Surface Excess Energy Governs the Non-Monotonic Behavior of Active Diffusivity with Activity

Abstract

Self-propulsion of particles is typically explained by phoretic mechanisms driven by externally imposed chemical, electric, or thermal gradients. In contrast, chemical reactions can enhance particle diffusion even in the absence of such external gradients. We refer to this increase as active diffusivity, often attributed to self-diffusiophoresis or self-electrophoresis, although these mechanisms alone do not fully account for experimental observations. Here, we investigate active diffusivity in catalytic Janus particles immersed in reactive media without imposed gradients. We show that interfacial reactions generate excess surface energy and sustained interfacial stresses that supplement thermal energy, enabling diffusion beyond the classical thermal limit. We consistently quantify this contribution using both dissipative and non-dissipative approaches, assuming that the aqueous bath remains near equilibrium. Our framework reproduces experimentally observed trends in diffusivity versus activity, including the non-monotonic behaviors reported in some systems, and agrees with data for nanometric Janus particles catalyzing charged substrates as well as vesicles with membrane-embedded enzymes driven by ATP hydrolysis. These results demonstrate that chemical reactions can induce and sustain surface-tension gradients and surface excess energy, providing design principles for tuning mobility in synthetic active matter.