1. 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

2. Ternary microemulsion systems water + oil + surfactant

3. 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

5. 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

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

7. 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

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

9. 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

10. SANS measurement upper part lower part
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

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)

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 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

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 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

22. 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)

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

24. Result of SANS T=25 ˚C → 65˚C R0 ~ 32Å → 28Å p ~ 0.16 → 0.1810
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

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

26. 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

27. Effective diffusion constant12 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

28. 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  

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

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

31. Schematic picture
Temperature
Pressure

32. Pressure- and temperature dependences of head area64 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

33. 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 phase droplet
spontaneous curvature Rs
bending modulus for Gaussian curvature k