Entropy in Self-Assembly - Lecture 1

Explore the fundamental concepts of entropy in soft matter self-assembly through this comprehensive lecture by Francesco Sciortino at the International Centre for Theoretical Sciences. Delve into topics such as translational and rotational entropy, phase transitions in hard sphere systems, the isotropic-nematic transition, and entropy calculations in fluids. Examine the role of entropy in crystal selection, predictive self-assembly of polyhedra, and depletion interactions. Discover how entropy influences the stability of various phases and structures in colloidal systems, including DNA-coated patchy colloids and lock-and-key particles. Gain insights into cutting-edge research on shape-dependent colloidal separations and surface roughness-directed self-assembly, providing a deep understanding of entropy's crucial role in soft matter phenomena.

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