Surface excess molecules

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

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. 

The surface excess F can be obtained - cf. Eq. (4.3) - from a plot of surface tension y vs log activity (concentration) of adsorbate. The area occupied per molecule or ion adsorbed can be calculated. 

Measurement of intermolecular distances between fluorescent surface-bound molecules in the presence of a large excess of fluorophore or background fluorescence in the bulk. 

Surface excess concentration, r, in mol cm", and area/molecule, A, in nm, at the liquid/air interface were calculated from the relationships ... 

From the plots of y versus concentration, the slope is related to the surface excess, Fsaikyisuifate- The area/molecule values indicate that the molecules are aligned vertically on the surface, irrespective of the alkyl chain length. If the molecules were oriented flat, then the value of area/molecule would be much larger (approximately 100 A2). Further, the fact that the alkyl chain length has no effect on the area also proves this assumption. These conclusions have been verified from spread monolayer studies. Further, it is also found that the polar group, that is, -SO4-, would occupy something like 50 A2. Later, it will be shown that other studies conhrm that the area per molecule is approximately 50 A2. 

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. 

On the assumption of the uniinolecular character of the Gibbs film we can, as Langmuir has indicated, obtain some idea as to the size of the solvent molecules. If the thickness of the film be t and the bulk concentration G, the quantity of solute which has left the film, on the hypothesis of a unimolecular film of pure solvent existing at the surface, will be Gr this is equivalent to the negative surface excess or... 

Subtractively normalized interfacial FTIR has been employed [242] to study the changes in the surface coordination of pyridine molecules on Au(lll). It has been deduced from the experiments that pyridine molecule is positioned upright at positive potentials and its plane rotates somewhat with respect to the electrode surface. In situ FTIR has also been used [243] to investigate adsorption of pyridine on Au(lll), Au(lOO), andAu(llO) electrodes. For the low-index electrodes, the behavior of band intensity located at 1309 cm and corresponding to the total adsorbed pyridine, agreed with the surface excess results obtained earlier from chronocoulometry. 

In Section 6.4.2 we will find that T represents the Gibbs-surface excess, i.e., T=N/A -N°/A, where is the number of molecules that would have been there if there had been no double layer, and N is the actual number of molecules in the interfacial region. However, when the bulk concentration of the spedes is small, i.e., tfi — 0, then the number of adsorbed molecules tends to f, i.e., f — N/A. 

Fig. 6.58. Three-dimensional graphs representing the surface excess (approximately equivalent to the number of adsorbed molecules) of fer-amyl alcohol calculated with respect to (a) the electrode potential and (b) the charge density. The electrical variable varies along the axis normal to the plane of the figure. The maximum surface excess corresponding to the plateau on both graphs is equal to 4.4 x 1(T10 mol cm-2. In this figure oM = qM. (Reprinted from J. Richer and J. Lipkowski, J. Electroanal. Chem. 251 217, copyright 1988, Fig. 12, with permission of Elsevier Science.)...

EXAMPLE 7.4 Determination of Surface Excess Concentration from Surface Tension Data. The slope of the 25°C line in Figure 7.15 on the low-concentration side of the break is about -16.7 mN m 1. Calculate the surface excess and the area per molecule for the range of concentrations shown. How would Figure 7.15 be different if accurate measurements could be made over several more decades of concentration in the direction of higher dilution Could the data still be interpreted by Equation (49) in this case ... 

For use in these equations, n2s is obtained from Equation 6. The volume of a sodium beta-naphthalenesulfonate molecule, calculated from bond lengths and appropriate van der Waals radii, is taken to be 330 A.3. An average molecular volume of water of 30 A.3 was calculated from the density of water at 25.0°C. Most of the numerical work was done on a Honeywell 800 digital computer. The symmetric surface excess and the surface charge densities were calculated over a wide range of surface potentials and concentrations. 

In TIRF protein adsorption experiments, it is desirable to correlate the intensity of excited fluorescence with excess protein concentration at the interface. Such an adsorbed layer is often in equilibrium with bulk-nonadsorbed protein molecules which are also situated inside the evanescent volume and thus contributing to the overall fluorescence. Various calibration schemes were proposed, using external nonadsorbing standards40,154 , internal standard in a form of protein solution together with a type of evanescent energy distribution calculation 154), and independent calibration of protein surface excess 155). Once the collected fluorescence intensity is correlated with the amount of adsorbed protein, TIRF can be applied in the study of various interactions between surface and protein. 

