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

Entropy in Self-Assembly - Lecture 1

International Centre for Theoretical Sciences
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