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Comments on ‘Diffuse double-layer models, long-range forces, and ordering of clay colloids’
Dep. of Crop and Soil Sciences Cornell University Ithaca, NY 14853
mbm7{at}cornell.edu
We are grateful to Professor Quirk for the interest he has shown in our article, and for the comprehensive exposé he provides of a number of traditional views on clay aggregation, swelling, and stability in soils. Much of this exposé deals with clay domains, and is therefore not directly relevant to the scope of our original article. Nevertheless, we appreciate the opportunity that is given to us to pursue one step further the reflection started in our article.
In our paper, 
Diffuse double-layer models, long-range forces, and ordering in clay colloids,
(McBride and Baveye, 2002) we wanted to emphasize the most current developments in colloid science and focus on the issues about which current theory and experiment deviate from generally accepted views of the past. A review of the immense literature in this field would have been impossible, but we did hope to redress in a small way the lack of attention among clay and soil scientists that the Coulombic attraction theory received since its presentation by Langmuir (1938), despite its revival with supporting experimental results over the past few decades.
We do not take issue with Dr. Quirk's assertion that the Coulombic attraction (Sogami-Ise) theory, the main focus of our article, has limited relevance to the structure of clay domains in soils. However, to put things in the right perspective, we would like to re-emphasize that no diffuse double layer theory, DLVO and the Coulombic attraction theory included, can properly describe the behavior of condensed silicate clay phases on which Dr. Quirk focuses in his comment. These theories are only relevant to dispersed systems in which particle separations are many times the molecular dimensions of water molecules; otherwise, hydration forces play a dominant role. This means that the exchange of Na+ ions on smectites by Ca2+, with consequent contraction of the interlayer spacing to about 1.0 nm, creates a condensed quasi-crystalline phase that must be described by stronger short-range forces. The generally accepted theory is one in which hydration of Ca2+ counterions and surfaces create a repulsive pressure that is balanced by strong electrostatic attraction across the mid-plane of the interlayer. Our only disagreement with Dr. Quirk on this explanation is whether it is necessary to invoke a fluctuational Ca2+ ion-ion correlation force (Kjellander et al., 1988) to generate this electrostatic attraction. The assumption of Kjellander et al. (1988) is that, because of symmetry, the electrostatic forces across the clay interlayer's mid-plane are balanced, so that the static view of the Ca2+–layer silicate system has no contraction (bridging) force resulting from the Ca2+ cations' attraction for the negatively charged silicate sheets. Yet, the bridging force created by Ca2+ and other polyvalent cations in drawing together anionic macromolecules is widely accepted in biochemistry (e.g., Huster and Arnold, 1998), and has also been advocated to play a significant role in the attraction of inorganic colloids (e.g., Israelachvili and Adams, 1978; Parker, 1985).
In our view, then, a reduction of the d-spacing of Ca2+–smectite would lower the electrostatic energy of the system in a manner analogous to the lowering of the electrostatic energy in three-dimensional ionic lattices as described by the Born-Landé equation (Langmuir, 1938). In fact, van Olphen (1977) gave the equation for the attractive electrostatic energy, 
E, for two negatively charged layers with a layer of cations mid-way between as
 |
is the dielectric constant, x is the interlayer spacing, and 
is the layer charge density. Thus, as the spacing, x, is decreased, the electrostatic potential is decreased.
Although Kjellander et al. (1988) predicted a potential energy minimum in Ca-smectite at the actual measured d-spacing (around 1.9 nm), this may not be a robust test of the importance of their ion-ion correlation force in holding the layers together. The Ca2+–smectite d-spacing appears insensitive to extreme environmental conditions, such as high temperature and pressure (Wu et al., 1998). We have observed no measurable change in the 1.9 nm spacing of Ca2+–smectite in the presence of excess water as the temperature was raised by 50°C or more (M. McBride, unpublished data. 1995). These facts would suggest that the potential energy well is much deeper than kT (thermal energy), preventing the Ca2+–clay d-spacing from expanding at higher temperature. The d-spacing is therefore not very sensitive to the magnitude of the electrostatic attraction force, as it is stabilized by the strong barrier to collapse below 1.9 nm, due to a steep rise in the opposing hydration forces of Ca cations as silicate layers move closer together. The barrier to collapse is enhanced by reduced entropy of the system as the hydrated Ca2+ ions are forced into less rotationally mobile states in the restricting interlayers.
The main part of our paper dealt, not with these short-range forces in quasi-crystalline clays, but with the long-range forces occurring in colloidal dispersions. Ten or 20 yr ago, one might have questioned the relevance of such long-range forces between clay particles in soils. However, in the intervening years, significant research has shown the practical importance of clay particles in, for example, the facilitated transport of a range of chemicals (McCarthy, 2002; McGechan and Lewis, 2002), a process in which the transition from flocculation to medium- and long-range spacings between clay particles undoubtedly plays a significant role. It is in this context in particular that interest in long-range interactions between soil colloids finds its justification. Additional stimulus is provided by the fact that the classical theory of colloid flocculation/dispersion in soils, described by Quirk, suffers from a number of well-documented flaws. For example, the standard DLVO model of clay flocculation is at odds with the spontaneous dispersion of clays at low ionic strength or high SAR value because the flocculated system is assumed to reside in a deep primary energy minimum (van Olphen, 1977). A number of other features of the classical theory of clay flocculation/dispersion in soils are also in question. Among them, the edge-to-face layer silicate clay interaction, referred to by Dr. Quirk as an important contributor to the flocculation process, is no longer accepted to be a valid description of flocculated clay domains as face-to-face attraction is the prevalent force in condensed layer silicate phases (Ben-Rhaïm et al., 1987).
