Reduced adsorption surface excess

Equation (6.87) is the basis for most adsorption measurements associated with liquid solutions. When(d(j/dfi )T is negative, Tg is positive and there is an excess of the solute at the interface. For (dct/dfiB)r > 0, Tg is negative and there is a deficiency of the solute at the interface. In other words, solutes that reduce the surface tension are enriched at the surface. 

Substitution of these relations into the expression of Ax,(= x - x,) and simple algebraic transformations leads to the usual adsorption equation for the reduced surface excess... 

For ionic surfactants another effect often dominates and usually salt tends to stabilize emulsions. Reason without salt the distance between surfactants in the interface is large because the molecules electrostatically repel each other. This prevents a high surface excess. The addition of salt reduces this lateral repulsion and more surfactant molecules can adsorb at the interface. Then, according to the Gibbs adsorption isotherm Eq. (3.52), the surface tension is reduced and the emulsion is stabilized. 

With surfactant the surface tension is reduced according to the Gibbs adsorption isotherm Eq. (3.52). To apply Eq. (3.52) we need to know the surface excess ... 

In general the values of rA and rB depend on the position chosen for the Gibbs dividing surface. However, two quantities, TB(A) and rB(n) (and correspondingly wBa(A) and nB°(n)), may be defined in a way that is invariant to this choice (see [l.e]). TB(A) is called the relative surface excess concentration of B with respect to A, or more simply the relative adsorption of B it is the value of rB when the surface is chosen to make rA = 0. rB(n) is called the reduced surface excess concentration of B, or more simply the reduced adsorption of B it is the value of rB when the surface is chosen to make the total excess r = rt = 0. 

Adsorption isotherms expressed in reduced surface excess... 

When the adsorption is studied from dilute solutions (where by convention, we shall consider that component 1 is the solvent), the experimental isotherms are still plotted, strictly speaking, in terms of reduced surface excess. Nevertheless, since... 

Since the reduced and relative surface excess isotherms convey composite information on the adsorption of the two components, there is a strong incentive to determine the individual (or separate ) isotherms, i.e. the adsorbed amount n (or ) versus concentration, mole fraction or mass fraction. It will be recalled that this implies some assumptions about the thickness, composition and structure of the adsorbed layer, and therefore is not to be recommended for reporting adsorption from solution data in a standard form. Indeed, this second step is already part of the theoretical interpretation of the adsorption mechanisms. 

Just as for gas adsorption, we can define a partial differential enthalpy of adsorption of a component, A ads/i(, which would correspond to the adsorption, from a solution of molality b, of an infinitesimal amount of component i, dn, on a solid surface already covered with solute at a reduced surface excess concentration J (n) ... 

The principle of the null procedure (Nunn and Everett, 1983) is to restore, by injection of an appropriate dose of initial solution, the concentration prior to adsorption. This is done at each adsorption step. A refinement is to arrange that the sample cell is bypassed during the injection of a new dose of solution until the determination of a new amount concentration d2. The flow through is re-started and, as the concentration decreases, it is restored to its initial value d2 by addition of a volume A Va of a solution of amount concentration c2. The determination of the increase in reduced surface excess amount of 2 simply requires a knowledge of the void volume of the bypassed section and the concentration d 1 of the former adsorption equilibrium. Thus,... 

An early normalizing procedure, proposed by Kiselev (1957) to compare adsorption isotherms of hydrocarbons, water vapour, etc. on a series of different adsorbents, was simply to plot the surface excess concentration F (=n/A), obtained from a knowledge of the BET-nitrogen surface area, A (BET), versus p/p°. It is also possible to plot, instead of f, the reduced adsorption , n/nm, which still relies on the BET method to determine the monolayer capacity nm but does not require knowledge of the molecular cross-sectional area a. 

Fig. 53. Schematic isotherms (density p versus chemical potential pi) corresponding to the gas-liquid condensation in capillaries of thickness D, for the case without (a) and with (b) prewetting, and adsorption isotherm (c) for a semi-infinite system, where the surface excess density pjs is plotted vs. pi. Full curves in (a) and (b) plot the density p vs. pi for a bulk system, phase coexistence occurs there between p,p, (bulk gas) and pn, (bulk liquid), while in the capillary due to the adsorption of fluid at the walls the transition is shifted from paKX to a smaller value rc(D, 7) (with pic(7>, T) 1 /D, the Kelvin equation ), and the density jump (from ps D) to pt D)) is reduced. Note also that in the ease where a semi-infinite system exhibits a first-order wetting transition 7W, for 7 > 7W one may cross a line of (first-order) prewetting transitions (fig. 54) where the density in the capillary jumps from p to p>+ or in the semi-infinite geometry, the surface excess density jumps from p to p +, cf. (c), which means that a transition occurs from a thin adsorbed liquid film to a thick adsorbed film. As pi the thickness of the adsorhed liquid film in the semi-infinite...

To remedy this situation and reduce the often excessive gel s polarity, the silanol groups are exploited in order to provide sites of covalent bonding for organic molecules. Bonded silica gel, modified in this way, behave as a liquid in that the separation mechanism now depends on the partition coefficient instead of adsorption coefficient. These covalently bonded phases, whose polarity can be easily adjusted, constitute the bases of the reversed phase polarity partition chromatography or RP-HPLC, used in the majority of HPLC separations. Two types of syntheses lead to monomeric or polymeric bonded surfaces ... 

Surface Adsorption. As we have already mentioned, the surface of the precipitate will have a primary adsorbed layer of the lattice ions in excess. This results in surface adsorption, the most common form of contamination. After the barium sulfate is completely precipitated, the lattice ion in excess will be barium, and this will form the primary layer. The counterion will be a foreign anion, say, a nitrate anion, two for each barium ion. The net effect then is an adsorbed layer of barium nitrate, an equihbrium-based process. These adsorbed layers can often be removed by washing, or they can be replaced by ions that are readily volatilized. Gelatinous precipitates are especially troublesome, though. Digestion reduces the surface area and the amount of adsorption. 

Surface Excess Isotherm A function relating, at constant temperature and pressure, the relative adsorption, reduced adsorption, or similar surface excess quantity to the concentration of component in the equilibrium bulk phase. 

Kxpcrimcntal data for adsorption from solution are usually expressed as specific reduced surface excess isotherms, sometimes called composite isotherms, in which n()Ax, /m is plotted as a function... 

Surfaces always differ in behaviour from the bulk of a material because of the abrupt changes that occur at and near phase boundaries. Surface atoms and molecules are not in equilibrium states, since they are neither in one phase nor in the other. Unsaturated bonds abound. This leads to an excess energy associated with the surface, the so-called surface free energy which has different values for different crystallographic orientations. There are different ways to minimize surface energy. A simple way would be to reduce the surface area under the influence of surface tension. But this is not realistic with solid materials. Surface free energy, however, can also be lowered by adsorption and segregation phenomena. 

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