Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Self Assembly, Clustering, Structural arrestBernal Spiral Clusters in Colloid-Polymer MixturesHard spheres colloidal particles in suspension withsmall non-adsorbing polymers interact via aneffective attractive depletion potential, controlled inrange by the polymer-to-colloid size ratio and inmagnitude by the polymer concentration. Often,colloidal particles are also slightly charged, so that along-ranged repulsion of screened electrostatic typecomplements the short-range attraction. In theabsence of charge, at low densities, colloidalparticles undergo gas-liquid (colloid poor-colloid rich)phase separation, before the dynamics becomessufficiently slow. However, when electrostaticrepulsion becomes non-negligible, the competitionbetween the short-range attraction and the longrangerepulsion produces what may be viewed as amicrophase separation into colloidal aggregates offinite size, also called `equilibrium cluster phase'.This corresponds to a fluid made on average ofclusters, which can break and reform in equilibrium,but whose properties as a structurally distinct stateare clearly visible, as for example in the staticstructure factor which displays a characteristic peakat a finite wave-vector, much smaller than thetypical nearest-neighbour wave-vector. Modeling theeffective colloidal pair interactions as the sum of ageneralized Lenard-Jones potential with exponent♋ mimicking the hard-core repulsion and theshort-range attraction, and of a Yukawa term ofamplitude A and screening length ξ, ground statecalculations[1] have shown that cluster formation isfavoured with respect to bulk liquid separation, uponvarying the potential parameters, and that,moreover, the shape of such clusters can be tunedfrom spherical to linear, when the repulsion changesfrom long-ranged to relatively short-ranged, i.e.comparable to the particle radius. In the latter case,confocal microscopy experiments [2] have providedevidence of the existence of such clusters, organisedin the structure of the so-called Bernal spiral, i.e. athree-stranded spiral of face-sharing tetrahedra (seeFig.1a). At high enough density clusters are found tobranch and percolate, forming a disordered arrestednetwork, i.e. a gel.Focusing on the potential parameters related to theexperimental results [2], extensive molecular andbrownian dynamics simulations were carried out [3]in order to check whether such elongated clustersexist and if a simple pair potential of the kinddescribed above is sufficient to reproduce theexperimental results. We find that, indeed, at lowtemperature the system structure is of the Bernalspirall type. At low packing fractions 0.1, since the residual interactionsbetween the spirals are small, they can branchthrough some defects allowed by the finiteFig. 1. Bernal SpiralFig. 2a. High TFig. 2c. Low TFig. 2b.Intermediate Ttemperature and thus forming a solid percolatingstate with non-ergodic features. Interestingly, in thislatter case, by decreasing temperature from high tolow, a reentrant percolation is observed. This isshown in Fig.2. At first, temperature is too high, andcluster just percolate transiently in a totally randomway. As temperature is lowered, a competitionbetween entropic and energetic effects takes place,so that the clusters become smaller in size, they donot percolate any more and they start to displayfeatures of the Bernal spiral. Further lowering of thetemperature produces a stable network ofpercolating spirals, again of random nature. Thus atransition from monomers to spiral clusters takesplace as subunits of the system.References[1] S.Mossa, F.Sciortino, P.Tartaglia, and E.Zaccarelli, Langmuir 20, 10756 (2004).[2] A. I. Campbell, V. J. Anderson, J. van Duijneveldtand P. Bartlett, Phys. Rev. Lett. 94, 208301 (2005).[3] F. Sciortino, P. Tartaglia, and E. Zaccarelli,Journal of Physical Chemistry B 109, 21942 (2005).AuthorsE. Zaccarelli(a,b), F. Sciortino(a), P.Tartaglia(c)(a) Dipartimento di Fisica and CNR-INFM-SOFT,Università di Roma La Sapienza, P.le A. Moro 2, I-00185 Roma, Italy; (b) ISC-CNR, Via dei Taurini 19,I-00185, Roma, Italy; (c) Dipartimento di Fisica andCNR-INFM-SMC, Università di Roma La Sapienza,P.le A. Moro 2, I-00185 Roma, ItalySOFT Scientific Report 2004-0696