Determination of Pore Radius Distribution of Porous Polymeric Membranes by Electron Microscopic Method

Abstract

An attempt was made to establish a method for evaluating the pore characteristics of porous polymeric membrane having the mean pore diameter larger than 10 nm through electron micrograph with help of stereology (EM method). For this purpose, ellipsoidal, spherical, and straight-through cylindrical pore models were adopted. Theoretical equations relating the pore radius distribution function N(r) to the distribution function F(x) of the length x of test lines cut off by pores in an electron micrograph were derived as follows;

Some Morphological Characteristics of Porous Polymeric Membranes Prepared by “Micro-Phase Separation Method”

“…The lengthy, cut·off with pores, of the test line was measured and the distribution function of y, F(y), was evaluated. Under the assumptions that the cylindrical pores dispersed randomly within a thin section and the dispersed state was homogeneous in this section, F(y) was converted to the pore radius distribution N(r) with the help of the stereology by the method proposed by Manabe et al 5 From N(r), the i-th mean pore radius, for example, can be calculated.…”

“…In this article, an attempts were made to prepare a series of very thin (at most, 1 Jlm) sheets by slicing the MF membrane with a diamond knife in parallel to the surface and to evaluate the pore radius distribution N(r) as a function of Z, by applying the EM method proposed so far 5 and to show that the development of the layer structure is theoretically explained by comparing the observed N(r) with the theoretical N(r), calculated from experimental S 2 and R values.…”

Thermodynamics of Formation of Porous Polymeric Membrane by Phase Separation Method IV. Pore Formation by Contacting Secondary Particles: Computer Simulation Experiments

“…26, No. 5,1994 subsequent piling-up of the collapsed layers. Therefore, membrane in actual use can be approximately regarded as the membrane which is produced by single step under R :-;:; I.…”

Probabilities of Finding Isolated, Semi-Open, and Through Pores in Porous Polymeric Membrane Prepared by Micro-Phase Separation Method

“…That is, eq 2 holds (2) Equation 2 indicates that if two of these three probabilities and P,e are known in advance, the remaining probability can be readily evaluated.…”

“…The validity of their theory was experimentally confirmed for cellulose cuprammonium solutions and cellulose membranes regenerated from them: The pore size distribution N(r) (r, pore radius) of the regenerated cellulose membrane surface, indirectly· estimated by the theory using the two-phase volume ratio of the phase separated solution and ·the average diameter of the secondary particles constituting the membrane cast from the solution, agrees fairly well with the pore size distribution directly determined by the electron microscopic (EM) method proposed before. 2 The phase-separation proceeded from the top to bottom surface for the case of cellulose cuprammonium solution. 3 Although the overall supermolecular structure changes significantly depending on the distance Z from the top surface of the membrane, it was ascertained that within a given thin layer with constant Z the particular supermolecular structure of the layer remained almost uniform.3 Accordingly, N(r) for each portion of the ultra-thin layer was constant for a given Z. These experimental facts clearly lead us to the following concept that the porous polymeric membrane prepared by the micro-phase separation method should be considered as a composite, in which many hypothetical ultrathin layers are piled up and when the polymer concentration is lower than the critical concentration, the ultra-thin layer is twodimentionally composed of many small particles.…”