The system of polymers in solvent mixtures is a widely-used model to represent biomolecular condensates in intracellular environments. Here, we apply a variational theory based on the 2n-power modified Gaussian to control the center-of-mass of two polymers in solvent mixtures and perform the first quantification of their interactions. The theory self-consistently introduces a mean force that controls the average position of the center-of-mass and a self-adjustable harmonic potential that counters the fluctuation of the center-of-mass position. Even both solvent and cosolvent are good to the polymer, we demonstrate that strong polymer-cosolvent affinity induces the formation of a single-chain condensate. Even though all the molecular interactions are soft, the PMF between two condensates exhibits an anomalous long-range hard-wall repulsion, which cannot be categorized into any classical types of inter-chain interactions. This repulsion is enhanced as either the affinity or the bulk cosolvent fraction increases, leading to a higher kinetic barrier to stabilize individual condensates. The emergence of the hard-wall repulsion is attributed to cosolvent regulation. The overlapping of the cosolvent excess layers triggers a local cosolvent condensation, dramatically increasing the energy. The hard-wall kinetic barrier prevents coalescence of condensates and hence highlights the intrinsic role of proteins as a cosolvent in stabilizing biomolecular condensates.
