The golden aspect ratio for ion transport.
Access resistance indicates how well current carriers from the bulk medium can converge to a pore or opening, and is important in many fields, such as cell biology, electronics, electrochemical engineering, thermal transport, among others. In simplified scenarios, it depends only on the resistivity and pore radius when the bulk dimensions are infinite in all directions. These conditions are often not valid in simulations of transport due to the computational cost of large simulation cells, and can even break down in micro- and nano-scale systems due to strong confinement. Here, we examine a scaling theory for the access resistance that predicts there should be a special simulation cell aspect ratio -- the golden aspect ratio -- where finite size effects are eliminated. We demonstrate that this golden aspect ratio exists and that it takes on a universal value in linear response and moderate concentrations, i.e., regimes of interest to transport through biological ion channels and nanopores. Outside of linear response, it gains an apparent dependence on characteristics of the transport scenario (concentration, voltages, etc.) for small simulation cells, but this dependence vanishes at larger length scales. These results will enable the use of all-atom molecular dynamics to study contextual properties of access resistance -- i.e., its dependence on protein and molecular-scale fluctuations, the presence of charges, etc. -- and yield the opportunity to quantitatively compare computed and measured resistances.
Publisher URL: http://arxiv.org/abs/1711.00472
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