Calculation of hydrophobic interactions from molecular dynamics,surface areas,and experimental hydrocarbon solubilities

Using experimental solubilities and partial pressures for hydrocarbon solution in water and molecular dynamics calculations of hydrocarbon water interaction energies, hydrocarbon–water cavity potentials are obtained and then plotted vs. accessible surface area. The data used is mainly for aliphatic hydrocarbons, but benzene is included. Molecular dynamics calculations of pairs of hydrocarbon molecules together with the cavity potential curve are then used to obtain hydrophobic interaction free energies between the hydrocarbon pairs. While the cavity potential change is related to a change in surface area for hydrocarbon systems, the hydrocarbon–water interaction energy is not, so that the hydrophobic binding energy is not. The results are in agreement with previous results by a different method (R.B. Hermann, In Seventh Jerusalem Symposium on Quantum Pharmacology, E. Bergman and B. Pullman, Eds., D. Reidel, Dordrecht, 1974, p. 441) in that there is little or no solvent-induced binding free energy between small hydrocarbon molecules in a dilute aqueous solution. It is proposed that the cavity potential vs. accessible surface area curve obtained here can be used together with OPLS parameters to calculate both hydrocarbon–water solvation free energies and hydrophobic interactions. © 1993 John Wiley & Sons, Inc.     

Solubilization of hydrocarbons and resulting aggregate shape transitions in aqueous solutions of Pluronic (PEO–PPO–PEO) block copolymers

Pluronic^® block copolymers are commercially available symmetric triblock copolymers with poly(ethylene oxide), PEO, as the hydrophilic end blocks and poly(propylene oxide), PPO, as the hydrophobic middle block. In this paper, the solubilization of hydrocarbons by aggregates of Pluronic^® block copolymers in water is examined in the framework of a simple molecular theory of solubilization. The aggregates have an inner core region made up of PPO and the solubilizate and an outer corona region made up of PEO and water. Expressions for the standard state free energy change associated with solubilization of hydrocarbons by aggregates having spherical, cylindrical, and lamellar shapes are presented. These free energy contributions account for the mixing of the core block with the solubilizate, the consequent changes in the state of deformation of the core block, the changes in the state of dilution and deformation of the corona block, the formation of the core-solvent interface, and the backfolding of the triblock copolymer which ensures that the two end blocks are in contact with the solvent. Utilizing these free energy expressions, we predict the core size, the corona thickness, and the aggregation number of the micelle and also the volume fraction of the hydrocarbon solubilized in the core, for seven aromatic and aliphatic hydrocarbon solubilizates incorporated within numerous Pluronic^® compounds. The calculated results show that a growth in aggregate size occurs both because of the incorporation of the hydrocarbon and also the increase in the intrinsic number of block copolymer molecules per aggregate. More interestingly, solubilization is shown to induce a transition in aggregate shapes from spheres to cylinders and then to lamellae. The shape transition is found to be critically controlled by the free energy of mixing of the solubilizate with the core forming PPO block.     

The hydrophobic effect

This review is a brief discussion on the development of the understanding of hydrophobicity, or the hydrophobic effect. The hydrophobic effect is primarily discussed in terms of partitioning of hydrocarbons between a hydrophobic environment and water as well as solubility of hydrocarbons in water. Micellization of surfactants is only briefly reviewed.It is emphasized that (i) the cause of the hydrophobic effect, e.g. the low solubility of a hydrocarbon in water, is to be found in the high internal energy of water resulting in a high energy to create a cavity in order to accommodate the hydrophobe, (ii) the “structuring” of water molecules around a hydrophobic compound increases the solubility of the hydrophobe. The “structuring” of water molecules around hydrophobic compounds is discussed in terms of recent spectroscopic findings. It is also emphasized that (iii) the lowering of entropy due to a structuring process must be accompanied by an enthalpy that is of the same order of magnitude as the TΔS for the process. Hence, there is an entropy–enthalpy compensation leading to a low free energy change for the structuring process. The assumption of a rapid decay of the entropy with temperature provides an explanation of the enthalpy–entropy compensation so often found in aqueous systems. It is also emphasized (iv) that the free energy obtained from partitioning, or solubility limits, needs to be corrected for molecular size differences between the solute and the solvent. The Flory–Huggins expression is a good first approximation for obtaining this correction. If the effect of different molecular sizes is not corrected for, this leads to erroneous conclusions regarding the thermodynamics of the hydrophobic effect. Finally, (v) micellization and adsorption of surfactants, as well as protein unfolding, are briefly discussed in terms of the hydrophobic effect.     

