elastic theory of nanocolloidal systems

ELASTIC THEORY OF NANOCOLLOIDAL SYSTEMS

LABRINI [email protected]

supervisor: dr. Primoz Ziherl

OUTLINE

Labrini ATHANASOPOULOULabrini 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

SOFT MATTER


• Subfield of condensed matter

• Energy scale comparable to kBT

• Building blocks’ sizes nm to μm

LIQUID CRYSTALS POLYMERS COLLOIDS

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, …


STAR POLYMERS

• Novel class of highly-branched polymers

• Functionality: number of arms

DENDRIMERS

NANOCOLLOIDS

arms

core

monomersN


HOW NANOCOLLOIDS INTERACT

STAR POLYMERS

Likos et al. (2002)Georgiou (2012)

DENDRIMERS

effec

tive

pote

ntial

distance between two centers

Labrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOU

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

Labrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOULabrini ATHANASOPOULOU

HYPOTHESIS


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


HERTZ ELASTIC MODEL


contact zone

2D case for disks

• Small deformations

• Contact area: flat and small

• Normal stresses


PHASE DIAGRAM OF HERTZIAN SPHERES


Pamies et al. (2009)density

tem

pera

ture

Prestipino et al. (2009)


LIMITED VALIDITY OF HERTZ MODEL


unit cell

Square lattice

density

Hertz regimea)

b) c) d) fr

ee e

nerg

y ?

DEFORMATIONSMALL LARGE

e)


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


Columnar lattice

Honeycomb lattice

Square lattice

Hexagonal lattice

2D LATTICES

• Regular lattices

unit cell

• Irregular lattices

Rhombic lattice

cage


3D LATTICES

FCC

BCC

• Unit cells in 3D

unit cell

SC

σ latticeΑ15

cage


• Stress field:

compression tension shear

• Deformation field: strain tensor: free energy density

THEORY OF ELASTICITY

Hookean free energy Non-Hookean: Neo-Hookean free energy


Quarter of a disk in a columnar lattice

Displacement fieldInitial shape Deformed disk

elements

dynamical boundary conditions

FINITE ELEMENT METHOD


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


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

elastic theory of nanocolloidal systems

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