Influence of gas rarefaction on the lateral resolution achievable by thermocapillary patterning

Molten polymer nanofilms subject to a large transverse thermal gradient can undergo a thermocapillary instability leading to the growth of nanopillar arrays on the cooler side. The array pitch can be estimated from the fastest growing wavelength from linear stability analysis. Here we quantify the influence of gas rarefaction on thermal conduction for cases in which the gas layer thickness above the film approaches dimensions of the molecular mean free path. For experimentally relevant parameters, rarefaction increases the pitch by as much as 65%, an important consideration for noncontact three-dimensional structure formation by thermocapillary lithography