Cavitation free energy for organic molecules having various sizes and shapes

Cavitation free energy DeltaG(cav), corresponding to the formation of an excluded volume cavity in water, is calculated for a large set of organic molecules employing the thermodynamic integration procedure, which is realized as the original two-step algorithm for growing the interaction potential between the hard cavity wall and the water molecules. A large variety of solute systems is considered. Their characteristic radii change in the range 3-7 A; spherical cavities with radii 3-6 A are also studied. The interaction between water molecules is described by the four-site nonpolarizable TIP4P model. The diversity of the trial molecular set is provided by using a specially formulated nonspherical criterion classifying the cavity shapes according to their deviation from a sphere. Molecular objects were partly taken from the data base NCI Diversity with the aid of this criterion. The so-computed free energies are approximated by the linear volume dependence DeltaG(cav)V = XiV, where V is the cavity volume. This relation works fairly well until the cavity size becomes very large (the effective radius larger than 7 A). The volume dependence valid for solutes of arbitrary shapes can be included in a calculation of the nonpolar free energy component as required in the implicit water model.     

Interaction between water molecules and zinc sulfide nanoparticles studied by temperature-programmed desorption and molecular dynamics simulations

We have investigated the bonding of water molecules to the surfaces of ZnS nanoparticles (approximately 2-3 nm sphalerite) using temperature-programmed desorption (TPD). The activation energy for water desorption was derived as a function of the surface coverage through kinetic modeling of the experimental TPD curves. The binding energy of water equals the activation energy of desorption if it is assumed that the activation energy for adsorption is nearly zero. Molecular dynamics (MD) simulations of water adsorption on 3 and 5 nm sphalerite nanoparticles provided insights into the adsorption process and water binding at the atomic level. Water binds with the ZnS nanoparticle surface mainly via formation of Zn-O bonds. As compared with bulk ZnS crystals, ZnS nanoparticles can adsorb more water molecules per unit surface area due to the greatly increased curvature, which increases the distance between adjacent adsorbed molecules. Results from both TPD and MD show that the water binding energy increases with decreasing the water surface coverage. We attribute the increase in binding energy with decreasing surface water coverage to the increasing degree of surface under-coordination as removal of water molecules proceeds. MD also suggests that the water binding energy increases with decreasing particle size due to the further distance and hence lower interaction between adsorbed water molecules on highly curved smaller particle surfaces. Results also show that the binding energy, and thus the strength of interaction of water, is highest in isolated nanoparticles, lower in nanoparticle aggregates, and lowest in bulk crystals. Given that water binding is driven by surface energy reduction, we attribute the decreased binding energy for aggregated as compared to isolated particles to the decrease in surface energy that occurs as the result of inter-particle interactions.     

THERMODYNAMIC PROPERTIES OF THE DISSOLUTION OF FATTY ACID SALTS IN WATER*

The enthalpy, entropy and heat capacity change of the dissolution of calcium and barium laurates, myristates and palmitates were determined by reaction calorimetry and by solubility at different temperatures. Heat capacity change, due to water restructuring or "iceberg" formation, was found to increase with the chain length. Linearity was observed up to 12 C-atoms in the chain, while the dissolution of chains with 16 C-atoms was accompanied by a significantly higher increase in the heat capacity than it would be expected. This phenomenon was explained on the basis of synergistic effect, i.e. by mutual promotion in the water restructuring.     

Enthalpies of aqueous solution of noble gases at 25°C

The standard enthalpies of solution of rare gases (helium, neon, argon, krypton, and xenon) in water at 25°C have been measured by a high precision steady-state calorimetric method. The aqueous solvation process is energetically favorable at 25°C for the gases studied. Values of the standard free energy, enthalpy, and entropy changes are found to be well correlated with cavity surface areas and the number of water molecules in the first solvation shell. Also, the values of the standard enthalpy and entropy of solution for the rare gases are found to have the same dependence on the number of solvation shell water molecules as inorganic and hydrocarbon gases. These results imply that the dominant source of enthalpy and entropy change resides in the first solvation shell.     

