Surface excesses of substances

Equation 4.5 represents the surface excess of substance i relative to an aqueous solution that contains kilograms of water plus substance i at molality m,-. This surface excess is assigned to a surface at which there is no net accumulation of water. If water in the interstitial space is not adsorbed (in the sense defined in Chap. 2), then this surface can be taken as congruent with the geometric boundaries of the adsorbing soil particles. If some of the interstitial water is adsorbed, say, within the region bounded by a surface 1.0 nm from the boundary of a soil particle, then the surface of zero net accumulation of water could differ slightly from the soil particle surface. 

More commonly used is another definition of Gibbs surface excesses, according to which r, is equal to the amount of substance j that must be added to the system (with a constant amount of the substance j = 0) so that the composition of the bulk phases will remain unchanged when the interface area is increased by unity. This definition can also be used when chemical reactions take place in the surface layer. In the case discussed here, the two definitions coincide. The set of surface excesses of all components is sometimes called the surface phase (in contrast to the real surface layer or interphase). 

The basic quantity in the study of adsorption is the surface excess of the surface-active substance. In the formation of a monomolecular film of the... 

We have noted previously that measuring 7 as a function of concentration is a convenient means of determining the surface excess of a substance at a mobile interface. In view of the complications arising from charge considerations, the need for an independent method for measuring surface excess becomes apparent. Some elaborate techniques have been developed that involve skimming a thin layer off the surface of a solution and comparing its concentration with that of the bulk solution. 

Electrocapillary methods, described in Sections 13.2 and 13.3, are very useful in the determination of relative surface excesses of specifically adsorbed species on mercury. As discussed in Section 13.4, such methods are less straightforward with solid electrodes. For electroactive species and products of electrode reactions, the faradaic response can frequently be used to determine the amount of adsorbed species (Section 14.3). Nonelectro-chemical methods can also be applied to both electroactive and electroinactive species. For example, the change in concentration of an adsorbable solution species after immersion of a large-area electrode and application of different potentials can be monitored by a sensitive analytical technique (e.g., spectrophotometry, fluorimetry, chemiluminescence) that can provide a direct measurement of the amount of substance that has left the bulk solution upon adsorption (7, 44). Radioactive tracers can be employed to determine the change in adsorbate concentration in solution (45). Radioactivity measurements can also be applied to electrodes removed from the solution, with suitable corrections applied for bulk solution still wetting the electrode (45). A general problem with such direct methods is the sensitivity and precision required for accurate determinations, since the bulk concentration changes caused by adsorption are usually rather small (see Problem 13.7). 

Daumas et al. (1976) have compared the operation of the rotating drum and screen types of samplers in the field. A detailed examination of their results shows clearly that the surface excesses of different substances analysed in microlayers collected with each device on the same water surface are not equal but vary considerably. There are even cases where some species are enriched in one type of microlayer and depleted in another. This is not so difficult to understand the very wide diversity in surface concentrations in the same patch of water at the same time is well-known (e.g., Parker and Zeitlin, 1972). This type of surface heterogeneity should be borne in mind when the results of different studies are compared. It is possible, nevertheless, that some of this variation arises firom a disturbance of the original surface film by one or both of the sampling devices, i.e., they lose some of the film or its components in an unknown and irregular way. 

The L curve isotherm is characterized by an initial slope that does not increase with the concentration of a substance in the soil solution. This property is the result of a high relative affinity of the soil solid phases for the substance at low concentrations coupled with a decreasing amount of adsorbing surface as the surface excess of the adsorbate increases. The example of o-phosphate adsorption in Fig. 4.1 illustrates a universal L-curve feature an isotherm that is concave to the concentration axis because of the combination of affinity and steric factors. 

Figure 4.6 Schematic presentation of the relative surface excess. c x) and cj x) are the concentration of substance i and solvent s in front of the surface. Usually large excess of the solvent in the electrolyte, represented by the ratio xjx, reduces the concentration of the solvent to the concentration of the substance i. The relative surface excess is the hatched area in the diagram. If (Xj/x, )Cj Cj the relative surface excess is approximately the surface excess of the adsorbed substance over its bulk concentration.

Here, F is the surface excess of the solute and a is its activity. The change in surface tension of the liquid is at constant temperature that is the reason why Eq. (6.65) is called isotherm. Equation (6.65) tells us that when a solute is enriched at the interface (F > 0), the surface tension decreases when the solution concentration is increased. Such solutes are said to be surface active and they are called surfactants or surface-active agents. Often, the term amphiphilic molecule or simply amphi-phUe is used. When a solute avoids the interface (F < 0), the surface tension increases by adding the substance. Experimentally, Eq. (6.65) can be used to determine the surface excess by measuring the surface tension versus the bulk concentration. If a decrease in the surface tension is observed, the solute is enriched in the interface. If the surface tension increases upon addition of solute, then the solute is depleted in the interface. 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

