3) Thermodynamic equation to characterize interfaces

Transcription

1 3) Thermodynamc equaton to characterze nterfaces 3.1) Gbbs Model Realty: rapd contnuous change of chemcal and thermodynamc propertes Replaced by model (constant propertes up to the surface) uv bulk uv bulk thn nterface U σ Uσ = U uv u V n = cv n = cv component Amount of component n the surface n = n cv cv σ σ =Γ n A μ = μ = μ σ n : total number of moles of component Surface excess of component : Γ > 0: excess, adsorpton Γ < 0: depleton

2 3.) Gbbs adsorpton equaton Relaton between surface excess Γ, surface tenson γ and chem. Potental μ nternal energy (U(S,V,n)): bulk: surface: U = ST pv + μ n du = TdS pdv + μ dn σ σ σ = + γ + μ σ SdT+ Adγ + ndμ = 0 σ du TdS da dn n γ = μ = Γ μ σ d d d A d γ = ( Γ dμ +Γ d μ ) 1 1 T=const, dt=0 Relaton between change n surface tenson and change n chem. potental va surface excess Relaton between surface excess Γ and bulk concentraton? Smplfcaton by the rght locaton of the surface.

3 Gbbs adsorpton lqud surface, surface and subphase are n equlbrum:exchange possble Problem: Locaton of a surface at a lqud/vapor nterface? Lqud surface: nterfacal regon a few molecular damters thck (nm) Sold surface: nterfacal regon on a Å scale

4 Gbbs adsorpton equaton Δ c(z) = c(z) c Δ c(z) = c(z) c lq vap Γ= Δc(z)dz Γ= (c(z) c )dz + (c(z) c )dz vap lq Γ =Γ = + 0 (c(z) c )dz (c(z) c )dz z 0 1 H O H O,v H O,lq Γ =Γ = + 0 (c(z) c )dz (c(z) c )dz 0 SDS z SDS,v SDS,lq z z = 0 dγ dμ = Γ SDS 1 dγ Γ surfactan t = RT d ln c surfactan t

5 Γ = surfactan t 1 dγ RT d ln c surfactan t γ / mn/m saturaton below cmc Slope => adsorbed amount Value => change n free energy for brngng molecules at the nterface The longer the hydrocarbon chan, the lower the CMC e.g. SDS n water: CMC=8*10-3 mol/l, γ=40 mj/m, Γ=1Molkül / 50Å NaCl n water: 1mol/l, γ=74 mj/m, depleton

6 3.3) Monolayers of soluble amphphles: Gbbs sotherm ( ) RT ln ( X ) μ = μ + RT ln X = μ = μ + μ w w w s s s μ X RT ln w s w = X s SDS DS - + Na + dγ =Γ dμ => Electroneutralty => μ = μ + RT ln c + RT ln c DS Na dγ = RT Γ (dlnc + dlnc ) dγ dlnc DS SDS X w,x s : molar ratos DS = RTΓ + + dγ Excess of electrolyte: = RTΓ 0.1 M NaCl: a 0 (SDS)=38Å dlnc Na a 0 (SDS)=5Å Equlbrum between soluton and surface: below cmc No change of soluton wthout changng the surface

7 surafec tenson / mn/m conc (C 1 TAC) / mol/l wthout salt 0. NaCl Γ = surfac tan t Γ = surfac tan t 1 dγ RT d ln c surfactan t 1 dγ RT d ln c surfac tan t Wth salt, non-onc surfactant Wthout salt

8 3.4) Langmur nterfaces No change n surface tenson accessble Cannot be characterzed by Gbbs sotherm Langmur sotherm: D lattce model: N ndependent bndng ste, N adsorbed molecules, N-N stes occuped by solvent molecules, X =N /N (Index : solute, 1: solvent) Interacton between molecules gnored, monolayer { μ μ } { } G = G + Nμ + RT NlnX + (N N)ln(1 X) 0 s s s G X N 1 X = μ(s) = μ(s) + RT ln μ (b) = μ (b) + RTln c (b) Θ= X = adsorpton Kc (b) Kc (b) + 1 RT ln K = (b) (s) entropy bulk surface μ (b) = μ (s) Equlbrum: c (b)k>>1 => Θ 1 c (b)k<<1 => Θ c (b)

9 3.5) Monolayers of nsoluble amphphles Preparaton: dssolve nsoluble amphphles n a volatle organc solvent and depost drops of soluton onto the ar/water nterface S>0 => spreadng, evaporaton of solvent => monolayer of amphphles Pressure s needed to prevent flm from spreadng: Π = 0 s γ γ

10 3.5.1) Monolayers of nsoluble amphphles: Π(a 0 ) sotherms Collapse G: gas phase L1: lqud expanded phase (e.g. saturated unbranched carbon chans: a Å ) L: lqud condensed phase (stronger molecular nteractons, lower compressblty S: sold (e.g. alcohols, esters: a 0 19 Å ) G->L1: typcal gas lqud transton lke n 3D L1->L: transton not fnally explaned.

11 Gas phase D 3D Ideal gas equaton Devaton from deal gas: Π sa= nrt Π sa0 = kt Πsa0 Z = kt pv= nrt pv Z = nrt Compressblty factor 1 C 4 C 5 3 C 6 4 C 8 5 C 10 6 C 1 Z < 1: attracton Z > 1: repulson

12 Vsualzaton of phase transton 3.5.) Fluorescence mcroscopy Doman sze determned by balance between electrostatc repulson and lne tenson Amphphle: DMPA (dmyrstoylphosphatdc acd) Dye: DP-NBD-PE (L-α-dpalmtoyl.ntrobenzoxadazol-phosphatdylethanolamne) 1%

13 3.6) Langmur-Blodget flms Mono- or multlayers Hghly ordered flms Problem: long-term stablty