Breakdown of Langmuir Adsorption Isotherm in Small Closed Systems.

For more than a century, monolayer adsorptions in which adsorbate molecules and adsorbing sites behave ideally have been successfully described by Langmuir's adsorption isotherm. For example, the amount of adsorbed material, as a function of concentration of the material which is not adsorbed, obeys Langmuir's equation. In this paper, we argue that this relation is valid only for macroscopic systems. However, when particle numbers of adsorbate molecules and/or adsorbing sites are small, Langmuir's model fails to describe the chemical equilibrium of the system. This is because the kinetics of forming, or the probability of observing, occupied sites arises from two-body interactions, and as such, ought to include cross-correlations between particle numbers of the adsorbate and adsorbing sites. The effect of these correlations, as reflected by deviations in predicting composition when correlations are ignored, increases with decreasing particle numbers and becomes substantial when only few adsorbate molecules, or adsorbing sites, are present in the system. In addition, any change that augments the fraction of occupied sites at equilibrium (e.g., smaller volume, lower temperature, or stronger adsorption energy) further increases the discrepancy between observed properties of small systems and those predicted by Langmuir's theory. In contrast, for large systems, these cross-correlations become negligible, and therefore when expressing properties involving two-body processes, it is possible to consider independently the concentration of each component. By applying statistical mechanics concepts, we derive a general expression of the equilibrium constant for adsorption. It is also demonstrated that in ensembles in which total numbers of particles are fixed, the magnitudes of fluctuations in particle numbers alone can predict the average chemical composition of the system. Moreover, an alternative adsorption equation, predicting the average fraction of occupied sites from the value of the equilibrium constant, is proposed. All derived relations were tested against results obtained by Monte Carlo simulations.

Multimerizations, Aggregation, and Transfer Reactions of Small Numbers of Molecules.

Chemical equilibria of multimerizations in systems with small numbers of particles exhibit a behavior seemingly at odds with that observed macroscopically. In this paper, we apply the recently proposed expression of equilibrium constant for binding, which includes cross-correlations in reactants' concentrations, to write an equilibrium constant for the formation of clusters larger than two (e.g., trimer, tetramer, and pentamer) as series of two-body reactions. Results obtained by molecular dynamics simulations demonstrate that the value of this expression is constant for all concentrations and system sizes, as well as at an onset of a phase transition to an aggregated state, where densities in the system change discontinuously. In contrast, the value of the commonly utilized expression of equilibrium constant, which ignores correlations, is not constant and its variations can reach few orders of magnitude. Considering different paths for the same multimer formation, with elementary reactions of any order, yields different expressions for the equilibrium constant, yet, with exactly the same value. This is also true for routes with essentially zero probability to occur. Existence of different expressions for the same equilibrium constant imposes equalities between averages of correlated, along with uncorrelated, concentrations of participating species. Moreover, a relation between an average particle number and relative fluctuations derived for two-body reactions is found to be obeyed here as well despite couplings to additional equilibrium reactions in the system. Analyses of transfer reactions, where association and dissociation events take place on both sides of the chemical equation, further indicate the necessity to include cross-correlations in the expression of the equilibrium constant. However, in this case, the magnitudes of discrepancies of the uncorrelated expression are smaller, likely because of partial cancellation of correlations, which exist on both the reactant and product sides.

Binding reactions at finite systems.

