Structural Arrest in Dense Star-Polymer SolutionsG. Foffi,1F. Sciortino,1P. Tartaglia,1E. Zaccarelli,1F. Lo Verso,2L. Reatto,2K. A. Dawson,3and C. N. Likos41Dipartimento di Fisica and INFM Center for Statistical Mechanics and Complexity, Universita`di Roma La Sapienza,Piazzale Aldo Moro 2, I-00185 Rome, Italy2Istituto Nazionale di Fisica della Materia and Dipartimento di Fisica, Universita`di Milano, Via Celoria 16, I-20133 Milano, Italy3University College Dublin, Irish Center for Colloid Science and Biomaterials, Department of Chemistry,Belfield, Dublin 4, Ireland4Institut fu¨r Theoretische Physik II, Heinrich-Heine-Universita¨tDu¨sseldorf, D-40225 Du¨sseldorf, Germany(Received 29 January 2003; published 9 June 2003)The dynamics of star polymers is investigated via extensive molecular and Brownian dynamicssimulations for a large range of functionality f and packing fraction . The calculated isodiffusivitycurves display both minima and maxima as a function of and minima as a function of f. Simulationresults are compared with theoretical predictions based on different approximations for the structurefactor. In particular, the ideal glass transition line predicted by mode-coupling theory is shown toexactly track the isodiffusivity curves, offering a theoretical understanding for the observation ofdisordered arrested states in star-polymer solutions.DOI: 10.1103/PhysRevLett.90.238301 PACS numbers: 83.80.Uv, 64.70.Pf, 82.70.Dd, 83.60.HcStar polymers play an important role in soft condensedmatter systems, since they have been shown to interpolatebetween hard colloids with a strong repulsive core on oneside and the soft flexible polymeric systems on the other[1]. Star polymers are constituted by a given number ofpolymeric arms, called functionality f, tied to a commoncenter. As the functionality increases, the system becomesmore similar to a hard sphere (HS) system, while low-ering the functionality the interparticle potential be-comes increasingly soft. Recently, many interestingproperties of star polymers have been clarified on thebasis of an effective interaction potential betweenstar polymer centers [2]. In line with their hybridpolymer-hard colloid character, star polymers displayno crystallization transition when the functionality f islow, f 34. At higher functionalities, a freezing transi-tion takes place at about the overlap concentration of thesystem, into a bcc solid for lower functionalities and intoan fcc solid for higher functionalities [3]. The freezing issucceeded by either a reentrant melting transition to thefluid for intermediate functionalities, 34 & f & 54,orbya cascade of structural phase transitions at higher valuesof f. The functionality-dependent bcc and fcc solids [4,5],as well as the reentrant melting transition [6], have beenexperimentally observed in solutions of starlike blockcopolymer micelles. Though the crystalline solids arethe phases of thermodynamic equilibrium at such highconcentrations, the experimental situation is often some-what different. A variety of studies with star polymers orstarlike systems of various functionalities has shown thatit is quite difficult to nucleate a crystal. Especially at highfunctionalities, the solutions display a gelation transition,i.e., a dynamical arrest into an amorphous crowded statein which the characteristic relaxation time of the systembecomes extremely long [7–12]. The onset of gelation, asopposed to crystallization, is further enhanced by thepresence of some polydispersity in the samples, whichgets indeed more pronounced as functionality increases.The purpose of this work is to analyze the dynamics ofstar polymers in athermal solvents theoretically, by em-ploying a combination of methods. Using the star-stareffective interaction potential, in which all microscopi-cally fluctuating degrees of freedom are averaged out,we carry out detailed molecular dynamics (MD) andBrownian dynamics (BD) simulations to measure thediffusivity of the star-polymer fluids down to the homo-geneous nucleation limit. Moreover, we carry out a mode-coupling theory (MCT) analysis [13] of the long-timelimit of the correlation functions, which allows us tolocate the nonergodicity (ideal glass) transition line ofthe system. We find that, on increasing the number densityof polymer, the characteristic time of the system goesthrough a sequence of maxima and minima which weshow to be related to the oscillatory behavior of theeffective HS diameter [14]. We also find a strong correla-tion between the equilibrium phase diagrams of the sys-tem and the ideal glass line. The equilibrium reentrantmelting transition is shown to have its counterpart in thereentrant melting of the disordered glass nested betweentwo stable fluid phases. Finally, we discover a strikingsimilarity in the shape of the isodiffusivity and MCTideal glass curves, regardless of the detailed approxima-tion employed in the calculation of the structure factorSq and the type of dynamics (MD or BD). These find-ings strongly support the interpretation that the structuralarrest of star polymers is a glass transition of ‘‘effectivehard spheres’’ characterized by an -andf -dependent HSdiameter, despite the fact that the liquid structure and thevariety and nature of the equilibrium phases themselvesis very different from the HS case.PHYSICAL REVIEW LETTERSweek ending13 JUNE 2003VOLUME 90, NUMBER 23238301-1 0031-9007=03=90(23)=238301(4)$20.00 2003 The American Physical Society 238301-1Standard MD and BD techniques have been employedin order to study the dynamic behavior of the star-poly-mer system [15]. MD and BD lead to identical predictionsfor the long-time dynamics of the system within theframework of the MCT [13,16]. Thus, though BD offersa more realistic description of the short-time diffusion ofthe particles, the long-time behavior which is the relevantbehavior for the glass transition is the same in both.Hydrodynamic interactions are ignored and the analysisis based on the effective center-center interaction poten-tialVr 518f3=2lnr 11 fp=2;r 518f3=2=r1 fp=2expfpr 2;r ;(1)where 1=kBT and r is the distance between the twocenters. This potential is a combination of a logarithmicinteraction at short distances, which gives the interactionits ultrasoft character and stems from the scaling analysisof Witten and Pincus [17], and a Yukawa form for
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