On the cavity size distribution in water and n-hexane

Gaussian and Non-Gaussian Solvent Density Fluctuations within Solute Cavities in a Water-like Solvent

We report a Monte Carlo simulation study of length-scale-dependent density fluctuations in cavities in the coarse-grained mW representation of water at ambient conditions. Specifically, we use a combination of test particle insertion and umbrella sampling techniques to examine the full range of water occupation states in spherical cavities up to 6.3 Å radius in water. As has previously been observed, water density fluctuations are found to be effectively Gaussian in nature for atomic-scale cavities, but as the cavities get larger, they exhibit a non-Gaussian "fat-tail" distribution for lower occupancy states. We introduce a new statistical thermodynamic approach to analyze non-Gaussian fluctuations based on the radial distribution of waters about cavities with varying numbers of waters within its boundaries. It is shown that the onset of these non-Gaussian fluctuations is a result of the formation of a bubble within the cavity as it is emptied, which is accompanied by the adsorption of waters onto its interior surface. We revisit a theoretical framework we previously introduced to describe Gaussian fluctuations within cavities to incorporate bubble formation by including surface tension contributions. This modified theory accurately describes density fluctuations within both atomic and meso-scale cavities. Moreover, the theory predicts the transition from Gaussian to non-Gaussian fluctuations at a specific cavity occupancy, in excellent agreement with simulation observations.

Role of Charge Ordering in the Dynamics of Cluster Formation in Associated Liquids

Liquids are archetypes of disordered systems, yet liquids of polar molecules are locally more ordered than nonpolar molecules, due to the Coulomb interaction based charge ordering phenomenon. Hydrogen bonded liquids, such as water or alcohols, for example, represent a special type of polar liquids, in that they form labile clustered local structures. For water, in particular, hydrogen bonding and the related local tetrahedrality, play an important role in the various attempts to understand this liquid. However, labile structures imply dynamics, and it is not clear how it affects the understanding of this type of liquids from purely static point of view. Herein, we propose to reconsider hydrogen bonding as a charge ordering process. This concept allows us to demonstrate the insufficiency of the analysis of the microscopic structure based solely on static pair correlation functions, and the need for dynamical correlation functions, both in real and reciprocal space. The subsequent analysis allows to recover several aspects of our understanding of hydrogen bonded liquids, but from the charge order perspective. For water, it confirms the jump rotation picture found recently, and it allows to rationalize the contradicting pictures that arise when following the interpretations based on hydrogen bonding. For alcohols, it allows to understand the dynamical origin of the scattering prepeak, which does not exist for water, despite the fact that both these liquids have very similar hydroxyl group chain clusters. The concept of charge ordering complemented by the analysis of dynamical correlation functions appear as a promising way to understand microheterogeneity in complex liquids and mixtures from kinetics point of view.

Some Clues about Enzymes from Psychrophilic Microorganisms

Enzymes purified from psychrophilic microorganisms prove to be efficient catalysts at low temperatures and possess a great potential for biotechnological applications. The low-temperature catalytic activity has to come from specific structural fluctuations involving the active site region, however, the relationship between protein conformational stability and enzymatic activity is subtle. We provide a survey of the thermodynamic stability of globular proteins and their rationalization grounded in a theoretical approach devised by one of us. Furthermore, we provide a link between marginal conformational stability and protein flexibility grounded in the harmonic approximation of the vibrational degrees of freedom, emphasizing the occurrence of long-wavelength and excited vibrations in all globular proteins. Finally, we offer a close view of three enzymes: chloride-dependent α-amylase, citrate synthase, and β-galactosidase.

Porous liquids - the future is looking emptier

The development of microporosity in the liquid state is leading to an inherent change in the way we approach applications of functional porosity, potentially allowing access to new processes by exploiting the fluidity of these new materials. By engineering permanent porosity into a liquid, over the transient intermolecular porosity in all liquids, it is possible to design and form a porous liquid. Since the concept was proposed in 2007, and the first examples realised in 2015, the field has seen rapid advances among the types and numbers of porous liquids developed, our understanding of the structure and properties, as well as improvements in gas uptake and molecular separations. However, despite these recent advances, the field is still young, and with only a few applications reported to date, the potential that porous liquids have to transform the field of microporous materials remains largely untapped. In this review, we will explore the theory and conception of porous liquids and cover major advances in the area, key experimental characterisation techniques and computational approaches that have been employed to understand these systems, and summarise the investigated applications of porous liquids that have been presented to date. We also outline an emerging discovery workflow with recommendations for the characterisation required at each stage to both confirm permanent porosity and fully understand the physical properties of the porous liquid.

