Extended law of corresponding states: square-well oblates

Abstract

The vapour-liquid coexistence collapse in the reduced temperature, Tr=T/Tc, reduced density, ρr= ρ/ρc, plane is known as a principle of corresponding states, and Noro and Frenkel have extended it for pair potentials of variable range. Here, we provide a theoretical basis supporting this extension and show that it can also be applied to short-range pair potentials where both repulsive and attractive parts can be anisotropic. We observe that the binodals of oblate hard ellipsoids for a given aspect ratio (κ=1/3) with varying short-range square-well interactions collapse into a single master curve in the Δ B*2--ρr plane, where Δ B*2= (B2(T)-B*2(Tc))/v0, B2 is the second virial coefficient, and v0 is the volume of the hard body. This finding is confirmed by both REMC simulation and second virial perturbation theory for varying square-well shells, mimicking uniform, equator, and pole attractions. Our simulation results reveal that the extended law of corresponding states is not related to the local structure of the fluid.

The Relationship between Protein–Protein Interactions and Liquid–Liquid Phase Separation for Monoclonal Antibodies

“…In Figure , the binodals for COE-01 under low ionic strength conditions and for COE-07 under salting-out conditions are plotted in terms of Δ b 22 = b 22 – b 22 c and compared against experimental data for lysozyme and results obtained from molecular simulations of square-well fluids for two different ranges given by λ = 1.1, 1.25, where λ is the range of the square well normalized by the hard sphere diameter. It has been shown that an extended law of corresponding states is applicable when the binodal is plotted in terns of Δ b 22 for nonspherical convex particles interacting through isotropic and weakly anisotropic interactions. , For lysozyme the dilute branch is captured by both models, but the dense branch is better fit to the shorter-ranged potential as the binodal is thinner for λ > 1.25. While the behavior of lysozyme agrees reasonably well with the phase diagrams of model potentials, the binodals of the mAbs deviate greatly from the behavior.…”

“…It has been shown that an extended law of corresponding states is applicable when the binodal is plotted in terns of Δb 22 for nonspherical convex particles interacting through isotropic and weakly anisotropic interactions. 65,66 For lysozyme the dilute branch is captured by both models, but the dense branch is better fit to the shorter-ranged potential as the binodal is thinner for λ > 1.25. While the behavior of lysozyme agrees reasonably well with the phase diagrams of model potentials, the binodals of the mAbs deviate greatly from the behavior.…”

“…Predictions based on models covering spheres and particles with convex shapes for varying aspect ratios interacting through weakly anisotropic potentials indicate that b 22 c values fall in a relatively small window. 65 , 66 For spherical models interacting through sticky patches, the values of b 22 c become greater than approximately −3 for models with 5 or greater patches or for 4 patch models, when the fraction of patchy surface coverage exceeds 0.5. 27 , 30 While capturing antibody solution properties often requires models reflecting highly directional protein–protein interactions, there are also cases where spherically symmetric models or coarse-grained bead models with uniform bead–bead interactions accurately reproduce thermodynamic properties.…”

“…As yet, there have been no investigations into the utility of using b 22 as a predictor of LLPS. Predictions based on models covering spheres and particles with convex shapes for varying aspect ratios interacting through weakly anisotropic potentials indicate that b 22 c values fall in a relatively small window. , For spherical models interacting through sticky patches, the values of b 22 c become greater than approximately −3 for models with 5 or greater patches or for 4 patch models, when the fraction of patchy surface coverage exceeds 0.5. , While capturing antibody solution properties often requires models reflecting highly directional protein–protein interactions, there are also cases where spherically symmetric models or coarse-grained bead models with uniform bead–bead interactions accurately reproduce thermodynamic properties. ,, Furthermore, under conditions dominated by electrostatic attraction, there can still be large large variability in the anisotropic nature of the protein–protein interactions. ,, It is then not clear to what extent mAb solutions will exhibit universal values of b 22 c and how the values will compare against the critical point solution properties of globular proteins such as lysozyme or γB-crystallin. As such, we have investigated the liquid–liquid phase boundaries in terms of b 22 for three mAbs.…”

Special issue on soft matter research in Latin America

“…The first contribution of this section is written by de Santiago et al [13] and shows that the extended law of corresponding states of Noro and Frenkel, originally developed for pair potentials of variable range, can also be applied to short-range pair potentials with both attractive and repulsive anisotropic interactions. As an illustrative example the authors considered oblate hard ellipsoids with varying short-range square-well interactions using perturbation theory and simulations.…”