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

Ternary microemulsion systems water + oil + surfactant

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

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

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

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

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

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

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

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

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)

Pressure dependence of W

Pressure-induced transition

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.

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

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

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

Dense droplet

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

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

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

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

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

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

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

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

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

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

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

Schematic picture Temperature Pressure

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

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