A perpetual yearn exists among computational scientists to scale down the size of physical systems, a desire shared as well with experimentalists able to track single molecules. A question then arises whether averages observed at small systems are the same as those observed at large or macroscopic systems. Utilizing statistical-mechanics formulations in ensembles in which the total numbers of particles are fixed, we demonstrate that properties of binding reactions are not homogeneous functions. This means that averages of intensive parameters, such as the concentration of the bound-state, at finite systems are different than those at large systems. The discrepancy increases with decreasing temperature, volume, and to some extent, numbers of particles. As perplexing as it may sound, despite variations in average quantities, extracting the equilibrium constant from systems of different sizes does yield the same value. The reason is that correlations in reactants' concentrations ought to be accounted for in the expression of the equilibrium constant, being negligible at large-scale but significant at small-scale. Similar arguments pertain to the calculations of the reaction rate constants, more specifically, the bimolecular rate of the forward reaction is related to the average of the product (and not to the product of the averages) of the reactants' concentrations. Furthermore, we derive relations aiming to predict the composition only from the equilibrium constant and the system's size. All predictions are validated by Monte-Carlo and molecular dynamics simulations. An important consequence of these findings is that the expression of the equilibrium constant at finite systems is not dictated solely by the chemical equation of the reaction but requires knowledge of the elementary processes involved.

Statistical mechanics of dimerizations and its consequences for small systems.

Utilizing a statistical mechanics framework, we derive the expression of the equilibrium constant for dimerization reactions. An important feature arising from the derivation is the necessity to include two-body correlations between monomer's number of particles, reminiscent to those recently found crucial for binding reactions. However in (homo-) dimerizations, particles of the same type associate, and therefore, self-correlations are excluded. As a result, the mathematical form of the equilibrium constant differs from the well-known expression given in textbooks. For systems with large number of particles the discrepancy is negligible, whereas, for finite systems it is significant. Rationalized by collision probability between monomers, the bimolecular rate for dimer formation is proportional to concentration the same way correlations are accounted for. That is average of squared, and not square of averaged, monomer concentration should be considered in such a way that inconceivable collisions between a tagged particle with itself are excluded. Another consequence emerging from these two-body correlations, is an inhomogeneous function behavior of system's properties upon scaling-down the system to a regime smaller than the thermodynamic limit. Thus, averages of properties observed at small systems are different than those observed at macroscopic systems. All predictions are verified by Monte Carlo and molecular dynamics simulations.

Adsorption-induced clustering of CO2 on graphene.

Utilization of graphene-based materials for selective carbon dioxide capture has been demonstrated recently as a promising technological approach. In this study we report results from density functional theory calculations and molecular dynamics simulations on the adsorption of CO2, N2, and CH4 gases on a graphene sheet. We calculate adsorption isotherms of ternary and binary mixtures of these gases and reproduce the larger selectivity of CO2 to graphene relative to the other two gases. Furthermore it is shown that the confinement to two-dimensions, associated with adsorbing the CO2 gas molecules on the plane of graphene, increases their propensity to form clusters on the surface. Above a critical surface coverage (or partial pressure) of the gas, these CO2-CO2 interactions augment the effective adsorption energy to graphene, and, in part, contribute to the high selectivity of carbon dioxide with respect to nitrogen and methane. The origin of the attractive interaction between the CO2 molecules adsorbed on the surface is of electric quadrupole-quadrupole nature, in which the positively-charged carbon of one molecule interacts with the negatively-charged oxygen of another molecule. The energy of attraction of forming a CO2 dimer is predicted to be around 5-6 kJ mol-1, much higher than the corresponding values calculated for N2 and CH4. We also evaluated the adsorption energies of these gases to a graphene sheet and found that the attractions obtained using the classical force-fields might be over-exaggerated. Nevertheless, even when the magnitudes of these (classical force-field) graphene-gas interactions are scaled-down sufficiently, the tendency of CO2 molecules to cluster on the surface is still observed.

Shedding light on the different behavior of ionic and nonionic surfactants in emulsion polymerization: from atomistic simulations to experimental observations.

