Adsorption surface excess concentration

Charge transfer reactions at ITIES include both ET reactions and ion transfer (IT) reactions. One question that may be addressed by nonlinear optics is the problem of the surface excess concentration during the IT reaction. Preliminary experiments have been reported for the IT reaction of sodium assisted by the crown ether ligand 4-nitro-benzo-15-crown-5 [104]. In the absence of sodium, the adsorption from the organic phase and the reorientation of the neutral crown ether at the interface has been observed. In the presence of the sodium ion, the problem is complicated by the complex formation between the crown ether and sodium. The SH response observed as a function of the applied potential clearly exhibited features related to the different steps in the mechanisms of the assisted ion transfer reaction although a clear relationship is difficult to establish as the ion transfer itself may be convoluted with monolayer rearrangements like reorientation. 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

A net surface charge can be acquired by the unequal adsorption of oppositely charged ions. Ion adsorption may involve positive or negative surface excess concentrations. 

The surface excess concentration (T), which is the surface concentration of surfactant, can be determined by the representative Gibbs adsorption equation. The T can be obtained from the slope of a plot shown in Figure 2.1 (y versus log[C] at constant temperature). 

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. 

Equation (2.34) is often referred to as the Gibbs adsorption equation where the interdependence of r and p is given by the adsorption isotherm. TTie Gibbs adsorption equation is a surface equation of state which indicates that, for any equilibrium pressure and temperature, the spreading pressure II is dependent on the surface excess concentration r. The value of spreading pressure, for any surface excess concentration, may be calculated from the adsorption isotherm drawn with the coordinates n/p and p, by integration between the initial state (n = 0, p = 0) and an equilibrium state represented by one point on the isotherm. 

The integral molar energy of adsorption is therefore obtained by integrating the differential energy of adsorption between the limits 0 and n°. It equals the mean of the differential energy of adsorption over the range of surface excess concentration from 0 to r. 

If we differentiate Equation (2.48) with respect to the adsorption temperature, so that the surface excess concentration T (or n) remains constant, and assume that fir.r nd A d° not vary> we obtain ... 

We can verify with Equation (2.68) that Aads/i<0 since, for physical adsorption, the equilibrium pressure necessary to obtain the surface excess concentration r (or n) increases with the adsorption temperature. It follows that A is necessarily negative. However, since the differential entropy of adsorption, at constant T, given by Equation (2.56) is directly proportional to the differential enthalpy of adsorption, its calculation is not of great value. 

The simplest interpretation of the behaviour of the adsorbed phase is to suppose at very low surface excess concentration, the adsorbate molecules are independe each other. By assuming that the dilute adsorbed phase behaves as a two-dimens ideal gas, regardless of the nature of the adsorption, we may write the limiting t tion of state in the form... 

An adsorption step, during which an amount of liquid na is vaporized from the liquid phase (with a molar energy of vaporization Avap ) and adsorbed on the solid surface (with an integral molar adsorption energy A k, precisely defined for an adsorption process at constant volume (cf. Equation (2.59)), at temperature T and for the surface excess concentration r=n°/A. 

It thus becomes possible to assess the net molar integral energy of adsorption (u° - ux) from the difference between the energy of immersion of the outgassed adsorbent and that of the adsorbent with a pre-adsorbed surface excess concentration, as was originally pointed out by Hill (1949). 

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) ... 

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. 

Therefore, when studying interfacial reactions on rocks and soils, it must always be determined what the mechanism of the interfacial reaction is, and what kind of processes take place. Also, it must identify the dominant processes responsible for surface excess concentration. If this is not done, and the resultant process is evaluated without knowing it in conventional ways, incorrect thermodynamic data are obtained. The concepts of adsorption, ion exchange, and surface precipitation have to be clearly differentiated, as done previously. When the character of the process can be neglected, only surface accumulation is considered, and we can speak about sorption, including all of the surface processes. In this case, only aphenomenological description can be given, and no thermodynamics can be applied. 