Enthalpy-entropy contributions to the potential of mean force of nanoscopic hydrophobic solutes

Entropic and enthalpic contributions to the hydrophobic interaction between nanoscopic hydrophobic solutes, modeled as graphene plates in water, have been calculated using molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble with free energy perturbation methodology. We find the stabilizing contribution to the free energy of association (contact pair formation) to be the favorable entropic part, the enthalpic contribution being highly unfavorable. The desolvation barrier is dominated by the unfavorable enthalpic contribution, despite a fairly large favorable entropic compensation. The enthalpic contributions, incorporating the Lennard-Jones solute-solvent terms, largely determine the stability of the solvent separated configuration. We decompose the enthalpy into a direct solute-solute term, the solute-solvent interactions, and the remainder that contains pressure-volume work as well as contributions due to solvent reorganization. The enthalpic contribution due to changes in water-water interactions arising from solvent reorganization around the solute molecules is shown to have major contribution in the solvent induced enthalpy change.     

Permeability of rat and rabbit erythrocyte membranes for a series of amides

Permeability coefficients of rat and rabbit erythrocyte membranes for a series of amides, as well as for erythrocytes treated with p-chloromercuribenzenesulfonic acid monosodium salt (pCMBS) have been determined at 25 and 37 degrees C. Directly proportional dependence of the pCMBS treated erythrocyte permeability for investigated substances and their partition coefficients between the hydrophobic phase and water as well as the values of activation energy of this process indicate that penetration of small hydrophilic molecules is realized by passive diffusion through the lipid bilayer. The results obtained indicate that penetration of small hydrophilic molecules of formamide through lipids is determined by the existence of a free space between hydrocarbon chains that arises from kink formation. The differences in permeability between rat and rabbit erythrocyte membranes could arise in particular as a result of the differences in lipid composition.     

Electrostatic free energy of weakly charged macromolecules in solution and intermacromolecular complexes consisting of oppositely charged polymers

When oppositely charged polyelectrolytes are mixed in water, attraction between oppositely charged groups may lead to the formation of polyelectrolyte complexes (associative phase separation, complex coacervation, interpolymer complexes). Theory is presented to describe the electrostatic free energy change when ionizable (annealed) (macro-)molecules form a macroscopic polyelectrolyte complex. The electrostatic free energy includes an electric term as well as a chemical term that is related to the dissociation of the ionic groups in the polymer. An example calculation for complexation of polyacid with polybase uses a cylindrical diffuse double layer model for free polymer in solution and electroneutrality within the complex and calculates the free energy of the system when the polymer is in solution or in a polyelectrolyte complex. Combined with a term for the nonelectrostatic free energy change upon complexation, a theoretical stability diagram is constructed that relates pH, salt concentration, and mixing ratio, which is in qualitative agreement with an experimental diagram obtained by Bungenberg de Jong (1949) for complex coacervation of arabic gum and gelatin. The theory furthermore explains the increased tendency toward phase separation when the polymer becomes more strongly charged and suggests that complexation of polyacid or polybase with zwitterionic polymer (e.g., protein) of the same charge sign (at the "wrong side" of the iso-electric point) may be due (in part) to an induced charge reversal of the protein.     

Characteristic property in aqueous solutions: effect of iceberg formation of water surrounding solute on the solubility(or cmc) and its peculiar temperature dependence.

The solubilities and the peculiar temperature dependence of hydrophobic substances in water were coherently explained in 1977 taking into account 1) the strong solidification tendency of water, 2) the large enthalpy of solution evident from the low solubilities, 3) the large entropy of dilution due to the small solubility, and 4) the large negative enthalpy and entropy of iceberg formation. As far as the author knows, there is no paper contradicting this interpretation. The present paper reviews the thermodynamic reasoning and experimental evidences confirming the interpretation. The phenomena are now much better understood due to new experimental evidences.     

Measuring the extent and width of internal energy deposition in ion activation using nanocalorimetry

The recombination energies resulting from electron capture by a positive ion can be accurately measured using hydrated ion nanocalorimetry in which the internal energy deposition is obtained from the number of water molecules lost from the reduced cluster. The width of the product ion distribution in these experiments is predominantly attributable to the distribution of energy that partitions into the translational and rotational modes of the water molecules that are lost. These results are consistent with a singular value for the recombination energy. For large clusters, the width of the energy distribution is consistent with rapid energy partitioning into internal vibrational modes. For some smaller clusters with high recombination energies, the measured product ion distribution is narrower than that calculated with a statistical model. These results indicate that initial water molecule loss occurs on the time scale of, or faster than energy randomization. This could be due to inherently slow internal conversion or it could be due to a multi-step process, such as initial ion-electron pair formation followed by reduction of the ion in the cluster. These results provide additional evidence for the accuracy with which condensed phase thermochemical values can be deduced from gaseous nanocalorimetry experiments.     