Electroneutral substances that are less polar than the solvent and also those that exhibit a tendency to interact chemically with the electrode surface, e.g. substances containing sulphur (thiourea, etc.), are adsorbed on the electrode. During adsorption, solvent molecules in the compact layer are replaced by molecules of the adsorbed substance, called surface-active substance (surfactant).t The effect of adsorption on the individual electrocapillary terms can best be expressed in terms of the difference of these quantities for the original (base) electrolyte and for the same electrolyte in the presence of surfactants. Figure 4.7 schematically depicts this dependence for the interfacial tension, surface electrode charge and differential capacity and also the dependence of the surface excess on the potential. It can be seen that, at sufficiently positive or negative potentials, the surfactant is completely desorbed from the electrode. The strong electric field leads to replacement of the less polar particles of the surface-active substance by polar solvent molecules. The desorption potentials are characterized by sharp peaks on the differential capacity curves. 

A qualitatively new approach to the surface pretreatment of solid electrodes is their chemical modification, which means a controlled attachment of suitable redox-active molecules to the electrode surface. The anchored surface molecules act as charge mediators between the elctrode and a substance in the electrolyte. A great effort in this respect was triggered in 1975 when Miller et al. attached the optically active methylester of phenylalanine by covalent bonding to a carbon electrode via the surface oxygen functionalities (cf. Fig. 5.27). Thus prepared, so-called chiral electrode showed stereospecific reduction of 4-acetylpyridine and ethylph-enylglyoxylate (but the product actually contained only a slight excess of one enantiomer). 

The end points of precipitation titrations can be variously detected. An indicator exhibiting a pronounced colour change with the first excess of the titrant may be used. The Mohr method, involving the formation of red silver chromate with the appearance of an excess of silver ions, is an important example of this procedure, whilst the Volhard method, which uses the ferric thiocyanate colour as an indication of the presence of excess thiocyanate ions, is another. A series of indicators known as adsorption indicators have also been utilized. These consist of organic dyes such as fluorescein which are used in silver nitrate titrations. When the equivalence point is passed the excess silver ions are adsorbed on the precipitate to give a positively charged surface which attracts and adsorbs fluoresceinate ions. This adsorption is accompanied by the appearance of a red colour on the precipitate surface. Finally, the electroanalytical methods described in Chapter 6 may be used to scan the solution for metal ions. Table 5.12 includes some examples of substances determined by silver titrations and Table 5.13 some miscellaneous precipitation methods. Other examples have already been mentioned under complexometric titrations. 

The sources of error indicated above were avoided in a series of experiments carried out by Donnan and Barker, which in principle resemble those made by Lewis, so that only a brief reference to them is necessary. The dissolved substance was nonylic acid, and a drop method. The results could be reproduced with very great accuracy, i.e., to a fraction of one drop in 300—500 drops. Adsorption was produced at a surface air-liquid, air being passed through the solution in bubbles of known size and number, so that the total active surface could be calculated. The bubbles, on reaching the surface, burst, hence the excess of solute carried by them remained in the surface very effective precautions were used to prevent diffusion backwards from this portion into... 

The investigations described in the preceding pages have been directed to one point Only the exact determination of the excess of dissolved substance in the surface layer at one particular concentration. There are, however, some further questions of great importance, the answers to which must be sought by other experimental methods. The first of these is does adsorption lead to a well-defined equilibrium in a short space of time the second is this equilibrium, assuming it to exist, a simple function of the concentration ... 

Investigations have shown that, if one carefully sucked a small amount of the surface solution of a surfactant, then one can estimate the magnitude of E The concentration of the surface-active substance was found to be 8 pmol/mL. The concentration in the bulk phase was 4 pmol/L. The data show that the surface excess is 8 pmol/mL - 4 pmol/mL = 4 pmol/mL. Further, this indicates that, when there is 8 pmol/L in the bulk of the solution, the SDS molecules completely cover the surface. The consequence of this is that, at a concentration higher than 8 pmol/L, no more adsorption at the interface of SDS takes place. Thus, y remains constant (almost). This means that the surface is completely covered with SDS molecules. The area-per-molecule data (as found to be 50 A2) indicates that the SDS molecules are oriented with the S04- groups pointing toward the water phase, while the alkyl chains are oriented away from the water phase. 

The occurrence and deactivation of excited states of the first type are schematically shown in Fig. 35. Let the minority carriers (holes) be injected into the semiconductor in the course of an electrode reaction (reduction of substance A). The holes recombine with the majority carriers (electrons). The energy, which is released in the direct band-to-band recombination, is equal to the energy gap, so that we have the relation ha> = Eg for the emitted light quantum (case I). More probable, however, is recombination through surface or bulk levels, lying in the forbidden band, which successively trap the electrons and holes. In this case the excess energy of recombined carriers is released in smaller amounts, so that hco < Eg (case II in Fig. 35). Both these types of recombination are revealed in luminescence spectra recorded with n-type semiconductor electrodes under electrochemical generation of holes (Fig. 

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