arXiv subjects

L. R. Pratt

Publications and source records attributed to L. R. Pratt.

At least 19 recordsLinked to original sources

arXiv2021

Shapes of Non-symmetric Capillary Bridges

Here we study the shapes of droplets captured between chemically distinct parallel plates. This work is a preliminary step toward characterizing the influence of second-phase bridging between biomolecular surfaces on their solution contacts, i.e., capillary attraction or repulsion. We obtain a simple, variable-separated quadrature formula for the bridge shape. The technical complication of double-ended boundary conditions on the shapes of non-symmetric bridges is addressed by studying waists in the bridge shape, i.e., points where the bridge silhouette has zero derivative. Waists are always expected with symmetric bridges, but waist-points can serve to characterize shape segments in general cases. We study how waist possibilities depend on the physical input to these problems, noting that these formulae change with the sign of the inside-outside pressure difference of the bridge. These results permit a variety of different interesting shapes, and the development below is accompanied by several examples.

cond-mat.soft↗

arXiv2019

Hydration Mimicry by Membrane Ion Channels

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if those protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry view depends on understanding the hydration structure and free energies of metal ions in water to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water, and the molecular quasi-chemical theory that provides hydration free energies. In that process, we note some current views of ion-binding to membrane channels and suggest new physical-chemical calculations and experiments that might further clarify the hydration mimicry view.

physics.chem-ph↗

arXiv2019

Quasi-Chemical Theory for Anion Hydration and Specific Ion Effects: Cl$^-$(aq) \emph{vs.} F$^-$(aq)

Anion hydration is complicated by H-bond donation between neighboring water molecules in addition to H-bond donation to the anion. This situation can lead to competing structures for chemically simple clusters like (H$_2$O)$_n$Cl$^-$ and to anharmonic vibrational motions. Quasi-chemical theory builds from electronic structure treatment of isolated ion-water clusters, partitions the hydration free energy into inner-shell and outer-shell contributions, and provides a general statistical mechanical framework to study complications of anion hydration. The present study exploits dynamics calculations on isolated (H$_2$O)$_n$Cl$^-$ clusters to account for anharmonicity, utilizing ADMP (atom-centered basis sets and density-matrix propagation) tools. Comparing singly hydrated F$^-$ and Cl$^-$ clusters, classic OH-bond donation to the anion occurs for F$^-$, while Cl$^-$ clusters exhibit more flexible but dipole-dominated interactions between ligand and ion. The predicted Cl$^-$ -- F$^-$ hydration free energy difference agrees well with experiment, a significant theoretical step for addressing issues like Hofmeister ranking and selectivity in ion channels.

physics.chem-ph↗

arXiv2018

Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F$^-$) Anion Hydration

Accurate predictions of the hydration free energy for anions typically have been more challenging than for cations. Hydrogen bond donation to the anion in hydrated clusters such as $\mathrm{F(H_2O)}_n{}^-$ can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that, even though anharmonic effects are interesting, they need not be troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed and application of implicit solvation models to these structures can incur more serious errors than for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

physics.chem-ph↗

arXiv2018

Comparison of Single-Ion Molecular Dynamics in Common Solvents

Laying a basis for molecularly specific theory for the mobilities of ions in solutions of practical interest, we report a broad survey of velocity autocorrelation functions (VACFs) of Li$^+$ and PF$_6{}^-$ ions in water, ethylene carbonate, propylene carbonate, and acetonitrile solutions. We extract the memory function, $γ(t)$, which characterizes the random forces governing the mobilities of ions. We provide comparisons, controlling for electrolyte concentration and ion-pairing, for van~der~Waals attractive interactions and solvent molecular characteristics. For the heavier ion (PF$_6{}^-$), velocity relaxations are all similar: negative tail relaxations for the VACF and a clear second relaxation for $γ\left(t\right)$, observed previously also for other molecular ions and with \emph{n}-pentanol as solvent. For the light Li$^+$ ion, short time-scale oscillatory behavior masks simple, longer time-scale relaxation of $γ\left(t\right)$. But the corresponding analysis of the \emph{solventberg} Li$^+\left(\mathrm{H}_2\mathrm{O}\right)_4$ does conform to the standard picture set by all the PF$_6{}^-$ results.

