Ultrathin Membrane Analysis

Membrane technology has been widely used for water purification and gas separation due to its inherent advantages over conventional separation technologies, such as high energy efficiency, simplicity in operation, compactness and ease of scale-up. Membrane processes have also emerged as the leading technology for seawater desalination, nitrogen enrichment from air, and CO2 removal from natural gas. Ultrathin composite membranes as shown in Figure 1 are of particular interest and use for industrial applications because of their enhanced performance (high permeance and selectivity) and low cost. In these structures an ultrathin (green) dense polymer layer (< 100 nm) performs molecular separation while the bulk porous support layer (150-200 µm) provides mechanical strength with negligible mass transport resistance. In a three layer membrane there is a highly permeable “gutter layer” between the selective layer and support that enhances the flux of penetrant through the membrane as shown in Figure 1. The characteristic flux for a gas A, i.e. the permeance (PA/leff), is defined as:

where PA is the permeability of penetrant A in the selective layer, leff is the effective diffusion length of the penetrant, NA is the steady-state flux of penetrant A through the membrane, Am is the membrane surface area, and p2A and p1A are the upstream (high) and downstream (low) partial pressure of A, respectively. The geometric restriction of the membrane nanostructures on the observed permeance of penetrant A can be characterized as membrane permeance efficiency,βA:

Where (PA)apparent is the membrane permeance modeled and PA,Ideal is the ideal permeance of the selective. Lower βA values indicate greater deviation from the ideal permeance, reflecting more severe effect from the porous support and/or the gutter layer.

We have recently developed 3D computational models to study the performance of untrathin composite membranes taking into account constituent material structures and properties. In these models the support layer is assumed to contain a 2D array of uniformly spaced cylindrical pores. We exploit the symmetry of this ordered pore structure and reduce the analysis to a unit cell of the membrane as shown in Figure 1.

Symmetry boundary conditions are applied on the sides of the unit cell to account for the surrounding membrane structure. The penetrant transport in the selective and gutter layers is diffusive and driven by the gradient in concentration following the solution-diffusion model. The equation that governs the steady-state concentration (CA) of a penetrant A in the membrane is:

The steady-state transport of penetrant A is obtained by solving Equation 3 subject to appropriate boundary conditions. The penetrant flux NA is also defined in Equation 3, where DA is the diffusion coefficient for penetrant A. The computational model predicts the concentration profile in the selective and gutter layers, and the resulting flux NA across the composite membrane.

Figure 2 ahowa a two-layer membrane, i.e. without a gutter layer, Figure 3a shows the membrane permeance efficiency βA as a function of the support porosity and the scaled selective layer thickness ( S = Ls/r). At a typical support porosity of 0.05 and a scaled selective layer thickness of 2, the permeance efficiency is as low as 0.17, indicating a significant flux restriction imposed by the porous support. Figure 3b illustrates the compromised benefits of decreasing selective layer thickness as a function of porosity (Φ). 

As illustrated in Figure 1, a gutter layer with negligible mass transfer resistance can channel the gas flow and thus mitigate geometric restriction by the porous support. Figure 4 depicts the magnitude of the 3D concentration of the penetrant for a three-layer membrane with a porous support of Φ=0.1. This provides a clear visualization of a significant concentration gradient near the pores, which indicates that the pores impose a substantial resistance to mass transport. The pores increase the effective path length leff of molecular transport and hence decrease the permeance. The increase in the path length is diminished with increasing porosity. Since the restriction is near the pore regions, it is expected that increasing the thickness of the selective layer and/or the gutter layer would minimize the pore restriction, and increase the concentration distribution in these layers.

Figure 5 illustrates the effect of the gutter layer on membrane permeance efficiency for porous supports with two extreme porosities (i.e., Φ = 0.01 and 0.1). The introduction of a gutter layer significantly increases permeance efficiency from 0.022 to as high as 0.13, a 5.9-fold increase at Φ = 0.01, and from 0.13 to 0.59, a 4.5-fold increase at Φ = 0.1.

Figure 5a also shows the membrane permeance efficiency for overall selective and gutter layers (βA'), which is defined as the apparent permeance to the ideal permeance of the combined selective and gutter layer (with a total length s+g), where the subscripts of s, g, s+g indicate the permeances for the selective layer only, gutter layer only, and the combined selective and gutter layer, respectively. Clearly, increasing the gutter layer thickness reduces the geometric restriction and thereby increases the βA' values. On the other hand, a further increase in the gutter layer thickness increases mass transport resistance in the gutter layer, which decreases the membrane permeance. Therefore, the benefit of reduced geometric restriction by the thicker gutter layer can be diminished by the increased mass transport resistance. There needs a judicious choice for the gutter layer material with high permeability and a balanced thickness to achieve the maximal improvement of membrane permeance.

There seems to be an optimal gutter layer thickness, denoted G, between 1 and 2 to achieve the highest increase in permeance efficiency for various S values.  Increasing the selective layer thickness increases the permeance efficiency, which is consistent to the study of two-layer composite membranes, as shown in Figure 3. Figure 5b directly exhibits the benefit of decreasing the selective layer thickness at different porosities.  The condition of G = 1 is chosen here for illustration, because it provides one of the greatest permeance efficiency values.  While decreasing the selective layer thickness from S = 10 to S = 1 increases the ideal permeance by 10 times, the enhancement in apparent permeance is only 2.0 at Φ = 0.01, and 6.7 at Φ = 0.1.  These results strongly indicate that the porous support and gutter layer are critical to designing high flux ultrathin membranes.

The 3D computational model described above is readily implemented in commercially available software (e.g Comsol) and enables rapid parametric analysis of membrane performance (selectivity and permeance) as a function of constituent material structures and properties. It provides clear and practical guidance in the design and optimization of ultrathin composite membranes and should find widspread use in the development of novel membrane structures.