Relaxations in gels: Analogies to α and β relaxations in glasses

Ren, Shisong; Sorensen, C. M.

doi:10.1103/physrevlett.70.1727

Cited by 123 publications

(77 citation statements)

References 25 publications

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“…A pioneering work putting forward the analogy between gel and glass transition was carried out by Ren and Sorensen [277], who studied a thermo-reversible gel-forming system (gelatin) by dynamic light scattering, identifying two relaxations that would be the analogous of the α and β relaxation in glasses [20]. The α relaxation equivalence was identified with a stretched exponential decay approaching the gel point, while the β relaxation was associated to the so-called 'gel mode', i.e.…”

Section: Discriminating Different Gels: Static and Dynamic Features; mentioning

confidence: 99%

Colloidal gels: equilibrium and non-equilibrium routes

Zaccarelli

2007

J. Phys.: Condens. Matter

720

915

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Abstract. We attempt a classification of different colloidal gels based on colloidcolloid interactions.We discriminate primarily between non-equilibrium and equilibrium routes to gelation, the former case being slaved to thermodynamic phase separation while the latter is individuated in the framework of competing interactions and of patchy colloids. Emphasis is put on recent numerical simulations of colloidal gelation and their connection to experiments. Finally we underline typical signatures of different gel types, to be looked at, in more detail, in experiments.

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Section: Discriminating Different Gels: Static and Dynamic Features; mentioning

confidence: 99%

Colloidal gels: equilibrium and non-equilibrium routes

Zaccarelli

2007

J. Phys.: Condens. Matter

720

915

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“…Unlike the boiling of an egg that involves an irreversible transition from a metastable to a stable state, this transition is reversible upon cooling, and the polymer is redissolved on subsequent cooling. In its high temperature phase, the Methyl Cellulose gel exhibits, like many other gels [6], glassy features. Non monotonic temperature dependence of the glassy order parameter has been already reported for a random heteropolymer in a disordered medium [7]; this may be considered as the glassy analogue of the flux line crystallization [4].…”

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confidence: 99%

Spin Model for Inverse Melting and Inverse Glass Transition

Schupper¹,

Shnerb²

2004

Phys. Rev. Lett.

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A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the "ferromagnetic" phase, while lower energy associated with the non-interacting states yields a "paramagnetic" phase as temperature decreases. An infinite range model is solved analytically for constant paramagnetic exchange interaction, while for its random exchange, analogous results based on the replica symmetric solution are presented. The qualitative features of this model are shown to resemble a large class of inverse melting phenomena. First and second order transition regimes are identified.PACS numbers: 05.70. Fh, 64.60.Cn, 75.10.Hk, 64.70.Pf We all tend to associate order parameter with order, namely, with less entropic microscopic realizations. This is indeed the general situation in nature: crystals are more ordered than liquids, ferromagnets have less entropy than paramagnets. Even the entropy associated with a glass, an out of equilibrium, frozen frustrated state, is less than that of a liquid phase of the same material.There are, however, exceptions, where an "order parameter" does not reflect order, and the entropy growth during crystallization or freezing. The prototype of these phenomena is inverse melting, i.e., a reversible transition between a liquid phase at low temperatures to a high temperature crystalline phase, observed in He 3 and He 4 at extreme conditions (temperature below 1 • K, pressure above 25 bar) [1]. A similar phenomenon was observed recently at room temperature and atmospheric pressure in P4MP1 polymer solutions [2]. Ferroelectricity in Rochelle salt is another example, where the spontaneous polarization is lost below the (lower) Curie temperature, this time the transition is second order in type [3]. The pinned-crystalline inverse transition of vortex lines in the presence of point disorder at high temperature superconductors [4] is also considered as an example of inverse melting. However, in that system, the intensive order parameter (bulk magnetization) is lower in the crystalline phase, and the response functions are higher, i.e., the disordered phase is stiffer than the ordered phase.Even if the crystalline state is the thermodynamically preferred one, the dynamics of the system may prevent its appearance. In glass forming materials ergodicity breaking takes place at a finite temperature and the system is trapped into a frozen disordered state. One expects that an "inverse" glass transition phenomenon, analogous to inverse melting, may also take place. An interesting example in polymeric systems is the reversible thermogelation of Methyl Cellulose solution in water [5]. When a (soft and transparent) solution of Methyl Cellulose is heated (above 50• C, for a 10 gr/liter solution) it turns into a white, turbid and mechanically strong gel. Unlike the boiling of an egg that involves an irreversible transition from a metastable to a stable state, this transition is reversible...

