OF NANOCOLLOIDAL SYSTEMS ELASTIC THEORY OF NANOCOLLOIDAL SYSTEMS LABRINI ATHANASOPOULOU labrinath@ijs.si supervisor: dr. Primoz Ziherl

Labrini ATHANASOPOULOU OUTLINE 1. INTRODUCTION Soft matter NANOCOLLOIDS Hard and soft colloids Soft spheres Hertz model MY AIM Theoretical framework Methodology Numerical approach CONCLUSIONS Expected results Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU SOFT MATTER Subfield of condensed matter Energy scale comparable to kBT Building blocks’ sizes nm to μm LIQUID CRYSTALS POLYMERS COLLOIDS Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU POLYMERS AND COLLOIDS Long chains of monomers Variety of polymeric properties Plastic, silicone, DNA, … Substance dispersed evenly in another substance Solid, liquid or gas Blood, milk, shaving cream, … Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU NANOCOLLOIDS Novel class of highly-branched polymers Functionality: number of arms arms core monomers N STAR POLYMERS DENDRIMERS Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU HOW NANOCOLLOIDS INTERACT STAR POLYMERS DENDRIMERS effective potential distance between two centers Likos et al. (2002) Georgiou (2012) Labrini ATHANASOPOULOU

CLOSE- PACKED AND OPEN LATTICES HARD COLLOIDS SOFT NANOCOLLOIDS BCC Jonas et al. (2004) A15 σ FCC Close-packed lattices quasicrystal Open lattices Zeng et al. (2004) Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU

HYPOTHESIS Many-body interactions Shape and deformation Percec (2003) Nanocolloids as soft elastic spheres Can we find an effective model? Framework: theory of elasticity Georgiou (2012) Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU

HERTZ ELASTIC MODEL 2D case for disks contact zone Small deformations Contact area: flat and small Normal stresses Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU

PHASE DIAGRAM OF HERTZIAN SPHERES temperature density Pamies et al. (2009) Prestipino et al. (2009) Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU

? LIMITED VALIDITY OF HERTZ MODEL Square lattice Hertz regime free energy unit cell b) c) d) e) density SMALL LARGE DEFORMATION Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU AIM Phase diagram of crystal lattices of elastic disks (2D) and spheres (3D) Theory of elasticity: stress, strain, Hookean, non-Hookean models for large deformations Numerical approach: finite element method Expected results Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU 2D LATTICES Regular lattices Hexagonal lattice unit cell cage Square lattice Honeycomb lattice Irregular lattices Rhombic lattice Columnar lattice Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU 3D LATTICES Unit cells in 3D unit cell cage BCC SC Α15 σ lattice FCC Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU THEORY OF ELASTICITY Stress field: compression tension shear Deformation field: strain tensor: free energy density Hookean free energy Non-Hookean: Neo-Hookean free energy Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU FINITE ELEMENT METHOD Quarter of a disk in a columnar lattice dynamical boundary conditions elements Initial shape Displacement field Deformed disk Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU EXPECTED RESULTS Phase diagram for 2D and 3D crystal lattices Poisson ratio vs. density Larger variety of lattices Coexistence T=0 Close-packed lattice Open lattices deformation Labrini ATHANASOPOULOU

Labrini ATHANASOPOULOU EXPECTED RESULTS Dendrimer Diffraction pattern 2 interacting dendrimers A15 lattice Columns in anisotropic coordination Iacovella et al. (2011) Labrini ATHANASOPOULOU

S UMMA R Y Soft nanocolloids Close-packed and open lattices Nanocolloids as elastic soft spheres Small and large deformations of elastic spheres Theory of elasticity and numerical approach Expectations Collaborations

THANKS