Ionic atmospheres

It should be noted that none of the foregoing equations relates to stoichiometric concentrations of additives. Quantitative treatment is precluded by ignorance of the effects of ionic atmosphere and of ionpairing in these media. 

At the shear plane, fluid motion relative to the particle surface is 2ero. For particles with no adsorbed surfactant or ionic atmosphere, this plane is at the particle surface. Adsorbed surfactant or ions that are strongly attracted to the particle, with their accompanying solvent, prevent Hquid motion close to the particle, thus moving the shear plane away from the particle surface. The effective potential at the shear plane is called the 2eta potential, It is smaller than the potential at the surface, but because it is difficult to determine 01 To usual assumption is that /q is effectively equal to which can be... 

Inorganic Ions. Because of electrostatic attraction, positive ions are attracted to negatively charged surfaces and have a higher concentration near the surface than in the bulk. Negative ions are repeUed from the negative surface and have a lower concentration near that surface. Ions which are very strongly bound (// ds Stem layer, whereas those that can move into and out of the ionic atmosphere < kT) are in the Helmholtz... 

It is shown that solute atoms differing in size from those of the solvent (carbon, in fact) can relieve hydrostatic stresses in a crystal and will thus migrate to the regions where they can relieve the most stress. As a result they will cluster round dislocations forming atmospheres similar to the ionic atmospheres of the Debye- Huckel theory ofeleeti oly tes. The conditions of formation and properties of these atmospheres are examined and the theory is applied to problems of precipitation, creep and the yield point."... 

Ionic atmosphere. An ion, on the average, is surrounded by more ions of opposite charge than of like charge. 

Because of electrostatic attraction, an ion in solution tends to surround itself with more ions of opposite than of like charge (Figure 10.12). The existence of this ionic atmosphere, first proposed by Peter Debye (1884-1966), a Dutch physical chemist in 1923, prevents ions from acting as completely independent solute particles. The result is to make an ion somewhat less effective than a nonelectrolyte molecule in its influence on colligative properties. 

When a charged particle is placed in aqueous media, however, the mobility may no longer be proportional to the intrinsic particle charge, since free counterions in solution will associate and move with the particle and thereby alter the net force exerted on the particle by the electric and fluid flow fields. The region of free or mobile counterions surrounding the particle has been termed the electrical double layer or ionic atmosphere. 

Ionic activity essentially represents the concentration of a particular type of ion in aqueous solution and is important in the accurate formulation of thermodynamic equations relating to aqueous solutions of electrolytes (Barrow, 1979). It replaces concentration because a given ion tends not to behave as a discrete entity but to gather a diffuse group of oppositely charged ions around it, a so-called ionic atmosphere. This means that the effective concentration of the original ion is less than its actual concentration, a fact which is reflected in the magnitude of the ionic activity coefficient. 

Debye-Huckel theory assumes complete dissociation of electrolytes into solvated ions, and attributes ionic atmosphere formation to long-range physical forces of electrostatic attraction. The theory is adequate for describing the behaviour of strong 1 1 electrolytes in dilute aqueous solution but breaks down at higher concentrations. This is due to a chemical effect, namely that short-range electrostatic attraction occurs... 

Oppositely charged ions are attracted to each other by electrostatic forces and so will not be distributed uniformly in solution. Around each ion or polyion there is a predominance of ions of the opposite charge, the counterions. This cloud of counterions is the ionic atmosphere of the polyion. In a dynamic situation, the distribution of counterions depends on competition between the electrostatic binding forces and the opposing, disruptive effects of thermal agitation. 

Not all ions are mobile within the ionic atmosphere of the polyion. A proportion are localized and site-bound-a concept apparently first suggested by Harris Rice (1954). Localized ion binding is equivalent to the formation of an ion-pair in simple electrolytes. Experimental evidence comes mainly from studies on monovalent counterions. 

An appreciable advance in the theory of electrostatic interaction between ions in solution was made in 1923 by Peter Debye and Erich Hiickel, who introduced the concept of ionic atmosphere to characterize the averaged distribution of the ions. In its initial form the theory was applied to fully dissociated electrolytes hence, it was named the theory of strong electrolytes. 

The ionic atmosphere has a blurred (diffuse) structure. Because of thermal motion, one cannot attribute precise locations to its ions relative to the central ion one can only dehne a probability to find them at a certain point or define a time-average ionic concentration at that point (the charge of the ionic atmosphere is smeared out around the centraf ion). In DH theory, the interaction of the central ion with specific (discrete) neighboring ions is replaced by its interaction with the ionic atmosphere (i.e., with a continuum). 

