The role of structural forces in membrane transport: Cellulose membranes.

The phenomena governing Transition RO/UF (nanofiltration) membrane transport have been critically studied. The residuals and predicted pore sizes of 965 individual permeation runs performed on 70 cellulose membranes were used to discriminate between several restricted transport models and various solute-solvent-membrane material interactions. Solute-membrane interactions were found to be mediated by the presence of structured solvent at the surface of the membrane. Two new interaction parameters, $\Psi\sb{DP}$ and $\kappa\sp\prime$ describing structural solvent forces at the surface of a membrane have been quantified. For solvent mediated interactions, the potential energy of a solute molecule $\phi\sbsp{DP}{\prime}(\underline d$) at a distance $\underline d$ from the membrane surface can be obtained by combining $\Psi\sb{DP}$ and $\kappa\sp\prime$ and the Stokes-Einstein radius a$\sb{s}$ of the solute as follows:$$\phi\sbsp{DP}{\prime}(\underline d) = -\Psi\sb{DP}\ a\sb{s}\ e\sp{-\kappa\sp\prime(\underline{d}-a\sb{s})}$$ A method to evaluate $\Psi\sb{DP}$ from simple permeation experiments and $\kappa\sp\prime$ from direct force measurements is given. This approach permits the decoupling of solute size and solute-membrane material interactions in predicting separation. The inverse of $\kappa\sp\prime$ was found to be approximately equal to the diameter of a solvent molecule. A linear correlation was obtained between the square root of $\Psi\sb{DP}$ and the solubility parameter $\delta\sb{SP}$ for all solutes tested in this work. The slope of this correlation reflects the ability of the membrane material to structure water dipoles at a solid-liquid interface. The ordinate's intercept of this correlation was equal to the solubility parameter of the solvent which implies that steric solute interactions $(\Psi\sb{DP}\to 0)$ occur when $\delta\sb{SP}$ of the solute approaches that of the solvent. The results of this study indicate that a solute molecule can penetrate hydrated layers of solvent at the surface of a material to different extents depending on its size and solvent compatibility. These findings are assumed to be applicable to reverse osmosis transport and indicate that if a membrane material is to be used in RO it must be capable of structuring solvent molecules at its surface. Several parametric studies were performed using the surface force pore flow (SFPF) model to determine the exact shape of the velocity profile in the membrane pore under conditions of solute adsorption and rejection. These studies were performed at various feed concentrations and values of $\lambda$ for polyethylene glycol, of molecular weight 1000, and casein. The shape of the solute separation vs. solute radius curve was studied parametrically as a function of pressure for four restricted transport models. The shape of this curve was also determined, using a radially dependent pore model (RDPM), for adsorptive and repulsive van der Waals interactions, electrical double layer (DLVO) interactions, increased viscosity in the membrane pore and effects of chain permeability and the shape of the interacting surface. Morphological reasons are given for the general inability to reduce the pore radius of cellulose membranes below 1.5 nm. Viscometric measurements performed on cellulose casting solutions indicate that the dissolved elements of the solution exist as rigid, rod-like structures. It is proposed, that the pore size of cellulose membranes be limited by the regular occurrence of indentations on the protofibril surface and by stacking limitations, enhanced by the geometry of the protofibrils. This interpretation is conform with the folded ribbon model of a cellulose protofibril described in the literature