DLVO model

However, the DLVO model cannot completely explain the stabiUzation properties of imidazoUum ILs towards the lr(0) nanoparticles as it treats counterions as mono-ionic point charges and was not designed to account for sterically stabiUzed systems. Together with the electrostatic stabilization provided by the intrinsic high charge of the IL, a steric type of stabilization can also be envisaged. This is due to the presence of anionic and cationic supramolecular aggregates of the type [(BMl),t(X),( ] [(BMl),t (X)J"T where BMl is the l- -butyl-3-methyUmidazoUum cation and X is the anion. 

Now let us see how this result is to be understood in terms of the DLVO theory. At first glance, it seems remarkable that any consistency at all can be found in tests as arbitrary as the CCC determination. It is not difficult, however, to show that these results are quite close to the values predicted in terms of the DLVO model for interacting blocks with flat faces. From an inspection of Figure 13.8, we concluded that the system at k = 108 m l would be stable with respect to coagulation, whereas the one at k = 3 108 m l would coagulate. Furthermore, we examined the energy barrier to draw these conclusions. Next we must ask how the qualitative criteria we used in discussing the curves can be translated into an analytical expression. 

The stability ratio decreases with the increase in the radius of the rigid core of a particle. This is consistent with the DLVO model together with the Fuches theory [8] for the case of rigid particles, and with the result obtained by Taguchi et al. [12] for ion-penetrable particles at low electrical potentials. 

How was the theoretical DLVO curve in Figure 1.12 obtained The DLVO model [18, 19] postulates that the appropriate thermodynamic potential energy of interaction between two parallel flat plates can be described in terms of two components a repulsive term VR, resulting from the overlap of electrical double layers, and an attractive van der Waals interaction, VA. It also assumes that these interactions are additive, so that the total potential energy can be written as... 

In contrast to what is clear from the DLVO model, early classical models of aggregation are based on an assumption that interparticle interactions are negligible until the particles contact. This contact then is assumed to result in adhesion 100% of the time. However, as particles are attracted together the fluid in the intervening space must be ejected, creating a hydrodynamic response in the particles, such as rotation. Neglect of... 

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 ...

Hildreth OJ, Rykaczewski K, Federov AG, Wong CP (2013) A DLVO model for catalyst motion in metal-assisted chemical etching based upon controlled out-of-plane rotational etching and force-displacement measurements. Nanoscale 5 961-970... 

The classic DLVO models are for flat planes and spheres, but more complex shapes arise in practice. For example, there will be some distortion of originally spherical emulsion droplets as they approach each other and begin to seriously interact, causing a flattening. The model has been extended to systems with particles that differ in size, shape, and chemical composition (64,65), and to those with particles that have an adsorbed layer of ions (7,8,10,11,31,35,64-66), as depicted in Figure 2. 

The DLVO model (named after its principal creators, Deqaguin, Landau, Verwey and Overbeek) is the most widely used to describe inter-particle surface force potential (1,2). It assumes that the total inter-particle potential is the sum of an attractive van der Waals force and a repulsive double-layer force. The repulsive force due to the double-layer coulombic interaction between equal spheres separated by a distance D generates a positive potential energy Vr. If the radius r of the spheres is large compared to the double-layer thickness 1/k (Kr l, with K the Debye-Hiickel parameter), Fr is described approximately by ... 

The stability of colloidal particles in suspension has been the focus of many research problems in literature. Central to many of these studies is the DLVO model, named after the pioneering work ofDerjaguin and Landau (1941) and Verwey and Overbeek (1948). The main idea of this theory is that the total interaction energy of coUoidal particles is given by the sum of the van der Waals and electrostatic interactions. 

Large spherical polyions are usually treated as an effective one-component system where the interaction between the polyions is given by a hard sphere potential plus a repulsive screened Coulomb potential (DLVO model) [31]. The screening of the polyion interactions is entirely due to the charges and concentrations of counterions and salt ions. As a result, the polyions interact via an effective charge Zeff or an effective surface potential. The value of z f depends on how the correlations between the polyions themselves and between polyions and counterions are theoretically formulated. All models discussed so far lead to an effective interaction in terms of screening arguments. A more detailed theory is required to consider the small ions in the system explicitly. Different approaches... 

Figure 10.5 Contour diagram for the interaction energy between two droplets with two minima corresponding to the primary and secondary minima in the DLVO model. The parameters used in the calculation are given in the text. Only the negative values of the energy are shown, starting from 0. The spacing between the contours corresponds to 100 kT...

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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