Problems from the last lecture

Transcription

1 Problems from the last lecture Problem 2.5 Use the Kelvn equaton to calculate the radus of an openended tube wthn whch capllary condensaton of ntrogen at 77 K and a relatve pressure of 0.75 mght be expected. Assume that pror adsorpton of ntrogen has formed a layer 0.9 nm thck coatng the nsde of the tube. For ntrogen at 77 K the surface tenson s 8.85 mn m -1 and the molar volume s 34.7 cm 3 mol -1. Answer: 2.57nm Problem 2.6 A jet arcraft s flyng through a regon where the ar s 10% supersaturated wth water vapour (.e. the relatve humdty s 110%). After coolng, the sold smoke partcles emtted by the jet engnes adsorb water vapour and can then be consdered as mnute sphercal droplets. What s the mnmum radus of these droplets f condensaton s to occur on them and a vapour tral form? Data: γ(h 2 O) = 75.2 mn m -1, M(H 2 O) = kg mol -1, ρ(h 2 O) = 1030 kg m -3, T = 275 K. Answer: 12nm

2 Lecture 2 Adsorpton and the thermodynamcs of surfaces Adsorpton at gas lqud nterface

3 Adsorpton Adsorpton - a tendency of one component to have a hgher or lower concentraton at the nterface n comparson to adjacent phase.

4 Models of the nterface A system contanng an nterface can be dvded nto 3 regons for an extensve property B: α β σ B= B + B + B 1. Surface phase approach nterfacal regon has fnte thckness; propertes n the bulk phases are unform

5 Models of the nterface 1. Surface excess propertes approach nterface s nfntely thn; propertes of bulk phases assumed to extend tll the nterface; dfference between the real property B and the model value s called excess extensve property: B = B = B B σ excess real model α β σ V = V + V, V = 0 ntensve property: b = B / V Example: concentraton excess n = c V + c V α α β β,model ( ) n = n c V + c V σ α α β β

6 surface excess: Adsorpton ( ) n = n c V + c V σ α α β β Γ = adsorpton n σ / A the value of adsorpton depends of the nterface poston! so, we need to agree on a conventon. Gbbs conventon: adsorpton of a major component s zero: σ Γ = n / A= 0 A A

7 relatve adsorpton Adsorpton ( ) ( ) n = n c V + c V = n c V + c c V σ α α β β α α β β ( ) n = n c V + c c V σ α α β β A A A A A elmnatng V b : Γ c c α β A =Γ ΓA α β ca ca Gbbs conventon: A Γ A = 0, Γ =Γ( Gbbs) adsorpton sotherm: dependence of the adsorpton vs. bulk concentraton at constant temperature

8 Thermodynamc propertes of nterfaces Other thermodynamcs excess propertes can be defned smlarly α α β β δwmech = P dv P dv + γda α α β β δw= P dv P dv + γ da+ µ dn α α β β du = δq + δw = TdS P dv P dv + γ da + µ dn α α β β H = U + PV, dh = TdS + P dv + P dv + γ da + µ dn α α β β G = H TS, dg = SdT + P dv + P dv + γ da + µ dn G A α β T, P, P, n = γ

9 Thermodynamc propertes of nterfaces α α β β dg = SdT + P dv + P dv + γ da + µ dn surface excess dg = dg + dg + dg dg = S dt + P dv + µ dn α α α α α dg = S dt + P dv + µ dn β β β β β dg = S dt + γ da + µ dn G A σ α β σ σ σ σ = γ + µ dγ σ σ σ σ U H TS σ = = + γ + µ dγ A A A σ σ σ α β

10 Measurement of adsorpton adsorpton from concentraton change ( ) n σ = n n = c c V 0 0 adsorpton from surface analyss (samplng at the surface) n = c V + c V + c V L L S S G G real, ( ) n = n n = c c V σ S L S, real,model adsorpton from surface tenson change Gbbs equaton: for 2 component system: dγ = Γ RT Γ = B ( dln( a )) ab dγ RT d( a ) B

