W. Richard Bowen and Nidal Hilal 4

116 4. INvEsTIgATINg MEMbRANEs ANd MEMbRANE PROCEssEs
Fraction of pores counted
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
AFM distribution
Theoretical distribution
0.00
0.00
2.0 2.5 3.0 3.5 4.0 4.5 5.0
Pore diameter/nm
FIgURE 4.9 AFM pore size distribution for Desal GM membrane and theoretical lognormal
distribution.
4.4 IMAgIng In LIqUID AnD ThE DETERMInATIOn OF
SURFACE ELECTRICAL PROPERTIES
For membranes that are used in liquid systems, it is very useful to
have the possibility of imaging in a solution corresponding to the processing
conditions of pH and ionic content. An Atomic Force Microscope
gives great control of imaging protocols, allowing investigation of the
procedures that give the best membrane images, in particular the imaging
force. Figure 4.10 shows the force of interaction between an AFM tip
and a Cyclopore membrane of specified pore diameter 0.1 �m in solutions
at constant pH but varying ionic strength [6].
It may be seen that the range of the interaction increases greatly as the
ionic strength decreases in accordance with electrical double layer theory. It
is then possible to image the membrane using a force at any point on the
curves in Figure 4.10. Two series of such images, one at various forces at
constant ionic strength and the other at approximately constant force at various
ionic strengths, are shown in Figure 4.11. It may be seen that the quality
of the images improves with increasing imaging force and with increasing
ionic strength. The derived pore diameter distributions also vary with the
imaging conditions, as shown in the corresponding graphs in Figure 4.11 [7].
The reason for this variation may be understood from Figure 4.12,
which shows calculated isopotential lines for a 10 �1 M solution and a
10 �4 M solution, respectively.
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
Probability density function fR(r)