Ion atmosphere

At this point an interesting simplification can be made if it is assumed that r, as representing the depth in which the ion discrimination occurs, is taken to be just equal to 1/x, the ion atmosphere thickness given by Debye-Hiickel theory (see Section V-2). In the present case of a 1 1 electrolyte, k = (8ire V/1000eitr) / c /, and on making the substitution into Eq. XV-7 and inserting numbers (for the case of water at 20°C), one obtains, for t/ o in millivolts ... 

The first tenn is the Coulomb field of the ion, and the second is the potential due to the ion atmosphere at an effective distance equal to 1/k. For a univalent aqueous electrolyte at 298 K,... 

The Dehye-Hbckel theory of electrolytes based on the electric field surrounding each ion forms the basis for modern concepts of electrolyte behavior (16,17). The two components of the theory are the relaxation and the electrophoretic effect. Each ion has an ion atmosphere of equal opposite charge surrounding it. During movement the ion may not be exacdy in the center of its ion atmosphere, thereby producing a retarding electrical force on the ion. 

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

The region of the gradual potential drop from the Helmholtz layer into the bulk of the solution is called the Gouy or diffuse layer (29,30). The Gouy layer has similar characteristics to the ion atmosphere from electrolyte theory. This layer has an almost exponential decay of potential with increasing distance. The thickness of the diffuse layer may be approximated by the Debye length of the electrolyte. 

At these high frequencies, the retarding effect of the ion-atmosphere on the movement of a central ion is greatly decreased and conductance tends to be increased. The capacitance effect is related to the absorption of energy due to induced polarisation and the continuous re-alignment of electrically unsymmetrical molecules in the oscillating field. With electrolyte solutions of low dielectric constant, it is the conductance which is mainly affected, whilst in solutions of low conductance and high dielectric constant, the effect is mostly in relation to capacitance. 

The Debye-Hiickel formula for the activity coefficient of an ion was developed by a consideration of ion atmosphere effects.10 It starts with an electrostatic expression for the free energy of interaction for one ion with one mole of others ... 

A number of analytical techniques such as FTIR spectroscopy,65-66 13C NMR,67,68 solid-state 13 C NMR,69 GPC or size exclusion chromatography (SEC),67-72 HPLC,73 mass spectrometric analysis,74 differential scanning calorimetry (DSC),67 75 76 and dynamic mechanical analysis (DMA)77 78 have been utilized to characterize resole syntheses and crosslinking reactions. Packed-column supercritical fluid chromatography with a negative-ion atmospheric pressure chemical ionization mass spectrometric detector has also been used to separate and characterize resoles resins.79 This section provides some examples of how these techniques are used in practical applications. 

Breithaupt DE. 2004. Identification and quantification of astaxanthin esters in shrimp (Pandalus borealis) and in a microalga (Haematococcus pluvialis) by liquid chromatography-mass spectrometry using negative ion atmospheric pressure chemical ionization. J Agric Food Chem 52 3870-3875. 

Fig. 19.2. Observed isotope pattern (upper panel) and predicted model (lower panel) for the [M+Na]+ of dioctyl tin EHTG, taken from a positive ion atmospheric pressure chemical ionization (APCI) LC-MS experiment.

The first half of this chapter concentrates on the mechanisms of ion conduction. A basic model of ion transport is presented which contains the essential features necessary to describe conduction in the different classes of solid electrolyte. The model is based on the isolated hopping of the mobile ions in addition, brief mention is made of the influence of ion interactions between both the mobile ions and the immobile ions of the solid lattice (ion hopping) and between different mobile ions. The latter leads to either ion ordering or the formation of a more dynamic structure, the ion atmosphere. It is likely that in solid electrolytes, such ion interactions and cooperative ion movements are important and must be taken into account if a quantitative description of ionic conductivity is to be attempted. In this chapter, the emphasis is on presenting the basic elements of ion transport and comparing ionic conductivity in different classes of solid electrolyte which possess different gross structural features. Refinements of the basic model presented here are then described in Chapter 3. 

