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 Cerbinos 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