PHYSICAL CHEMISTRY
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SURFACE TENSION
NOMENCLATURE
General definition σ
= ∂ G ∂ A P ,T
where G is the Gibbs free energy and A is the area. Pressure drop across a spherical surface (Young-Laplace (Y oung-Laplace equation) ∆P = 2 ⋅ σ R where R is the radius of the sphere Abov e a certa in surfac tant conce Above concentrantration, called the critical micelle conSurface enthalpy centration, the surfactant molecules H = σ − T ∂σ form spherical-shaped aggregates in ∂ T P solution. In water, for example, the Temperature dependence hydrocarbon tail assemble together to (Katayama-Guggenheim equation) form an oil-like droplet with the polar heads forming an outer shell (dian T gram). The presence of micelles is what σ = σ 0 1− enables detergent solutions to dissolve T C where 0 and n are empirical param- oils and fats. eters of a given liquid, and T C is the critical temperature. For organic com- ADSORPTION ISOTHERMS pounds, n = 11/9.
ADSORPTION Definitions
Gibbs adsorption isotherm
= −kT ∑ Γ i d ln ci dσ = i
A Area B Empirical constant for adsorption isotherms c i i Bulk concentration concentration of ith component G Gibbs free energy H Enthalpy k Boltzmann constant K i i Equilibrium constant n An empirical constant in the relation describiong the temperature dependence of surface tension ni Number of adsorbed molecules or atoms on a surface (n (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 component ∞ Γ i Surface concentration of ith component at large concentrations ΓF An empirical parameter of the Freundlich isotherm σ Surface tension σo Surface tension of pure solvent
where k is the Boltzmann constant T is the temperature, in Kelvin Γi is the surface concentration of ith component c i i is the bulk concentration of the ith component
Henry adsorption isotherm Adsorption is a process whereby a gas Adsorption is or liquid (adsorbate (adsorbate ) accumulates on the Γ i = c i surface of a solid or liquid (adsorbent ( adsorbent ) to Γ i ∞ B form a molecular or atomic film. In con where B is an empirical constant. trast, absorption absorption is is a process whereby a gas, liquid or solid diffuses into a liquid Freundlich adsorption isotherm or solid to form a solution. Langmuir adsorption isotherm m Physisorption is used when the adsorPhysisorption Γ i = c i Γ i c bate is physically bound to the adsorΓ F B F = i ∞ bate through weak bonds, such as van Γ i B + c i where ΓF , B F der Waals forces. Chemisorption Chemisorption is is used F and m are empirical where B is an empirical constant. This constants. when the adsorbate is chemically bound to the adsorbate, such as through cova- classical equation is useful for describing the adsorption of molecules onto a lent bonds. solid surface to form a monolayer. For � Surfactants,, or surface-active agents, multilayer adsorption, the BET isotherm Surfactants are wetting agents that lower the sur- is used: face tension of a liquid by lowering the interfacial tension between two liquids. BET (Brunauer, Emmett and Teller) Surfactants are typically long molecules adsorption isotherm composed of a hydrocarbon tail and a � � polar head. Surfactants can be classified Γ i K i ⋅ p i = according to the charge of the head: ∞ Γ i p i p i � • Anionic surfactants have negatively 1 + K i ⋅ p i − ⋅ 1− P P i i charged groups (such as sulfate, sulfo nate or carboxylate) where K i i is a constant, p i i is the pressure • Cationic surfactants have positively- of the adsorbable component i , and P i charged groups (such as quaternary its vapor pressure. Other isotherms of ammonium ions) importance include: � � • Zwitterionic surfactants have a polar head with both positively and nega- References tively charged groups. 1. Levine, I., “Physical Ch emistry,” 2nd ed., Mc3. Danov, K.D. and others, Equilibrium and Dy• Nonionic surfactants don't have any Graw Hill Book Co., N.Y., 1983, pp. 342–365. namics of Surfactant Adsorption Monolayers charged group for the polar head. Ex- 2. Perry, R.H. an d Green, D.W., “Perry’s Chemical and Thin Liquid Films, “Handbook of Detergents, Part A: Proper ties,” M.Dekker, N.Y., N.Y., pp. amples of non-ionic surfactants are alkyl Engineers’ Handbook,” 7th ed., McGraw Hill 303–418, 1999. Book Co., N.Y., p. 16-12–13. poly(ethylene oxide) and fatty alcohols. �
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