We present a theoretical analysis of the dynamics of crystal growth from a supercooled melt. A molecular theory of crystal growth that pays proper attention to the structure at the liquid-solid interface is discussed.

The canonical average of the Boltzmann factor of the interaction potential, as measured by a test particle, is shown to be equal to the inverse of the fraction of the average number $$(\bar m_1 )$$ of 1-particle Mayer clusters. The potential distribution theory is used to derive an analytic expression for a mean number of small clusters $$(\bar m_n {\text{ , 1 }} \leqslant {\text{ }}n < {\text{ }}N,$$ 1≤n<N, in anN-particle system) in the mean-field expression. Near the spinodal density, the average number of small clusters undergo a sharp change. Computation of pressure shows that only the first four clusters produce surprisingly good agreement with known pressure even beyond the spinodal density.

A microscopic theoretical calculation of time-dependent solvation energy shows that the solvation of an ion or a dipole is dominated by a single relaxation time if the translational contribution to relaxation is significant.

Microscopic expressions for the time dependence of solvation energies of newly created ions and dipoles in a dense dipolar liquid are presented. It is shown that: (i) the dynamics of solvation of an ion differ considerably from that of a dipole, especially that the long wavelength (k=0) component of solvent response is totally absent for dipoles, and (ii) the translational modes of the solvent molecules lead to a breakdown of Onsager’s conjecture on the distance dependence of solvent polarization relaxation.

In this article we present a new, general but simple, microscopic expression for time-dependent solvation energy of an ion. This expression is surprisingly similar to the expression for the time-dependent dielectric friction on a moving ion. We show that both the Chandra-Bagchi and the Fried-Mukamel formulations of solvation dynamics can be easily derived from this expression. This expression leads to an almost perfect agreement of the theory with all the available computer simulation results. Second, we show here for the first time that the mobility of a light solute ion can significantly accelerate its own solvation, specially in the underdamped limit. The latter result is also in excellent agreement with the computer simulations.

A recently developed microscopic theory of solvation dynamics in real dipolar liquids is used to calculate, for the first time, the solvation time correlation function in liquid acetonitrile, water and methanol. The calculated results are in excellent agreement with known experimental and computer simulation studies.

The solvation time correlation function for solvation in liquid water was measured recently. The solvation was found to be very fast, with a time constant equal to 55 fs. In this article we present theoretical studies on solvation dynamics of ionic and dipolar solutes in liquid water, based on the molecular hydrodynamic approach developed earlier. The molecular hydrodynamic theory can successfully predict the ultrafast dynamics of solvation in liquid water as observed from recent experiments. The present study also reveals some interesting aspects of dipolar solvation dynamics, which differs significantly from that of ionic solvation.

A microscopic theory is used to calculate the solvation-time correlation function, (S(t)), of a light, non-stationary charge bubble in water. The calculated correlation function is found to be similar to the energy-time correlation function of a solvated electron. The ionic mobility of a charge bubble of the size of the hydrated electron is also calculated. It is found that the mobility of the charge plays a very important role in its own solvation.

Non-exponential electron transfer kinetics in complex systems are often analyzed in terms of a quenched, static disorder model. In this work we present an alternative analysis in terms of a simple dynamic disorder model where the solvent is characterized by highly non-exponential dynamics. We consider both low and high barrier reactions. For the former, the main result is a simple analytical expression for the survival probability of the reactant. In this case, electron transfer, in the long time, is controlled by the solvent polarization relaxation—in agreement with the analyses of Rips and Jortner and of Nadler and Marcus. The short time dynamics is also non-exponential, but for different reasons. The high barrier reactions, on the other hand, show an interesting dynamic dependence on the electronic coupling element,V_el.

