Diffusion of Submicron Particles on Biological Surfactant Monolayers Governed by the Viscoelasticity and Interfacial Dynamics

Abstract

The diffusion of microscale and nanoscale particles on biological membranes plays a critical role in understanding various physiologic processes and optimizing drug delivery. In this study, we investigate the diffusive motion of submicron particles on in vitro porcine pulmonary surfactant monolayers at the air–water interface using single-particle tracking. The viscoelastic response of the monolayer becomes apparent only when particle sizes fall below the Saffman and Delbrück length. Hydrodynamic and nonhydrodynamic interfacial dynamics induce distinct anomalous diffusion behaviors for small and large particles, respectively. For smaller particles, their thermal velocities approach the minimum phase velocity of interfacial capillary waves, causing a hydrodynamic wave drag, whose magnitude can be approximately modeled using the sudden accelerated/decelerated rectilinear motion of an object at the interface. In contrast, larger particles do not exhibit wave drag due to their lower thermal velocities. Instead, their displacement correlation functions reveal unusually slow-decaying oscillations─a phenomenon fundamentally stemmed from nanoscale contact-line interfacial dynamics. These oscillations are linked to the diffusion coefficient that varies instantaneously with the particle’s immersion depth. By performing Langevin dynamics simulations of the particle’s perpendicular motion, we confirmed that the oscillation period precisely coincides with the cyclic time of the particle’s motion along the interfacial normal direction. These simulations explicitly account for subtle contact-line perturbations to the interfacial free energy, which arise from nanoscale surface heterogeneity of the particle. This behavior demonstrates strong dynamic coupling between in-plane and out-of-plane particle motions. Crucially, the oscillation amplitude becomes magnified when the particle’s transverse displacement per unit time decreases, explaining why these oscillations are exclusively observable in larger particles. The displacement probability distributions (DPDs) remain non-Gaussian even at long elapsed times when the diffusion becomes linear. This non-Gaussianity stems from variations in the diffusion coefficients of individual particles, which originate from the heterogeneity of the monolayer’s structure.