Soft Report - Dipartimento di Fisica - Sapienza

Clustering and Cooperative Dynamics in Reactive MixturesDisparate fluids can evolve into structurally arrestedstates, either of glass or gel type, with differentvariables serving as a control parameter [1]. Weconcentrate on the idea that clusters of correlatedparticles are at the basis of glass formation andinvestigate how the dynamics and clustering are, infact, intimately related [2, 3].Experimental studies providing evidence for aquantitative connection of this type are generallyprevented by the absence of direct access to relevantcluster properties in real systems. We have exploitedparticle clustering that occurs by stepwiseaggregation in a two-component reactive mixture(DGEBA-DETA N e:N a). Step polymerization is a selforganizationprocess able to generate permanentmolecular clusters similar in shape to the transientones observed in cooperativity studies. While theirgeometry and mass distribution depends on anumber of factors, their average size x n (i.e., theaverage number of monomers per molecule) turnsout to be only dependent on the functionality (i.e.,reactive groups per molecule) of the reagents andthe number of bonds created, according tox n(α)=1/(1-f α), where α is the chemical conversion,and f=2N e/(N e+N a) denotes the average functionalityof the system. Thus, knowing f for a given mixtureand measuring α by differential scanning calorimetry,enabled us to calculate the average size x n ofmolecular clusters making up the system at any timeof reaction. x n displays critical behavior at α=1/f.The structural dynamics of our reactive system wasmonitored throughout reaction by VH depolarizedphoton correlation spectroscopy, probing opticalanisotropy fluctuations, which arrest at the glasstransition. Instead, the technique is blind to theformation of a gel phase. The structural relaxationtime τ exhibits a strongly nonlinear dependence onα. Figure 1, showing logτ versus x n for differentreactions, reveals how the x n and the τ data,independently determined, relate to each other. Wefind that the x n dependence of τ is expressedremarkably well by an exponential law, that is,τ ∝ exp(Bx n). This means that the relaxation timediverges, determining a structurally arrested glassstate, when the average size of particle clustersbecomes infinite.The Adam-Gibbs model provides a convenientframework for interpreting our finding. One canargue that a monomer involved in a rearrangementis likely to take its bonded monomers along, so thatthe average number of particles in the system thatcooperate to move grows proportionally to x n. Thus,an exponential variation of τ with x n would beexpected, as we find to be the case.In conclusion, our data reveal the cluster propertyinvolved in the glasslike arrest and its quantitativelink with the structural relaxation time. We find thatincreasing the average size of clusters of bondedparticles causes the dynamics to slowdownprogressively in such a way that, differently fromgelation, an arrested glass state forms (τ→∞) whenx n diverges. The behavior of x n correlates to the sizeof the ‘cooperatively rearranging regions’ postulatedby the Adam-Gibbs model for glass forming liquids.These results have two implications. First, they bringout a major difference between the glass andgelation transitions in terms of the cluster propertywhich is relevant to the transition [2]: a glass resultswhen the average number of particles in a cluster(x n) tends to infinity; by contrast, the gelationtransition is known to occur when the weightaveragecluster size (x w) diverges due to theformation of the first particle network of macroscopicsize. Second, our findings suggest that the steppolymerization process generates clusters that,although they are of a non-transient nature, behavemuch like dynamical heterogeneities observed insupercooled liquids [3]. Their size, in particular,identifies a growing, diverging lengthscale associatedwith the cooperative dynamics of the system.2N e:N a1 10:35:25:2.804:310:9-1N a/N e0.2 0.4 0.6 0.8 1.0-21.00.9-3α 00.80.7-40.62 3 4 5 6 7 8 9 10xFig.1. Semilogarithmic plot n of the structuralrelaxation time τ, vs the average size x n of clustersgrown by polymerization, for five DGEBA-DETA N e:N acompositions as indicated. The data follow straightlines for more than five decades in τ. In the frame ofthe Adam-Gibbs model, an exponential variation of τwith x n, in a process at constant temperature,supports a direct relationship between x n and the sizeof the CRRs. In the inset: Dependence on the molarratio N a/N e between the reagents, of the values α 0 atwhich the τ data (directly analyzed as a function of α)tend to diverge. They match the expected variationof 1/f=[1+(N a/N e)]/2 (solid line).log 10τ(s)References[1] S. Corezzi, D. Fioretto, P. Rolla, Nature 420, 653(2002)[2] S. Corezzi, L. Palmieri, J.M. Kenny, D. Fioretto, J.Phys.: Condens. Matter 17, S3557 (2005)[3] S. Corezzi, D. Fioretto, J.M. Kenny, Phys. Rev.Lett. 94, 065702 (2005)Authors:S. Corezzi (a), D. Fioretto (b), and J.M. Kenny (c)(a) CRS-SOFT and Dipartimento di Fisica, Universitàdi Roma La Sapienza, Roma (Italy); (b) CRS-SOFTand Dipartimento di Fisica, Università di Perugia,Perugia (Italy); (c) Materials Engineering Center,Università di Perugia, Terni (Italy)89SOFT Scientific Report 2004-06