Overview
Syllabus
INTERNATIONAL
Francesco Sciortino
Outline
Translational entropy Rotational Mixing entropy Packing entropy entropy entropy
Phase Transition for a Hard Sphere System
Which one is more disordered
Hard Spheres HS
Sterically stabilized PMMA particles polydispersity 5-10 %
At constant V, we need to maximize the entropy
Which one is more disordered
A proxy to translational Entropy...
Stable Crystal
Orientation Entropy
Isotropic-Nematic Transition Onsager Theory
Dashed -Isotropic Full - Nematic
In the case of the nematic, there is an additional contribution equal to
Nematic to...
How do we calculate the fluid entropy numerically
Entropy and flexibility translation+rotation
Example of patchy particles
DNA constructs: Limited-valence patchy particles
DNA-coated patchy colloids
Entropy decides the most stable phase exactly as in HS!
Key elements for liquid stability at T=0 K: ultrastable liquids !
Crystal Selection by Entropy
S=LIL2
Predictive Self-Assembly of Polyhedral into Complex Structures
Entropic Attraction Large HS in a bath of small HS
Depletion interaction
Let's assume we have A large HS and M small HS.
AT Oc Op
M13M [V - 2Vo + Voverlap R JM _ V -2VoM
Same story from a different perspective
Real hard-spheres
Visualization of depletion forces
Vol 453| 22 May 2008 | doi:10.1038/nature06931
Depletion: shape and roughness
Osmotically driven shape-dependent colloidal separations
Another example
Lock and key colloids
Surface roughness directed self-assembly of patchy particles into colloidal micelles
Playing with the properties of the co-solute
Taught by
International Centre for Theoretical Sciences