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The excess free energy of mixing Δ G ex governs the phase behavior of mixtures and controls material properties. It is challenging, however, to measure Δ G ex in simulations. Previously, we developed a method that combines molecular dynamics (MD) simulations with thermodynamic integration along the path of transformation of chains to predict the Flory Huggins interaction parameter χ for polymer mixtures and block copolymers. However, this method is best applied when the constituent molecules of the blends are structurally related. To overcome this limitation, we have developed a new method to predict Δ G ex for mixtures. We perform simulations to induce phase separation within a mixture by gradually weakening the interaction between different species. To compute Δ G ex we measure the thermodynamic work required to modify the interactions and the interfacial energy between the separated phases. We validate our method by applying it first to equimolar mixtures of labeled and unlabeled Lennard-Jones (LJ) beads, and labeled and unlabeled benzene, which results in good agreement with ideal solution theory. Then we compute the excess free energy of mixing for equimolar mixtures of benzene and pyridine, using both united-atom (UA) and all-atom (AA) potentials. Our results using UA potentials predict a value for Δ G ex about four times the experimental value, whereas using AA potentials gives results consistent with experiment, highlighting the need for good potentials to faithfully represent mixture behavior. 

Predicting the mixing free energy of mixing for binary mixtures using simulations is challenging. We present a novel molecular dynamics (MD) simulation method to extract the chemical potential μ ( X ) for mixtures of species A and B. Each molecule of species A and B is placed in equal and opposite harmonic potentials ±(1/2) U ex ( x ) centered at the middle of the simulation box, resulting in a nonuniform mole fraction profile X ( z ) in which A is concentrated at the center, and B at the periphery. Combining these, we obtain U ex ( X ), the exchange chemical potential required to induce a given deviation of the mole fraction from its average. Simulation results for U ex ( X ) can be fitted to simple free energy models to extract the interaction parameter χ for binary mixtures. To illustrate our method, we investigate benzene–pyridine mixtures, which provide a good example of regular solution behavior, using both TraPPE united-atom and OPLS all-atom potentials, both of which have been validated for pure fluid properties. χ values obtained with the new method are consistent with values from other recent simulation methods. However, the TraPPE-UA results differ substantially from the χ obtained from VLE experimental data, while the OPLS-AA results are in reasonable agreement with experiment, highlighting the importance of accurate potentials in correctly representing mixture behavior. 

When oppositely charged polyelectrolytes mix in an aqueous solution, associative phase separation gives rise to coacervates. Experiments reveal the phase diagram for such coacervates, and determine the impact of charge density, chain length and added salt. Simulations often use hybrid MC-MD methods to produce such phase diagrams, in support of experimental observations. We propose an idealized model and a simple simulation technique to investigate coacervate phase behavior. We model coacervate systems by charged bead-spring chains and counterions with short-range repulsions, of size equal to the Bjerrum length. We determine phase behavior by equilibrating a slab of concentrated coacervate with respect to swelling into a dilute phase of counterions. At salt concentrations below the critical point, the counterion concentration in the coacervate and dilute phases are nearly the same. At high salt concentrations, we find a one-phase region. Along the phase boundary, the total concentration of beads in the coacervate phase is nearly constant, corresponding to a “Bjerrum liquid''. This result can be extended to experimental phase diagrams by assigning appropriate volumes to monomers and salts. 

This paper presents a new method to simulate the osmotic pressure of an ionic solution. Previous simulation methods confine ions between walls, and the osmotic pressure is inferred from the force required to maintain this confinement. In this work, we impose a harmonic potential on the ions to form a nonuniform concentration profile in the solution. As this profile arises from the force balance of the harmonic potential with the osmotic pressure, it can be used to determine the osmotic pressure across the entire concentration profile. This method can be performed without specialized programming, making it accessible to the general user. Using our method, we find that standard potentials for Na + and Cl − ions need adjustments to be consistent with experimental osmotic pressure at high concentrations.