11 Probelms Problem 3.2 From surface tenson measurements on aqueous solutons of butanol, t was found that the slope of the graph of surface tenson aganst concentraton was mn m 2 mol -1 at a bulk concentraton of 6.40 mol m -3. Calculate the adsorpton at ths concentraton and state any assumptons made. Problem 3.3 An aqueous soluton of acetc acd (50 cm3) was shaken wth charcoal (2.5 g) untl equlbrum was reached. The concentraton of the orgnal soluton was mol dm -3, whle after adsorpton the concentraton had fallen to mol dm -3. Calculate the amount of acetc acd adsorbed on 1.0 g of charcoal.

12 Adsorpton at Gas-Lqud nterface Measurements of equlbrum adsorpton surface tenson measurements (Wlhelmy plate) surface analyss rado-labelled solutes neutron reflectometry (deuterated solutes) X-ray reflectometry formaton and collecton of foam

13 Adsorpton at Gas-Lqud nterface Observaton of adsorpton knetcs adsorpton at freshly formed nterfaces surface waves: transverse capllary waves (rpples generated by an oscllatng hydrophobc knfe edge, f= Hz). Energy dsspaton caused by compressonexpanson cycle. longtudnal waves (horzontal movement of barrer, <0.1 Hz)

14 Adsorpton of non-electrolyte solutes expermental: surface tenson vs. butanol concentraton n aqueous soluton ab dγ Γ B = RT da ( ) calculated: adsorpton B

15 Adsorpton of non-electrolyte solutes Szyszkowsk-Langmur adsorpton * γ = γ bγ * ln(1 + c / a) A A B constants Szyszkowsk-Langmur sotherm a dγ a bγ / a Γ αc Γ B = = = RT da ( ) RT1 + c / a 1+ αc * B B A B B cb 1 c = + Γ Γ α Γ B B B B B B B vald at low concentratons

16 Adsorpton of non-electrolyte solutes Equaton of state (Schonfeld and Rdeal) Π Aˆ Aˆ = qkt 0 ( ), where surface pressure Π= γ γ, Aˆ = 1/ Γ, solvent soluton q measure of the affnty of the adsorbed molecules Negatve adsorpton observed n dlute aqueous solutons of e.g. glycne and sucrose Knetcs of adsorbton n case of no strrng and no energy barrer: 1/2 1/2 d Γ D ct 1/2, 2ct D = Γ= dt π π

17 Adsorpton of onzed solute n case onzed solute the Gbbs equaton must nclude contrbuton of all ons: from electro neutralty: dγ =Γ + dln c + +Γ dln c M M X X RT c = c = c and Γ =Γ =Γ + + M X M X 1 dγ Γ= 2RT dc

18 Absorpton of surfactants surfactants (stands for: surface actve agents) belong to a class of amphphles Gbbs monolayers

19 Absorpton of surfactants Surfactants can be: anonc, catonc, non-onc

20 Absorpton of surfactants Surface tenson of surfactant usually falls to a lower lmt and becomes a constant after saturaton adsorpton

21 Absorpton of surfactants Gbbs equaton occasonaly reveals dscrepances wth expermentally measured values. surface hydrolyss: one of the ons s not adsorbed by the surface and replaced by H +. dγ =Γ + dln( c + ) +Γ dln( c ) +Γ + dln( c + ) M M X X H H RT =0 =const dγ =Γ RT X dln( c ) X ndfferent electrolyte: same stuaton can be created artfcally to avod ambgutes that mght arse due to surface hydrolyss by addng large amounts of M + Y - : dγ dγ =Γ + dln( c + ) +Γ dln( c ) +Γ dln( c ) =Γ dln( c ) M M X X Y Y X X RT RT =0 =const

22 Mcelles above certan crtcal concentraton the surface tenson becomes ndependent of concentraton: crtcal mcelle concentraton (cmc). dγ =Γ X dln( c ) ln( ) S X +Γ S X d c M XM RT not all amphphles form mcelles. at cmc other propertes show dstnct changes as well (e.g. osmotc pressure ndcate that the number of solute partcles stays the same above cmc). formaton of mcelles means decrease n G, prmarly due to large ncrease n entropy: hydrophobc nteracton.

