Adsorption of geses on liquids.Surface-active and surface-inactive substances. Gibbs’s

equation, Shyshkovsky’s equations and Langmuir’s equations

Plan1. Surfactants and nonsurfactants subsances

2. Gibbs and Szyszkowski equations

Assistant Kozachok S.S. prepared

Ionic The hydrophilic part of the most effective soluble surfactants (e.g. soaps,"synthetic detergents and dyestuffs) is often an ionic group. Ions have a strong affinity for water owing to their electrostatic attraction to the water dipoles and are capable of pulling fairly long hydrocarbon chains into solution with them; for example, palmitic acid, which is virtually un-ionised, is insoluble in water, whereas sodium palmitate, which is almost completely ionised, is soluble

Anionic (soap, sulphoacids and their salts)Cationic (organic N – containing bases and their salts)

Classification of surfactants

Molecular (non-ionic) –It is possible to have non-ionic hydrophilic groups

which alsoexhibit a strong affinity for water; for example, the

monomer units ina poly (ethylene oxide) chain each show a modest

affinity for waterand the sum effect of several of these units in the

polymer chain is anoverall strong affinity for water.

Ampholyticaccording to the charge carried by the surface-active part of the molecule.

In addition, surfactants are often named in relation to their technological application; hence names such as detergent, wetting agent, emulsifier and dispersant,Anionics are the most widely used surfactants on account of cost and performance. Cationics are expensive, but their germicidal action makes them useful for some applications. An advantage enjoyed by non-ionics is that the lengths of both hydrophilic and hydrophobic groups can be varied.

Adsorption of surface-active molecules as an orientated monolayer at air-water interfaces with the increasing of their concentrations.

Langmuir’ s type

The scheme of the monomolecular layer’s transfer

on the solid surface

Spreading of oil on the water surface

Gas

Water

Oil

Condition of Spreading:- σ of oil is less then σ of water- a big difference between surface tension of oil and water

Isotherms of the surface tension

1 – for solution of surfactant,2 – for solution of non surfactantnon surfactant 3 – for solution of surface inactive substance

Dependence of the surface tension on the concentration of surfactant’s solution

1, 3 – Henry’s linear relationship, :σ0- σ = КС

2- Szyszkowski equation: σ = σ0 – a ln (1+ bc)

11

22

3 3

The excess concentration of surfactant at the surface is called the Gibbs surface excess and is given the symbol Γ. The surface excess is named after Gibbs who developed a model for describing the interfacial region between two bulk phases. From this model a relationship (the Gibbs adsorption isotherm) was developed between the surface excess (Γ), the bulk concentration of surfactant (c), and the surface tension (γ ).

The relationship between the surface tension of the solution and the concentration of surfactants is described by Gibbs equation:

where Г – adsorption, units = mol/m2

This is the important Gibbs adsorption isotherm. (Note that for concentrated solutions the activity and for ideal gases the pressure will be used in this equation.)

Experimental measurements of γ over a range of concentrations allows us to plot γ against lnc1 and hence obtain Г1, the adsorption density at the surface. The validity of this fundamental equation of adsorption has been proven by comparison with direct adsorption measurements. Themethod is best applied to liquid/vapour and liquid/liquid interfaces, where surface energies can easily be measured.

Conclusion from Gibbs equationat – dγ/dc > 0 Г > 0,at – dγ/dc < 0 Г < 0,at – dγ/dc = 0 Г = 0,Ribender proposed, that – dγ/dc = g is a surface activity The strong adsorption of such materials at surfaces or interfaces in the form of an orientated monomolecular layer (or monolayer) is termed surface activity.

Figure shows the effect of lower members of the homologousseries of normal fatty alcohols on the surface tension of water. The longer the hydrocarbon chain, the greater is the tendency for the alcohol molecules to adsorb at the air-water surface and, hence, lower the surface tension. A rough generalisation, known as Traube's rule, is that for a particular homologous series of surfactants theconcentration required for an equal lowering of surface tension in dilute solution decreases by a factor of about 3 for each additional CH2 group.If the interfacial tension between two liquids is reduced to asufficiently low value on addition of a surfactant, emulsification will readily take place, because only a relatively small increase in the surface free energy of the system is involved.

Szyszkowski equation:

σ = σ0 – a ln (1+ bc)or

Δσ = σ0 – σ = a ln (1+ bc)

where σ0 and σ are surface tension of the solvent and solute; c- surfactant’s concentration; a, b – empirical constants.Szyszkowski equation is used for the surface tension calculation of the fat acids ( or other surfactants) with non large number of carbon atom’s chain ( till C8)

Using Szyszkowski equation you can transfer from Gibbs to Langmuir equations if differentiate the Szyszkowski equation on the concentration:

Langmuir equation:KС

KСГГ

1

K is the equilibrium constant for adsorption. is a limiting value of adsorption. It’s a quantity of adsorbate which is adsorbed by the mass units of adsorbant (observed at a high concentration of surfactants).

The surface excess is the concentration of surfactant at the surface in excess of the bulk concentration and as such the bulk concentration must be added to the surface excess to obtain the actual surface concentration. However, for most surfactants the surface excess is muchgreater than the bulk concentration and this correction is typically neglected. We can integrate this equation to get the surface tension as a function of surfactant concentration if we know the relationship between the surface excess and the concentration. If we assume thatthe free energy of adsorption is constant, this relationship is given by the Langmuir isotherm:

Г

KCГГ ГГ

сКГГГ

1111

The linear form of the equation:

RTaГ /

If С <<1: If С >>1:

Г = а/RT * bc/1+bc

ГUsing the value of calculate two important molecular constants: S – the area is taken by a separated molecule on the saturated monolayer surface and δ – thickness of this layerSince the quantity of molecules that are on the monolayer surface in 1 m2 equals Г·NA , that

S = 1/ Г·NA

In the volume of the surface layer:δ = Г M/ρWhere ρ is a density of the adsorbed substance, M is a molar mass of adsorbed substance.Value of S characterizes the polar group of surfactants that is located on the saturated monolayer surface. According to the Langmuir researching with fat acids the area that is taken by a one molecule in the saturated monolayer equals 20,5 . 10-20 m2, it does not depend on the molecule’s length at the present of 14-34 Carbon atoms inside.

Absence of the dependence of the cross-sectional area from the chain length of a fat acid CH3 – (CH2)n – COOH denotes that the molecules orientate vertically to the surface