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

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Presentation on theme: "ELASTIC THEORY OF NANOCOLLOIDAL SYSTEMS LABRINI ATHANASOPOULOU supervisor: dr. Primoz Ziherl."— Presentation transcript:

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

2 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

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

4 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, …

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

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

7 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

8 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

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

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

11 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)

12 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

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

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

15 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

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

17 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

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

19 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

20 THANKS


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