Francesco Sciortino Simple models of competitive interactions in soft-matter: re-entrant liquids and gels on heating Workshop on Soft Matter Self Assembly and Dynamics, January 9- 10th, 2014 Hyderabad.

Outline of the talk Unconventional Gas-Liquid Phase Behaviors. Re-entrant liquids (J. Russo, L. Rovigatti, J. Tavares, Texeira, M. Telo da Gama) A patchy particle model that gels on heating (S. Roldan, F. Smallenberg, W. Kob) A possible DNA implementation (F. Romano)

Unconventional (gas-liquid) phase diagrams standard Gas-dominated liquid-dominated valence-dominated Bianchi et al, PRL 97, , 2006, Russo et al PRL 1a06, (2011); Rovigatti et al Phys.Rev.Lett. 111, (2013) FS et al PRL 103, (2009)

Competitive Interactions Modulate the entropy-enthalpy balance to stabilize different local structures: In this talk, the entropy-enthalpy balance promotes the emergence of a structure controlled by energy (stable at low T) which competes with a structure stabilized by entropy at intermediate T.

Dipolar Hard Spheres… competition between chaining and branching Tlusty-Safram, Science (2000) Camp et al PRL (2000)

Can we reproduce this “pinched” phase diagram with a simple patchy model ? Well defined pair-interaction potential Exploit the Wertheim theory as a tool J. M. Tavares, et al Mol. Phys. 107, , Phys. Rev. E 80,

PATCHY PARTICLES THAT FORM CHAINS:  AA

PATCHY PARTICLES THAT FORM CHAINS:  AA ADD BRANCHING POSSIBILITIES ABAB

How the ground state looks like ? Start from an infinite chain of AA bonds

Splitting the chain in two parts costs  AA How the ground state looks like ? Start from an infinite chain of AA bonds

Chains win at low T Branching wins even at low T Splitting the chain in two parts costs  AA How the ground state looks like ? Start from an infinite chain of AA bonds  AB /  AA =0.5 Chaining wins at low T Branching wins even at low T  E=  AA -2  AB >0 Joining the two newly created ends provides a gain of -2  AB

Branching at finite T ? Entropy ! Which Entropy ? Bonding Volume Entropy and “configurational” Entropy

  B /   A =0.37 J. Russo, et al Reentrant Phase Diagram of Network Fluids Phys. Rev. Letts. 106, (2011) A patchy model with a “pinched” phase diagram Russo et al PRL 106, (2011);

Evolution of the phase diagram on modulating the branching strength  AB

Effective temperature valence

Part II

How do we form an equilibrium gel ? reducing “valence” Small Valence The essence of the gel state of matter

How do we break a gel ? Competing interactions…. Add a new species that compete for the bonding sites  AA  AB  AB  AA /2 Network Blocked particle

How to stabilize the network: Entropy Bonding volume AA >> Bonding volume AB

Gel bonds Blocking bonds Forming and melting the gel !

Low and high T Intermediate T

Projection in the 4-1 composition ratio (stochiometric mixture) Slower

Can we design a system that does it ?

Experiments: DNA Hydrogels

Phase behavior of DNA hydrogels

Can we realize this with the Biffi et al DNA particles ? STAR-ARM -3’(TGA)GCGTACGC(AAT)-5’ 3’-ATTGCG-5’ 3’-CGCTCA-5’ STAR-ARM -3’-TGAGCGTACGCAAT-5’ 5’-GCGTTA-3’ 5’-ACTCGC-3’ STAR-ARM -3’(TGA)GCGTACGC(AAT)-5’ AA-bonding: 8 bases paired AB-bonding: 12 bases paired (Flavio Romano)

AA-bonding: 8 bases paired AB-bonding: 12 bases paired

Nupack Evaluations: Gel bonds Blocking bonds Gel bonds Patchy model DNA

Conclusions Competitive interactions: very powerful concept for designing sensitive structured materials DNA constructs are very versatile in this respect. Hopefully, DNA re-entrant gels will be realized. Waiting for experimental realization (Milan-Rome)

Thanks to… Emanuela Bianchi, Piero Tartaglia, Emanuela Zaccarelli – Valence Phase Diagram Flavio Romano (Oxford) - DNA gels Walter Kob, (Montpellier), Sandalo Roldan, Frank Smallenburg - Gel on heating John Russo, J. M. Tavares, P. I. C. Teixeira, M. Telo da Gama(Lisbon) - Chaining and Branching Lorenzo Rovigatti - 2D SUS Tommaso Bellini, Roberto Cerbino, Silvia Biffi, Francesca Bomboi – experiments on DNA