Langmuir 1988,4, 611-626
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Colloid Vibration Potential and the Electrokinetic Characterization of Concentrated Colloids B. J. Marlow* and D. Fairhurst Pen Kem, Inc., 341 Adams St., Bedford Hills, New York 10507
H. P. Pendse Chemical Engineering Department, Urtiversity of Maine, Orono, Maine 04469 Received January 23, 1987. I n Final Form: November 25,1987 Subjecting charged colloidal particles to a compressional sound wave gives rise to a periodic polarization of the ionic atmosphere surrounding the particles. This periodic polarization causes each particle to act as a vibrating dipole resulting in an alternating voltage, termed the colloid vibration potential (CVP), between any two points in space separated by a phase distance other than an integral multiple of the wavelength and normal to the propagation direction. The present work shows that the CVP is analogous in many respects to the Dorn effect (sedimentation potential) and reflects the same intrinsic phenomena where double-layer relaxation is the dominant process. Both Smoluchowski’s theory of the Dorn effect and Ehderby’s treatment of a charged particle in a sound field are reviewed. Expressions are presented showing the relationship of the CVP to the I; potential for dilute colloids. It is also shown how the theory can be extended to particle concentrations as high as 50% by volume using the Levine et al. cell model theory. An apparatus for making electrokinetic measurements using continuous wave ultrasonics is described in detail. Data are presented comparing mobilities obtained from CVP measurements and microelectrophoresis. Data are also shown for the dependence of the CVP on particle concentration and compared to predictions based on the proposed modifications using the cell model theory. Also included are data showing the versatility and advantages of acoustical electrokinetic techniques over conventional methods.
Introduction Electrokinetic measurements have long been used to probe interfacial phenomena and the stability of colloidal systems. Below we describe the use of acoustics in the ultrasonic frequency range in making electrokinetic measurements. As shown in this work, acoustics offer distinct advantages over conventional electrokinetic techniques such as microelectrophoresis, namely: (i) colloids containing particles with sizes ranging from a few nanometers to several micrometers can be analyzed, (ii) samples having a wide range of particle concentration can be measured, from the ppm range (which overlaps with conventional electrokinetic techniques such as microelectrophoresis) to essentially volume-filling systems, i.e., up to 75% by weight particles or greater, (iii) measurements can be made in flowing streams relevant to on-line applications, (iv) opaque or photosensitive materials can be analyzed because no optical imaging is required, and (v) mobile living organisms can be analyzed. In 1933 Debyel predicted that a compressional ultrasonic sound wave passing through an electrolytic solution would result in alternating potentials having the same frequency as the sound wave between any two points normal to the sound wave and separated by a distance other than an integral multiple of the wavelength or (2n 1)X/2. The basis of the “Debye effect” is that the dynamic reactions of ions in an ultrasonic field will be different for ions of different masses. These differences result in different displacement amplitudes and phases between anions and cations. The relative displacement of anions and cations produces a separation of charge accompanying the sound wave resulting in potential differences. The mechanism of the Debye effect and the resulting alternating potential, termed the ion vibration potential (Np), are shown pictorially in Figure 1. The figure shows the displacement of anion and cation produced by the sound wave at a particular instant along the direction of propagation. The arrows represent the respective dis-
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*Author to whom all correspondence should be addressed.
placements. As depicted, the anion is displaced to a greater extent than the cation. The net effect is that region A will have a negative potential and region B a positive potential. If two electrodes are placed a t points A and B, the IVP can be measured. Measurements of the IVP lead to information about the effective masses and nature of the ions producing the effect. Debye considered only frictional, dynamical, and electrical forces acting on the ions. The original theory of Debye has since been modified to account for electrophoretic, relaxational, and pressure gradient forces2 and experimentally verified, a review of which can be found in ref 3. Modification of Debye’s original theory shows that the IVP results not from the masses of the ions alone but rather their effective masses, Le., the ionic masses minus the mass of the free displaced solvent. Thus, for ordinary electrolytes the effect yields information about differences in partial molar volumes and not strictly the differences in ionic masses. In 1938 Hermans4p5and Rugers6J reported an effect similar to the Debye effect when ultrasonic waves were propagated through a colloidal system. In contrast to the IVP,where the relative displacement of anions and cations produces an alternating potential, the displacement of a charged particle from its surrounding “ion atmosphere” induces a similar alternating potential termed the colloid vibration potential (CVP). Typically, the CVP is orders of magnitude grater than the IVP. Theoretical treatments of the CVP have been presented by her man^,^^^ Rutgers?,’ Enderby,* and Enderby and Booth: all of whom consider an “isolated” colloid particle or colloidal system as having low particle concentrations. Theory indicates that the CVP is dependent on the { poDebye, P. J . Chem. Phys. 1933,1,13. Bugoeh, J.; Yeager, E.; Hovarka, F. J.Chem. Phys. 1947,15(8),542. Zana, R.; Yeager, E. Mod. Aspects Electrochem. 1982,14, 1. Hermans, J. Philos. Mag. 1938,25, 426. (6) Hermans, J. Philos. Mag. 1938,26,674. (6)Rutgers, A. Physica 1938,5,46. (7)Rutgers, A. Nature (London) 1946,157, 74. (8)Enderby, J. R o c . Phys. SOC.l951,207A,321. (9)Booth, F.; Enderby, J. hoc. Phys. SOC.1952,208A,351.
0743-7463/88/2404-0611$01.50/00 1988 American Chemical Society
612 Langmuir, Vol.4,No. 3, 1988
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Figure 1. Ion vibration potentials (IVPs). Separation of equilibrium charge densities due to ultrasonic disturbances leads to an oscillatory potential at points A and B having the same frequency as the ultrasonic source. tential, concentration and nature of the particles, frequency
of the acoustic wave, and supporting electrolyte nature and concentration. The first experimental work on the CVP was performed by Yeager et al.'*12 on silica suspensions. Since that time many diverse colloidal systems have been studied acoustically including polyelectrolytes,ls cellulose fibers,14 and micellar systems.16 The objective of this work is to present expressions relating the CVP to the 5 potential and to provide perspective as to how the CVP can be quantitatively described in concentrated colloidal systems. It is shown how the CVP and the Dorn effect or sedimentation potentidle are analogous and reflect the same intrinsic phenomena. The analysis further shows how the CVP in dilute colloidal systems can be explained by classical electrokinetic theory first described by Smoluchowski," the final result being the same under the appropriate conditions as that obtained by the rigorous treatment of Enderbf and Enderby and Booth.v Furthermore, it is shown how the dilute theory can be extended to concentrated systems via the Levine and co-worker's cell model theory of this sedimentation potential.18 An apparatus employing continuous wave electronics for measuring colloid vibration potentials is described in detail, and experimental data are presented verifying both the dilute theory and the relevance of the cell model approach to the CVP in concentrates. Also included are data showing the versatility and advantages of acoustical electrokinetic techniques over conventional methods. Theory Spherical Particles i n a S o u n d Field. Consider a colloid containing rigid spherical particles a t a concentration less than 1?% by volume. Under such conditions the distance between particles is much greater than the particle size, and the particles can be treated as "isolated" from one another; hence, particleparticle interactions can be neglected. When this colloid is subjected to a monochromatic plane progressive sound wave where the wavelength X is much greater than the particle radius a,i.e., 2 ~ a l X
