(297h) Correction for Sample Conductance in the Measurement of the Zeta Potentials of Porous Samples by the Rotating Disk Technique

The zeta potentials of porous materials are important quantities for post chemical mechanical planarization processes in which highly porous brushes clean particles and debris from wafers after planarization.  It is particularly important to know the zeta potential in order to design the brush material to repel particles removed from the wafers.  If the particles electrostatically adsorb on the brush material, the effectiveness of the brush declines and the potential for scratching the wafer increases.

The use of the rotating disk geometry for determining the zeta potential of porous materials is the topic of this contribution. The zeta potential of  a non-porous material is determined from streaming potential measurements acquired near a planar disk sample affixed to the end of a spindle and rotated. The theory underlying the method makes use of the well established hydrodynamics of the rotating disk.¹

While the rotating disk approach was originally developed for determination of the zeta potential of planar disk-shaped samples, it has been found that an amplified streaming potential is measured when the sample is porous. For example, one measures several mV of streaming potential in the vicinity of a disk-shaped porous quartz frit rotating on its axis in 1 mM electrolyte. Naïve application of the theory developed for planar surfaces gives absurdly large apparent zeta potentials. A new theory of the streaming potential caused by a rotating porous body,² based on hydrodynamics developed for a rotating filter,³ was applied to the experimental results. The exercise showed that the large streaming potentials were clearly related to the porosity of the sample; a predicted dependence of the streaming potential on the square of the rotation rate was confirmed. It was found that the permeability of the quartz frit could be found, but the magnitudes of the zeta potential determined from the theory were now much too small.

The shortcoming of the new theory was neglect of the sample conductance. The sample provides a channel for leakage of streaming current from the periphery backwards, much like surface conductivity provides a path for streaming current to flow back to its origin without contributing to the streaming potential.   Analytical and numerical analysis of the streaming potential near a rotating porous sample of finite thickness reveals that two parameters control the short-circuiting.  The first is the ratio of the sample thickness to the sample radius. The second parameter is the ratio of the conductance of the porous layer to the conductance of the electrolyte, given by s_ph/s_ea, where s is ionic conductivity, p denotes the porous sample, e denotes the liquid electrolyte, h is the sample thickness, and a is the sample radius.  When the dimensionless sample thickness is less than 0.2 and the conductivity parameter is less than 0.01, the short-circuiting of the streaming current is small and the analytical solution provides a good result. Larger values of these parameters mean that correction for leakage of streaming current leakage is necessary.   For example, the streaming potential measured in the vicinity of a 25 mm diameter porous quartz frit (porosity = 0.5) that is 5 mm thick is only about 50% of what is expected if the short circuiting effect is neglected.

1. P. Sides, J. Newman, J. Hoggard, D. Prieve, "Calculation of the Streaming Potential Near a Rotating Disk," Langmuir, (2006) 22 9765-9769.
2. P. Sides, S. Mukka, D. Prieve, “Measurement of the zeta potential of open porous structures by means of a sample rotating on its axis,” AIChE Annual Meeting 2011, Minneapolis, MN. 18OCT2011.
3. Joseph, D. D., “Note on Steady Flow Induced by Rotation of a Naturally Permeable Disk,” Quart. J. Mech. Appl. Math. (1965) 18 325-331.