Lecture 3. Phenomena at Liquid-gas and Liquid-Liquid interfaces. I

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1 Lecture 3 Phenomena at Liquid-gas and Liquid-Liquid interfaces. I

2 Adsorption at Gas-Liquid interface Measurements of equilibrium adsorption surface tension measurements (Wilhelmy plate) surface analysis radio-labelled solutes neutron reflectometry (deuterated solutes) X-ray reflectometry formation and collection of foam

3 Adsorption at Gas-Liquid interface Observation of adsorption kinetics adsorption at freshly formed interfaces surface waves: transverse capillary waves (ripples generated by an oscillating hydrophobic knife edge, f= Hz). Energy dissipation caused by compressionexpansion cycle. longitudinal waves (horizontal movement of barrier, <0.1 Hz)

concentration curve is measured and experimental points fitted to a curve 2.

4 Adsorption of non-electrolyte solutes Calculating the adsorption from measured surface tension vs. concentration curve 1. surface tension vs. concentration curve is measured and experimental points fitted to a curve 2. Gibbs equation is used to calculate the adsorption Γ = ab dγ RT da ( ) calculated: adsorption B B

5 Adsorption of non-electrolyte solutes For many binary systems the surface tension follows Szyszkowski-Langmuir equation: * γ = γ bγ * ln(1 + c / a) A A B constants followed well at low concentrations, significantly deviates at higher due to solvent competition

Adsorption of non-electrolyte solutes Szyszkowski-Langmuir adsorption * γ = γ bγ * ln(1 + c / a) A A B Szyszkowski-Langmuir isotherm a dγ a bγ / a Γ αc Γ B = = = RT da ( ) RT1 + c / a 1+ αc * B B

6 Adsorption of non-electrolyte solutes Szyszkowski-Langmuir adsorption * γ = γ bγ * ln(1 + c / a) A A B Szyszkowski-Langmuir isotherm a dγ a bγ / a Γ αc Γ B = = = RT da ( ) RT1 + c / a 1+ αc * B B A B B B B B form suitable for linear plotting cb 1 c = + Γ Γ α Γ B B B B and Γ = B ab dγ RT da ( ) B Szyszkowski-Langmuir isotherm has a form similat to Langmuir equation valid at low concentrations

Adsorption of non-electrolyte solutes Equation of state (Schonfield and Rideal) Π Aˆ Aˆ = qkt 0 ( ), where surface pressure Π= γ γ, Aˆ = 1/ Γ, solvent solution i i q measure of the affinity of the

7 Adsorption of non-electrolyte solutes Equation of state (Schonfield and Rideal) Π Aˆ Aˆ = qkt 0 ( ), where surface pressure Π= γ γ, Aˆ = 1/ Γ, solvent solution i i q measure of the affinity of the adsorbed molecules egative adsorption observed in dilute aqueous solutions of e.g. glycine and sucrose Kinetics of adsorbtion in case of no stirring and no energy barrier, initial stages of adsorption are limited by the solute diffusing to the surface: 1/2 1/2 d Γ D ct 1/2, 2ct D = Γ= dt π π

8 Adsorption of ionized solute in case ionized solute the Gibbs equation must include contribution of all ions: from electro neutrality: 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

9 Absorption of surfactants surfactants (stands for: surface active agents) belong to a class of amphiphiles Gibbs monolayers

10 Absorption of surfactants Surfactants can be: anionic (the most used), cationic, non-ionic zwitterionic

11 Unconventional surfactants

12 Absorption of surfactants Gibbs equation occasionaly reveals discrepancies with experimentally measured values. surface hydrolysis: one of the ions is 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 indifferent electrolyte: same situation can be created artificially to avoid ambiguities that might arise due to surface hydrolysis by adding 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

13 Absorption of surfactants Surface tension of surfactant usually falls to a lower limit and becomes a constant after saturation adsorption

at cmc other properties show distinct change

14 Micelles above certain critical concentration the surface tension becomes independent of concentration: critical micelle concentration (cmc). dγ =Γ X dln( c ) ln( ) S X +Γ S X d c M XM RT not all amphiphiles form micelles. at cmc other properties show distinct changes as well (e.g. osmotic pressure indicate that the number of solute particles stays the same above cmc). formation of micelles means decrease in G, primarily due to large increase in entropy: hydrophobic interaction.