A Rationalization of the Effect That TMAO, Glycine, and Betaine Exert on the Collapse of Elastin-like Polypeptides

Elastin-like polypeptides (ELPs) are soluble in water at low temperature, but, on increasing the temperature, they undergo a reversible and cooperative, coil-to-globule collapse transition. It has been shown that the addition to water of either trimethylamine N-oxide (TMAO), glycine, or betaine causes a significant decrease of T(collapse) in the case of a specific ELP. Traditional rationalizations of these phenomena do not work in the present case. We show that an alternative approach, grounded in the magnitude of the solvent-excluded volume effect and its temperature dependence (strictly linked to the translational entropy of solvent and co-solute molecules), is able to rationalize the occurrence of ELP collapse in water on raising the temperature, as well as the T(collapse) lowering caused by the addition to water of either TMAO, glycine, or betaine.

Noria and its derivatives as hosts for chemically and thermally robust Type II porous liquids

Porous Liquids (PLs) are a new class of material that possess both fluidity and permanent porosity. As such they can act as enhanced, selective solvents and may ultimately find applications which are not possible for porous solids, such as continuous flow separation processes. Type II PLs consist of empty molecular hosts dissolved in size-excluded solvents and to date have mainly been based on hosts that have limited chemical and thermal stability. Here we identify Noria, a rigid cyclic oligomer as a new host for the synthesis of more robust Type II PLs. Although the structure of Noria is well-documented, we find that literature has overlooked the true composition of bulk Noria samples. We find that bulk samples typically consist of Noria (ca. 40%), a Noria isomer, specifically a resorcinarene trimer, “R3” (ca. 30%) and other unidentified oligomers (ca. 30%). Noria has been characterised crystallographically as a diethyl ether solvate and its ¹H NMR spectrum fully assigned for the first time. The previously postulated but unreported R3 has also been characterised crystallographically as a dimethyl sulfoxide solvate, which confirms its alternative connectivity to Noria. Noria and R3 have low solubility which precludes their use in Type II PLs, however, the partially ethylated derivative Noria-OEt dissolves in the size-excluded solvent 15-crown-5 to give a new Type II PL. This PL exhibits enhanced uptake of methane (CH₄) gas supporting the presence of empty pores in the liquid. Detailed molecular dynamics simulations support the existence of pores in the liquid and show that occupation of the pores by CH₄ is favoured. Overall, this work revises the general accepted composition of bulk Noria samples and shows that Noria derivatives are appropriate for the synthesis of more robust Type II PLs.

Porous Liquids (PLs) are a new class of material that possess both fluidity and permanent porosity. Here we identify Noria, a rigid cyclic oligomer as a new host for the synthesis of more robust Type II PLs.

A driving force for polypeptide and protein collapse

Polypeptide collapse is driven by the solvent-excluded volume decrease, the presence of nonpolar side chains is not so important.

Ligand Entropy in Gas-Phase, Upon Solvation and Protein Complexation. Fast Estimation with Quasi-Newton Hessian

A method of rapid entropy estimation for small molecules in vacuum, solution, and inside a protein receptor is proposed. We show that the Hessian matrix of second derivatives built by a quasi-Newton optimizer during geometry optimization of a molecule with a classical molecular potential in these three environments can be used to predict vibrational entropies. We also show that a simple analytical solvation model allows for no less accurate entropy estimation of molecules in solution than a physically rigorous but computationally more expensive model based on Poisson's equation. Our work also suggests that scaled particle theory more precisely estimates the hydrophobic part of solvation entropy than the using a simple surface area term.

On the mechanism of cold denaturation

A theoretical rationalization of the occurrence of cold denaturation for globular proteins was devised, assuming that the effective size of water molecules depends upon temperature [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252]. In the present work, it is shown that the latter assumption is not necessary. By performing the same type of calculations in water, 40% (by weight) methanol, methanol, and carbon tetrachloride, it emerges that cold denaturation occurs only in water due to the special temperature dependence of its density and the small size of its molecules. These two coupled factors determine the magnitude and the temperature dependence of the stabilizing term that measures the gain in configurational/translational entropy of water molecules upon folding of the protein. This term has to be contrasted with the destabilizing contribution measuring the loss in conformational entropy of the polypeptide chain upon folding.

