c = pc p regime III: surface tension nearly constant because chemical potential depends only weakly on surfactant concentration chemical potential:

Transcription

1 regime III: surface tension nearly constant because chemical otential deends only weakly on surfactant concentration chemical otential: below CMC: c c s i.e. total surfactant concentration unimer concentration far above CMC: c c Kc s c s c 1/ ( K) 1/ : association number, i.e. average number of molecules er micelle, tyically K: equilibrium constant of micellization chemical otential µ s RT ln c RT RT chemical otential deends weakly on surfactant concentration s µ θ s + ln c ln 1 [ K]

2 Influence of head grou on CMC for ionic surfactants, CMC higher than for nonionic surfactants reason: electrostatic reulsions between head grous must be overcome to form micelles CMC increases with head grou charge Influence of salt on CMC for ionic surfactants, addition of salt decreases the CMC because it reduces the reulsion between charged head grous. 2

3 Influence of hydrohobic grou on CMC hydrohobicity: the more hydrohobic the chain is, the lower the CMC (e.g. fluorinated surfactants) log(cmc) number of carbon atoms length of hydrohobic chain: the longer the hydrohobic chain, the lower the CMC: log(cmc) A B n C A, B: constants n c : number of carbon atoms ionic surfactants : CMC decreases by a factor of ~2 er CH 2 added nonionic surfactants: CMC decreases by a factor of ~3 er CH 2 added 3

4 4.3.3 The Krafft temerature solubility curve CMC solubility of ionic surfactants deends strongly on temerature: increases raidly in narrow temerature range Krafft temerature: temerature at which the solubility curve meets the CMC curve Krafft temerature deends on: length of alkyl chain crystal structure interactions between head grous salt content interlay between T-deendent CMC curve and T-deendent solubility of the surfactant osition of the Krafft oint 4

5 4.3.4 The closed association model dynamic equilibrium between unimers and micelles containing unimers S S disersity in is ~20-30% equilibrium constant: K c c s c : concentration of micelles of association number, [mol/l] c s : concentration of unimers Gibbs energy change of micellization er mole of micelles: mic G θ RT ln K RT ln c c s er mole of micelles: mic G θ RT RT ln K ln c + RT ln c s für large and at the CMC: mic G θ RT ln c CMC 5

6 for ionic surfactant, include counterions C: S x + ) y α α n/ degree of dissociation of the surfactant ( n C S x, y: charges of surfactant/counterion G n RT 2 ln θ mic c CMC above CMC: added molecules go into micelles concentration of secies CMC unimers micelles surfactant concentration 6

7 unimers + CMC surfactant concentration aggregation number (number of unimers er micelles) indeendent of surfactant concentration number of micelles increases with surfactant concentration 7

8 for nonionic surfactant: θ mic H R d ln c d(1/ T ) CMC θ ln c mich CMC + const. RT lot lnc CMC vs. 1/T to determine enthaly of micellization driving force for micelle formation: increase in entroy of system of molecules in micelles comared to unassociated molecules reason: unassociated molecules ordering of surrounding water gain in entroy of water uon micelle formation >> loss of configurational entroy 8

9 4.3.5 Hydrohobic effect liquid water molecule has 4 H-bonds in a tetrahedral geometry hydrogen bond life time ~1 s. 3D hydrogen bonding network hydrohobic interactions: entroic hydrohobic units induce some order in the surrounding water. D. Chandler, Nature437 (2005) water molecules surrounding a small molecule (left) or a cluster of small molecules (right) 9

10 4.3.6 Molecular structure and interfacial curvature rediction of shae of micelles (sheres, cylinders, bicontinuous, lamellar) two models: 1. curvature model elastic energy related to curved surface 2. shae of surfactant molecule acking of molecules C. Tauin, in Soft Matter Physics, M. Daoud, C.W. Williams (Eds.), Sringer Berlin

11 Micellar shae and size: General considerations 1st condition: sace requirements of olar head and hydrohobic chain define sontaneous curvature c 0 of the interface minimization of elastic energy in absence of constraints 2nd condition: size of micelle smaller than or equal to the stretched length of hydrohobic tail area er headgrou: geometric electrostatic for uncharged membranes: F elastic < k B T membranes highly flexible G. Porte, in Soft Matter Physics, M. Daoud, C.W. Williams (Eds.), Sringer Berlin

12 Model 1: Curvature model calculation of morhology based on the curvature of a continuous surfactant film differential geometry of surfaces in each oint P: mean curvature and Gaussian curvature R 1, R 2 : radii of curvature saddle surface in bicontinuous structure c 1 < 0, c 2 > 0 1 c 1, c2 R1 c 1 + c H 2 2 K c c R mean curvature 2 Gaussian curvature 12

13 elastic free energy of a curved surface: F el κ,κ : F mean + F Gauss 1 κ ( c1 + c2 c0 ) κc1c 2 elastic moduli for mean and Gaussian curvature can be measured using dynamic light scattering related to membrane flexibility κ : κ : bending modulus, imortant for 1D deformation saddle slay modulus, imortant for saddle where c 1 -c 2 13

14 Effect of cosolutes on curvature ure surfactant monolayer insertion of short amhihiles oil in water emulsion comensation by swelling with oil molecules C. Tauin, in Soft Matter Physics, M. Daoud, C.W. Williams (Eds.), Sringer Berlin

15 Packing model 1/3 1/2 1 N s micelle cylinder vesicle bilayer inverse micelle definition of acking arameter N s V al V: surfactant volume a: area of head grou l: tail length 15

16 Packing arameter association number 3 4πRmic / 3 V volume 4πR a 2 mic surface area V armic V: volume er molecule R mic : micellar radius a: head grou area l: tail length 1 3 V al 1 3 surfactant acking arameter: N s V al variation of N s ossible mainly by altering a by variation of solvent 16

17 Packing arameter for surfactant with alkyl chain OSO3 - SDS: dodecylsulfate length of alkyl chain: l / nm n C nm: C-C bond length nm: rojection of C-C bond length onto chain axis volume of alkyl chain: ( ) 3 V / nm n C + n Me n Me 1 or 2: number of methyl grous SDS: l 1.551nm V a 0.324nm OSO nm 2 N s 0.33 association number sherical micelle 4πl 2 49 a 17

18 4.4 Liquid crystal hases at high concentrations The Gibbs hase rule relation between the number of hases that can exist in amhihile solution, P the number of comonents, C the number of degrees of freedom, F number of indeendent intensive variables i.e. for surfactant solutions: P + F C + 2 temerature, ressure, comosition one-comonent systems: C 1 F 3 P single hase (P 1): F 2, e.g. T, can take any air of values 2 hases (P 2): F 1 T and cannot be varied indeendently 3 hases (P 3): F 0 T and are fixed 18

19 4.4 Liquid crystal hases at high concentrations The Gibbs hase rule binary solvent / surfactant mixture: P + F 4 in one-hase region: T,, comosition free in two-hase region: 2 degrees of freedom, e.g. T, comosition three-hase region: e.g. eutectic line at fixed comosition (T-variation) four-hase region: oint on eutectic line where vaor ressure 19

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