W. Richard Bowen and Nidal Hilal 4

4.3 CORREsPONdENCE bETwEEN sURFACE PORE dIMENsIONs FROM AFM ANd MwCO 115
expressions. Depending on the expression used, the ratio of the mean pore
diameters obtained from MWCO data and AFM measurements was in the
range 1.04–2.42. Agreement between the diameters obtained in the two ways
was best for the membranes with the lowest MWCO values. The two measurements
are probing the membrane properties in different ways, but the
overall correlation is encouraging.
However, AFM has the important advantage of providing a measure
of pore size distribution. This is indicated in Table 4.2 by the
standard deviations. A full distribution for one of the membranes is given
in Figure 4.9.
Knowledge of such distributions is very important if the membrane is
to be selected for a fractionation process, where a narrow distribution is
highly desirable. Further, theoretical modelling to predict membrane process
performance often assumes a log-normal distribution of pore sizes.
Figure 4.9 shows that this is a reasonable assumption in this case.
TAbLE 4.1 surface Characteristics of desal g Membranes Over Areas of
3 �m � 3 �m (R p−v, Peak to valley distance; Rms, Root-Mean-square).
Membrane MWCO R p–v (nm) Rms roughness (nm)
GE 1000 26.6 3.6
GH 2500 58.7 8.4
GK 3500 53.9 8.4
GM 8000 63.7 9.2
GN 10 000 88.1 11.7
TAbLE 4.2 Pore diameters for desal g-series Membranes Obtained from AFM
Measurements and MwCO.
AFM mean pore
diameter Mean pore diameters from MWCO (nm)
Membrane (nm) * Ex. 1 Ex. 2 Ex. 3
GE 1.8 (�0.3) 1.9 2.4 2.0
GH 2.2 (�0.5) 2.6 3.8 3.2
GK 2.5 (�0.5) 3.0 4.4 4.2
GM 2.8 (�0.7) 4.4 6.4 6.8
GN 3.1 (�0.9) 4.8 7.2 7.6
* Numbers in brackets are standard deviations.