In its supercritical state water exhibits anomalous solvent properties, the most important being its ability to solubilize organic solutes of various sizes which are sparingly soluble under ambient conditions. This phenomenon occurs at high pressure where the density is rather large (0.6–0.9 gm/cm³). In this work, a microscopic explanation for the anomalous solubility of organic substances in supercritical water is presented by using the quasi-chemical approximation of Bethe and Guggenheim. The theory suggests the enhanced anomalous solubility arises because the critical temperature of the binary mixture (waterplus organic solute) could be slightly lower than the gas-liquid critical temperature of pure water. Several exotic solvent properties may arise due to the subtle interplay between these two critical temperatures.

Binary mixtures show many kinds of fascinating dynamical behaviour which has eluded microscopic description till very recently. In this work we show that much of the anomalous behaviour can be explained by building suitable models and carrying out theoretical and simulation studies. Specifically, three well-known problems have been addressed here. (a) Non-ideality in composition dependence of viscosity, (b) re-entrant behaviour of orientational relaxation, and (c) heterogeneity in supercooled binary mixtures. The physical origin of the dynamical behaviour of binary mixtures can be understood in terms of composition fluctuation, a study of which has also been presented in this paper.

Folding dynamics and energy landscape picture of protein conformations of HP-36 andβ-amyloid (Aβ) are investigated by extensive Brownian dynamics simulations, where the inter amino acid interactions are given by a minimalistic model (MM) we recently introduced [J. Chem. Phys.118 4733 (2003)]. In this model, a protein is constructed by taking two atoms for each amino acid. One atom represents the backbone C_αs atom, while the other mimics the whole side chain residue. Sizes and interactions of the side residues are all different and specific to a particular amino acid. The effect of water-mediated folding is mapped into the MM by suitable choice of interaction parameters of the side residues obtained from the amino acid hydropathy scale. A new non-local helix potential is incorporated to generate helices at the appropriate positions in a protein. Simulations have been done by equilibrating the protein at high temperature followed by a sudden quench. The subsequent folding is monitored to observe the dynamics of topological contacts (N_topo), relative contact order parameter (RCO), and the root mean square deviation (RMSD) from the real-protein native structure. The folded structures of different model proteins (HP-36 and Aβ) resemble their respective real native state rather well. The dynamics of folding showsmultistage decay, with an initial hydrophobic collapse followed by a long plateau. Analysis ofN_topo and RCO correlates the late stage folding with rearrangement of the side chain residues, particularly those far apart in the sequence. The long plateau also signifies large entropic free energy barrier near the native state, as predicted from theories of protein folding.

Fluorescence resonance energy transfer (FRET) is a popular tool to study equilibrium and dynamical properties of polymers and biopolymers in condensed phases and is now widely used in conjunction with single molecule spectroscopy. In the data analysis, one usually employs the Förster expression which predicts (l/R⁶) distance dependence of the energy transfer rate. However, critical analysis shows that this e_xpression can be of rather limited validity in many cases. We demonstrate this by explicitly considering a donor-acceptor system, polyfluorene (PF₆)-tetraphenylporphyrin (TPP), where the size of both donor and acceptor is comparable to the distance separating them. In such cases, one may expect much weaker distance (as l/R² or even weaker) dependence. We have also considered the case of energy transfer from a dye to a nanoparticle. Here we find l/R⁴ distance dependence at large separations, completely different from Förster. We also discuss recent application of FRET to study polymer conformational dynamics.

Many recent experimental studies have reported a surprising ultraslow component (even >10 ns) in the solvation dynamics of a polar probe in an organized assembly, the origin of which is not understood at present. Here we propose two molecular mechanisms in explanation. The first one involves the motion of the `buried water’ molecules (both translation and rotation), accompanied by cooperative relaxation (‘local melting’) of several surfactant chains. An estimate of the time is obtained by using an effective Rouse chain model of chain dynamics, coupled with a mean first passage time calculation. The second explanation invokes self-diffusion of the (di)polar probe itself from a less polar to a more polar region. This may also involve cooperative motion of the surfactant chains in the hydrophobic core, if the probe has a sizeable distribution inside the core prior to excitation, or escape of the probe to the bulk from the surface of the self-assembly. The second mechanism should result in the narrowing of the full width of the emission spectrum with time, which has indeed been observed in recent experiments. It is argued that both the mechanisms may give rise to an ultraslow time constant and may be applicable to different experimental situations. The effectiveness of solvation as a dynamical probe in such complex systems has been discussed.