15 Micelles For ionic surfactants: the solubility of surfactants exhibits a sharp rise in above a certain temperature: Krafft temperature. Below Krafft temperature solubility is lower than CMC, otherwise, solubility doesn t depend significantly on temperature bu depends on the ionic strength for non-ionic surfactants raising temperature appears to decrease solubility, so above cloud point large aggregates of surfactant appear

Micelle structure the shape of micelle depends of several factors at low concentrations micelles are spherical with diameter slightly less than twice the

16 Micelle structure the shape of micelle depends of several factors at low concentrations micelles are spherical with diameter slightly less than twice the length of the molecule at higher concentration, more complex structures are formed if organic solvent are used, reverse (inverted) micelles will be formed

17 Micelle structure

18 Solubilization micelles can increase solubility of otherwise sparingly soluble substances, as the centre of a micelle is a liquid hydrocarbon

19 Self-Assembly of Amphiphilic Molecules sometimes can be hard and solid, but most of the time are soft and fluid like. Commonly referred as complex fluids. usually characterized by size distribution most important interactions: ionic repulsion of head groups and hydrophobic interaction of the tails.

20 Thermodynamics of Self-Assembly Let s consider surfactant in the solvent and in the micelle: 0 µ ( solvent) = µ + RT lns sur sur at [S]=CMC the chemical potential of the surfactant in micelles and solution is equal: µ micelle µ kt CMC 0 sur ( ) = sur + ln the molar Gibbs energy of micelle formation: G = micelle = RT CMC micelle 0 m µ sur( ) µ sur ln

21 Thermodynamics of Self-Assembly If several aggregated structures are in equilibrium than the chemical potential of surfactant molecules in every structure is the same: µ = µ + kt ln X = µ + kt ln X =... = µ + kt ln X

22 Thermodynamics of Self-Assembly or, from kinetics 1 1 ( / ) kx = k X 0 0 K = k1/ k = exp ( µ µ 1)/ kt (( / ) exp ( µ 0 µ 0 ) / ) / ( ) ( 0 0 exp µ µ )/ 1 1 X = X M M kt M M ( ) X = X kt M

23 Formation of aggregates aggregates are formed if µ < µ rod-like aggregates µ = ( 1) αkt µ = µ + α kt /

24 Formation of aggregates 2D aggregates µ = µ + αkt / D aggregates µ = µ + αkt /

25 CMC ( ( ) ) 0 0 exp µ µ / 1 1 X = X kt = ( exp ( 1 1/ ) ) α α α = X 1 X1e as concentrations cannot be larger than 1 X1 < e α ( ) ( 0 0 ) 1 µ 1 µ X = CMC = exp / kt e α crit

26 Aggregate distribution above CMC discs, p=1/2 spheres, p=1/3 α = 1 X X e e α = 1 X X e e α α for disks and spheres there are very few aggregates of finate size, the transition goes to an aggregate of infinite size rods, p=1 1 α X = X e e α for rods we expect a polydispersed distribution

27 Aggregate distribution above CMC Mean aggregation number: max = M = Ce α

28 Optimal head group area hydrophobic interaction (attractive) can be measured as decrease of water-oil surface tension. Thus it can be written as : ga, g=20-50 mj/m 2. head-head interaction: K/a 2 Π+ a/ A A b = kt compare: 2D van der Waals equation: ( )( ) µ γ = a+ K / a = 2 a ; a = K µ γ γ _min 0 0 γ = 2 a + a a a µ γ optimal head group area, mainly depends on the head (not the tail length) ( ) 2 0 0

29 Optimal headgroup area Optimal headgroup area approach: contains essential features of interlipid interaction doesn t include into account specific headgroup interaction, e.g. ionic bridging specific chain-chain interaction effect of surface curvature on the energy

Geometric packing The geometry of aggregate is defined by the following factors: optimal headgroup area a 0 ; maximum effective length of the chain, critical chain length l

30 Geometric packing The geometry of aggregate is defined by the following factors: optimal headgroup area a 0 ; maximum effective length of the chain, critical chain length l c ; volume of the hydrocarbon chain v. for saturated hydrocarbons: c max ( ) ( ) 10 l l + n nm v + n nm 3 3 packing parameter (shape factor): v al 0 c

