Pressure- and temperature- dependences of shape fluctuations in a microemulsion system

1. Pressure- and temperature- dependences of shape fluctuations in a microemulsion system Hideki Seto Department of Physics, Kyoto University, Japan Michihiro NagaoISSP, The University of Tokyo Takayoshi TakedaFIAS, Hiroshima Univ. Youhei Kawabata Tokyo Metropolitan Univ. …and many other colleagues with collaborations of

2. Ternary microemulsion systemswater + oil + surfactant

3. bending modulus Bending energy Spontaneous curvature Helfrich’s approach W. Helfrich, Z. Naturforsch. C28 (1973) 693 mean curvature Gaussian curvature

5. Phase transitions SANS/SAXS and NSE studies Phase transitions are observed with increasing temperature, pressure, ... spontaneous curvatures bending moduli change with changing conditions

6. AOT + D2O + n-decane water-in-oil droplet

7. T [˚C] 2 phase lamellae 50 binodal line 40 30 droplet 1 phase 20 f 0 0.1 0.2 0.3 0.4 0.5 0.6 T-f(droplet volume fraction) phase diagram Cametti et al.Phys. Rev. Lett. 64 (1990) 1461.

8. Origin of temperature dependence T lamellar structure R ~ 0 s R > 0 s w/o droplet R > > 0 s

9. P [ MPa ] 40 30 binodal line 2 phase Lamellae 20 droplet 1 phase 10 percolation line 0 f 0 0.1 0.2 0.3 0.4 0.5 0.6 Pressure dependence Saïdi et al.J. Phys. D : Appl. Phys. 28 (1995) 2108.

10. SANS measurement Nagao and Seto, Phys. Rev. E 59 (1999) 3169 upper part lower part

11. Determination of P(Q) and S(Q) P(Q):form factor of droplet polydisperse droplet with Schultz size distribution Kotlarchyk and Chen, J. Chem. Phys. 79 (1983) 2461. (R0: mean radius of water core) S(Q):inter-droplet structure factor hard core and adhesive potential Liu, Chen, Huang, Phys. Rev. E 54 (1996) 1698 L(Q)=1/(xr2Q2+1) :surfactant concentration fluctuation

12. Result of fitting I(Q)=P(Q)S(Q)+L(Q) R=51.9(Å) f=0.28 W=-3kBT e=0.0013 Z=26.1 R0=40.5 (Å) xr=10.6(Å)

13. Pressure dependence of W

14. Pressure-induced transition pressure

15. Dynamical behavior Pressure-dependence Temperature-dependence SAME? or DIFFERENT? dilute droplet Y. Kawabata, Ph. D thesis to Hiroshima Univ. dense droplet M. Nagao et al., JCP 115 (2001) 10036.

16. Neutron Inelastic/Quasielastic Scattering Low wavelength resolution Low energy resolution High resolution Less intensity

17. Neutron Spin Echo Larmor precession in a magnetic field Wavelength resolution and engergy resolution are decoupled

18. Advantages of NSE Highest energy resolution ~ neV I(Q,t) is observed : better to investigate relaxation processes BEST for SLOW DYNAMICS in SOFT-MATTER

19. Dense droplet

20. Model of membrane fluctuation Zilman and Granek, Phys. Rev. Lett. 77 (1996) 4788) The Stokes-Einstein diffusion coefficient is, The relaxation rate is, Thus they obtained the stretched exponential form of the relaxation function as, where

21. k k k ambient-T,P high-P high-T 0.4 k T 1.4 k T 2.6 k T B B B Bending modulus G(Q)= 0.024(kBT)2/3k 1/3h -1Q3

22. Dilute droplet temperature / pressure AOT / D2O / d-decane (film contrast) fs=0.37 (AOT volume fraction) f =0.1 (droplet volume fraction)

23. Measured points AOT / D2O / d-decane (film contrast) fs=0.37 (AOT volume fraction) f =0.1 (droplet volume fraction)

24. T=298.15K P=22 MPa 100 ] -1 10 I(Q) [cm T=329.15K P=0.1MPa 1 T=298.15K P=0.1MPa 2 3 4 5 6 7 8 9 2 0.01 0.1 -1 ] Q [Å T=25 ˚C → 65˚C R0 ~ 32Å → 28Å p ~ 0.16 → 0.18 P=0.1 MPa → 60 MPa R0 ~ 32 Å → 30Å p ~ 0.16 Result of SANS

25. T=43˚C/ P=0.1MPa Room temperature/pressure T RT/ P=20MPa P NSE profiles

26. Expansion of the shape fluctuation into spherical harmonics damping frequency of the 2nd mode deformation up to n=2 mode gives mean-square displacement of the 2nd mode deformation shape deformation translational diffusion where Milner and Safran model Huang et al. PRL 59 (1987) 2600. Farago et al. PRL 65 (1990) 3348. n=0 mode n=2 mode

27. T= 19˚C T= 25˚C T= 35˚C 12 T= 49˚C temperature T= 55˚C P= 21MPa 10 P= 40MPa P= 60MPa Deff [10-7 cm2/s] 8 6 4 pressure 2 0.04 0.06 0.08 0.10 0.12 0.14 -1 Q [Å ] Effective diffusion constant

28. EXPERIMENTALY OBTAINED PARAMETERS KNOWN PARAMETERS From SANS experiments  Seki and Komura Physica A 219 (1995) 253  Expansion of the theory Y. Kawabata, Ph. D thesis

29. Pressure- and temperature-dependence of k and <|a2|2> k (B): Pressure dependence of (A) : Temperature dependence of k

30. TB , PB : binodal point T0 , P0 : ambient temperature/pressure ambient temperature/pressure binodal point Introducing reduced pressure / temperature

31. Temperature Pressure Schematic picture

32. 64 62 60 aH[Å2] 58 56 54 52 -0.8 -0.4 0.0 0.4 ^ ^ T, P Pressure- and temperature dependences of head area temperature area per molecule a H= number of surfactants per droplet pressure number of surfactants number of surfactants per droplet = number of droplets Whole volume of droplets number of droplets = volume of a droplet

33. pressure temperature structure dilute droplet 2-phase droplet dense droplet lamellar/bicontinuous k increase decrease microscopic tail-tail interaction counter-ion dissociation spontaneous curvature Rs k bending modulus for Gaussian curvature Summary Pressure- and temperature-dependences of the structure and the dynamics of AOT/D2O/decane were investigated.