Recent optical kerr effect (OKE) studies have revealed that orientational relaxation of rodlike nematogens near the isotropic-nematic (I-N) phase boundary and also in the nematic phase exhibit temporal power law decay at intermediate times. Such behaviour has drawn an intriguing analogy with supercooled liquids. Here, we have investigated the single-particle and collective orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I-N phase boundary, the system behaves like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system.

Processes in complex chemical systems, such as macromolecules, electrolytes, interfaces, micelles and enzymes, can span several orders of magnitude in length and time scales. The length and time scales of processes occurring over this broad time and space window are frequently coupled to give rise to the control necessary to ensure specificity and the uniqueness of the chemical phenomena. A combination of experimental, theoretical and computational techniques that can address a multiplicity of length and time scales is required in order to understand and predict structure and dynamics in such complex systems. This review highlights recent experimental developments that allow one to probe structure and dynamics at increasingly smaller length and time scales. The key theoretical approaches and computational strategies for integrating information across time-scales are discussed. The application of these ideas to understand phenomena in various areas, ranging from materials science to biology, is illustrated in the context of current developments in the areas of liquids and solvation, protein folding and aggregation and phase transitions, nucleation and self-assembly.

Dielectric dispersion and NMRD experiments have revealed that a significant fraction of water molecules in the hydration shell of various proteins do not exhibit any slowing down of dynamics. This is usually attributed to the presence of the hydrophobic residues (HBR) on the surface, although HBRs alone cannot account for the large amplitude of the fast component. Solvation dynamics experiments and also computer simulation studies, on the other hand, repeatedly observed the presence of a non-negligible slow component. Here we show, by considering three well-known proteins (lysozyme, myoglobin and adelynate kinase), that the fast component arises partly from the response of those water molecules that are hydrogen bonded with the backbone oxygen (BBO) atoms. These are structurally and energetically less stable than those with the side chain oxygen (SCO) atoms. In addition, the electrostatic interaction energy distribution (EIED) of individual water molecules (hydrogen bonded to SCO) with side chain oxygen atoms shows a surprising two peak character with the lower energy peak almost coincident with the energy distribution of water hydrogen bonded to backbone oxygen atoms (BBO). This two peak contribution appears to be quite general as we find it for lysozyme, myoglobin and adenylate kinase (ADK). The sharp peak of EIED at small energy (at less than 2 $k_{B}T$) for the BBO atoms, together with the first peak of EIED of SCO and the HBRs on the protein surface, explain why a large fraction (∼ 80%) of water in the protein hydration layer remains almost as mobile as bulk water. Significant slowness arises only from the hydrogen bonds that populate the second peak of EIED at larger energy (at about 4 k$_B$T). Thus, if we consider hydrogen bond interaction alone, only 15-20% of water molecules in the protein hydration layer can exhibit slow dynamics, resulting in an average relaxation time of about 5-10 ps. The latter estimate assumes a time constant of 20-100 ps for the slow component. Interestingly, relaxation of water molecules hydrogen bonded to back bone oxygen exhibit an initial component faster than the bulk, suggesting that hydrogen bonding of these water molecules remains frustrated. This explanation of the heterogeneous and non-exponential dynamics of water in the hydration layer is quantitatively consistent with all the available experimental results, and provides unification among diverse features.

