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where  is the surface excess of the -th component,  are the moles,  and  are the phases, and  is the area of the dividing surface.

Adsorption and the Gibbs Surface Excess

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  • The derivation of the Gibbs equation assumed that the system could be divided into the two bulk phases separated by an infinitely sharp interface. The surface thermodynamic properties, are then those of the real system less the ideal sharply divided bulk phases. The surface excesses Γ literally measure the difference in the actual amount of in the system compared with that given by the sharp distribution, divided by the area. It may be positive (adsorption) or negative (depletion). This definition is very clear from a thermodynamic view but is only simple when there is strong adsorption from dilute solution. The surface excess of the solvent in the left hand side of the figure below is obtained by summing the red (negative excess relative to the uniform solvent) and green (positive excess). On the right hand side the dividing surface has been moved so that the red and green regions sum to zero, the dividing surface has been placed so that there is no adsorption of solvent. The dividing surface is often taken as being at the point where there is no nett adsorption of solvent. Note that the surface excess of solute is different between the left and right hand sides of the diagram. This difference is insignificant in most cases of amphiphile adsorption because adsorption is strong and the bulk solution concentration is low. The difference would not be insignificant for ethanol/water.

    In the thermodynamics of adsorption to surfaces the concept of surface excess is used. The surface excess is the extra amount per unit area of the solute that is present at or near the surface, when the surface is equilibrated with the mobile phase containing the solute.

  • The derivation of the Gibbs equation assumed that the system could be divided into the two bulk phases separated by an infinitely sharp interface. The surface thermodynamic properties, are then those of the real system less the ideal sharply divided bulk phases. The surface excesses Γ literally measure the difference in the actual amount of in the system compared with that given by the sharp distribution, divided by the area. It may be positive (adsorption) or negative (depletion). This definition is very clear from a thermodynamic view but is only simple when there is strong adsorption from dilute solution. The surface excess of the solvent in the left hand side of the figure below is obtained by summing the red (negative excess relative to the uniform solvent) and green (positive excess). On the right hand side the dividing surface has been moved so that the red and green regions sum to zero, the dividing surface has been placed so that there is no adsorption of solvent. The dividing surface is often taken as being at the point where there is no nett adsorption of solvent. Note that the surface excess of solute is different between the left and right hand sides of the diagram. This difference is insignificant in most cases of amphiphile adsorption because adsorption is strong and the bulk solution concentration is low. The difference would not be insignificant for ethanol/water.

    The situation for water soluble surfactants is quite different from that described in the previous paragraphs. There has to be equilibrium with the underlying solution. For solutions ofsurfactants below the CMC, progressive addition of surfactant lowers thesurface tension of the solution. This occurs for two reasons. The first isbecause at the air water interface the hydrophilic group can remain incontact with the water while the hydrophobic group can partially escapefrom the water. The second is that the surface energy of a hydrocarbonlayer is lower than that of water. The adsorption of surfactant at theinterface will be opposed, however, by the loss of entropy of mixing. Thebalance between the two leads to the very important , whichrelates the change of surface tension with concentration to the amountadsorbed at the surface. This can be used experimentally to determine howclosely the amphiphiles pack and this, in turn, gives the value of thearea occupied by the hydrophilic head group, which is the most convenientmeasure of the water hydrophilic head group interaction. The basis of theGibbs equation is given in the panel below the next figure. Its derivation requires the definitionof a dividing surface. This is a hypothetical surface which isregarded as making a perfect division between the two uniform bulk phaseson either side of the surface. The contributions to the thermodynamicproperties of the surface can then be separated into those of the twouniform bulk phases and an excess associated with the deviations fromuniformity in the surface region. The surface excess of the solvent in the left hand side of the figure below is obtained by summing the red (negative excess relative to the uniform solvent) and green (positive excess). On the right hand side the dividing surface has been moved so that the red and green regions sum to zero. This move of the dividing surface has little effect on the surface excess of the very surface active solute in the figure.

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  • Adsorption and the Gibbs Surface Excess
    D. Chattoraj
    Limited preview - 2012

    J. Willard Gibbs in his pioneering work on the influence of surfaces discontinuity upon the equilibrium of heterogene-ous masses suggested for the measurement of the quantities of a system a geometrical surface dividing the interfacial layer. Surface excess is the difference between the amount of a component actually present in the system, and that which would be present in a reference system if the bulk concentration in the adjoining phases were maintained up to the arbitrary chosen but precisely determined in position dividing surface.

Calculations of surface excess Nguyen, Yen V.; Phillips, Colin R

There are various factors affecting surface tension, one of which is that the of the surface may be different from the bulk. For example, if water is mixed with a tiny amount of (for example, ), the bulk water may be 99% water molecules and 1% soap molecules, but the topmost surface of the water may be 50% water molecules and 50% soap molecules. In this case, the soap has a large and positive "surface excess". In other examples, the surface excess may be negative: For example, if water is mixed with an like , the surface of the water is on average salty and more pure than the bulk average.