On the Origin of Interfacial Resistance in Ideal Nanomaterials

Abstract

Interfacial resistance significantly hinders transport in nanomaterials and membranes, limiting efficiency improvement as system size is reduced. While slow transport of fluids in finitesized materials, found in experiment and simulation, has been imputed to interfacial resistance, the underlying mechanism is unclear, and no theory exists for its prediction. A kinetic theorybased approach for low-density transport in finite nanopores is developed here, which demonstrates interfacial resistance to arise from an entry region of developing flow, in which the transport coefficient is nonuniform. The origin of interfacial resistance is shown to lie in the enhanced influence of short molecular trajectories in the entry region, with increased frequency of wall collision, which reduces the local transport coefficient. It is shown that the relative interfacial resistance is a universal function of a parameter related to length and surface momentum accommodation factor for a given fluid−solid interaction potential. While interfacial resistance is system size-dependent, it approaches a limiting value in long nanopores that is readily determined. Application of the approach to H 2 transport in carbon nanotubes using molecular dynamics simulation results shows the apparent interfacial resistance to increase with decrease in nanotube diameter and with increase in fluid−solid interaction strength.

On the increased interfacial resistance of hydrogen in carbon nanotube arrays and its effect on gas mixture separation

“…29 We may now use the new α hex values listed in Table II to determine the τ term, and then, using the finite difference method that was developed prior, we may determine the molar flux through a nanopore similar to those found in the VACNT arrays developed by Holt et al, 6 which we model as a collection of 3 μm (10,10) CNT's (d ¼ 1:35 nm). It is immediately noticeable that since here the predicted α hex values are approximately ten times greater than EMD simulations predict 24 the effective friction is overestimated, with L eff values for H 2 being 39.6, which is far greater than the value utilized prior of approximately 5. Despite this issue of total magnitude, we use the α hex values in Table II to determine the molar flux of each species, to then determine the molar selectivity (which denotes the ratio of mass flux for each species) of each gas against He, which is presented in Fig.…”

“…While this model can provide approximate values for the TMAC value in nanoscale materials, it was noted in the work that the estimates are orders of magnitude larger than numerical simulations predict, with the MD simulations presented in a recent work by Bhatia and Dutta, 24 finding TMAC values of order 0.001 for H 2 at 300K traveling through narrow armchair CNTs of type (6,6) to (12,12). This discrepancy between theory and numerical experiment may be attributed to the spacing utilized for the hard-sphere model wall in the LSR model.…”

“…This corresponds to a decrease in α hex of approximately 10, roughly agreeing with the EMD results reported by Bhatia and Dutta. 24 Currently, this scaling is empirical, and we have not presented a direct derivation for this scaling. In spite of this fact, a single scaling value seems to function well for all gas species considered, and as such, this model could allow for the extrapolation of results for different species from a single value calculated from MD simulations.…”