Elementary models of low-pressure plasma polymerisation into nanofibrous mats

Abstract Deposition penetration depth into nanofibrous materials is a crucial but underexplored parameter for their modification using low-pressure plasma polymerisation. This work studies it using Monte Carlo simulations and two analytical approaches, a classic continuum diffusion model and a new abstract discrete model, which is fully solvable using the method of generating functions. The discrete model represents the material as a stack of cells with no further geometry and is only characterised by the sticking coefficient η of film-forming species. The models are used to investigate other properties, such as directional coverage of fibres by the deposited film, anisotropy of the mean free path in the nanofibrous material, or the effective sticking coefficient of the material as a whole. The two very different analytical approaches are found to complement each other. When the derived expressions are compared with Monte Carlo results, we find that the discrete model can provide surprisingly relevant formulae despite the very high level of abstraction. The clearest example is the sticking coefficients of the material as a whole, for which the discrete model achieves almost perfect agreement. The other two properties require dimensional scaling factors. It shows that certain aspects of the process are fundamental and mostly independent on details of the interactions and that the dependencies on the sticking coefficient are in some sense separable. By combining the analytical and Monte Carlo results we can also obtain elementary practical formulae for the studied quantities as functions of the sticking coefficient and/or porosity. They are directly applicable to the deep penetration of low- η species or deposition of thin coatings and can be used as local description in more complex cases.