Unexpected effect of charge density of the aromatic guests on the stability of calix[6]arene-phenol host-guest complexes

The pi-pi interaction-based inclusion complexation of calix[6]arene hexasulfonate as host with neutral aromatic guest molecules was studied in aqueous media. To vary the electron density on the guest's aromatic rings, the phenol parent compound was functionalized in the para-position with different electron-withdrawing groups, such as NO2 and Cl, as well as H and CH3 groups. To study the interaction between calixarene and the guests, PL, DSC, and quantum-chemical methods were used. The results indicate 1:1 stoichiometry for all examined host-guest complexes. Although the enthalpy change predicts strong interaction between the host and the guest, the Gibbs free energy change of the complex formation is small, resulting in a relatively low complex stability. This property is due to the high and negative entropy change during the complex formation. Comparing the thermodynamic parameters observed on the series of the guests, we observed a decrease of the enthalpy change when the electron density on the guest's aromatic ring increased. However, the Gibbs free energy and therefore, the stability of the complexes increased when the enthalpy change lowered. These unexpected results are based on the enthalpy-entropy compensation effect and probably due to the quite different entropy change related to the high and low electron density on the aromatic rings of different guest molecules. Using molecular dynamic calculations, a redistribution of the electron density of calixarene rings, followed by the reordering of the solvent molecules, was identified as a background of this unexpected entropy change at molecular level.     

Energetics of low-molecular-mass products of mechanical fracture of poly(methyl methacrylate)

It is experimentally revealed that monomer and water molecules released during the fracture of PMMA have a bimodal velocity distribution. The first distribution peak for the monomer corresponds to energetic (hot) MMA molecules (0.13–0.70 eV), and the second peak is attributed to MMA molecules bearing a low energy (0.016–0.060 eV). On the basis of the results of earlier theoretical studies of the mechanically induced polymer-chain scission, it was concluded that the energetic monomer molecules are produced immediately in the event of mechanical chain rupture and are nonthermal in nature. In the bimodal velocity distribution of occluded water molecules desorbed from a subsonic crack, the first and the second peaks are attributed to “hot” and “cold” molecules with translational temperatures of 605 ± 180 K and 53 ± 5 K, respectively. A possible mechanism of the mechanically induced desorption of occluded water is discussed. The mechanodesorption of water molecules is due to the portion of vibrational energy transferred to side methyl carboxylate groups that retain water molecules by the unloading-wave front traveling along the main chain from a macromolecule scission site. Along with hot water molecules, a considerable amount of hot free hydroxyls were detected. The mechanism of formation of the latter species is associated with the double-well structure of the hydrogen bond potential and similar to the mechanism of mechanodesorption of hot molecules of water.     

Selective guest encapsulation by a cobalt-assembled cage molecule

Metal-assembled resorcinarene-based cages enclose space and entrap organic molecules from water. Addition of cobalt(II) ions to a neutral, aqueous solution of a resorcinarene that has iminodiacetic acids attached to its upper rim results in the formation of cages. These cages not only entrap organic molecules, but they do so in a selective manner. Guests with optimum size, shape, and polarity are preferentially entrapped. For example, selection of p-xylene is twenty thousand times more favorable than that of m-xylene. The enthalpy of resorcinarene deprotonation and cage formation was calculated by performing calorimetry studies and ranged from -305 to -348 kJ mol(-1). The change in enthalpy of guest encapsulation varied by as much as 43 kJ mol(-1). The differences in change in free energy of guest encapsulation varied by -16 kJ mol(-1). The changes in enthalpy and free energy of guest encapsulation were used to calculate the changes in entropy, which ranged from -97 to +37 J mol(-1) K(-1). An enthalpy-entropy compensation of guest encapsulation was observed.     

