Structural studies of cubic phases Marianne Impéror-Clerc LPS -UMR 8502-, UPS, Orsay
Ia3d
Im3m
Molecules, phases and self-assembly Wide range of molecular compounds Self-assembly Supramolecular structures, periodic at the nanoscale The symmetry of these organised phases are the same for all molecular compounds Templating of nanostructured materials
Molecules and self-assembly organic chemistry compounds OH Cn H
NO 2
O O Cn H
O 2n+1 O
2n+1
OH
NO 2
two immiscible parts at the molecular level : - hydrophilic/hydrophobic - polar/apolar
metallomesogens, dendrimers
self-assembly
industrial compounds : surfactants, cosmetics, food, biochemistry O
supramolecular structures, periodic at the nanoscale
O-Na+
EOmPOnEOm CH3(CH2)10COO-Na+
biological molecules : fatty acids, lipids
tribloc copolymers
Sequence of mesophases balance between the two parts –hydrophilic/hydrophobic or polar/apolarphases directes
Micellaire 3D
hex 2D
phases inverses
intermédiaire 3D lamellaire
courbure
courbure positive
courbure nulle
courbure négative frac vol para
The mesophase morphology results from the global optimisation of the nanosegregation between the two immiscible parts
Micellar cubic phases Different types of packing of micelles Non-ionic CnEOm/water systems hcp packing Anne-Marie Levelut (LPS, Orsay) Jean-François Sadoc (LPS, Orsay) Xiangbing Zeng (Sheffield University, UK)
Types of observed packing of micelles hard sphere packing fcc
tetrahedral close packing –tcp-
hcp
Pm3n
120°
Z = 12
Fm3m
P63/mmc
Z = 14
hard-sphere potential
Fd3m
Z = 15
bcc
Z = 16 b
repulsive long-range potential
y z
x
P42/mnm c
Im3m
a
Packing of hard spheres How to stack oranges ???
hard sphere packing fcc and hcp
conjecture de Kepler, 1611: No packing of balls of the same radius in three dimensions has density greater than the face-centered cubic packing. T. C. Hales, A proof of the Kepler conjecture. 1998-2005 …. C
A
fcc and hcp : same compacity
B
B
fcc has a very slightly more high entropy than hcp
A
A
fcc
hcp
Packing of « soft » spheres ? area minimisation
tetrahedral close packing –tcpFranck, Kasper, 1958
micellar phases of surfactants J. Charvolin, J. F. Sadoc, 1988
soap foams
dendrimers
Soap film area minimisation
P. Ziherl, P., R. D. Kamien, 2001 maximizing entropy of the dendrimer corona chains by minimizing the contact area
Geometrical approach
D. Weaire, R. A. Phelan, 1994
Pm3n
Pm3n is an ideal periodic foam with equal cell volumes -Kelvin conjecture-
Non-ionic CnEOm micellar phases O
O
CH3(CH2)n-1 (OCH2CH2)mOH
O
O
OH
C12EO12
C12EO8
hcp
Pm3n Pm3n
M. Clerc J. Phys. II France (1996)
M. Imai J. Chem. Phys. (2005)
P. Sakya, J.M. Seddon Langmuir (1997)
hcp packing in C12E8
single-crystal analysis P63/mmc c/a=(8/3)1/2 c
A B A B A
M. Clerc J. Phys. II France (1996)
b
b
b a
c
a
a
c
120 100 80
FF : form factor core/shell model (110)
(a)
(102)
140
(100) (002)
Bragg peak intensities
(101)
hcp packing in C12E8
60
(103)
40 20 1
2
3
4
electron density around a micelle electron density reconstruction
X. Zeng, M. Impéror-Clerc, J. Phys. Chem B (2007)
Conclusion about micellar cubic phases
In project : electron density reconstructions for bcc and Pm3n link between the shape of the micelles and the type of packing : hard sphere packing or tcp
Thermotropic cubic phases Many examples of Ia3d bicontinuous phases A complex tri-continuous Im3m cubic phase : structure solving using the inverse method Anne-Marie Levelut, Michèle Veber (LPS, Orsay) Goran Ungar, Xiangbing Zeng (Sheffield University, UK)
Bicontinuous Ia3d cubic phase r l
ε
surface G
electron density reconstruction
V. Luzzati Nature (1967)
Gyroid bicontinuous cubic O. Terasaki and coll. JACS (2004)
Two cubic phases formed by the ANBC-n compounds NO 2 O
OH Cn H
O Cn H
O 2n+1 O
2n+1
ANBC-n
OH
NO 2
Im3m Structural model ?
M. Impéror-Clerc, M. Veber, A.M. Levelut ChemPhysChem (2001)
n : alkyl chain length S. Kutsumizu et al. Liquid Crystals. (2002)
10 % mixture : Ia3d-Im3m reversible phase transition NO 2 OH
pure ANBC-18
Cn H
O O Cn H
O 2n+1 O
2n+1
OH
NO 2
K
125°C
SmC
156°C
Ia3d
197°C
I O C 12H 25
mixture with 10 % 3,5-didodecyloxobenzoic acid K
120°C
SmC
125°C
Ia3d Ia3d
175°C 145°C
Im3m
200°C
O OH
I
Im3m
aIm3m = 17.3 nm
aIa3d = 11.7 nm dSmC = 4.6 nm d211 = 4.8 nm
O C 12H 25
size ratio 1.5
d321 = 4.6 nm
Im3m single-crystal data After slow cooling from the isotropic liquid phase … 258< α