Phase Equilibria of Polydisperse Square-Well Chain Fluid Confined in Random Porous Media: TPT of Wertheim and Scaled Particle Theory

Phase behavior of patchy colloids confined in patchy porous media

A simple model for functionalized disordered porous media is proposed and the effects of confinement on self-association, percolation and phase behavior of a fluid of patchy particles are studied. The media are formed by randomly distributed hard-sphere obstacles fixed in space and decorated by a certain number of off-center square-well sites. The properties of the fluid of patchy particles, represented by the fluid of hard spheres each bearing a set of the off-center square-well sites, are studied using an appropriate combination of the scaled particle theory for the porous media, Wertheim's thermodynamic perturbation theory, and Flory-Stockmayer theory. To assess the accuracy of the theory a set of computer simulations have been performed. In general, predictions of the theory appeared to be in good agreement with the computer simulation results. Confinement and competition between the formation of bonds connecting the fluid particles, and connecting fluid particles and obstacles of the matrix, gave rise to a re-entrant phase behavior with three critical points and two separate regions of the liquid-gas phase coexistence.

Behaviour of the model antibody fluid constrained by rigid spherical obstacles: Effects of the obstacle-antibody attraction

This study investigates the behaviour of a fluid of monoclonal antibodies (mAbs) when trapped in a confinement represented by rigid spherical obstacles that attract antibodies. The antibody molecule is depicted as an assembly of seven hard spheres (7-bead model), organized to resemble a Y-shaped object. The model antibody has two Fab and one Fc domains located in the corners of letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pairs of interactions are effective. The confinement is formed by the randomly distributed hard-spheres fixed in space. The spherical obstacles, besides the size exclusion, interact with beads of the antibody molecules via the Yukawa attractive potential. We applied the combination of the scaled particle theory, replica Ornstein-Zernike equations, Wertheim's thermodynamic perturbation approach and the Flory-Stockmayer theory to calculate: (i) the phase diagram of the liquid-liquid phase separation and the percolation threshold, (ii) the cluster size distributions, and (iii) the second virial coefficient of the protein fluid distributed among the obstacles. All these quantities were calculated as functions of the strength of the attraction between the monoclonal antibodies, and the monoclonal antibodies and obstacles. The conclusion is that while the hard-sphere obstacles decrease the critical density and the critical temperature of the mAbs fluid, the effect of the protein-obstacle attraction is more complex. Adding an attractive potential to the obstacle-mAbs interaction first increases the wideness of the T*-ρ envelope. However, with the further increase of the obstacle-mAbs attraction intensity, we observe reversal of the effect, the T*-ρ curves become narrower. At some point, depending on the obstacle-mAbs interaction, the situation is observed where two different temperatures have the same fluid density (re-entry point). In all the cases shown here the critical point decreases below the value for the neat fluid, but the behaviour with respect to an increase of the strength of the obstacle-mAbs attraction is not monotonic. Yet another interesting phenomenon, known in the literature as an approach toward the "empty liquid" state, is observed. The stability of the "protein droplets", formed by the liquid-liquid phase separation, depends on their local environment and temperature.

Equation of state for confined fluids

Fluids confined in small volumes behave differently than fluids in bulk systems. For bulk systems, a compact summary of the system’s thermodynamic properties is provided by equations of state. However, there is currently a lack of successful methods to predict the thermodynamic properties of confined fluids by use of equations of state, since their thermodynamic state depends on additional parameters introduced by the enclosing surface. In this work, we present a consistent thermodynamic framework that represents an equation of state for pure, confined fluids. The total system is decomposed into a bulk phase in equilibrium with a surface phase. The equation of state is based on an existing, accurate description of the bulk fluid and uses Gibbs’ framework for surface excess properties to consistently incorporate contributions from the surface. We apply the equation of state to a Lennard-Jones spline fluid confined by a spherical surface with a Weeks–Chandler–Andersen wall-potential. The pressure and internal energy predicted from the equation of state are in good agreement with the properties obtained directly from molecular dynamics simulations. We find that when the location of the dividing surface is chosen appropriately, the properties of highly curved surfaces can be predicted from those of a planar surface. The choice of the dividing surface affects the magnitude of the surface excess properties and its curvature dependence, but the properties of the total system remain unchanged. The framework can predict the properties of confined systems with a wide range of geometries, sizes, interparticle interactions, and wall–particle interactions, and it is independent of ensemble. A targeted area of use is the prediction of thermodynamic properties in porous media, for which a possible application of the framework is elaborated.

Aggregation, liquid-liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles

This study is concerned with the behaviour of proteins within confinement created by hard-sphere obstacles. An individual antibody molecule is depicted as an assembly of seven hard spheres, organized to resemble a Y-shaped (on average) antibody (7-bead model) protein. For comparison with other studies we, in one case, model the protein as a hard sphere decorated by three short-range attractive sites. The antibody has two Fab and one Fc domains located in the corners of the letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pair interactions are possible. The confinement is formed by the randomly distributed hard-sphere obstacles fixed in space. Aside from size exclusion, the obstacles do not interact with antibodies, but they affect the protein-protein correlation. We used a combination of the scaled-particle theory, Wertheim's thermodynamic perturbation theory and the Flory-Stockmayer theory to calculate: (i) the second virial coefficient of the protein fluid, (ii) the percolation threshold, (iii) cluster size distributions, and (iv) the liquid-liquid phase separation as a function of the strength of the various pair interactions of the protein and the model parameters, such as protein concentration and the packing fraction of obstacles. The conclusion is that hard-sphere obstacles strongly decrease the critical density and also, but to a much lesser extent, the critical temperature. Also, the confinement enhances clustering, making the percolating region broader. The effect depends on the model parameters, such as the packing fraction of obstacles η0, the inter-site interaction strength εIJ, and the ratio between the size of the obstacle σ0 and the size of one bead of the model antibody σhs; the value of this ratio is varied here from 2 to 5. Interestingly, at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), and the slope depends on the observation temperature, but then at higher values of η0 it increases. The calculated values of the second virial coefficient also depend on the size of the obstacles.