Reduced ionic cloud

A well-known result of the DH theory is that the charge dq in the volume element 4ttr2dr has a maximum value at a distance k 1 from the central ion (Figure la)2. The ionic cloud can be reduced to a charge on an infinitesimally thin shell placed at a distance (a + k 1) from the center of the central ion such that the potential caused by the reduced ionic cloud is... 

Figure la. Left a segment of the spherical ionic atmosphere. Right the reduced ionic cloud of Debye and Hiickel. 

Boundary Conditions Solution of the Problem of the Reduced Ionic Cloud. For equipotential conditions the total potential at the surface of the... 

A new theory of electrolyte solutions is described. This theory is based on a Debye-Hiickel model and modified to allow for the mutual polarization of ions. From a general solution of the linearized Poisson-Boltzmann equation, an expression is derived for the activity coefficient of a central polarized ion in an ionic atmosphere of non-spherical symmetry that reduces to the Debye-Hiickel limiting laws at infinite dilution. A method for the simultaneous charging of an ion and its ionic cloud is developed to allow for ionic polarization. Comparison of the calculated activity coefficients with experimental values shows that the characteristic shapes of the log y vs. concentration curves are well represented by the theory up to moderately high concentrations. Some consequences in relation to the structure of electrolyte solutions are discussed. 

A structure may be imposed on the ionic cloud by supposing that dq in the volume element dv = r2 sin OdOdipdr has a finite number, n, of maxima similarly situated at k 1 from the surface of the central ion (Figure lb). By analogy, this non-radial atmosphere is reducible to a corresponding array of point charges, and this device later enables us to formulate the necessary boundary conditions. 

All symbols have their usual meaning in the c.g.s. system of units, as given in Ref. 3. The common interpretation that the central ion sees its ionic cloud at a distance k 1 away is valid for the point-charge model only. For the DH second approximation the ionic cloud can be reduced to a charge located on a spherical surface at k 1 so as to maintain a constant potential at the surface of the central ion. Therefore, it cannot be replaced by a point charge. 

For 1 1 electrolytes the simplest choice for n is unity (as in Figure lb) and is shown to be appropriate by comparison with experiment. Thus we have n = 1, X = 1 (cos 0i = 1, 0i = 0), and can take any value, since m = 0 and does not depend on (p. Variants of Equation 39 are easily obtained for other than uni-univalent salts by choosing a structure for the reduced ionic atmosphere in the light of symmetry and chemical intuition. This is illustrated with reference to the divalent ion of a 1 2 electrolyte, where it is reasonable as a first approximation to suppose that the ionic cloud will have two diametrically opposed maxima, each at a distance 1 /k from the reference ion. It is easy to see that dipoles induced on the central ion by these two charge centers will cancel, as well all higher terms of odd Z, but that quadrupolar effects (Z = 2) and other terms of even Z will not. For the structure factor the coordinates of the two maxima in dq are 0i = 0 and 02 = 7r, while the atmosphere is still symmetrical with respect to the angular coordinate [Pg.211]

Multivalent Electrolytes. For 2 1 electrolytes we assume n = 2 for the divalent ion and n = 1 for the monovalent ion. The latter is a necessary choice which supposes that a monovalent ion sees a singly charged ionic cloud represented by a reduced ionic atmosphere with one maximum. This model gives log 7 vs. a/7 plots which are remarkably like the experimental pictures. The... 

Based on this postulate and the pronounced effect of agitation on particle incorporation Buelens et al7X77 proposed a five-step mechanism for composite deposition. In the first step particles in the bulk of the electrolyte obtain an ionic cloud by adsorbing ions from the electrolyte. In the second and third step the particles are transported by bath agitation to the hydrodynamic boundary layer and by diffusion through the diffusion layer to the cathode surface. Finally, the particles adsorb on the cathode surface still surrounded by their ionic cloud and are incorporated by the reduction of some of the adsorbed ions. A model for the calculation of the weight percent of incorporated particles was developed consistent with this mechanism. The basic hypothesis of the model is that a certain amount, x, out ofX ions adsorbed on a particle must be reduced at the... 