cond-mat.soft↗

arXiv2016

Statistical analyses of hydrophobic interactions: A mini-review

This review focuses on the striking recent progress in solving for hydrophobic interactions between small inert molecules. We discuss several new understandings. Firstly, the _inverse _temperature phenomenology of hydrophobic interactions, _i.e., strengthening of hydrophobic bonds with increasing temperature, is decisively exhibited by hydrophobic interactions between atomic-scale hard sphere solutes in water. Secondly, inclusion of attractive interactions associated with atomic-size hydrophobic reference cases leads to substantial, non-trivial corrections to reference results for purely repulsive solutes. Hydrophobic bonds are _weakened by adding solute dispersion forces to treatment of reference cases. The classic statistical mechanical theory for those corrections is not accurate in this application, but molecular quasi-chemical theory shows promise. Finally, because of the masking roles of excluded volume and attractive interactions, comparisons that do not discriminate the different possibilities face an interpretive danger.

physics.chem-ph↗

arXiv2016

Molecular-scale Description of SPAN80 Desorption from the Squalane-Water Interface

Extensive all-atom molecular dynamics calculations on the water-squalane interface for nine different loadings with sorbitan monooleate (SPAN80), at $T=300$K, are analyzed for the surface tension equation of state, desorption free energy profiles as they depend on loading, and to evaluate escape times for absorbed SPAN80 into the bulk phases. These results suggest that loading only weakly affects accommodation of a SPAN80 molecule by this squalane-water interface. Specifically, the surface tension equation of state is simple through the range of high tension to high loading studied, and the desorption free energy profiles are weakly dependent on loading here. The perpendicular motion of the centroid of the SPAN80 head-group ring is well-described by a diffusional model near the minimum of the desorption free energy profile. Lateral diffusional motion is weakly dependent on loading. Escape times evaluated on the basis of a diffusional model and the desorption free energies are $7\times 10^{-2}$ s (into the squalane) and $3\times 10^2$ h (into the water). The latter value is consistent with irreversible absorption observed by related experimental work.

physics.chem-ph↗

arXiv2015

Molecular theory and the effects of solute attractive forces on hydrophobic interactions

The role of solute attractive forces on hydrophobic interactions is studied by coordinated development of theory and simulation results for Ar atoms in water. We present a concise derivation of the local molecular field (LMF) theory for the effects of solute attractive forces on hydrophobic interactions, a derivation that clarifies the close relation of LMF theory to the EXP approximation applied to this problem long ago. The simulation results show that change from purely repulsive atomic solute interactions to include realistic attractive interactions \emph{diminishes} the strength of hydrophobic bonds. For the Ar-Ar rdfs considered pointwise, the numerical results for the effects of solute attractive forces on hydrophobic interactions are of opposite sign and larger in magnitude than predicted by LMF theory. That comparison is discussed from the point of view of quasi-chemical theory, and it is suggested that the first reason for this difference is the incomplete evaluation within LMF theory of the hydration energy of the Ar pair. With a recent suggestion for the system-size extrapolation of the required correlation function integrals, the Ar-Ar rdfs permit evaluation of osmotic second virial coefficients $B_2$. Those $B_2$ also show that incorporation of attractive interactions leads to more positive (repulsive) values. With attractive interactions in play, $B_2$ can change from positive to negative values with increasing temperatures. This is consistent with the historical work of Watanabe, \emph{et al.,} that $B_2 \approx 0$ for intermediate cases. In all cases here, $B_2$ becomes more attractive with increasing temperature.

physics.chem-ph↗

arXiv2014

Hydration of Kr(aq) in dilute and concentrated solutions

Molecular dynamics simulations of water with both multi-Kr and single Kr atomic solutes are carried out to implement quasi-chemical theory evaluation of the hydration free energy of Kr(aq). This approach obtains free energy differences reflecting Kr-Kr interactions at higher concentrations. Those differences are negative changes in hydration free energies with increasing concentrations at constant pressure. The changes are due to a slight reduction of packing contributions in the higher concentration case. The observed Kr-Kr distributions, analyzed with the extrapolation procedure of Krüger, \emph{et al.}, yield a modestly attractive osmotic second virial coefficient, $B_2\approx -60~\mathrm{cm}^3$/mol. The thermodynamic analysis interconnecting these two approaches shows that they are closely consistent with each other, providing support for both.

physics.chem-ph↗

arXiv2014

The role of attractive interactions in the dynamics of molecules in liquids

The friction kernel (or memory function) $γ(t)$ characterizing single-molecule dynamics in strongly bound liquids exhibits two distinct relaxations with the longer time-scale relaxation associated with attractive intermolecular forces. This observation identifies differing roles of repulsive and attractive interaction in the motions of molecules in equilibrium liquids, and thus provides a basis for a renewed investigation of a van der Waals picture of the transport properties of liquids. This conclusion is supported by extracting $γ(t)$ from molecular dynamics simulation data for four common molecular liquids.