23 Mcelles solublty of surfactants: there s a sharp rse n solublty of onc surfactant above a certan temperature: Krafft temperature for non-onc surfactants rasng temperature appears to decrease solublty, so above cloud pont large aggregates of surfactant appear

24 Mcelle structure at low concentratons mcelles are sphercal wth dameter slghtly less than twce the length of the molecule at hgher concentraton, more complex structures are formed f organc solvent are used, reverse (nverted) mcelles wll be formed

25 Mcelle structure

26 Solublzaton mcelles can ncrease solublty of otherwse sparngly soluble substances, as the centre of a mcelle s a lqud hydrocarbon

27 Factors affectng cmc cmc s affected by factors changng solublty and nteracton n the soluton: Amphphle chan length (l): longer chan means lower solublty. ln( cmc) = a bλ Salt concentraton: as onc strength ncrease the nteracton between the charged head groups of onc surfactants wll decrease,.e. cmc wll decrease. Head group structure: cmc can be affected (but not much) Structure of the alkyl chan: ncrease n bulkness rases cmc, addton of benzene rng lowers cmc Other surfactants Polar addtves: long-chan materals wth polar group lower cmc and ncorporate n the mcelles.

28 Impurty effects mpurtes can lead to a mnmum on surface tenson vs. concentraton curve. another (better) test for mpurtes s based on varaton of surface tenson when area of the surface s changed.

29 Applcaton of surfactants Wettng: contact angle s reduced. Detergency: detergent: mxture of surfactants wth other addtves for effectve cleansng (bulders, brghteners and bleaches, electrolyte fller) cleansng effcency grows wth the concentraton up to cmc Water repulson hydrophlc surface can be made hydrophobc Emulsfcaton Froth flotaton n ore treatment: partcles wth hydrophobc surface stck to bubbles and are carred upwards when foam s formed (lead and copper sulfde ores, oxdes, coal etc.) Ol recovery Membrane dsrupton absorpton on the nterface emulsfyng sol

30 Flms and Foams Structure of a foam layer: Foam layer has a surface tenson, therefore foam flm tres to mnmze the area: Laplace equaton s applcable as well: when a foam thckness decreases due to lqud dranage t forms black flms: common black flm (lqud core) and Newton black flm (no lqud core)

31 Flms and Foams Permeablty to gases monolayer permeaton: J = km cm dffuson through the soluton: J 1 zb = c km DH km J DH = c z b b k

32 Flms and Foams Foam formaton (by bubblng)

33 Flms and Foams the Plateau border as the curvature radus s smaller at the trple pont, the pressure wll be lower and the lqud wll flow there druptng the foam foam can be stablzed by repulsve pressure between the adsorbed layers: dsjonng pressure

34 Tears of wne Flms and Foams

35 Flms and Foams The Marangon effect buoyancy-drven convecton presence of surfactant s mpedng convecton

36 Aerosols Formaton: dsperson method aggregaton methods monodsperse sze dstrbuton can be created by controlled nucleaton Precptaton, e.g. electrostatc

37 Problems 3.2 From surface tenson measurements on aqueous solutons of butanol, t was found that the slope of the graph of surface tenson aganst concentraton was mn m 2 mol -1 at a bulk concentraton of 6.40 mol m -3. Calculate the adsorpton at ths concentraton and state any assumptons made. 4.1 A surfactant soluton of sodum dodecyl sulfonate (concentraton 1.7 mmol kg -1 ) s found to have a surface tenson of 63 mn m -1 at 25ºC. Calculate the adsorpton of the surfactant at the ar/soluton nterface and state the two assumptons that are requred. The surface tenson of pure water at ths temperature s 72.0 mn m -1.