It is now time to reconsider the simple case of a two-phase system that contains two different types of molecules. If molecules of phase a are polar and molecules of phase [3 are nonpolar, the introduction of amphiphilic molecules that are capable of associating with either one of the two bulk phase molecules will result in an accumulation at the interface. Hence, these molecules will have a true excess concentration at the interface. Figure D3.5.4 illustrates that once surfactants adsorb at interfaces, the concentration within the interface may be larger than in any of the other phases. In order to predict the influence that these adsorbed surfactant molecules can have on the properties of the bulk system, interfacial chemists must be able to quantify the number of molecules that are adsorbed at the interface, that is, they must be able to measure the interfacial coverage. Unfortunately, it is extremely difficult, if not impossible, to directly measure the concentration of surface-active molecules adsorbed in a two-dimensional plane. This is where the thermodynamic concepts discussed earlier prove to be very useful, because a relationship between the interfacial coverage (G) and the interfacial tension (y) can be derived. 

In the Gibbs model of an ideal interface there is one problem where precisely do we position the ideal interface Let us therefore look at a liquid-vapor interface of a pure liquid more closely. The density decreases continuously from the high density of the bulk liquid to the low density of the bulk vapor (see Fig. 3.2). There could even be a density maximum in between since it should in principle be possible to have an increased density at the interface. It is natural to place the ideal interface in the middle of the interfacial region so that T = 0. In this case the two dotted regions, left and right from the ideal interface, are equal in size. If the ideal interface is placed more into the vapor phase the total number of molecules extrapolated from the bulk densities is higher than the real number of molecules, N < caVa + c V13. Therefore the surface excess is negative. Vice versa if the ideal interface is placed more into the liquid phase, the total number of molecules extrapolated from the bulk densities is lower than the real number of molecules, N > caVa + surface excess is positive. 

Soap bubbles To stabilize a bubble, surfactants are usually added to water. Assume we add a surfactant to a concentration of 2 mM. At this concentration we have a positive surface excess. As an average, each surfactant molecule occupies a surface area of 0.7 nm2. Estimate the change in pressure inside a soap bubble with a radius of 1 cm compared to a hypothetical bubble formed from pure water. 

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. 

The adsorption of amphiphilic molecules at the surface of a liquid can be so strong that a compact monomolecular film, abbreviated as monolayer, is formed. There are amphiphiles which, practically, do not dissolve in the liquid. This leads to insoluble monolayers. In this case the surface excess T is equal to the added amount of material divided by the surface area. Examples of monolayer forming amphiphiles are fatty acids (CH3(CH2) c 2COOH) and long chain alcohols (CH3(CH2)nc iOH) (see section 12.1). 

At this point we need to be careful with the use of the symbol a a- Here, it is the average area available for one molecule and defined to be the inverse of the surface excess. In chapter 9 it is the related to the geometric size of a molecule. For example, if a molecule has a diameter of say 1 nm and it is adsorbed to a surface, its contact area is roughly (lnm)2. This is independent of the surface excess, except for very high surface coverage. 

This equivalence between the charge of surface-bound molecules and the current of solution soluble ones is due to two main reasons first, in an electro-active monolayer the normalized charge is proportional to the difference between the total and reactant surface excesses ((QP/QP) oc (/> — To)), and in electrochemical systems under mass transport control, the voltammetric normalized current is proportional to the difference between the bulk and surface concentrations ((///djC) oc (c 0 — Cq) [49]. Second, a reversible diffusionless system fulfills the conditions (6.107) and (6.110) and the same conditions must be fulfilled by the concentrations cQ and cR when the process takes place under mass transport control (see Eqs. (2.150) and (2.151)) when the diffusion coefficients of both species are equal. 

Figure 6.29a-c can be used as working curves to accurately determine the values of AEf and the total surface excess / , for immobilized surface molecules. 

Calculate surface excess concentrations and the average area occupied by each adsorbed molecule for bulk concentrations of 0.01,0.02,0.04 and 0.08 mol dm-3. Plot a ir-A curve for the adsorbed n-pentanol monolayer and compare it with the corresponding curve for an ideal gaseous him. 

Type 2 solutes moderately decrease surface tension in aqueous solution and, thus, have positive surface excess concentrations. This class of solutes includes organic molecules with polar groups that give them some water solubility. Short-chain organic acids, amines, and alcohols are of this type. 

The more compact arrangement of surfactant molecules on a surface of lower curvature suggests that dyfdr < 0 and hence that Cis a positive quantity. In addition, the surface excess is expected to increase with increasing radius, because the molecules can more easily pack on a surface of lower curvature. This means that 8Cj8pi is also a positive quantity. 

Here II = yo - y is the surface pressure, k the Boltzmann constant, and (Oo the solvent molecule molecular area. An important feature of Eq. (6) is that it involves solvent characteristics only. The (Oo value depends on the choice of the position of the dividing surface. Assuming the solvent adsorption to be positive, the equation was proposed30 which relates the surface excesses H of the solvent (subscript i = 0) and dissolved species (i > 1) with any molecular area (fy ... 

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