Although surfactants are known to play a vital role in polymerization reactions carried out in dispersed media, many aspects of their use are poorly understood, perhaps none more so than the vastly different action of ionic and nonionic surfactants in emulsion polymerization. In this work, we combine experimental measurements of emulsion polymerization of styrene with atomistic molecular dynamics simulations to better understand the behavior of surfactants at monomer/polymer-water interfaces. In a batch emulsion polymerization of styrene, the nonionic surfactant Disponil AFX 1080 leads to two nucleation periods, in contrast to the behavior observed for the ionic surfactant SDS. This can be explained by the absorption of the nonionic surfactant into the organic phase at the early stages of the polymerization reaction which is then released as the reaction progresses. Indeed, we find that the partition coefficient of the surfactant between the organic phase and water increases with the amount of monomer in the former, and preferential partitioning is detected to organic phases containing at least 55% styrene. Results from molecular dynamics simulations confirm that spontaneous dissolution of the non-ionic surfactant into a styrene-rich organic phase occurs above a critical concentration of the surfactant adsorbed at the interface. Above this critical concentration, a linear correlation between the amount of surfactant adsorbed at the interface and that absorbed inside the organic phase is observed. To facilitate this absorption into a completely hydrophobic medium, water molecules accompany the intruding surfactants. Similar simulations but with the ionic surfactant instead did not result in any absorption of the surfactant into a neat styrene phase, likely because of its strongly hydrophilic head group. The unusual partitioning behavior of nonionic surfactants explains a number of observable features of emulsion polymerization reactions which use nonionic surfactants and should help with future development of processes for improved control over polymerization.

Adsorption mechanism of an antimicrobial peptide on carbonaceous surfaces: A molecular dynamics study.

Peptides are versatile molecules with applications spanning from biotechnology to nanomedicine. They exhibit a good capability to unbundle carbon nanotubes (CNT) by improving their solubility in water. Furthermore, they are a powerful drug delivery system since they can easily be uptaken by living cells, and their high surface-to-volume ratio facilitates the adsorption of molecules of different natures. Therefore, understanding the interaction mechanism between peptides and CNT is important for designing novel therapeutical agents. In this paper, the mechanisms of the adsorption of antimicrobial peptide Cecropin A-Magainin 2 (CA-MA) on a graphene nanosheet (GNS) and on an ultra-short single-walled CNT are characterized using molecular dynamics simulations. The results show that the peptide coats both GNS and CNT surfaces through preferential contacts with aromatic side chains. The peptide packs compactly on the carbon surfaces where the polar and functionalizable Lys side chains protrude into the bulk solvent. It is shown that the adsorption is strongly correlated to the loss of the peptide helical structure. In the case of the CNT, the outer surface is significantly more accessible for adsorption. Nevertheless when the outer surface is already covered by other peptides, a spontaneous diffusion, via the amidated C-terminus into the interior of the CNT, was observed within 150 ns of simulation time. We found that this spontaneous insertion into the CNT interior can be controlled by the polarity of the entrance rim. For the positively charged CA-MA peptide studied, hydrogenated and fluorinated rims, respectively, hinder and promote the insertion.

Strings-to-Rings Transition and Antiparallel Dipole Alignment in Two-Dimensional Methanols.

Structural order emerging in the liquid state necessitates a critical degree of anisotropy of the molecules. For example, liquid crystals and Langmuir monolayers require rod- or disc-shaped and long-chain amphiphilic molecules, respectively, to break the isotropic symmetry of liquids. In this Letter we present results from molecular dynamics simulations demonstrating that in two-dimensional liquids, a significantly smaller degree of anisotropy is sufficient to allow structural organization. In fact, the condensed phase of the smallest amphiphilic molecule, methanol, confined between two, or adsorbed on, graphene sheets forms a monolayer characterized by long chains of molecules. Intrachain interactions are dominated by hydrogen bonds, whereas interchain interactions are dispersive. Upon a decrease in density toward a gaslike state, these strings are transformed into rings. The two-dimensional liquid phase of methanol undergoes another transition upon cooling; in this case, the order-disorder transition is characterized by a low-temperature phase in which the hydrogen bond dipoles of neighboring strings adopt an antiparallel orientation.

Adsorption and desorption behavior of ionic and nonionic surfactants on polymer surfaces.

