OUTLINE
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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
SOFT MATTER
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• Subfield of condensed matter
• Energy scale comparable to kBT
• Building blocks’ sizes nm to μm
LIQUID CRYSTALS POLYMERS COLLOIDS
POLYMERS AND COLLOIDS
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• 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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STAR POLYMERS
• Novel class of highly-branched polymers
• Functionality: number of arms
DENDRIMERS
NANOCOLLOIDS
arms
core
monomersN
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HOW NANOCOLLOIDS INTERACT
STAR POLYMERS
Likos et al. (2002)Georgiou (2012)
DENDRIMERS
effec
tive
pote
ntial
distance between two centers
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CLOSE- PACKED AND OPEN LATTICES
Zeng et al. (2004)
Open lattices
BCC
σ
Jona
s et
al.
(200
4)
HARD COLLOIDS SOFT NANOCOLLOIDS
quasicrystal
A15
FCCClose-packed lattices
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HYPOTHESIS
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Geo
rgio
u (2
012)
Perc
ec (2
003)
• Many-body interactions
• Shape and deformation
• Nanocolloids as soft elastic spheres
• Can we find an effective model?
• Framework: theory of elasticity
Labrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOU
HERTZ ELASTIC MODEL
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contact zone
2D case for disks
• Small deformations
• Contact area: flat and small
• Normal stresses
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PHASE DIAGRAM OF HERTZIAN SPHERES
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Pamies et al. (2009)density
tem
pera
ture
Prestipino et al. (2009)
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LIMITED VALIDITY OF HERTZ MODEL
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unit cell
Square lattice
density
Hertz regimea)
b) c) d) fr
ee e
nerg
y ?
DEFORMATIONSMALL LARGE
e)
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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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Columnar lattice
Honeycomb lattice
Square lattice
Hexagonal lattice
2D LATTICES
• Regular lattices
unit cell
• Irregular lattices
Rhombic lattice
cage
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3D LATTICES
FCC
BCC
• Unit cells in 3D
unit cell
SC
σ latticeΑ15
cage
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• Stress field:
compression tension shear
• Deformation field: strain tensor: free energy density
THEORY OF ELASTICITY
Hookean free energy Non-Hookean: Neo-Hookean free energy
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Quarter of a disk in a columnar lattice
Displacement fieldInitial shape Deformed disk
elements
dynamical boundary conditions
FINITE ELEMENT METHOD
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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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Dendrimer
2 interactingdendrimers
Diffraction pattern
Iacovella et al. (2011)
EXPECTED RESULTS
A15 lattice
Columns in anisotropic coordination
• 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
SUMMARY
SUMMARY
THANKS