Particle/solution interactions

The particle/solution interactions of REEs have attracted the attention of a number of workers trying to model the REE pattern of seawater or groundwaters (e.g., Turner et al, 1981 Erel and Stolper, 1992 Byrne and Kim, 1990). Ereshwater systems are more complex and, as of early 2000s, no model taking into account complexation by colloids, surface adsorption and complexation by inorganic ligands has been attempted. The question of the adsorption of REEs onto suspended solids in freshwaters has been addressed by Elderfield et al. (1990) and Sholkovitz (1995). 

Equations 1 and 2 indicate that the diffusiophoretic velocities of a particle are independent of the particle size and shape (and there is no rotational motion of the particle). However, their validity is based on the assumptions that the local radii of curvature of the particle are much larger than the thickness of the particle-solute interaction layer (diffuse layer) at the particle surface and that the effect of polarization (relaxation effect) of the diffuse solute species in the interfacial layer due to nonuniform osmotic flow is negligible. Important advances have been made in the past in the evaluation of the diffusiophoretic velocities of colloidal particles relaxing these assumptions and will be discussed below. 

On the other hand, the extension of Eqs. 5 and 11 to the diffusiophoretic velocity of spheroidal [4] and cylindrical [3, 5] particles with thin but polarized particle-solute interaction layers was also derived. A remarkable feature was found that the diffusiophoretic velocity of a long circular cylinder in a transversely applied solute gradient is exactly the same as that of a sphere with an equal radius, given by Eqs. 5 and 11. 

For the case of diffusiophoretic motion of a colloidal sphere of radius a with a thin but polarized particle-solute interaction layer in a gradient of nonelectrolyte solute, the... 

As developed in sect. 6.2, Sholkovitz et al. (1994) noted that there is systematic fractionation between the surface coatings of suspended particles and filtered seawater (fig. 17). Observation of surface coatings allows insight into particle/solution interactions responsible for fractionation. Vertical profiles of the La/Nd and La/Yb ratios of filtered... 

In summary, the distinct Nd isotopic composition of the major ocean basins and the rivers feeding these basins make Nd unique amongst other tracers. This feature has been exploited as provenance indicators of wind- and ocean-bome sediments, as tracers for water circulation within and between ocean basins and as probes for particle-solution interactions in seawater. Reliable values for ocean residence times of the lanthanides are still needed. The inter-oceanic differences in Nd isotopic composition suggest short residence times whereas river/estuarine studies points to long residence times. This dilemma has lead to the hypothesis that Nd (and other lanthanides) are being added to the oceans from the sediments. 

The Stokes-Einstein equation has already been presented. It was noted that its vahdity was restricted to large solutes, such as spherical macromolecules and particles in a continuum solvent. The equation has also been found to predict accurately the diffusion coefficient of spherical latex particles and globular proteins. Corrections to Stokes-Einstein for molecules approximating spheroids is given by Tanford. Since solute-solute interactions are ignored in this theory, it applies in the dilute range only. 

If a substance is to be dissolved, its ions or molecules must first move apart and then force their way between the solvent molecules which interact with the solute particles. If an ionic crystal is dissolved, electrostatic interaction forces must be overcome between the ions. The higher the dielectric constant of the solvent, the more effective this process is. The solvent-solute interaction is termed ion solvation (ion hydration in aqueous solutions). The importance of this phenomenon follows from comparison of the energy changes accompanying solvation of ions and uncharged molecules for monovalent ions, the enthalpy of hydration is about 400 kJ mol-1, and equals about 12 kJ mol-1 for simple non-polar species such as argon or methane. 

Solute molecules which diffuse into the stationary phase particles and interact with them are left behind by those molecules that bypass the stationary phase. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

Electrostatic fluidized-bed coating, 7 55-56 Electrostatic forces, 9 569, 570 11 800 and adsorbent selectivity, 1 584 in adsorption, 1 583 in solvent-solute interactions, 23 91-92 Electrostatic particle forces, in depth filtration theory, 11 339 Electrostatic precipitators (ESP), 11 714 13 180 23 552 26 699-706 advantages of, 26 700 applications of, 26 701-703, 705t design considerations related to,... 

Several different approaches can be used to model the interaction of solutes with reactive mineral surfaces. The conceptual approaches differ in the degree to which they account for observed or postulated solution and surface reactions. Whatever the approach, the description of interactions at the particle/solution interface must inevitably take into account the effect of pH on solute adsorption. 

General Observations About x. its Relationship to the Overall Partitioning Coefficient and to the Concept of Surface-Site Heterogeneity. One approach to metal/particle surface interactions which has been developed, historically, in a variety of forms, is a conceptual model that assumes only two conditions for surface sites occupied by an adsorbate or unoccupied. In applying this approach to the solid/aqueous solution interface, the adsorption... 

In a solntion, the solnte particles (molecules, ions) interact with solvent molecnles and also, provided the concentration of the solute is sufficiently high, with other solnte particles. These interactions play the major role in the distribution of a solnte between the two liquid layers in liquid-liquid distribution systems. Conseqnently, the nnderstanding of the physical chemistry of liquids and solntions is important to master the rich and varied field of solvent extraction. 

In Section 3.4a we examine a model for the second virial coefficient that is based on the concept of the excluded volume of the solute particles. A solute-solute interaction arising from the spatial extension of particles is the premise of this model. Therefore the potential exists for learning something about this extension (i.e., particle dimension) for systems for which the model is applicable. In Section 3.4b we consider a model that considers the second virial coefficient in terms of solute-solvent interaction. This approach offers a quantitative measure of such interactions through B. In both instances we only outline the pertinent statistical thermodynamics a somewhat fuller development of these ideas is given in Flory (1953). Finally, we should note that some of the ideas of this section are going to reappear in Chapter 13 in our discussions of polymer-induced forces in colloidal dispersions and of coagulation or steric stabilization (Sections 13.6 and 13.7). 

Solvation is a process in which solute particles (molecules or ions) in a solution interact with the solvent molecules surrounding them. Solvation in an aqueous solution is called hydration. The solvation energy is defined as the standard chemical potential of a solute in the solution referred to that in the gaseous state.11 The solvation of a solute has a significant influence on its dissolution and on the chemical reactions in which it participates. Conversely, the solvent effect on dissolution or on a chemical reaction can be predicted quantitatively from knowledge of the solvation energies of the relevant solutes. In this chapter, we mainly deal with the energetic aspects of ion solvation and its effects on the behavior of ions and electrolytes in solutions. 

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