DLVO Lifshitz

Correspondence with the DLVO-Lifshitz Theory of Colloid Stability... 

Adsorption of enteric viruses on mineral surfaces in soil and aquatic environments is well recognized as an important mechanism controlling virus dissemination in natural systems. The adsorption of poliovirus type 1, strain LSc2ab, on oxide surfaces was studied from the standpoint of equilibrium thermodynamics. Mass-action free energies are found to agree with potentials evaluated from the DLVO-Lifshitz theory of colloid stability, the sum of electrodynamic van der Waals potentials and electrostatic double-layer interactions. The effects of pH and ionic strength as well as electrokinetic and dielectric properties of system components are developed from the model in the context of virus adsorption in extra-host systems. 

Application of DLVO Theory. Our approach to determine the contribution of double-layer interaction and van der Waals potentials to AGads involves comparing differences in the magnitudes of AGads found on the same solid but with different solution conditions, to potentials (U), or theoretical free energy components, evaluated from the DLVO-Lifshitz theory of colloid stability. 

To evaluate DLVO-Lifshitz potentials we approximate the highly complex interaction of a spherical-icosahedral, deformable virus adsorbing to a real surface (Figure 1) with sphere-plate models (Figure 5). The complex real interactions, even if they were well defined, cannot be quantified by present ab initio quantum mechanical procedures. 

To adjust for errors introduced by modeling these highly complex interactions with simple geometries, we consider the characteristic interaction-separation distances in expressions derived for the models to be adjustable parameters. The DLVO-Lifshitz potentials are evaluated for characteristic distances found to fit data for Si02, where AGads and U determinations are most accurate. These distances are then used for all other solids. Since the assumptions used in the double-layer and van der Waals models (described in following sections) are quite... 

This suggests that if covalent-ionic interactions control adsorption, we could expect viruses to be strongly adsorbed to CuO, but only weakly adsorbed, if at all, to our other oxide surfaces. This is clearly inconsistent with observed trends in virus adsorption, suggesting that here, covalent-ionic interactions are not involved to any major extent, especially considering the good correspondence obtained with the DLVO-Lifshitz theory. 

We have presented considerable evidence that poliovirus type 1, strain LSc2ab, adsorbs on inorganic surfaces according to the electrodynamic and electrostatic potentials defined by the DLVO-Lifshitz theory of colloid stability. We shall now present a general discussion concerning the predicted implications these findings have in regard to the overall problem of virus transport in the environment. 

Our analysis describes virus adsorption from the standpoint of chemical equilibrium. Since adsorption equilibrium appears to be approached closely in our systems in less than or equal to 2 hr, and since the residence time of viruses in natural water systems is greater than 2 hr for many cases (for example, lakes, groundwaters, rivers, etc.), equilibrium considerations are entirely appropriate. In other situations, where residence times of the virus in the system are small compared to expected times required for adsorption to approach equilibrium (for example, sand filters in water treatment, water distribution systems, etc.), the DLVO-Lifshitz theory may still be applied directly. The work of Fitzpatrick and Spielman (57) concerning filtration and that of Zeichner and Schowalter (58) concerning colloid stability in fiow fields demonstrate this clearly. Their developments of hydrodynamic trajectory analysis coupled to DLVO-Lifshitz considerations can be extended... 

For example, dissolved carbonate species present in our 0.02 I buflFer system, predominantly CO2, H2CO3 , HCOa, COa, and various car-bonato complexes, had a marked elfect concerning adsorption to transition metal oxides. The zeta potential of CuO in 0.02 I buffer was —17.6 6.1 mV, while in 0.02M NaCl that contained only traces of total dissolved carbonate (approximately lO M), it was -f32.0 it 5.8 mV. This shows marked alteration of the electrical structure of double layers by some carbonate species. The same effects were seen to lesser extents on Fc203 and Mn02 (8). Double-layer interaction potentials calculated with zeta potentials measured in 0.02 I reaction buffers matched adsorption free energy differences well, and these potentials included the effects of carbonate species. Where effects of dissolved constituents have not been accounted for intrinsically, predictions made on the basis of the DLVO-Lifshitz considerations alone must be made with care. 

In any case, we did not attempt to predict adsorption characteristics of all viruses on all solids in any aqueous system in this study. In this discussion of environmental implications, we merely attempted to extract salient features of the importance of the DLVO-Lifshitz theory in regard to problems concerning virus adsorption. Additional implications and specialized cases will be the subjects of future investigations. 