We report combined experimental and computational studies aiming to elucidate the adsorption properties of ionic and nonionic surfactants on hydrophobic polymer surface such as poly(styrene). To represent these two types of surfactants, we choose sodium dodecyl sulfate and poly(ethylene glycol)-poly(ethylene) block copolymers, both commonly utilized in emulsion polymerization. By applying quartz crystal microbalance with dissipation monitoring we find that the non-ionic surfactants are desorbed from the poly(styrene) surface slower, and at low surfactant concentrations they adsorb with stronger energy, than the ionic surfactant. If fact, from molecular dynamics simulations we obtain that the effective attractive force of these nonionic surfactants to the surface increases with the decrease of their concentration, whereas, the ionic surfactant exhibits mildly the opposite trend. We argue that the difference in this contrasting behavior stems from the physico-chemical properties of the head group. Ionic surfactants characterized by small and strongly hydrophilic head groups form an ordered self-assembled structure at the interface whereas, non-ionic surfactants with long and weakly hydrophilic head groups, which are also characterized by low persistence lengths, generate a disordered layer. Consequently, upon an increase in concentration, the layer formed by the nonionic surfactants prevents the aprotic poly(ethylene glycol) head groups to satisfy all their hydrogen bonds capabilities. As a response, water molecules intrude this surfactant layer and partially compensate for the missing interactions, however, at the expense of their ability to form hydrogen bonds as in bulk. This loss of hydrogen bonds, either of the head groups or of the intruding water molecules, is the reason the nonionic surfactants weaken their effective attraction to the interface with the increase in concentration.

Molecular dynamics study of the recognition of dimethylated CpG sites by MBD1 protein.

The cell is able to regulate which genes to express via chemical marks on the DNA and on the histone proteins. In all vertebrates, the modification on the DNA is methylation at position 5 of the two cytosines present in the dinucleotide sequence CpG. The information encoded by these chemical marks on the DNA is processed by a family of protein factors containing a conserved methyl-CpG binding domain (MBD). Essential to their function, the MBD proteins are able to bind DNA containing dimethylated CpG sites, whereas binding to unmethylated sites is not observed. In this paper, we perform molecular dynamics simulations to investigate the mechanism by which the mCpG binding domain of MBD1 is able to bind specifically dimethylated CpG sites. We find that the binding affinity of MBD1 to a DNA containing dimethylated CpG site is stronger by 26.4 kJ/mol relative to binding the same DNA but with an unmethylated CpG site. The contribution of each of the methyl groups to the change in free energy is very similar and additive. Therefore, this binding affinity (to a dimethylated DNA) is halved when considered relative to binding a hemimethylated DNA, a result that is also supported by experimental observations. Despite their equal contributions, the two methyl groups are recognized differently by MBD1. In one case, demethylation induces conformational changes in which the hydrophobic patch formed by the conserved residues Val20, Arg22, and Tyr34 moves away from the (methyl)cytosine, weakening the DNA-protein interactions. This is accompanied by an intrusion of a bulk water into the binding site at the protein-DNA interface. As a consequence, there is a reduction and rearrangements of the protein-DNA hydrogen bonds including a loss of a crucial hydrogen bond between Tyr34 and the (methyl)cytosine. The methylcytosine on the opposite strand is recognized by conformational changes of the surrounding conserved hydrophobic residues, Arg44 and Ser45, in which Arg44 participate in the 5mC-Arg-G triad. More specifically, the hydrogens of the methyl group form weak hydrogen bonds with the guanidino group and backbone carbonyl of the conserved Arg44, interactions that are absent when the cytosine is unmethylated. The results presented in this paper contribute to our knowledge of the different ways the chemical mark on the DNA is recognized by the epigenetic machinery.

Aggregation and cooperative effects in the aldol reactions of lithium enolates.