On the molecular origin of cold denaturation of globular proteins

A polypeptide chain can adopt very different conformations, a fundamental distinguishing feature of which is the water accessible surface area, WASA, that is a measure of the layer around the polypeptide chain where the center of water molecules cannot physically enter, generating a solvent-excluded volume effect. The large WASA decrease associated with the folding of a globular protein leads to a large decrease in the solvent-excluded volume, and so to a large increase in the configurational/translational freedom of water molecules. The latter is a quantity that depends upon temperature. Simple calculations over the -30 to 150 °C temperature range, where liquid water can exist at 1 atm, show that such a gain decreases significantly on lowering the temperature below 0 °C, paralleling the decrease in liquid water density. There will be a temperature where the destabilizing contribution of the polypeptide chain conformational entropy exactly matches the stabilizing contribution of the water configurational/translational entropy, leading to cold denaturation.

Blowing bubbles in Lennard-Jonesium along the saturation curve

Extensive molecular simulations of the Lennard-Jones fluid have been performed to determine its liquid-vapor coexistence properties and solvent contact densities with cavities up to ten times the diameter of the solvent from the triple point to the critical point. These simulations are analyzed using a revised scaled-particle theory [H. S. Ashbaugh and L. R. Pratt, Rev. Mod. Phys. 78, 159 (2006)] to evaluate the thermodynamics of cavity solvation and curvature dependent interfacial properties along the saturation curve. While the thermodynamic signatures of cavity solvation are distinct from those in water, exhibiting a chemical potential dominated by a large temperature independent enthalpy, the solvent dewets cavities of increasing size similar with water near coexistence. The interfacial tension for forming a liquid-wall interface is found to be consistently greater than the liquid-vapor surface tension of the Lennard-Jones fluid by up to 10% and potentially reflects the suppression of high amplitude fluctuations at the cavity surface. The first-order curvature correction for the surface tension is negative and appears to diverge to negative infinity at temperatures approaching the critical point. Our results point to the success of the revised scaled-particle theory at bridging molecular and macroscopic descriptions of cavity solvation.

Scaled particle theory study of the length scale dependence of cavity thermodynamics in different liquids

It has been noted that the work of cavity creation in water exhibits a crossover behavior, in that its cavity size dependence changes from volume dependence for small cavities to area dependence for larger cavities [Lum, K.; Chandler, D.; Weeks, J. D. J. Phys. Chem. B 1999, 103, 4570]. It is shown here that this behavior can be reproduced using the scaled particle theory in a straightforward manner for six different liquids (water, methanol, ethanol, benzene, cyclohexane, and carbon tetrachloride). It has also been suggested that the crossover is due to a change in the physical mechanism of the process, from one entropy-dominated to another enthalpy-dominated. However, the crossover behavior can be produced using the scaled particle theory without invoking any change in any physical mechanism. Also, the crossover occurs at a length scale of the size of the liquid molecules, as has been pointed out by others. This is the length regime where the work of cavity creation bears little relation to the bulk liquid surface tension. In addition, it is pointed out that cavity creation can always be considered as a purely entropy-driven process, which is usually accompanied by another process with compensating enthalpy and entropy changes.

Contrasting nonaqueous against aqueous solvation on the basis of scaled-particle theory

Normal hexane is adopted as a typical organic solvent for comparison with liquid water in modern theories of hydrophobic hydration, and detailed results are worked-out here for the C-atom density in contact with a hard-sphere solute, rhoCG(R), for the full range of solute radii. The intramolecular structure of an n-hexane molecule introduces qualitative changes in G(R) compared to scaled-particle models for liquid water. Also worked-out is a revised scaled-particle model implemented with molecular simulation results for liquid n-hexane. The classic scaled-particle model, acknowledging the intramolecular structure of an n-hexane molecule, is in qualitative agreement with the revised scaled-particle model results, and is consistent in sizing the methyl/methylene sites which compose n-hexane in the simulation model. The classic and revised scaled-particle models disagree for length scales greater than the radius of a methyl group, however. The liquid-vapor surface tension of n-hexane predicted by the classic scaled-particle model is too large, though the temperature variation is reasonable; this contrasts with the classic scaled-particle theory for water which predicts a reasonable magnitude of the water liquid-vapor surface tension, but an incorrect sign for the temperature derivative at moderate temperatures. Judging on the basis of the arbitrary condition that drying is indicated when G(R)<1, hard spheres dry at smaller sizes in n-hexane than in liquid water.

