Hydrophobic Hydration in an Orientational Lattice Model

Thermally reversible pattern formation in arrays of molecular rotors

Control over the mesoscale to microscale patterning of materials is of great interest to the soft matter community. Inspired by DNA origami rotors, we introduce a 2D nearest-neighbor lattice of spinning rotors that exhibit discrete orientational states and interactions with their neighbors. Monte Carlo simulations of rotor lattices reveal that they exhibit a variety of interesting ordering behaviors and morphologies that can be modulated through rotor design parameters. The rotor arrays exhibit diverse patterns including closed loops, radiating loops, and bricklayer structures in their ordered states. They exhibit specific heat peaks at very low temperatures for small system sizes, and some systems exhibit multiple order-disorder transitions depending on inter-rotor interaction design. We devise an energy-based order parameter and show via umbrella sampling and histogram reweighting that this order parameter captures well the order-disorder transitions occurring in these systems. We fabricate real DNA origami rotors which themselves can order via programmable DNA base-pairing interactions and demonstrate both ordered and disordered phases, illustrating how rotor lattices may be realized experimentally and used for responsive organization. This work establishes the feasibility of realizing structural nanomaterials that exhibit locally mediated microscale patterns which could have applications in sensing and precision surface patterning.

Solvation theory to provide a molecular interpretation of the hydrophobic entropy loss of noble-gas hydration

An equation for the chemical potential of a dilute aqueous solution of noble gases is derived in terms of energies, force and torque magnitudes, and solute and water coordination numbers, quantities which are all measured from an equilibrium molecular dynamics simulation. Also derived are equations for the Gibbs free energy, enthalpy and entropy of hydration for the Henry's law process, the Ostwald process, and a third proposed process going from an arbitrary concentration in the gas phase to the equivalent mole fraction in aqueous solution which has simpler expressions for the enthalpy and entropy changes. Good agreement with experimental hydration free energies is obtained in the TIP4P and SPC/E water models although the solute's force field appears to affect the enthalpies and entropies obtained. In contrast to other methods, the approach gives a complete breakdown of the entropy for every degree of freedom and makes possible a direct structural interpretation of the well-known entropy loss accompanying the hydrophobic hydration of small non-polar molecules under ambient conditions. The noble-gas solutes experience only a small reduction in their vibrational entropy, with larger solutes experiencing a greater loss. The vibrational and librational entropy components of water actually increase but only marginally, negating any idea of water confinement. The term that contributes the most to the hydrophobic entropy loss is found to be water's orientational term which quantifies the number of orientational minima per water molecule and how many ways the whole hydrogen-bond network can form. These findings help resolve contradictory deductions from experiments that water structure around non-polar solutes is similar to bulk water in some ways but different in others. That the entropy loss lies in water's rotational entropy contrasts with other claims that it largely lies in water's translational entropy, but this apparent discrepancy arises because of different coordinate definitions and reference frames used to define the entropy terms.

Molecular correlations and solvation in simple fluids

We study the molecular correlations in a lattice model of a solution of a low-solubility solute, with emphasis on how the thermodynamics is reflected in the correlation functions. The model is treated in the Bethe-Guggenheim approximation, which is exact on a Bethe lattice (Cayley tree). The solution properties are obtained in the limit of infinite dilution of the solute. With h(11)(r), h(12)(r), and h(22)(r) the three pair correlation functions as functions of the separation r (subscripts 1 and 2 referring to solvent and solute, respectively), we find for r > or = 2 lattice steps that h(22)(r)/h(12)(r) is identical with h(12)(r)/h(11)(r). This illustrates a general theorem that holds in the asymptotic limit of infinite r. The three correlation functions share a common exponential decay length (correlation length), but when the solubility of the solute is low the amplitude of the decay of h(22)(r) is much greater than that of h(12)(r), which in turn is much greater than that of h(11)(r). As a consequence the amplitude of the decay of h(22)(r) is enormously greater than that of h(11)(r). The effective solute-solute attraction then remains discernible at distances at which the solvent molecules are essentially no longer correlated, as found in similar circumstances in an earlier model. The second osmotic virial coefficient is large and negative, as expected. We find that the solvent-mediated part W(r) of the potential of mean force between solutes, evaluated at contact, r = 1, is related in this model to the Gibbs free energy of solvation at fixed pressure, DeltaG(p)(*), by (Z/2)W(1) + DeltaG(p)(*) is identical with pv(0), where Z is the coordination number of the lattice, p is the pressure, and v(0) is the volume of the cell associated with each lattice site. A large, positive DeltaG(p)(*) associated with the low solubility is thus reflected in a strong attraction (large negative W at contact), which is the major contributor to the second osmotic virial coefficient. In this model, the low solubility (large positive DeltaG(p)(*)) is due partly to an unfavorable enthalpy of solvation and partly to an unfavorable solvation entropy, unlike in the hydrophobic effect, where the enthalpy of solvation itself favors high solubility, but is overweighed by the unfavorable solvation entropy.