Density functional theory and Car-Parrinello molecular dynamics simulations have been carried out for model aldol reactions involving aggregates of lithium enolates derived from acetaldehyde and acetone. Formaldehyde and acetone have been used as electrophiles. It is found that the geometries of the enolate aggregates are in general determined by the most favorable arrangements of the point charges within the respective Lin On clusters. The reactivity of the enolates follows the sequence monomer≫dimer>tetramer. In lithium aggregates, the initially formed aldol adducts must rearrange to form more stable structures in which the enolate and alkoxide oxygen atoms are within the respective Lin On clusters. Positive cooperative effects, similar to allosteric effects found in several proteins, are found for the successive aldol reactions in aggregates. The corresponding transition structures show in general sofa geometries.

Attraction between like-charged monovalent ions.

Ions with like-charges repel each other with a magnitude given by the Coulomb law. The repulsion is also known to persist in aqueous solutions albeit factored by the medium's dielectric constant. In this paper, we report results from molecular dynamics simulations of alkali halides salt solutions indicating an effective attraction between some of the like-charged monovalent ions. The attraction is observed between anions, as well as between cations, leading to the formation of dimers with lifetimes on the order of few picoseconds. Two mechanisms have been identified to drive this counterintuitive attraction. The first is exhibited by high-charge density ions, such as fluoride, at low salt concentrations, yielding effective attractions with magnitude up to the order of 1-2 kT. In this case, the stronger local electric field generated when the two ions are in contact augments the alignment of neighboring waters toward the ions. This results in a gain of substantial favorable ion-water interaction energy. For fluorides, this interaction constitutes the major change among the different energy components compensating for the anion-anion repulsion, and therefore, rendering like-charge association possible. The second mechanism involves mediation by counterions, the attractions increase with salt concentration and are characterized by small magnitudes. In particular, clusters of ion triplets, in which a counterion is either bridging the two like-charged ions or is paired to only one of them, are formed. Although these two mechanisms may not yield net attractions in many cases, they might still be operational and significant, explaining effective repulsions between like-charged ions with magnitudes much smaller than expected based on continuum electrostatics.

Tandem [8 + 2] cycloaddition--[2 + 6 + 2] dehydrogenation reactions involving imidazo[1,2-a]pyridines and imidazo[1,2-a]pyrimidines.

The reaction between benzynes and imidazo[1,2-a]pyridines (pyrimidines) to form benzo[a]imidazo[5,1,2-cd]indolizines and 2,3,9c-triazocyclopenta[j,k]fluorenes has been studied computationally and experimentally. It is found that these reactions take place via tandem [(pi)8(s) + (pi)2(s)] and [(sigma)2(s) + (pi)6(s) + (sigma)2(s)] processes. The [8 + 2] cycloaddition steps are essentially barrierless, and the aromatization steps occur via highly synchronous aromatic transition structures. From an experimental standpoint, the reaction is feasible under microwave irradiation and using 2-(trimethylsilyl)phenyl triflates as benzyne precursors. Depending on the substitution pattern in the starting triflate a complete regiocontrol of the reaction can be achieved. The tetracyclic compounds thus prepared emitted blue light when excited at 365 nm and exhibited interesting photophysical properties.

Reduced Graphene Oxide/Polymer Monolithic Materials for Selective CO2 Capture.

Polymer composite materials with hierarchical porous structure have been advancing in many different application fields due to excellent physico-chemical properties. However, their synthesis continues to be a highly energy-demanding and environmentally unfriendly process. This work reports a unique water based synthesis of monolithic 3D reduced graphene oxide (rGO) composite structures reinforced with poly(methyl methacrylate) polymer nanoparticles functionalized with epoxy functional groups. The method is based on reduction-induced self-assembly process performed at mild conditions. The textural properties and the surface chemistry of the monoliths were varied by changing the reaction conditions and quantity of added polymer to the structure. Moreover, the incorporation of the polymer into the structures improves the solvent resistance of the composites due to the formation of crosslinks between the polymer and the rGO. The monolithic composites were evaluated for selective capture of CO2. A balance between the specific surface area and the level of functionalization was found to be critical for obtaining high CO2 capacity and CO2/N2 selectivity. The polymer quantity affects the textural properties, thus lowering its amount the specific surface area and the amount of functional groups are higher. This affects positively the capacity for CO2 capture, thus, the maximum achieved was in the range 3.56-3.85 mmol/g at 1 atm and 25 °C.