Experimental evidence shows that long-range ordering in colloidal dispersions (in directions other than that of the gravitational field) can only be explained by long-range electrostatic attraction delicately balanced by a repulsive osmotic force, contrary to the standard DLVO model. Historically, spontaneous liquid-crystalline behavior was observed for the first time in tactoid and Schiller layer formation (Langmuir, 1938), but more recently has been observed with dilute like-charged spherical latex particles. The large (µm-scale) distances between colloids means that the forces involved in the ordered phases cannot be surface hydration or van der Waals dispersion forces. There is considerable experimental evidence for a long-range electrostatic attraction (e.g., Crocker and Grier, 1996; Smalley, 1990; Ise et al., 1990; Ito et al., 1994). The physical explanation for this attraction is simply the redistribution of counter-cation swarms around the negatively charged colloids to produce a net attractive force between the like-charged particles. The balance of attractive (electrostatic) and repulsive (osmotic) forces is delicate, however, and the attractive energy at particle separation distances of microns is only a few kT units. Consequently, reversible phase transitions from the ordered arrays in suspension to a disordered state may occur with a slight rise in temperature. The fact that voids form in colloidal dispersions as particles cluster into ordered arrays is direct evidence of the failure of the DLVO model, as this model assumes that only repulsive interparticle forces operate at these distances, and therefore particles should always repel and uniformly occupy the total volume of the suspension. In contradiction to this, it is common for presumed homogeneous dispersions to have ordered domains or clusters, and therefore to have voids as well (Ise et al., 1999).
Recent observations indicate that the confinement of like-charged colloids in small solution volumes may favor particle attraction (Crocker and Grier, 1996). Nikolaides et al. (2002) very recently observed that like-charged methacrylate colloidal particles confined to an oil-water interface formed a stable ordered array with a relatively long interparticle spacing of 5.7 µm, indicating a long-ranged attractive interaction. The potential energy minimum holding these particles in a hexagonal array was 
3 kT units, sufficient to maintain order in a 7-particle cluster for more than 30 min. Although these authors hypothesized a novel capillary force to explain the attraction, we suspect that further experiments on colloid behavior at interfaces may implicate long-range Coulombic attractive forces. It is reasonable to suggest that confinement of particles, by reducing degrees of freedom of particle motion, shifts the balance of forces to favor electrostatic attraction over entropy (osmotic pressure), and favors ordered arrays.
Sogami and Ise (1984) provided a theoretical framework for the long-range attractive and repulsive forces in like-charged colloidal dispersions. This Coulombic attraction theory has raised controversy by challenging the long-accepted DLVO theory. We do not agree with Dr. Quirk that Overbeek's 1987 and 1993 critiques of the Coulombic attraction theory exposes significant errors in the theory. In fact, Overbeek's arguments were countered by Smalley (1990) and Ise et al. (1990); the two sides of this debate are also discussed by Schmitz (1993). It is apparent from the arguments presented that Overbeek misapplied the Gibbs-Duhem equation, and therefore reached an invalid conclusion. Despite Dr. Quirk's implication that the Sogami-Ise theory has been discredited for some time, the original Sogami and Ise (1984) paper has been cited over 200 times, and the citation rate has increased in recent years.
Dr. Quirk's statement that Petris and Chan (2002) successfully treated the formation of a liquid crystalline phase without recourse to the Coulombic attractive theory is misleading. These authors calculated from the mean spherical approximation that in an idealized colloidal dispersion, the bare Coulomb repulsion between the colloid-colloid species and between the ionic species of the same valence are outweighed by the bare Coulomb attraction between the colloid-counterion species and ions of opposite valence. That is, the Coulombic contribution to colloid pressure is always negative and contributes to a destabilization of dispersions, a description that is essentially the same paradigm adopted by Langmuir (Petris and Chan, 2002). Petris and Chan suggest that the Coulombic attractive force is a possible explanation for the observed phase separation in monodisperse colloids. This explanation for reversible phase transitions in colloids is substantively the same as that of Ise and coworkers, attributable to the counterion-mediated attraction among like-charged colloids.
Current debates about which diffuse double layer theory is most correct, as we are reminded by Smalley (1990), miss a basic principle of science, that experiment is the sole judge of scientific truth (Feynman, 1963). The experimental evidence is now convincing that a long-range electrostatic attraction exists in dispersions of like-charged colloids.
As a last point, we would like to reiterate a side remark made in our original article, namely that one should exert caution in applying the Coulombic attraction theory to the real colloids found in soils. There are numerous reasons for this, as we alluded to in our paper, including the complex interactions of particles of different surface chemistry and charge, and the fact that the relatively dilute mono-disperse like-charge colloidal systems in which diffuse double layer theories can be tested (e.g., Na+–smectites) are too idealized to represent situations encountered by clays in most soils, where clay particles are typically partially weathered and covered with various mineral or organic phases, like amorphous oxides or organic matter. Nevertheless, diffuse double-layer models, like the Coulombic attraction theory, are potentially useful in understanding the forces driving spontaneous clay dispersion in soils, as described by Dr. Quirk, and therefore a number of related important phenomena (e.g., facilitated transport of contaminants). The fundamental forces contributing to flocculation, dispersion, and ordering in simple model colloid systems must be understood before progress can be made in understanding the much more complex soil-water system.
REFERENCES
homogeneous dispersions? Counterion-mediated attraction between like-charged species. Langmuir 15:4176–4184.
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