Francesco Sciortino Gelling on heating. A patchy particle story

Outline of the talk Mini-review on competitive interactions (chaining/branching, intra-inter bonding) A patchy particle model that gels on heating (S. Roldan, F. Smallenberg, W. Kob) A possible DNA implementation (F. Romano)

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.

Long range repulsion – short range attraction (charged colloids in the presence of a depletant) Suppress the phase separation in favor of a cluster phase S. Mossa, FS, P. Tartaglia, E. Zaccarelli Ground-state clusters for short-range attractive and long-range repulsive potentials Langmuir 20, , 2004 Campbell, A. I.; Anderson, V. J.; van Duijneveldt, J.; Bartlett, P. Phys. ReV. Lett. 2005, 94, A. Stradner, H. Sedgwick2, F. Cardinaux, W.C. K. Poon, S. U. Egelhaaf & P. Schurtenberger Nature 432, (2004) |

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

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 Chains win 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

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

Stable also against crystallization ! E. Bianchi, J. Largo, P. Tartaglia, E. Zaccarelli, FS Phase diagram of patchy colloids: towards empty liquids Phys. Rev. Lett. 97, , 2006 (limited valence + flexibility)

DNA gels (Cerbino, Rovigatti talks) Limited valence + flexibility

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

Wertheim theory... different densities.... Parameter-free Theory Simulation

Two-component phase-diagram.... Wertheim theory (black)... MC simulation (2SUS) (red)

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

Can we realize this with the Biffi et al DNA particles ? (Roberto Cerbino’s talk) STAR-ARM-3’-CGATCG-5’ (Flavio Romano)

Can we realize this with the Biffi et al DNA particles ? STAR-ARM-3’-CGATCGGG-5’ 3’-CCCG-5’ AA-bonding: 6 bases paired AB-bonding: 4 bases paired (Flavio Romano) STAR-ARM-3’-CGATCGGG-5’ 3’-CCCG-5’ Blocking sequence

Gel bonds Blocking bonds Nupack Evaluations: Blocking bonds Gel bonds

How can we increase the entropic cost of blocking ? 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

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