Isodesmic self-assembly in lyotropic chromonic systems

We have developed simple models of chromonic molecules and by carrying out Monte Carlo simulation in a binary mixture of model chromonic and water molecules, have studied the effect of concentration and molecular shape on the pattern of molecular aggregation. We have also computed the free energy change associated with the formation of chromonic columnar aggregates by umbrella sampling. This helps us to verify the isodesmic behaviour which is characteristic of chromonic systems.     

Isodesmic self-assembly in lyotropic chromonic systems

We have developed simple models of chromonic molecules and by carrying out Monte Carlo simulation in a binary mixture of model chromonic and water molecules, have studied the effect of concentration and molecular shape on the pattern of molecular aggregation. We have also computed the free energy change associated with the formation of chromonic columnar aggregates by umbrella sampling. This helps us to verify the isodesmic behaviour which is characteristic of chromonic systems.     

Formation of dimers in lipid monolayers

In this work, we analyse theoretically the hypothesis that zwitterionic lipids form dimers in adsorption monolayers on water/ hydrocarbon phase boundary. A dimer can be modelled as a couple of lipid molecules whose headgroup lateral dipole moments have antiparallel orientation. Properties including surface pressure, chemical potentials and activity coefficients are deduced from a general expression for the free energy of the monolayer. The theoretical model is in a good agreement with experimental data for surface pressure and surface potential of lipid monolayers. The results favour the hypothesis about formation of dimers in equilibrium with monomers, with the amount of the species depending on the area per molecule and temperature. The reaction of dimerisation turns out to be exothermic with a heat of about 2.5kT per dimer. The results may be applied to the molecular models of membrane structures and mechanisms.     

Novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: free energy calculation for the Beckmann rearrangement promoted by proton transfers in the supercritical water

The Beckmann rearrangement of acetone oxime promoted by proton transfers in the supercritical water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER) recently developed. The transition state (TS) structures have been explored by ab initio calculations for the reaction of hydrated acetone oxime on the assumption that the reaction is catalyzed by proton transfers along the hydrogen bonds connecting the solute and the solvent water molecules. Up to two water molecules have been considered as reactants that take part in the proton transfers. As a result of the density functional theory calculations with B3LYP functional and aug-cc-pVDZ basis set, it has been found that participation of two water molecules in the reaction reduces the activation free energy by -12.3 kcal/mol. Furthermore, the QM/MM-ER simulations have revealed that the TS is more stabilized than the reactant state in the supercritical water by 2.7 kcal/mol when two water molecules are involved in the reaction. Solvation free energies of the reactant and the TS have been decomposed into terms due to the electronic polarization of the solute, electron density fluctuation, and others to elucidate the origin of the stabilization of the TS as compared with the reactant. It has been revealed that the promotion of the chemical reaction due to the hydration mainly originates from the interaction between the nonpolarized solute and the solvent water molecules at the supercritical state.     

Interfacial behavior of ACORGA CLX-50 and surface kinetics of copper extraction

Interfacial tension isotherms were determined and interpreted for ACORGA CLX-50. The hydration of extractant molecules in aqueous solution and at hydrocarbon/water interfaces was studied by molecular modelling. The usefulness of this technique to interpret the adsorption behavior was demonstrated. The interfacial kinetics was considered and relationships for various models of interfacial mechanism were derived and discussed. Despite its high hydrophobicity, ACORGA CLX 50 strongly adsorbs at the hydrocarbon/water interfaces and thus decreases effectively the interfacial tension. This high interfacial activity of ACORGA CLX 50 can be explained by the formation of hydrates. The interfacial tension isotherm can be well matched with the Szyszkowski equation. Molecular modelling suggests that ACORGA CLX 50 adsorbs at the hydrocarbon/water interface probably as a tetrahydrate containing two water molecules bonded to the same carbonyl oxygen atom (e.g., at position 3), one water molecule bonded to the oxygen atom of the second alkoxyl group (i.e., at position 5 when the hydration of carbonyl oxygen at position 3 is previously considered) and, finally, one water molecule bonded with the pyridine nitrogen atom. Positions 3 and 5 are equivalent. It is also shown that when the extraction of copper takes place in the kinetic regime, the reaction order with respect to ACORGA CLX 50 can change depending on the limiting step and the range of extractant concentration considered. Thus, a decrease of the extractant concentration from 10^?5M to 3·10^?3M causes a fall of the order with respect to ACORGA CLX 50 from 1 to 0 and 2 to 1 when the formation of the intermediate 1∶1 and final 2∶1 complexes are considered to be the limiting step, respectively.