A solvent-topology perspective on hydrophobic aggregation

Hydrophobic aggregation is often described in terms of effective attractive forces between apolar units. In aqueous and soft-matter environments, however, aggregation necessarily involves a collective reorganization of the solvent, whose connectivity and confinement properties may play a central role. Here we investigate a deliberately minimal lattice model in which hydrophobic (apolar) segments interact with the solvent only through a local restriction rule, without introducing explicit solute-solute attractions. Each lattice site is occupied either by solvent or by an apolar segment at a fixed composition. Solvent sites are classified as restricted when the local density of nearby apolar segments exceeds a prescribed threshold, and configurations are sampled with a Boltzmann-like weight that penalizes the total number of restricted-solvent sites. Within this framework, aggregation can only arise through the reorganization of solvent restriction fields. By decomposing the solvent into free and restricted subsets, we analyze their connectivity using standard percolation diagnostics alongside conventional measures of solute clustering. Baseline simulations reveal that while amphiphile aggregation evolves smoothly with concentration, the restricted-solvent subset can undergo a sharp, kernel-dependent connectivity crossover: for sufficiently isotropic interaction neighborhoods, restricted water becomes a system - spanning only over an intermediate range of solute fractions. Free solvent, by contrast, remains spanning across the explored parameter range. Notably, these solvent-topology signatures are significantly sharper and more structured than the corresponding solute-ordering metrics. A systematic extension to larger system sizes refines this picture. The onset of restricted-solvent spanning remains localized and kernel selective, while high-density behavior becomes smoother and more fluctuation dominated, consistent with finite-size effects. Importantly, the amount of restricted solvent grows monotonically and robustly with system size, whereas its global connectivity reorganizes nontrivially. Taken together, these results support a restrained interpretation of hydrophobic aggregation as a solvent-driven topological crossover rather than a sharp thermodynamic phase transition, highlighting solvent topology as a sensitive diagnostic even when solute ordering remains gradual.