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ELASTIC THEORY OF NANOCOLLOIDAL SYSTEMS

ELASTIC THEORY OF NANOCOLLOIDAL SYSTEMS. LABRINI ATHANASOPOULOU. labrinath@ijs.si. supervisor: dr. Primoz Ziherl. OUTLINE. 1. INTRODUCTION Soft matter. NANOCOLLOIDS Hard and soft colloids Soft spheres Hertz model. MY AIM Theoretical framework Methodology Numerical approach.

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ELASTIC THEORY OF NANOCOLLOIDAL SYSTEMS

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

  2. 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

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

  4. 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

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

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

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

  8. 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

  9. 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

  10. 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

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

  12. 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

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

  14. 3D LATTICES • Unit cells in 3D unit cell cage BCC SC Α15 σ lattice FCC Labrini ATHANASOPOULOU

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

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

  17. 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

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

  19. 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

  20. THANKS

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