An intermediate of the type Co(NH3)4NH + is postulated in (4.45). The subsequent reactions of this intermediate should be independent of the nature of the X group in the starting material. The results of early experiments to verify this point have represented some of the most powerful support for the mechanism. Base hydrolysis of Co(NH3)jX + in an H2 0/H2 0 mixture was found, as required, to give a constant proportion of Co(NH3)5 OH + and Co(NH3)5> OH +, independent of X being Cl, Br or NO3-. The competition experiments described in Sec. 2.2.1 (b) support a five-coordinate intermediate which is so short lived that it retains the original ion-atmosphere of Co(NH3)jX "1+ but has lost memory of the X group. ... 

Kauppila, T. J. Kotiaho, X Kostiainen, R. Bruins, A. P. Negative ion-atmospheric pressure photoionization-mass spectrometry. J Am Soc Mass Spectrom 2004, 15, 203-211. 

S. Hamilton, A. Ray and K. Dennis, LC/MS of alkyl iodides using HPLC with negative ion atmospheric pressure chemical ionisation. Unpublished Work. 2003. 

A term used in electrostatic descriptions of ions to denote the continuous electric charge density [p(r)] surrounding an ionic species. On average, an ion will be surrounded by a spherically symmetrical distribution of counterions that form its ion atmosphere. See Hydration Atmosphere... 

As expected, the D-H theory tells us that ions tend to cluster around the central ion. A fundamental property of the counterion distribution is the thickness of the ion atmosphere. This thickness is determined by the quantity Debye length or Debye radius (1/k). The magnitude of 1/k has dimension in centimeters, as follows ... 

The data in Table 7.1 show values of D-H radius in various salt concentrations. The magnitude of 1/k decreases with I and with the number of charges on the added salt. This means that the thickness of the ion atmosphere around a reference ion will be much compressed with increasing value of I and zion. 

Emulsions and foams are two other areas in which dynamic and equilibrium film properties play a considerable role. Emulsions are colloidal dispersions in which two immiscible liquids constitute the dispersed and continuous phases. Water is almost always one of the liquids, and amphipathic molecules are usually present as emulsifying agents, components that impart some degree of durability to the preparation. Although we have focused attention on the air-water surface in this chapter, amphipathic molecules behave similarly at oil-water interfaces as well. By their adsorption, such molecules lower the interfacial tension and increase the interfacial viscosity. Emulsifying agents may also be ionic compounds, in which case they impart a charge to the surface, which in turn establishes an ion atmosphere of counterions in the adjacent aqueous phase. These concepts affect the formation and stability of emulsions in various ways ... 

Beyond the Stern layer, the remaining z counterions exist in solution. These ions experience two kinds of force an electrostatic attraction drawing them toward the micelle and thermal jostling, which tends to disperse them. The equilibrium resultant of these opposing forces is a diffuse ion atmosphere, the second half of a double layer of charge at the surface of the colloid. Chapter 11 provides a more detailed look at the diffuse part of the double layer. 

The diffuse part of the double layer is of little concern to us at this point. Chapters 11 and 12 explore in detail various models and phenomena associated with the ion atmosphere. At present it is sufficient for us to note that the extension in space of the ion atmosphere may be considerable, decreasing as the electrolyte content of the solution increases. As micelles approach one another in solution, the diffuse parts of their respective double layers make the first contact. This is the origin of part of the nonideality of the micellar dispersion and is reflected in the second virial coefficient B as measured by osmometry or light scattering. It is through this connection that z can be evaluated from experimental B values. 

Ionic micelles will migrate in an electric field, and the ion atmosphere of the colloidal particle is dragged along with it. Interpretation of micellar mobility (conductivity experiments) must take this into account. The same is true, however, of the mobility of simple ions, but the situation is more involved here since the micelle and the ion atmosphere have comparable dimensions. We see in Chapter 12 how particle and double-layer dimensions affect the interpretation of mobility experiments. 

If the surfactant is ionic and imparts a charge to the interface, then the dispersed particle will be surrounded by an ion atmosphere. We see in Chapters 11 and 13 how an ion atmosphere surrounding a particle may slow down the rate at which such particles come together. This is one of the ways by which an emulsion may achieve some degree of kinetic stability. 

Our discussion of the repulsion between particles requires a more drawn out development. In Chapter 11 we consider the effects of ion atmosphere as the origin of repulsion. In Chapter 13, we discuss polymer-induced repulsive forces, which are often used to screen out the van der Waals forces. In these cases also, we are interested in both the magnitude and the distance dependence of these interactions. 

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