Porous Liquids

The aim of this article is to put forward the novel concept of porous liquids, or, more precisely, liquids with permanent microporosity. In contrast to the small, transient cavities that exist between the molecules of any liquid (here called "extrinsic" porosity), we suggest that a truly microporous liquid could exist if it had empty pores within the molecules of the liquid ("intrinsic" porosity). By using rigid host molecules with restricted access windows, any unwanted occupation of the pores could be prevented (i.e., the pores could be kept empty and available so that the liquid would be genuinely microporous). The liquid could have permanent, well-defined, empty pores capable of molecular recognition when exposed to other species (e.g., gases etc.). We stress that these phases are not the same as simple solutions of host species, in which any pores would normally be occupied by solvent molecules. In microporous liquids, any solvent molecules, if present, would be deliberately sterically excluded from the host cavities, to leave them readily accessible. Microporous liquids would be of considerable fundamental interest. They could combine properties of microporous solids, such as size- and shape-selective sorption and so forth, with the rapid mass transfer, fluidity and fast kinetics of liquids. Some synthetic approaches to these materials are discussed in this article. Also, whilst the overall concept of microporous liquids is new, literature is described which suggests that some examples have arguably already been reported, even if they have not previously been recognised and characterised in such terms.

Entropy Convergence in the Hydration Thermodynamics of n-Alcohols

Using experimental data from the literature, entropy convergence in the hydration thermodynamics of n-alcohols is shown to occur at about 125 degrees C. The phenomenon is reproduced in a more-than-qualitative manner by means of a theoretical approach that accounts for the entropy contributions associated with (a) creation of a cavity in water, (b) turning on solute-water van der Waals interactions, and (c) turning on the solute-water H-bonding potential. The density of water and the effective size of water molecules with their temperature dependence play the pivotal role for the occurrence of entropy convergence, together with the property of the alcohol hydroxyl group to form the same number of H-bonds with water molecules regardless of the length of the alkyl chain.

Solvation Thermodynamics of Water in Nonpolar Organic Solvents Indicate the Occurrence of Nontraditional Hydrogen Bonds

Experimental data for the solvation of water in nonpolar organic solvents indicate that the process is spontaneous under the Ben-Naim standard conditions, due to a large and negative enthalpy change. The process is analyzed by considering that the solvation Gibbs energy change is given by the sum of two opposing terms: the work to create a suitable cavity and the work to turn on the attractive solute-solvent interactions. Basic calculations point out unequivocally that, beyond the van der Waals contributions, additional favorable interactions occur between water and the surrounding solvent molecules. These additional favorable interactions should be nontraditional hydrogen bonds such as those between the delocalized pi-electron cloud of the aromatic ring and the hydrogen atoms of water, and those between the CH groups of both aliphatics and aromatics and the oxygen atom of water.

Aliphatics vs. aromatics hydration thermodynamics

By comparing the hydration thermodynamics of benzene with that of a hypothetical aliphatic hydrocarbon having the same accessible surface area (ASA) of benzene, Makhatadze and Privalov concluded that the whole difference is due to the weak H-bonds that water forms with the aromatic ring. The formation of such H-bonds would be characterized by a negative Gibbs energy change, slightly increasing in magnitude with temperature, and a positive entropy change over a large temperature range. The latter thermodynamic feature is not physically reliable for the formation of H-bonds. In the present article, by using a statistical mechanical dissection scheme of hydration, a microscopic interpretation for the numbers obtained by Makhatadze and Privalov is proposed. The difference in hydration Gibbs energy should be attributed to the different strength of van der Waals interactions that benzene can do with water, owing to the larger polarizability of the aromatic ring with respect to an aliphatic hydrocarbon of equal size. In addition, the difference in hydration entropy should account for the different extent of H-bond reorganization upon the insertion of benzene and the corresponding aliphatic hydrocarbon in water.

Relationship between cohesive energy density and hydrophobicity

It has been recently claimed that the large cohesive energy density of water is the ultimate cause of the poor solubility of nonpolar compounds in water. In order to test the validity of this idea, we analyze the difference in solubility between light water and heavy water of several nonpolar compounds. Even though the cohesive energy density of D(2)O is larger than that of H(2)O, nonpolar compounds are slightly more soluble in D(2)O than H(2)O. In such case experimental data do not support the correctness of the large cohesive energy density as the ultimate cause of hydrophobicity. We show that D(2)O is a slightly better solvent than H(2)O for nonpolar compounds because it is slightly less costly to create a cavity in the former liquid. This is because there is slightly more void volume in heavy water than in light water.