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“…These results very well reproduce the relaxation patterns in the experiments as reported in ref. [4,5,6]. The relaxation time diverges at the percolation threshold due to the divergence of the connectivity and this correponds to the occurrence of the power law behaviour, also observed in the gel phase in TMOS silica gels [4] and in N IP A gel [5].…”

Section: Relaxation Properties: Permanent Bond Casementioning

confidence: 99%

“…Infact the relaxation functions in most of the experiments display a long time stretched exponential decay ∼ e −( t τ 0 ) β in the critical solution approaching the gelation threshold [4,5,6,7]. The relaxation process becomes critically slow at the gel point, where the onset of a power law decay is typically observed.…”

Section: Introductionmentioning

confidence: 99%

A unifying approach to relaxation properties of chemical and colloidal gels

Arcangelis¹,

Gado²,

Fierro³

et al. 2003

Braz. J. Phys.

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We study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical mechanics model. The model is based on percolation and bond-fluctuation dynamics. By opportunely varying some model parameter we are able to describe a crossover from the chemical gelation behaviour to dynamics more typical of colloidal systems. The results suggest a novel connection linking classical gelation, as originally described by Flory, to more recent results on colloidal systems. I IntroductionThe gelation transition transforms a solution of polymeric molecules, the sol, which is essentially a viscous fluid, into an elastic solid. This happens when the bond formation between different molecules is induced and it is phenomenologically characterized by the divergence of the viscosity coefficient in the sol and by the appearence of an elastic response in the gel phase. This corresponds to the constitution inside the sol of a macroscopic polymeric structure [1], which characterizes the gel phase. This polymerization process leading to the formation of an interconnected stress-bearing network in the system is then responsible on one hand for the divergence of the viscosity coefficient η and on the other hand for the growing of a non-zero elastic modulus Y . The critical growth of the connectivity can be straightforwardly interpreted by means of a percolation transition, which starting from the work of Flory and Stockmayer [1,2,3] is practically considered as the basic model for gelation transition. Depending on the particular system the gelation can be observed by lowering the temperature, or as function of time or else of the monomer concentration in the sol. In any case close to the gelation transition the viscosity coefficient grows with a power law behaviour characterized by a critical exponent k. The onset of the elastic response in the system corresponds to a power law increasing of the elastic modulus described by a critical exponent f .Approaching the gelation threshold complex polymeric structures are formed, characterized by different relaxation processes over many different lenght scales. Infact the relaxation functions in most of the experiments display a long time stretched exponential decay ∼ e −( t τ 0 ) β in the critical solution approaching the gelation threshold [4,5,6,7]. The relaxation process becomes critically slow at the gel point, where the onset of a power law decay is typically observed.This complex relaxation somehow resembles what is typically observed in a supercooled liquid approaching the glass transition [8] and in general this form is interpreted in terms of many decay processes, occurring over different time scales. One has to recognize that here the relaxation process is actually controlled by the growth of the connectivity. At the gelation threshold τ 0 → ∞ and the relaxation functions decay as a power law [4,5]. In the gel phase the relaxation behaviour displays a variety of complex behaviours depending on the system. These features are actually common to ...

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Relaxations in gels: Analogies to α and β relaxations in glasses

Cited by 123 publications

References 25 publications

Colloidal gels: equilibrium and non-equilibrium routes

Colloidal gels: equilibrium and non-equilibrium routes

Spin Model for Inverse Melting and Inverse Glass Transition

A unifying approach to relaxation properties of chemical and colloidal gels

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