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

2. 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

3. Labrini ATHANASOPOULOU
SOFT MATTER
Subfield of condensed matter
Energy scale comparable to kBT
Building blocks’ sizes nm to μm
LIQUID CRYSTALS
POLYMERS
COLLOIDS
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4. 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, …
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5. Labrini ATHANASOPOULOU
NANOCOLLOIDS
Novel class of highly-branched polymers
Functionality: number of arms
arms
core
monomers N
STAR POLYMERS
DENDRIMERS
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6. Labrini ATHANASOPOULOU
HOW NANOCOLLOIDS INTERACT
STAR POLYMERS
DENDRIMERS
effective potential
distance between two centers
Likos et al. (2002)
Georgiou (2012)
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7. 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)
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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)
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9. HERTZ ELASTIC MODEL 2D case for disks contact zone Small deformations
Contact area: flat and small
Normal stresses
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10. PHASE DIAGRAM OF HERTZIAN SPHERES
temperature
density
Pamies et al. (2009)
Prestipino et al. (2009)
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11. ? LIMITED VALIDITY OF HERTZ MODEL Square lattice Hertz regime
free energy
unit cell b) c) d) e)
density
SMALL
LARGE
DEFORMATION
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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
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13. Labrini ATHANASOPOULOU
2D LATTICES
Regular lattices
Hexagonal lattice
unit cell
cage
Square lattice
Honeycomb lattice
Irregular lattices
Rhombic lattice
Columnar lattice
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14. Labrini ATHANASOPOULOU
3D LATTICES
Unit cells in 3D
unit cell
cage
BCC SC
Α15
σ lattice
FCC
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15. 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
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16. Labrini ATHANASOPOULOU
FINITE ELEMENT METHOD
Quarter of a disk in a columnar lattice
dynamical
boundary conditions
elements
Initial shape
Displacement field
Deformed disk
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17. 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
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18. Labrini ATHANASOPOULOU
EXPECTED RESULTS
Dendrimer
Diffraction
pattern
2 interacting
dendrimers
A15 lattice
Columns in anisotropic coordination
Iacovella et al. (2011)
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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