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PHYSICAL CHEMISTRY

SURFACE TENSION

General definition

σ ∂∂

=

GA P T,

where G is the Gibbs free energy and A is the area. Pressure drop across a spherical surface (Young-Laplace equation)

∆PR

= ⋅2 σ

where R is the radius of the sphere

Surface enthalpy

H TT P

= −

σ ∂σ

∂Temperature dependence(Katayama-Guggenheim equation)

σ σ= −

0 1 T

TC

n

where 0 and n are empirical param-eters of a given liquid, and TC is the critical temperature. For organic com-pounds, n = 11/9.

ADSORPTION

DefinitionsAdsorption is a process whereby a gas or liquid (adsorbate) accumulates on the surface of a solid or liquid (adsorbent) to form a molecular or atomic film. In con-trast, absorption is a process whereby a gas, liquid or solid diffuses into a liquid or solid to form a solution.Physisorption is used when the adsor-bate is physically bound to the adsor-bate through weak bonds, such as van der Waals forces. Chemisorption is used when the adsorbate is chemically bound to the adsorbate, such as through cova-lent bonds. Surfactants, or surface-active agents, are wetting agents that lower the sur-face tension of a liquid by lowering the interfacial tension between two liquids. Surfactants are typically long molecules composed of a hydrocarbon tail and a polar head. Surfactants can be classified according to the charge of the head: • Anionic surfactants have negatively

charged groups (such as sulfate, sulfo-nate or carboxylate)

• Cationic surfactants have positively-charged groups (such as quaternary ammonium ions)

• Zwitterionic surfactants have a polar head with both positively and nega-tively charged groups.

• Nonionic surfactants don't have any charged group for the polar head. Ex-amples of non-ionic surfactants are alkyl poly(ethylene oxide) and fatty alcohols.

Above a certain surfactant concentra-tion, called the critical micelle con-centration, the surfactant molecules form spherical-shaped aggregates in solution. In water, for example, the hydrocarbon tail assemble together to form an oil-like droplet with the polar heads forming an outer shell (dia-gram). The presence of micelles is what enables detergent solutions to dissolve oils and fats.

ADSORPTION ISOTHERMS

Gibbs adsorption isothermd kT d ci

iiσ = − ∑ Γ ln

where k is the Boltzmann constantT is the temperature, in KelvinΓi is the surface concentration of ith

componentci is the bulk concentration of the ith

component

Langmuir adsorption isotherm

ΓΓ

i

i

i

i

cB c∞ =

+

where B is an empirical constant. This classical equation is useful for describ-ing the adsorption of molecules onto a solid surface to form a monolayer. For multilayer adsorption, the BET isotherm is used:

BET (Brunauer, Emmett and Teller) adsorption isotherm

ΓΓ

i

i

i i

i ii

i

i

i

K p

K p pP

pP

∞ = ⋅

+ ⋅ −

⋅ −

1 1

where Ki is a constant, pi is the pressure of the adsorbable component i, and Pi its vapor pressure. Other isotherms of importance include:

Henry adsorption isothermΓΓ

i

i

icB∞ =

where B is an empirical constant.

Freundlich adsorption isotherm

ΓΓ

i

F

i

F

mcB

=

where ΓF, BF and m are empirical constants.

NOMENCLATURE A Area B Empirical constant for adsorption

isotherms ci Bulk concentration of ith component G Gibbs free energy H Enthalpy k Boltzmann constant Ki Equilibrium constant n An empirical constant in the rela-

tion describiong the temperature dependence of surface tension

ni Number of adsorbed molecules or atoms on a surface (ni = Γi A)

P Pressure pi Pressure of ith component R Radius of a spherical surface, such

as a bubble or meniscus T Temperature Tc Critical temperature Γi Surface concentration of ith compo-

nent Γ∞

i Surface concentration of ith compo-nent at large concentrations

ΓF An empirical parameter of the Freundlich isotherm

σ Surface tension σo Surface tension of pure solvent

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References1. Levine, I., “Physical Chemistry,” 2nd ed., Mc-

Graw Hill Book Co., N.Y., 1983, pp. 342–365.2. Perry, R.H. and Green, D.W., “Perry’s Chemical

Engineers’ Handbook,” 7th ed., McGraw Hill Book Co., N.Y., p. 16-12–13.

3. Danov, K.D. and others, Equilibrium and Dy-namics of Surfactant Adsorption Monolayers and Thin Liquid Films, “Handbook of Deter-gents, Part A: Properties,” M.Dekker, N.Y., pp. 303–418, 1999.