-diffusivity relationships of water models that can be compared with experiment and used to develop better atomistic and coarse-grained models for water.

A comparison of the efficiency of Fourier- and discrete time-path integral Monte Carlo

We compare the efficiency of Fourier and discrete time path integral Monte Carlo (PIMC) methods on a cluster of 22 hydrogen molecules at 6 K. The discrete time PIMC with a pair density matrix approximation to the path action is shown to be the most efficient for evaluating all the observables studied here. The Fourier PIMC technique has a comparable efficiency for observables diagonal in the coordinates but is significantly worse for estimating the kinetic and total energies. The superior performance of the discrete time PIMC is shown to be due to the more accurate treatment of the path action using the pair density matrix approach; the discrete time PIMC simulation within the primitive approximation is much less efficient. Complete details of the implementation of all algorithms are given.

Local order, energy, and mobility of water molecules in the hydration shell of small peptides.

The extent to which the presence of a biomolecular solute modifies the local energetics of water molecules, as measured by the tagged molecule potential energy (TPE), is examined using molecular dynamics simulations of the beta-hairpin of 2GB1 and the alpha-helix of deca-alanine in water. The CHARMM22 force field, in conjunction with the TIP3P solvent water model, is used for the peptides, with simulations of TIP3P and SPC/E water used as benchmarks for the behavior of bulk solvent. TIP3P water is shown to have significantly lower local tetrahedral order and higher binding energy than SPC/E at the same state point. The TIP3P and SPC/E water models show very similar dynamical correlations in the TPE fluctuations on frequency scales greater than 0.1 cm(-1). In addition, the two models show the same linear correlation between mean tetrahedral order and binding energy, suggesting that the relationship between choice of water models and simulated hydration behavior may involve a complex interplay of static and dynamic factors. The introduction of a peptide in water modifies the local TPE of water molecules as a function of distance from the biomolecular interface. There is an oscillatory variation in the TPE with distance from the peptide for water molecules lying outside a 3 A radius and extending to at least 10 A. These variations are of the order of 2-5% of the bulk TPE value and are anticorrelated with variations in local tetrahedral order in terms of locations of maxima and minima, which may be understood in terms of the relative contribution of van der Waals and Coulombic contributions to the TPE. The distance-dependent variations in local order and energetics are essentially the same for the beta-hairpin of 2GB1 as well as deca-alanine. Within a radius of 3 A, the perturbation of the solvent structure is very significant with local TPEs that are 10-15% lower than the bulk value. The chemical identity of side-chain residues and the secondary structure play an important role in determining residue-dependent variations in the TPEs. The variation in the residue-dependent tagged molecule potential energies is of the order of 3-5%, while the local residence times vary by a factor of approximately 5. The correlation of the local residence times with the local energetics within the innermost hydration layer is weak, though charged residues typically have low binding energies and large residence times.

The Rise and Fall of Anomalies in Tetrahedral Liquids

The thermodynamic liquid-state anomalies and associated structural changes of the Stillinger-Weber family of liquids are mapped out as a function of the degree of tetrahedrality of the interaction potential, focusing in particular on tetrahedrality values suitable for modeling C, H2O, Si, Ge and Sn. We show that the density anomaly, associated with a rise in molar volume on isobaric cooling, emerges at intermediate tetrahedralities (e.g. Ge, Si and H2O) but is absent in the low (e.g. Sn) and high (e.g. C) tetrahedrality liquids. The rise in entropy on isothermal compression associated with the density anomaly is related to the structural changes in the liquid using the pair correlation entropy. An anomalous increase in the heat capacity on isobaric cooling exists at high tetrahedralities but is absent at low tetrahedralities (e.g. Sn). Structurally, this heat capacity anomaly originates in a sharp rise in the fraction of four-coordinated particles and local tetrahedral order in the liquid as its structure approaches that of the tetrahedral crystal.

Water and water-like liquids: relationships between structure, entropy and mobility.

Liquids with very diverse underlying interactions share the thermodynamic and transport anomalies of water, including metalloids, ionic melts and mesoscopic fluids. The generic feature that characterises such water-like liquids is a density-driven shift in the nature of local order in the condensed phases. The key semiquantitative relationships between structural order, thermodynamics and transport that are necessary in order to map out the consequences of this common qualitative feature for liquid-state properties and phase transformations of such systems are reviewed here. The application of these ideas to understand and model tetrahedral liquids, especially water, is discussed and possible extensions to other complex fluids are considered.