The surface excess concentration ( surface concentration) at surface saturation Tm is a useful measure of the effectiveness of adsorption of the surfactant at the L/G or L/L interface, since it is the maximum value that adsorption can attain. The effectiveness of adsorption is an important factor in determining such properties of the surfactant as foaming, wetting, and emulsification, since tightly packed, coherent interfacial films have very different interfacial properties than loosely packed, noncoherent films. Table 2-2 lists values for the effectiveness of adsorption Tm, in mol/cm2, and the area per molecule at the interface at surface saturation asm, in square angstroms (which is inversely proportional to the effectiveness of adsorption) for a wide variety of anionic, cationic, nonionic, and zwitterionic surfactants at various interfaces. 

In general, the choice of the position of the Gibbs dividing surface is arbitrary. It is possible to define quantities which are invariant with respect to the choice of its location. If Fj or Fj, are the relative adsorption and F and Ff the Gibbs surface excess concentrations of components i and 1, respectively, then the relative adsorption of component i with respect to component 1 is defined by... 

Gibbs Surface A geometrical surface chosen parallel to the interface and used to define surface excess properties such as the extent of adsorption. The surface excess amount of adsorption is the excess amount of a component actually present in a system over that present in a reference system of the same volume as the real system, and in which the bulk concentrations in the two phases remain uniform up to the Gibbs dividing surface. The terms surface excess concentration or surface excess have now replaced the earlier term superficial density. 

For most of the conventional amphiphiles it was demonstrated by Rosen [141] that at a surface pressure H = 20 mN/m the surface excess concentration reaches 84-100 % of its saturation value. Then, the (l/c)n=2o value can be related to the change in free energy of adsorption at infinite dilution AG , the saturation adsorption F and temperature T using the Langmuir and von Szyszkowski equations. The negative logarithm of the amphiphile concentration in the bulk phase required for a 20 mN/m reduction in the surface or interfacial tension can be used as a measure of the efficiency of the adsorbed surfactant ... 

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

Here,, characterizes concentration of individual ion i in moles per square meter called surface excess concentration or Gibbs adsorption. It may be expressed in different units tied up by the following equality... 

In contrast to this, the adsorption of ions obeying GC theory is termed as nonspecific adsorption. It is important to emphasize that the distinction between specific and nonspecific adsorption is based on an arbitrarily chosen model assumption. It should, however, be borne in mind that it is impossible, by means of thermodynamic arguments, to determine the extent of the contribution of the specific adsorption to the overall surface excess concentration and to the charge density. 

The results of flic interfacial rheological studies on asphaltene adsorption at oil-water interfaces teach us a great deal about the behavior of asphaltenes and their role in emulsion stabili2ation. The conclusions drawn are based largely on the assumption that the rheological properties measured, namely flic elastic film modulus G are directly related to the surface excess concentration of asphaltenes. F. It is understood diat die elastic modulus actually depends on both the surface excess concenlration and the relative conformation (i.e., coimectivity) of the adsorbed asphaltenes. It is further understood that a minimum adsorbed level is required to observe a finite value of G and that the relationship between G and G is not linear. With these caveats in mind, we can conclude die following ... 

Adsorption is an entropically driven process by which molecules diffuse preferentially from a bulk phase to an interface. Due to the affinity that a surfactant molecule encounters towards both polar and non-polar phases, thermodynamic stability (i.e. a minimum in free energy or maximum in entropy of the system) occurs when these surfactants are adsorbed at a polar/non-polar (e.g. oil/water or air/water) interface. The difference between solute concentration in the bulk and that at the interface is the surface excess concentration. The latter... 

The preceding discussion of the Gibbs adsorption equation was referenced to a fluid-fluid interface in which the surface excess, T, is calculated based on a measured quantity, a, the interfacial tension. For a sohd-fluid interface, the interfacial tension cannot be measured directly, but the surface excess concentration of the adsorbed species can be, so that the equation is equally useful. In the latter case. Equation (9.16) provides a method for determining the surface tension of the interface based on experimentally accessible data. 

The principles given above allow one to derive an expression relating theoretical concepts of surface excess concentration and adsorption to experimentally obtainable quantities. But what is the practical importance of those ideas In fact, the phenomenon of adsorption at interfaces, tied to the resultant effects of such adsorption, carries with it a multitude of important consequences (some good and some bad) for many technological and biological processes. 

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