1. Nematic Elastomers (NLCEs)
NLCEs are a class of biocomposites which combine the entropic elasticity of a network of cross-linked polymeric chains with the peculiar optical properties of nematic liquid crystals. To sketch the internal organization of such materials, consider that nematic (rod-like) molecules are linked to long polymeric chains, forming an anisotropic solid structure which has extraordinary properties of deformability.
The unique properties of NLCEs arise from the rod orientation changing the chain shapes and when the chains are crosslinked, changes in the degree of order being reflected in changes of shape of the bulk material. NLCEs are a fascinating example of a multi-scale material (that is, a substance whose macroscopic behavior depends on the average properties of its microscopic structure) and of a multiphysics system (in the wake of the intricate strain-order-electro-magnetic interaction). As a result, NLCEs are endowed with striking properties that enable applications including sensors, artificial muscles and lenses, bioprostheses.
My recent research on NLCEs has focused on the following areas:
My recent research on NLCEs has focused on the following areas:
- investigation of the soft modes (and semi-soft modes) by computing the low-energy states, both with analytical and numerical methods (see Fig 2).
Fig. 2 a) Phase diagram and level curves of the relaxed (coarse-grained) energy model for isotropic nematic elastomers. The three regions correspond to the Solid (no microstructure), Smectic (shear bands) and Liquid (laminate-within-laminates) phases.
b) Level curves and relaxation of an anisotropic model for nematic elastomers. The green region in the relaxed energy corresponds to a constant-stress region obtained by formation of shear-bands.
- I showed that the use of anisotropic energies is crucial to avoid that imposed stretches may be accommodated at zero stress (ideally soft response, see Fig. 2 b)). In fact a non-vanishing shear moduli in the natural state of the material is in agreement with experimental observation (see Rogez et al., 2006).
- Computed the microstructure observed in large sample of nematic elastomers, both with analytical and numerical methods.
2. Pattern formation and disclinations
Martensitic phase transformation is observed in various metals, ceramics, biological systems and, most important for technological applications, shape-memory alloys. Despite the vast potential, incorporation of the shape-memory effect into application has been relatively slow and essentially limited to Ni-Ti for a variety of reasons. Therefore it is strategically important to improve and stabilize the shape-memory effect in known materials and develop new solutions.
My studies on the analysis of martensitic microstructure have been twofold.
1. Dynamics of interfaces: avalanches.
In several phase-transforming metals, nucleation of crystal phases is triggered by a temperature gradient and propagation occurs as a series of avalanches.
By using the language and the tools of stochastic methods I have modeled the dynamical evolution of the microscopic structure of a metal as a Poisson process. Interfaces propagate and cause the growth of a self-similar pattern. Preliminary results in collaboration with Ben Hambly (Oxford) show good match between our predictions and power law distributions derived from statistical manipulations of experimental observations available for various phase-transformations.
- Martensitic phase transformation is observed in various metals, ceramics, biological systems and, most important for technological applications, shape-memory alloys. Despite the vast potential, incorporation of the shape-memory effect into application has been relatively slow and essentially limited to Ni-Ti for a variety of reasons. Therefore it is strategically important to improve and stabilize the shape-memory effect in known materials and develop new solutions.
My studies on the analysis of martensitic microstructure have been twofold.
2. Material singularities and defects: disclinations.
Amongst the most common discrete topological singularities in crystals, disclinations are one of the main mechanisms of plastic deformations in metals.
In the framework of solid-to-solid transforming materials, disclinations may be originated by various causes. In relation with avalanches (Fig. 4), disclinations may arise in the wake of large rotations of the crystal lattice such as those occurring in a multiple line intersections structure. Another possibility is the rotation of twin boundaries and linking of different variants leading to self-similar tripole-star patterns as the ones observed in Pb3 (VO4)2 (see Fig. 5-LEFT).
Main results on disclinations:
- investigation of the analytical conditions which guarantee (or forbid) the creation of self-similar loops as the one in Fig. 5 LEFT
- analysis of several mechanical models accounting for interfacial energies (collaboration with S. Patching and A. Rueland)
- general models and theories for materials defects and singularities