facts at your fingertips - adsorption.pdf
TRANSCRIPT
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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.