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ELASTIC THEORY OF NANOCOLLOIDAL SYSTEMS LABRINI ATHANASOPOULOU supervisor: dr. Primoz Ziherl

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OUTLINE Labrini ATHANASOPOULOU 1.INTRODUCTION Soft matter 2.NANOCOLLOIDS Hard and soft colloids Soft spheres Hertz model 3.MY AIM Theoretical framework Methodology Numerical approach 4.CONCLUSIONS Expected results

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SOFT MATTER Labrini ATHANASOPOULOU Subfield of condensed matter Energy scale comparable to k B T Building blocks sizes nm to μm LIQUID CRYSTALSPOLYMERSCOLLOIDS

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POLYMERS AND COLLOIDS Labrini ATHANASOPOULOU 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, …

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

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

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

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

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

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

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

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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

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

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Labrini ATHANASOPOULOU 3D LATTICES FCC BCC Unit cells in 3D unit cell SC σ latticeΑ15 cage

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

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Labrini ATHANASOPOULOU Quarter of a disk in a columnar lattice Displacement fieldInitial shapeDeformed disk elements dynamical boundary conditions FINITE ELEMENT METHOD

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

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

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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 SUMMARYSUMMARY SUMMARYSUMMARY

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THANKS

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