Entropic interactions of 2D materials with cellular membranes: Parallel versus perpendicular approaching modes

Understanding the interaction of 2D materials including graphene, boron nitride and MoS₂ with biological systems is a growing topic of interest to many applications such as biosensors, drug delivery, gene therapy and nano-toxicity. In this paper, we show that the interaction of 2D materials with cellular membranes at its early stage of approaching is dominantly controlled by entropic forces. Recent experiments indicate that graphene sheets, depending on their size, can either undergo a near-orthogonal cutting or a parallel attachment mode of interaction with cell membranes. Here, we perform a set of integrated theoretical statistical mechanics analysis and coarse-grained molecular dynamics simulations to quantify the entropic energy barrier for these modes of interactions. Our results indicate that micro-sized graphene sheets prefer approaching a fluctuating membrane through a sharp corner, while nano-sized sheets are more likely to adhere to the cell membrane surface due to relatively low entropic energy cost that is comparable with thermal energy from random Brownian motions.