Tensorial Minkowski functionals of triply periodic minimal surfaces

Probing Water State during Lipidic Mesophases Phase Transitions

We investigate the static and dynamic states of water network during the phase transitions from double gyroid ( I a 3 ‾ d ) to double diamond ( P n 3 ‾ m ) bicontinuous cubic phases and from the latter to the reverse hexagonal (HII ) phase in monolinolein based lipidic mesophases by combining FTIR and broadband dielectric spectroscopy (BDS). In both cubic(s) and HII phase, two dynamically different fractions of water are detected and attributed to bound and interstitial free water. The dynamics of the two water fractions are all slower than bulk water due to the hydrogen-bonds between water molecules and the lipid's polar headgroups and to nanoconfinement. Both FTIR and BDS results suggest that a larger fraction of water is hydrogen-bonded to the headgroup of lipids in the HII phase at higher temperature than in the cubic phase at lower temperature via H-bonds, which is different from the common expectation that the number of H-bonds should decrease with increase of temperature. These findings are rationalized by considering the topological ratio of interface/volume of the two mesophases.

Vitreous Carbon, Geometry and Topology: A Hollistic Approach

Glass-like carbon (GLC) is a complex structure with astonishing properties: isotropic sp2 structure, low density and chemical robustness. Despite the expanded efforts to understand the structure, it remains little known. We review the different models and a physical route (pulsed laser deposition) based on a well controlled annealing of the native 2D/3D amorphous films. The many models all have compromises: neither all bad nor entirely satisfactory. Properties are understood in a single framework given by topological and geometrical properties. To do this, we present the basic tools of topology and geometry at a ground level for 2D surface, graphene being the best candidate to do this. With this in mind, special attention is paid to the hyperbolic geometry giving birth to triply periodic minimal surfaces. Such surfaces are the basic tools to understand the GLC network architecture. Using two theorems (the classification and the uniformisation), most of the GLC properties can be tackled at least at a heuristic level. All the properties presented can be extended to 2D materials. It is hoped that some researchers may find it useful for their experiments.

Mesoscale networks and corresponding transitions from self-assembly of block copolymers

A series of cubic network phases was obtained from the self-assembly of a single-composition lamellae (L)-forming block copolymer (BCP) polystyrene-block-polydimethylsiloxane (PS-b-PDMS) through solution casting using a PS-selective solvent. An unusual network phase in diblock copolymers, double-primitive phase (DP) with space group of [Formula: see text], can be observed. With the reduction of solvent evaporation rate for solution casting, a double-diamond phase (DD) with space group of [Formula: see text] can be formed. By taking advantage of thermal annealing, order-order transitions from the DP and DD phases to a double-gyroid phase (DG) with space group of [Formula: see text] can be identified. The order-order transitions from DP (hexapod network) to DD (tetrapod network), and finally to DG (trigonal planar network) are attributed to the reduction of the degree of packing frustration within the junction (node), different from the predicted Bonnet transformation from DD to DG, and finally to DP based on enthalpic consideration only. This discovery suggests a new methodology to acquire various network phases from a simple diblock system by kinetically controlling self-assembling process.