Urea's action on hydrophobic interactions.

For more than a century, urea has been commonly used as an agent for denaturing proteins. However, the mechanism behind its denaturing power is still not well understood. Here we show by molecular dynamics simulations that a 7 M aqueous urea solution unfolds a chain of purely hydrophobic groups which otherwise adopts a compact structure in pure water. The unfolding process arises due to a weakening of hydrophobic interactions between the polymer groups. We also show that the attraction between two model hydrophobic plates, and graphene sheets, is reduced when urea is added to the solution. The action of urea is found to be direct, through its preferential binding to the polymer or plates. It is, therefore, acting like a surfactant capable of forming hydrogen bonds with the solvent. The preferential binding and the consequent weakened hydrophobic interactions are driven by enthalpy and are related to the difference in the strength of the attractive dispersion interactions of urea and water with the polymer chain or plate. This relation scales with square root(epsilon(b)), where epsilon(b) is the Lennard Jones (LJ) energy parameter for each group on the chain. Larger values of epsilon(b) increase the preferential binding and result in a larger decrease of the hydrophobic interactions, with a crossover at very weak dispersions. We also show that the indirect mechanism, in which urea acts as a chaotrope, is not a likely cause of urea's action as a denaturant. These findings suggest that, in denaturing proteins, urea (and perhaps other denaturants) forms stronger attractive dispersion interactions with the protein side chains and backbone than does water and, therefore, is able to dissolve the core hydrophobic region.

Dissecting entropic coiling and poor solvent effects in protein collapse.

The early events in protein collapse and folding are guided by the protein's elasticity. The contributions of entropic coiling and poor solvent effects like hydrophobic forces to the elastic response of proteins are currently unknown. Using molecular simulations of stretched ubiquitin in comparison with models of proteins as entropic chains, we find a surprisingly high stiffness of the protein backbone, reflected by a persistence length of 1.2 nm, which is significantly reduced by hydrophobic forces acting between protein side chains to an apparent persistence length of 0.3-0.6 nm frequently observed in single-molecule stretching experiments. Thus, the poor solvent conditions of a protein in water lead to a protein compaction much beyond the coiling of an entropic chain and thereby allow a protein to appear softer than when using good solvents.

Temperature dependence of dimerization and dewetting of large-scale hydrophobes: a molecular dynamics study.

We studied by molecular dynamics simulations the temperature dependence of hydrophobic association and drying transition of large-scale solutes. Similar to the behavior of small solutes, we found the association process to be characterized by a large negative heat capacity change. The origin of this large change in heat capacity is the high fragility of hydrogen bonds between water molecules at the interface with hydrophobic solutes; an increase in temperature breaks more hydrogen bonds at the interface than in the bulk. With increasing temperature, both entropy and enthalpy changes for association strongly decrease, while the change in free energy weakly varies, exhibiting a small minimum at high temperatures. At around T=Ts=360 K, the change in entropy is zero, a behavior similar to the solvation of small nonpolar solutes. Unexpectedly, we find that at Ts, there is still a substantial orientational ordering of the interfacial water molecules relative to the bulk. Nevertheless, at this point, the change in entropy vanishes due to a compensating contribution of translational entropy. Thus, at Ts, there is rotational order and translational disorder of the interfacial water relative to bulk water. In addition, we studied the temperature dependence of the drying-wetting transition. By calculating the contact angle of water on the hydrophobic surface at different temperatures, we compared the critical distance observed in the simulations with the critical distance predicted by macroscopic theory. Although the deviations of the predicted from the observed values are very small (8-23%), there seems to be an increase in the deviations with an increase in temperature. We suggest that these deviations emerge due to increased fluctuations, characterizing finite systems, as the temperature increases.

