Context. The diffusion of volatile species on amorphous solid water ice affects the chemistry on dust grains in the interstellar medium as well as the trapping of gases enriching planetary atmospheres or present in cometary material. Aims. The aim of the work is to provide diffusion coefficients of CH4 on amorphous solid water (ASW) and to understand how they are affected by the ASW structure. Methods. Ice mixtures of H2O and CH4 were grown in different conditions and the sublimation of CH4 was monitored via infrared spectroscopy or via the mass loss of a cryogenic quartz crystal microbalance. Diffusion coefficients were obtained from the experimental data assuming the systems obey Fick's law of diffusion. Monte Carlo simulations were used to model the different amorphous solid water ice structures investigated and were used to reproduce and interpret the experimental results. Results. Diffusion coefficients of methane on amorphous solid water have been measured to be between 10-12 and 10-13 cm2 s-1 for temperatures ranging between 42 K and 60 K. We show that diffusion can differ by one order of magnitude depending on the morphology of amorphous solid water. The porosity within water ice and the network created by pore coalescence enhance the diffusion of species within the pores. The diffusion rates derived experimentally cannot be used in our Monte Carlo simulations to reproduce the measurements. Conclusions. We conclude that Fick's laws can be used to describe diffusion at the macroscopic scale, while Monte Carlo simulations describe the microscopic scale where trapping of species in the ices (and their movement) is considered.

We use experimental mid-infrared optical constants and extended effective medium approximations to determine the porosity and the band strengths of multi-phase composite ices grown at 30 K. A set of porous H₂O:CH₄ ices are taken as a prototypical example. As a benchmark and proof of concept, the stoichiometry of the ice constituents is retreived with good accuracy from the refractive indices and the extinction coefficients of the reference binary ice mixtures with known compositions. Accurate band strengths are then calculated from experimental mid-infrared spectra of complex ices. We notice that the presence of pores has only a small effect on the overall band strengths, whereas a water dilution can considerably alter them. Different levels of porosity are observed depending on the abundance of methane used as a gas contaminant premixed with water prior to background deposition. The absorption profiles are also found to vary with deposition rate. To explain this, we use Monte Carlo simulations and we observe that the deposition rate strongly affects the pore size distribution as well as the ice morphology through reorganization processes. Extrapolated to genuine interstellar ices, the methodology presented in this paper can be used to evaluate the porosity and to quantify the relative abundances from observational data.