Spherical micelles For a spherical micelle of radius R with aggregation number M: M 2 3 4π R 4π R = = R= 3v a0 a 3v 0 v la < c 0 1 3

31 Spherical micelles For a spherical micelle of radius R with aggregation number M: M 2 3 4π R 4π R = = R= 3v a0 a 3v 0 v la < c Example: SDS-micelle M=74; 12 carbon chain; from equation we get: v=0.35 nm 3 ; l c =1.67 nm; a0=0.57 nm 2 ; R=1.84 nm v/a 0 l c =0.37

32 Cylindrical micelles 1 v 1 < < 3 al 2 0 c lipids forming spherical micelles at low salt concentration might switch to cylindrical at higher ionic strength; from thermodynamics, the cylindrical micelles are large and polydisperse, mean aggregation number ~C ½. most energy is associated with ends of the micelle (spherical caps are unfavorable)

33 Bilayers 1 v < 1 2 al 0 c formed when the headgroup is small or chain is bulky, e.g. lipids with two chains lecitin bilayer

34 Bilayer: Some estimates residence time inside the membrane τ = τ / exp( E/ kt) = 55 τ / CMC R 0 0 time between colliding the interface τ τ τ 0 = s R ( micelles) /10 10 s; R ( bilayers) /10 10 s;

35 Bilayer: Some estimates elastic energy (stretching) of bilayer compare: 1 2 elastic energy = ka ( a a0) / a 2 0 γ 2 µ = 2 γa0 + ( a a0) a k k a a 2γ permonolayer; 4γ perbilayer

36 Vesicles at some condition it could be energetically favorable to eliminate the edges of a bilayer forming vesicles

37 Factors affecting structure changes factors affecting headgroup area: ionic strength, ph factors affecting chain packing (e.g. chain branching and unsaturation) effect of temperature, affects both a o and l c. lipid mixtures

38 Emulsion stability selection of emulsifier determines which type of emulsion will be formed Bancroft rule: the phase the emulsifier is more soluble in will be the continuous phase Harkins wedge theory: larger end of the emulsifier lies in the continuous phase Winsor theory: based on ratio of cohesive energies R E E LO = R<1 O/W emulsion is formed HW R>1 W/O emulsion is formed

39 Emulsion stability in case of ionic emulsifier, the droplets will interact via double layers Stern model Example: stabilization of oil-water emulsions with inorganic electrolytes (e.g. KCS) due to anions preferably adsorbed in oil

40 Steric interaction: Emulsion stability loss of configuration entropy due to the excluded volume higher osmotic pressure in the region where absorbed layers overlap changes in the conformation of polymer loops due to approached droplet stabilization by solid particles

emulsions or solid-stabilized emulsions)

41 Stabilization with solid particles For effective stabilization, the particles should assume a stable position on the interface with a non-zero contact angle (Pickering emulsions or solid-stabilized emulsions) liquid marble on solid surface stabilized with hydrophobic powder

Function: cuts the hydrophilic tail of k-casein, therefore destroying sterical stabilization of casein

42 Cheese case Casein micelles in milk are sterically stabilized by k-casein; Active enzyme: Proteinase rennin, originally obtained from calf stomach, currently synthesized in bacterial host, e.g. under a name Chymosin. Function: cuts the hydrophilic tail of k-casein, therefore destroying sterical stabilization of casein micelles Other substances involved: CaCl 2 accelerates aggregation by screening negative charges

43 Problems A surfactant solution of sodium dodecyl sulfonate (SDS) (concentration 1.7 mmol kg -1 ) is found to have a surface tension of 63 m m -1 at 25ºC. Calculate the adsorption of the surfactant at the air/solution interface and state the two assumptions that are required. The surface tension of pure water at this temperature is 72.0 m m -1. Below what aggregation number SDS micelles can be spherical? Estimate CMC for Hexane in water. Surface tension of Hexane-Water interface is 51.1m/m

Monolayers. Factors affecting the adsorption from solution. Adsorption of amphiphilic molecules on solid support

Monolayers. Factors affecting the adsorption from solution. Adsorption of amphiphilic molecules on solid support Monolayers Adsorption as process Adsorption of gases on solids Adsorption of solutions on solids Factors affecting the adsorption from solution Adsorption of amphiphilic molecules on solid support Adsorption