Poliovirus adsorption to many oxide surfaces is controlled principally by the combination of electrodynamic van der Waals interactions and electrostatic double-layer interactions, as demonstrated by the excellent correspondence of the DLVO-Lifshitz theory with experimentally determined adsorption free energies. 

The DLVO-Lifshitz theory should be regarded as a principal mechanism governing the adsorption of viruses on various inorganic surfaces. This finding has direct application to problems concerning transport of viruses in aquatic systems and soils. It is possible that it could lead to the design and optimization of adsorption-filtration processes for removing viruses and other particulates from contaminated water. 

R. O. James (currently at C.S.I.R.O. Textile Physics Division, Ryde, N.S.W., Australia) is thanked for his assistance with concepts of the DLVO-Lifshitz theory Gordon Brown and Milton Kerker are thanked for their helpful comments and John L. Murray, John R. Murray, and H. H. Huang are thanked for their financial assistance. Part of the materials used in this study were purchased with a Sigma-Xi Grant-in-Aid of Research. The final phase of the project was supported by the. S. Environmental Protection Agency Grant R-8050I6. 

Fig. 4. Attractive force law deduced from forces measured between mica surfaces immersed in CTAB solutions. Each point is the difference between the measured force and the expected DLVO interaction. For comparison, from Lifshitz theory calculated van der Waals force-law for two mica surfaces and two hydrocarbon surfaces in water is shown as shaded area. Adapted from Ref. [81]. 1984, with permission from Elsevier.

Values of e, n and ve and Hamaker constants for two identical types of a material in a vacuum, which are calculated from Equation (567) by taking e3 = 1 and 3 = 1, are given in Table 7.1. Unfortunately, the lack of material constants, such as the dielectric constant, as a function of frequency for most of the substances, and also the complexity of the derived formulae have hampered the general use of the Lifshitz model. However, Lifshitz theory made possible the advent of the first theories on the stability of hydrophobic colloids as a balance between London attraction and electrical double-layer repulsion. Later, these theories were further elaborated by Derjaguin and Landau, and independently by Verwey and Overbeek. The general theory of colloidal stability (which is beyond the scope of this book) is based on Lifshitz theory and has become known as the DLVO theory, by combining the initials of these four authors. 

Figure 24 Total free energy of interaction between solid colloidal panicles inmersed in solution, obtained as a sum of three contributions electrostatic (EL), Lifshitz-van der Waals (LW). and acid-base (AB), following the extended DLVO model, (a) Spherical hydrophilic panicles of radius 2(X) run in 10 M solution of ttidlfferent I. I clcclruiyle and neutral pH potential 22 mV Hamaker constant A 10" J and AC(H ) = 5,. 4 mJ/m (b) Identical hydrophobic particles but in this case AG(ffu) = -.10 mJ/m ...

Lev Davidovich Landau (1908-1968). .. was a Soviet physicist who worked in several fields of theoretical physics, e.g. in quantum mechanics, superfluidity, and superconductivity. Additionally, he is renowned for his textbook series in physics which he created together with Lifshitz. His contribution to colloid science concerns the stability of colloids (DLVO theory). He was awarded the Nobel Prize in Physics in 1962 for his pioneering theories of condensed matter, especially liquid helium . 

In this respect the approach by Ninham and Yaminsky is much easier to use. In principle the influence of solvent structure can be taken into account within the DLVO model by using a convenient Lifshitz-like ansatz. There, all non-electrostatic interactions are taken into account via frequency summations over all electromagnetic interactions that take place in the solutions. If done rigorously, the result should be more or less exact. As a proof of principle, Bostrom and Ninham made a first attempt in this direction. The classical DLVO ansatz was replaced by a modified Poisson-Boitzmann (PB) equation, in which a simplified so-called dispersion term was added to the electrostatic interaction. In this way ion specificity came in quite naturally via the polarisability and the ionisation potential of the ions. However, it turned out that this first-order approximation of the non-electrostatic interactions was not sufficient to predict the Hofineister series of surface tension. Heavier ions such as iodide had to be supposed to have smaller polarisabilities compared to smaller ions such as chloride. Although the exact polarisabilities of ions in water are still under debate, this is not physical. 

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