physics.chem-ph↗

arXiv2014

Concentration dependence of the Flory-Huggins interaction parameter in aqueous solutions of capped PEO chains

The dependence on volume fraction $φ$ of the Flory-Huggins $χ_{\mathrm{wp}}\left(φ\right)$ describing the free energy of mixing of polymers in water is obtained by exploiting the connection of $χ_{\mathrm{wp}}\left(φ\right)$ to the chemical potential of the water, for which quasi-chemical theory is satisfactory. We test this theoretical approach with simulation data for aqueous solutions of capped PEO oligomers. For CH$_3$(CH$_2$-O-CH$_2$)$_m$CH$_3$ ($m$=11), $χ_{\mathrm{wp}}\left(φ\right)$ depends strongly on $φ$, consistent with experiment. These results identify coexisting water-rich and water-poor solutions at $T$ = 300K and $p$ = 1atm. Direct observation of the coexistence of these two solutions on simulation time scales supports that prediction for the system studied. This approach directly provides the osmotic pressures. The osmotic second virial coefficient for these chains is positive, reflecting repulsive interactions between the chains in the water, a good solvent for these chains.

cond-mat.soft↗

arXiv2014

Loop-Closure and Gaussian Models of Collective Structural Characteristics of Capped PEO Oligomers in Water

Parallel-tempering MD results for a CH$_3$(CH$_2$-O-CH$_2$)$_m$CH$_3$ chain in water are exploited as a data-base for analysis of collective structural characteristics of the PEO globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of Corexit type. The chain structure factor, relevant to neutron scattering from a deuterated chain in neutral water, is considered specifically. The traditional continuum-Gaussian structure factor is inconsistent with the simple $k \rightarrow \infty$ behavior, but we consider a discrete-Gaussian model that does achieve that consistency. Shifting-and-scaling the discrete-Gaussian model helps to identify the low-$k$ to high-$k$ transition near $k \approx 2π/0.6 \mathrm{nm}$ when an empirically matched number of Gaussian links is about one-third of the total number of effective-atom sites. This short distance-scale boundary of 0.6 nm is directly verified with the $r$-space distributions, and this distance is thus identified with a natural size for coarsened monomers. The probability distribution of $R_g{}^2$ is compared with the classic predictions for both Gaussian model and freely-jointed chains. $\left\langle R_g{}^2(j)\right\rangle$, the contribution of the $j$-th chain segment to $\left\langle R_g{}^2\right\rangle$, depends on contour index about as expected for Gaussian chains despite significant quantitative discrepancies which express the swelling of these chains in water. Monomers central to the chain contour occupy the center of the chain globule. The density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due close proximity of central elements to the globule center. But that density structuring washes-out for longer chains where many chain elements additively contribute to the density profiles.

physics.chem-ph↗

arXiv2013

Multi-scale theory in the molecular simulation of electrolyte solutions

This paper organizes McMillan-Mayer theory, the potential distribution approach, and quasi-chemical theory to provide theory for the thermodynamic effects associated with longer spatial scales involving longer time scales, thus helping to define a role for AIMD simulation directly on the time and space scales typical of those demanding methods. The theory treats composition fluctuations which would be accessed by larger-scale calculations, and also longer-ranged interactions that are of special interest for electrolyte solutions. The quasi-chemical organization breaks-up governing free energies into physically distinct contributions: packing, outer-shell, and chemical contributions. Here we study specifically the outer-shell contributions that express electrolyte screening. For that purpose we adopt a primitive model suggested by observation of ion-pairing in tetra-ethylammonium tetra-fluoroborate dissolved in propylene carbonate. Gaussian statistical models are shown to be effective physical models for outer-shell contributions, and they are conclusive for the free energies within the quasi-chemical formulation. With the present data-set the gaussian physical approximation obtains more accurate mean activity coefficients than does the Bennett direct evaluation of that free energy.

physics.chem-ph↗

arXiv2013

Direct Numerical Test of the Statistical Mechanical Theory of Hydrophobic Interactions