Refinement of the OPLSAA Force-Field for Liquid Alcohols.

We employ the popular all-atom optimized potential for liquid simulations, OPLSAA, force-field to model 17 different alcohols in the liquid state. Using the standard simulation protocol for few hundred nanosecond time periods, we find that 1-octanol, 1-nonanol, and 1-decanol undergo spontaneous transition to a crystalline state at temperatures which are 35-55 K higher than the experimental melting temperatures. Nevertheless, the crystal structures obtained from the simulations are very similar to those determined by X-ray powder diffraction data for several n-alcohols. Although some degree of deviations from the experimental freezing points are to be expected, for 1-nonanol and 1-decanol, the elevation of the freezing temperature warrants special attention because at room temperature, these alcohols are liquids; however, if simulated by the OPLSAA force-field, they will crystallize. This behavior is likely a consequence of exaggerated attractive interactions between the alkane chains of the alcohols. To circumvent this problem, we combined the OPLSAA model with the L-OPLS force-field. We adopted the L-OPLS parameters to model the hydrocarbon tail of the alcohols, whereas the hydroxyl head group remained as in the original OPLSAA force-field. The resulting alcohols stayed in the liquid state at temperatures above their experimental melting points, thus, resolving the enhanced freezing observed with the OPLSAA force-field. In fact, the mixed-model alcohols did not exhibit any spontaneous freezing even at temperatures much lower than the experimental values. However, a series of simulations in which these mixed-OPLSAA alcohols started from a coexistence configuration of the liquid and solid phases resulted in freezing transitions at temperatures 14-25 K lower than the experimental values, confirming the validity of the proposed model. For all of the other alcohols, the mixed model yields results very similar to the OPLSAA force-field and is in good agreement with the experimental data. Thus, for simulating alcohols in the liquid phase, the mixed-OPLSAA model is necessary for large (7 carbons and above) hydrocarbon chains.

Frequency-dependent Stokes-Einstein relation in supercooled liquids.

We investigate by molecular dynamics simulations the validity of the frequency-dependent Stokes-Einstein (SE) relation in supercooled liquids at different temperatures. The results indicate that the SE relation holds at intermediate frequencies that correspond to the beta -relaxation and the onset of the alpha -relaxation regimes. Large deviations, which increase as the temperature decreases, are observed at frequencies well below the frequency at which the non-Gaussian parameter alpha2 is maximum. We argue that the breakdown of the SE relation in supercooled liquids arises from underestimation of the diffusion coefficient due to neglect of correlated motions.

Aggregation and dispersion of small hydrophobic particles in aqueous electrolyte solutions.

The effect of salts on the solvent-induced interactions between hydrophobic particles dispersed in explicit aqueous solution is investigated as a function of the salt's ionic charge density by molecular dynamics simulations. We demonstrate that aggregates of the hydrophobic particles can be formed or dissolved in response to changes in the charge density of the ions. Ions with high charge density increase the propensity of the hydrophobic particles to aggregate. This corresponds to stronger hydrophobic interactions and a decrease in the solubility (salting-out) of the hydrophobic particles. Ions with low charge density can either increase or decrease the propensity for aggregation depending on whether the concentration of the salt is low or high, respectively. At low concentrations of low charge density ions, the aggregate forms a "micelle-like" structure in which the ions are preferentially adsorbed at the surface of the aggregate. These "micelle-like" structures can be soluble in water so that the electrolyte can both increase the solubility and increase aggregation at the same time. We also find, that at the concentration of the hydrophobic particles studied (approximately 0.75 m), the aggregation process resembles a first-order transition in finite systems.