Membranes with nanometer scale pores are an important technology for the separation of proteins and small molecules, with use in research, industrial, and clinical arenas. Dialysis, a diffusion based separation modality requiring a nanoporous membrane, is a staple in laboratory purifications and buffer exchanges. Similarly, the clinical process of hemodialysis utilizes nanoporous membranes for the diffusive separation of proteins coupled with pressurized flow for fluid balance. The development of new membrane materials are needed to improve the precision and efficiency of these frequently used procedures [1
Many of the polymer based membranes currently used in dialysis have long tortuous pores and log normal pore distributions with extended tails [3
], resulting in low resolution molecular weight cutoffs. With pore characteristics such as these, only molecules differing significantly in size can be clearly separated. This is of significant concern to hemodialysis. Low-flux dialysis membranes are able to filter urea and small toxins while retaining serum albumin, but often unwanted middle weight molecules, including β2
-microglobulin, cytokines, and leptin, are retained as well [4
]. Retention of β2
-microglobulin in particular can cause amyloidosis and can be used as a predictor of patient mortality [5
]. High-flux membranes, which have larger pore sizes and cutoffs, are able to better clear middle weight species, but have been linked to serum albumin loss [7
In addition to having non-ideal pore distributions, traditional dialysis membranes are orders of magnitude thicker than their nominal pore size. The diffusion of molecules traversing this thickness is greatly reduced compared to free diffusion, requiring long times for laboratory and clinical separations. This has lead to a call for thin nanoengineered membranes to enable wearable dialysis units [9
]. In the case where filters are used for isolating small analytes, the thickness and tortuous pores present high surface area for adsorption, which may result in the significant loss of low abundance species.
Due to the infrastructure created by the microelectronics industry, silicon is an attractive fabrication platform for engineered nanomembranes [10
]. Silicon based membranes with arrays of well defined slit pores fabricated via photolithography techniques have been shown to be useful in a number of separation and biological experiments [11
]. Silicon has also been used as a platform for aligned carbon nanotube (CNT) growth and the creation of CNT membranes [12
]. However, both of these novel membranes are still many microns thick. In 2004, Tong et al.
fabricated an ultrathin (10 nm) silicon nitride nanosieve with precise, individually drilled pores, a process that is too time consuming for scale up [14
]. More recently, a thin (0.7 – 1 µm) anodized alumina membrane, in which the pores self-assemble, was developed with the use of thin film deposition on silicon, although the pore sizes 0.7–1 µm are not on the same scale as the nanosieve [15
We have previously reported an ultrathin porous membrane material with self-assembling pores called porous nanocrystalline silicon (pnc-Si) [16
]. Previous studies with these membranes have shown diffusion based separations of binary mixtures of proteins [16
] and the rapid diffusion of small molecules through the pores [17
]. In addition, recent experiments have shown that pnc-Si has high hydraulic permeability [18
], can precisely separate closely sized nanoparticles under pressure [18
], and can be used as a highly permeable cell culture substrate [19
]. Pnc-Si membranes are fabricated using standard photolithography and silicon chip manufacturing techniques. The free-standing membranes can be made between 7 and 30 nm thick, which is on the same order as their pore sizes. Pore sizes can be tuned by adjusting annealing temperature or ramp rate during pnc-Si production, and pore distributions, which are directly measured using transmission electron microscopy [18
], fall within the size scale of small molecules, proteins, and larger complexes. While pnc-Si membranes have a distribution of pores, the membranes have a distinctly sharp cutoff. Current processes enable the production of more than 100 membrane chips per 4″ wafer, and this process can be scaled up to a 6″, 8″, or 12″ substrate, which would enable the production of thousands of chips per wafer or whole wafer membrane cartridges for dialysis procedures.
Because of their thinness and unambiguous pore distributions, pnc-Si membranes can be used to test theories of molecular diffusion and can help in understanding how ultrathin membranes can impact diffusive separations. While a porous membrane will prevent any molecule larger than the largest pore from diffusing through, it also hinders the diffusion of molecules smaller than this pore size. Traditional theory suggests that the hindrance is due to 1) steric interactions between the molecule and the pore entrance and 2) frictional interactions between the molecule and the pore walls as it passes through [20
]. This theory has seen experimental verification with experiments using track etched mica [21
] and porous alumina membranes [22
]. Early hindrance models considered the diffusion solely along the central axis of the pore [20
], although newer treatments average the hindrance radially across the entire cross-section [25
]. An additional cause of hindrance arises from the parallel diffusion of molecules across the membrane surface between pores [17
]. The parallel diffusion and entrance effects are negligible for a thick membrane but significantly contribute to the total resistance of an ultrathin membrane; once a molecule finds a pore it needs only to diffuse a distance on the order of its own length to exit the other side.
In this work we have performed separations with proteins and small molecules using pnc-Si membranes. Using equations defining the resistance to diffusion along the surface of and through a membrane, we have developed 1-dimensional and 3-dimensional models of molecular diffusion. We used these models to analyze the influence of factors such as membrane thickness, porosity, pore size distribution, time of separations, and system geometry on separations. The experimental results were compared with the diffusion models, and good agreement was observed for small molecules. We consider the effect of protein adsorption, and we discuss the potential effects of additional factors including molecular shape, electrostatics, and convection.