This work tests the statistical mechanical theory of hydrophobic interactions, isolates consequences of excluded volume interactions, and obtains B2 for those purposes. Cavity methods that are particularly appropriate for study of hydrophobic interactions between atomic-size hard spheres in liquid water are developed and applied to test aspects of the Pratt-Chandler (PC) theory that have not been tested. Contact hydrophobic interactions between Ar-size hard-spheres in water are significantly more attractive than predicted by the PC theory. The corresponding results for the osmotic second virial coefficient are attractive (B2 <0), and more attractive with increasing temperature (Delta B2/Delta T < 0) in the temperature range 300K < T < 360K. This information has not been available previously, but is essential for development of the molecular-scale statistical mechanical theory of hydrophobic interactions, particularly for better definition of the role of attractive intermolecular interactions associated with the solutes.

physics.bio-ph↗

arXiv2013

Case study of Rb+(aq), quasi-chemical theory of ion hydration, and the no split occupancies rule

Quasi-chemical theory applied to ion hydration combines statistical mechanical theory, electronic structure calculations, and molecular simulation, disciplines which are individually subjects for specialized professional attention. Because it combines activities which are themselves non-trivial, quasi-chemical theory is typically viewed with surprise. Nevertheless, it provides a fully-considered framework for analysis of ion hydration. Furthermore, the initial calculations are indeed simple, successful, and provide new information to long-standing experimental activities such as neutron diffraction by hydrated ions. Here we review quasi-chemical theory in the context of a challenging application, Rb+(aq).

physics.chem-ph↗

arXiv2012

Pairing of 1-hexyl-3-methylimidazolium and tetrafluoroborate ions in n-pentanol

Molecular dynamics simulations are obtained and analyzed to study pairing of 1-hexyl-3-methylimidazolium and tetrafluoroborate ions in n-pentanol, in particular by evaluating the potential-of-mean-force between counter ions. The present molecular model and simulation accurately predicts the dissociation constant Kd in comparison to experiment, and thus the behavior and magnitudes for the ion-pair pmf at molecular distances, even though the dielectric constant of the simulated solvent differs from the experimental value by about 30%. A naive dielectric model does not capture molecule structural effects such as multiple conformations and binding geometries of the Hmim+ and BF4- ion-pairs. Mobilities identify multiple time-scale effects in the autocorrelation of the random forces on the ions, and specifically a slow, exponential time-decay of those long-ranged forces associated here with dielectric friction effects.

physics.chem-ph↗

arXiv2011

Generalizations of the Fuoss Approximation for Ion Pairing

An elementary statistical observation identifies generalizations of the Fuoss approximation for the probability distribution function that describes ion clustering in electrolyte solutions. The simplest generalization, equivalent to a Poisson distribution model for inner-shell occupancy, exploits measurable inter-ionic correlation functions, and is correct at the closest pair distances whether primitive electrolyte solutions models or molecularly detailed models are considered, and for low electrolyte concentrations in all cases. With detailed models these generalizations includes non-ionic interactions and solvation effects. These generalizations are relevant for computational analysis of bi-molecular reactive processes in solution. Comparisons with direct numerical simulation results show that the simplest generalization is accurate for a slightly supersaturated solution of tetraethylammonium tetrafluoroborate in propylene carbonate ([tea][BF$_4$]/PC), and also for a primitive model associated with the [tea][BF$_4$]/PC results. For [tea][BF$_4$]/PC, the atomically detailed results identify solvent-separated nearest-neighbor ion-pairs. This generalization is examined also for the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF$_4$]) where the simplest implementation is less accurate. In this more challenging situation an augmented maximum entropy procedure is satisfactory, and explains the more varied near-neighbor distributions observed in that case.

physics.chem-ph↗

arXiv2007

Balancing Local Order and Long-Ranged Interactions in the Molecular Theory of Liquid Water

A molecular theory of liquid water is identified and studied on the basis of computer simulation of the TIP3P model of liquid water. This theory would be exact for models of liquid water in which the intermolecular interactions vanish outside a finite spatial range, and therefore provides a precise analysis tool for investigating the effects of longer-ranged intermolecular interactions. We show how local order can be introduced through quasi-chemical theory. Long-ranged interactions are characterized generally by a conditional distribution of binding energies, and this formulation is interpreted as a regularization of the primitive statistical thermodynamic problem. These binding-energy distributions for liquid water are observed to be unimodal. The gaussian approximation proposed is remarkably successful in predicting the Gibbs free energy and the molar entropy of liquid water, as judged by comparison with numerically exact results. The remaining discrepancies are subtle quantitative problems that do have significant consequences for the thermodynamic properties that distinguish water from many other liquids. The basic subtlety of liquid water is found then in the competition of several effects which must be quantitatively balanced for realistic results.

physics.chem-ph↗