We explore the potential energy landscape of structure breaking binary mixtures (SBBM) where two constituents dislike each other, yet remain macroscopically homogeneous at intermediate to high temperatures. Interestingly, we find that the origin of strong composition dependent non-ideal behaviour lies in its phase separated inherent structure. The inherent structure (IS) of SBBM exhibits bi-continuous phase as is usually formed during spinodal decomposition.We draw analogy of this correlation between non-ideality and phase separation in IS to explain observation of non-ideality in real aqueous mixtures of small amphiphilic solutes, containing both hydrophilic and hydrophobic groups. Although we have not been able to obtain IS of these liquids, we find that even at room temperature these liquids sustain formation of fluctuating, transient bicontinuous phase, with limited lifetime ($\tau \lesssim$ 20 ps). While in the model (A, B) binary mixture, the non-ideal composition dependence can be considered as a fluctuation from a phase separated state, a similar scenario is expected to be responsible for the unusually strong non-ideality in these aqueous binary mixtures.

Using polydispersity index as an additional order parameter we investigate freezing/melting transition of Lennard-Jones polydisperse systems (with Gaussian polydispersity in size), especially to gain insight into the origin of the terminal polydispersity. The average inherent structure (IS) energy and root mean square displacement (RMSD) of the solid before melting both exhibit quite similar polydispersity dependence including a discontinuity at solid-liquid transition point. Lindemann ratio, obtained from RMSD, is found to be dependent on temperature. At a given number density, there exists a value of polydispersity index (𝛿_P) above which no crystalline solid is stable. This transition value of polydispersity (termed as transition polydispersity, 𝛿_P) is found to depend strongly on temperature, a feature missed in hard sphere model systems. Additionally, for a particular temperature when number density is increased, 𝛿_P shifts to higher values. This temperature and number density dependent value of 𝛿_P saturates surprisingly to a value which is found to be nearly the same for all temperatures, known as terminal polydispersity (𝛿_TP). This value (𝛿_TP ∼ 0.11) is in excellent agreement with the experimental value of 0.12, but differs from hard sphere transition where this limiting value is only 0.048. Terminal polydispersity (𝛿_TP) thus has a quasiuniversal character. Interestingly, the bifurcation diagram obtained from non-linear integral equation theories of freezing seems to provide an explanation of the existence of unique terminal polydispersity in polydisperse systems. Global bond orientational order parameter is calculated to obtain further insights into mechanism for melting.

It is commonly believed that melting occurs when mean square displacement (MSD) of a particle of crystalline solid exceeds a threshold value. This is known as the Lindemann criterion, first introduced in the year of 1910 by Lindemann. However, Chakravarty et al., demonstrated that this common wisdom is inadequatebecause the MSD at melting can be temperature dependent when pressure is also allowed to vary along the coexistence line of the phase diagram [Chakravarty C, Debenedetti P G and Stillinger F H 2007 J. Chem. Phys. 126 204508]. We show here by extensive molecular dynamics simulation of both two and three dimensional polydisperse Lennard-Jones solids that particles on the small and large limits of size distribution exhibit substantially different Lindemann ratio at melting. Despite all the dispersion in MSD, melting is found tobe first order in both the dimensions at 5–10% dispersity in size. Sharpness of the transition is incommensurate with the different rate of growth of MSD. The increased MSD values of smaller particles play a role in the segregation of them prior to melting.

Water-mediated, effective, long-range interaction between two hydrophobic surfaces immersed in water is of great importance in natural phenomena.We perform themolecular dynamics simulations to investigate the effect of temperature on the attractive force between two graphene-like hydrophobic surfaces in SPC/Ewater. We systematically calculate the force between two hydrophobic surfaces at different inter-wall separations (d) and subsequently determine the correlation lengths at different temperatures. A significant change in the strength of the attractive hydrophobic force is observed with the variation of temperature. The correlation length of effective hydrophobic force increases on lowering the temperature. We also examine the temperature effects on the behavior of confined water molecules by computing the density and orientational profiles. The analyses of these profiles suggest that the layering of water molecules induced by surfaces decreases with increase in temperature of the system. Critical dewetting distance (dc), where drying transition phenomenon occurs, shifts to the lower value of d upon cooling.