The potential energy of the dipole is pBi = —p2R. The part depending on (e — eo) represents the dipole-dipole interactions while the (k<7d)2 term concerns the dipole-ion interactions. For k 0, Eq. (10) reduces to the reaction-field expression of dielectric theory [54] derived from Laplace equation. Interestingly, even for e = eo a reaction field results because of the polarization of the ionic cloud. 

When a central ion moves in an electric field the ionic cloud surrounding the ion is permanently formed. This requires a certain time called the relaxation time. Therefore, as illustrated in Fig. 6-1, the charge density around the central ion is no longer symmetrical, but is lower in front of the central ion than behind it. This dissymmetry in charge distribution leads to an electrostatic deceleration of the central ion which reduces the ion mobility. 

A. Two copper particles are placed in an aqueous environment and an electric field is applied. The polarization of each particle is shown. Initially the particle on the right liberates copper ions r le the particle on the left reduces water. The shaded area represents a hypothetical distribution of the ionic cloud. (For clarity only the phenomena in the inteiparticle region are shown). 

The critical micelle concentration is affected by the presence of electrolytes and other components of the surfactant solution [142,168,192,193]. Electrolytes depress the cmc of ionic surfactants and increase the micellar size by decreasing the thickness of the ionic cloud around the ionic groups and reducing the electrostatic... 

As with the perturbed ionic cloud, the perturbed pseudolattice cell reduces the mobility of... 

Studies on non-ionic surfactants as effective drag-reducing additives have been submitted by Zakin (1972). He studied various effects on three non-ionic surfactants formed from straight-chain alcohols and ethyleneoxide. These surfactants have an upper and a lower temperature limit for solubility in water and prove effective drag reducers near their upper critical solubility temperature or clouding point. The clouding point is the point at which a solution of a non-ionic agent in water becomes turbid as the temperature is raised. 

Applications. Sarcosinates show low irritation potential and are good foamers. Due to these properties they find applications in personal care products where synergistic effects with other surfactants may also be exploited. In combination with other anionics, sarcosinates will often detoxify the formulation and give improved foaming and skin feel. Sarcosinates are also used for their hydrotropic properties - the addition of sarcosinate to other anionics often gives a reduced Kraft point or a raised cloud point if combined with non-ionic surfactants. Lauroyl sarcosinate is used to formulate SLS-free toothpastes which are claimed to have improved taste profile. 

We have examined the stmcture of both ionic and nonionic micelles and some of the factors that affect their size and critical micelle concentration. An increase in hydrophobic chain length causes a decrease in the cmc and increase of size of ionic and nonionic micelles an increase of polyoxyethylene chain length has the opposite effect on these properties in nonionic micelles. About 70-80% of the counterions of an ionic surfactant are bound to the micelle and the nature of the counterion can influence the properties of these micelles. Electrolyte addition to micellar solutions of ionic surfactants reduces the cmc and increases the micellar size, sometimes causing a change of shape from spherical to ellipsoidal. Solutions of some nonionic surfactants become cloudy on heating and separate reversibly into two phases at the cloud point. 

Another property of surfactants is the cloud point of non-ionic surfactants. Below this temperature a single phase of molecular or micellar solution exists above it, the surfactant has reduced water solubility, and a cloudy dispersion results [Biinz, Braun et al., 1998 Katritzky, Maran et al., 2000]. 

The recent investigation [71] of a nonionic system, hexaoxyethylene dodecyl ether and water, showed a hydrotrope molecule to be introduced into the micelle first at concentrations at which the hydrotrope self-associates.This increase of the minimum concentration at which the hydrotrope molecule enters the micelle from the values in ionic systems [61-66] is in all probability due to electrostatic effects. One essential result of the investigations into nonionic systems [71] is that the presence of the hydrotrope reduces the size of the micelle i.e., the radius of the curvature toward the hydrophobic region is reduced and, hence, the cloud point is enhanced in accordance with the views of Shinoda and Arai [70], Investigations of block copolymer systems [72-76] may now be interpreted in a similar manner and the coupling or linking action of a hydrotrope in a nonionic system is given a simple explanation in the form of a modified micellar structure. 

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