The most important parameters of the ionic atmosphere are the charge density Qv r) and the electrostatic potential /(r) at the various points. Each of these parameters is understood as the time-average value. These values depend only on distance r from the central ion, not on a direction in space. For such a system it is convenient to use a polar (spherical) coordinate system having its origin at the point where the central ion is located then each point can be described by a single and unique coordinate, r. 

The total charge, of the ionic atmosphere can be calcnlated by integrating the charge density over its total volnme. Since the system is electroneutral, the total charge of the ionic atmosphere mnst be eqnal in absolnte valne and opposite in sign to the central ion s charge <2m- The charge density is constant in an elementary volnme dV=4nr dr enclosed between two concentric spherical snrfaces with radu r and r + dr. Therefore,... 

The electrostahc potential /(r) at each point is reckoned relahve to the solution s constant average potential the latter is assnmed to be zero. The total value of potential /o(r) can be written as the sum of two components, one dne to the central ion / (r), and one due to the ionic atmosphere ... 

The energy of interaction of the central ion with its ionic atmosphere depends on the potential of this atmosphere t /atm(0) at a point where the central ion is located (r = 0). Therefore, it is the main task of the physical theory of ion-ion interaction to calculate the potential of the ionic atmosphere, j/a,ni. 

In the first version of DH theory it was shown that the potential of the ionic atmosphere can be represented by the equation... 

We can see from this equation that the potential / at the point r = 0 has the value that would exist if there were at distance 1/k a point charge -zj or, if we take into account the spherical symmetry of the system, if the entire ionic atmosphere having this charge were concentrated on a spherical surface with radius 1/k around the central ion. Therefore, the parameter = 1/k with the dimensions of length is called the ejfective thickness of the ionic atmosphere or Debye radius (Debye length). This is one of the most important parameters describing the ionic atmosphere under given conditions. 

The expression for the distribntion of potential of the ionic atmosphere becomes... 

Within a spherical space of radius a, by definition Qy = 0, so that the value of potential of the ionic atmosphere here is constant and equal to that at point r = a ... 

In practical applications of this equation, one must pick values for constant a. To a first approximation it can be regarded as equal to the sum of the radii of two solvated ions. It is not clear, however, whether the solvation sheaths of approaching ions would not be deformed. Moreover, in deriving Eq. (7.43) it was assnmed without sufficient reasoning that the constant a for a given central ion will be the same for different ions present in the ionic atmosphere. 

Ideas concerning the ionic atmosphere can be used for a theoretical interpretation of these phenomena. There are at least two effects associated with the ionic atmosphere, the electrophoretic effect and the relaxation effect, both lowering the ionic mobilities. Formally, this can be written as... 

The electrophoretic (cataphoretic) ejfect arises because the central ion and its ionic atmosphere, which differ in the sign of the charge, will move in opposite directions in an electric field (Fig. 7.6). The countermovement of the ionic atmosphere (as the surrounding medium) slows down the motion of the central ion. Usually, the value of the ionic atmosphere s own conductivity, A jj is adopted as the value of... 

AA-gpjj. Conditionally, the ionic atmosphere is regarded as a sphere with radius r. The valnes of approach the size of colloidal particles, for which Stokes s law applies (i.e., the drag coefficient 9 = where r is the liquid s viscosity) when they... 

The relaxation effect arises because a certain time, is required for the formation or collapse of an ionic atmosphere around the central ion. When an ion moves in an electric held, its ionic atmosphere lags somewhat behind, as it were its center (Fig. 7.7, point B) is at a point where the central ion had been a little earlier. The conhgurahon of the ionic atmosphere around the central ion (point A) will no longer be spherical but elongated (ovoid). Because of this displacement of the charges, the ionic atmosphere has an electrostahc effect on the central ion which acts in a direction opposite to the ion s motion. A rigorous calculation of this effect was made in 1927 by Lars Onsager. His solution was... 

According to the basic ideas concerning ionic atmospheres, the ions contained in them are in random thermal motion, uncoordinated with the displacements of the central ion. But at short distances between the central ion m and an oppositely charged ion j of the ionic atmosphere, electrostatic attraction forces will develop which are so strong that these two ions are no longer independent but start to move together in space like one particle (i.e., the ion pair). The total charge of the ion pair... 

We can find the potential of the ionic atmosphere by subtracting from the overall value of potential /(r) in accordance with Eq. (7.32) the value of potential of the central ion ... 

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