Frustration-limited Domains Research Articles

Transition from Arrhenius to non-Arrhenius temperature dependence of structural relaxation time in glass-forming liquids: continuous versus discontinuous scenario.

The temperature dependences of α relaxation time τ(α)(T) of three glass-forming liquids (salol, o-terphenyl, and α-picoline) were investigated by a depolarized light scattering technique. A detailed description of τ(α)(T) near T(A), the temperature of the transition from the Arrhenius law at high temperatures to a non-Arrhenius behavior of τ(α)(T) at lower temperatures, was done. It was found that this transition is quite sharp. If the transition is described as switching from the Arrhenius law to the Vogel-Fulcher-Tammann law, it occurs within the temperature range of about 15 K or less. Most of the known expressions for τ(α)(T) cannot describe this sharp transition. Our analysis revealed that this transition can be described either as a discontinuous transition in the spirit of the frustration-limited domain theory [D. Kivelson, G. Tarjus, X. Zhao, and S. A. Kivelson, Phys. Rev. E 53, 751 (1996)], implying a phase transition, or by a phenomenological expression recently suggested [B. Schmidtke, N. Petzold, R. Kahlau, M. Hofmann, and E. A. Rössler, Phys. Rev. E 86, 041507 (2012)], where the activation energy includes the term depending exponentially on temperature.

A Viewpoint, Model and Theory for Supercooled Liquids

In this article we describe a novel model of supercooled liquids, denoted the theory of frustration-limited domains. It is a scaling theory built about a narrowly avoided critical point, avoided because of weak, but long-range frustration. Because of space limitations we eschew details of both phenomenology and theory, as well as discussion of other work (including references), and we do not, unfortunately, include graphs; all these can be found elsewhere.

Hole-Induced Magnetic Solitons and Colossal Magnetoresistance Phenomena in Doped Manganites

We have introduced the hole-induced magnetic soliton by using the gauge-invariant Lagrangian density and the path-integral method. The percolation-like dynamics of hole-induced magnetic solitons and the colossal magnetoresistance mechanism in doped manganites have been proposed from the standpoint of the random resistor network and percolation-scaling method. The long-relaxation behaviour of the spin has been discussed by using the effective Hamiltonian and the frustration-limited domain model.

Dynamic Model of Super-Arrhenius Relaxation Rates in Glassy Materials

Super-Arrhenius relaxation rates in glassy materials can be associated with thermally activated rearrangements of increasing numbers of molecules at decreasing temperatures. We explore a model of such a mechanism in which stringlike fluctuations in the neighborhood of shear transformation zones provide routes along which rearrangements can propagate, and the entropy associated with critically long strings allows the rearrangement to be distributed stably in the surrounding material. We further postulate that, at low enough temperatures, these fluctuations are localized on the interfaces between frustration-limited domains, and in this way obtain a modified Vogel-Fulcher formula for the relaxation rate.

Nature of slow dynamics in a minimal model of frustration-limited domains.

We present simulation results for the dynamics of a schematic model based on the frustration-limited domain picture of glass-forming liquids. These results are compared with approximate theoretical predictions analogous to those commonly used for supercooled liquid dynamics. Although model relaxation times increase by several orders of magnitude in a non-Arrhenius manner as a microphase separation transition is approached, the slow relaxation is in many ways dissimilar to that of a liquid. In particular, structural relaxation is nearly exponential in time at each wave vector, indicating that the mode-coupling effects dominating liquid relaxation are comparatively weak within this model. Relaxation properties of the model are instead well reproduced by the simplest dynamical extension of a static Hartree approximation. This approach is qualitatively accurate even for temperatures at which the mode-coupling approximation predicts loss of ergodicity. These results suggest that the thermodynamically disordered phase of such a minimal model poorly caricatures the slow dynamics of a liquid near its glass transition.

The boson peak in supercooled metallic liquids and glasses and relation to the glass transition

We have presented a theory of three-dimensional supercooled metallic liquids and glasses, which is based on the gauge-invariant Lagrangian density with spontaneous breaking (Higgs mechanism), and compared it with the frustration-limited domain (FLD) theory. Using the present theoretical formulation, a qualitative picture of the boson peak is proposed.

H2O below 277 K: A Novel Picture†,‡

We present a mesoscopic picture of supercooled water in which we fit the properties of water into a general scheme applicable to all so-called fragile glass-forming liquids. Water is taken as a single liquid phase above its glass transition at about 136 K. It is the only liquid known to have a Kauzmann temperature that lies above (well above) the glass transition temperature; we discuss this phenomenon and its implications. We have also associated the metastable cubic ice Ic with the defect-ordered phase predicted by the theory of frustration-limited domains, thereby developing a general physical and theoretical picture that incorporates both the metastable low-temperature liquid and solid phases at 1 atm.

The viscousslowing down of supercooled liquids as a temperature-controlledsuper-Arrhenius activated process: a description in terms offrustration-limited domains

We propose that the salient feature to be explained about the glasstransition of supercooled liquids is the temperature-controlledsuper-Arrhenius activated nature of the viscous slowing down, morestrikingly seen in weakly bonded, fragile systems. In the light ofthis observation, the relevance of simple models of sphericallyinteracting particles and that of models based on free-volumecongested dynamics are questioned. Finally, we discuss how the mainaspects of the phenomenology of supercooled liquids, including thecrossover from Arrhenius to super-Arrhenius activated behaviour and theheterogeneous character of the α-relaxation, can be described by anapproach based on frustration-limited domains.

A heterogeneous picture of α relaxation for fragile supercooled liquids

We examine some of the consequences, and their connection to experiments on supercooled liquids, of a scaling model of heterogeneous relaxation that is based on the theory of frustration-limited domains. In particular, we focus on what appears to be the two slowest components of structural relaxation, the one usually described by a stretched exponential or a Cole–Davidson function and the somewhat faster, apparently power-law decay known as von-Schweidler relaxation. Based on our model we study the α-relaxation activation free energy, the imaginary part of the dielectric frequency-dependent susceptibility, the susceptibility-mastercurve of Dixon et al. [Phys. Rev. Lett. 65, 1108 (1990)], and the breakdown of the Stokes–Einstein relation for translational diffusion at low temperatures. We also obtain estimates for the characteristic domain sizes as a function of temperature. As with all mesoscopic approaches, a number of assumptions must be introduced, but they all fit the overall scaling picture that motivates this approach. The good agreement with experimental dielectric relaxation data on two representative supercooled liquids, salol and glycerol, though necessarily dependent upon adjustable parameters, gives support to the theory.

The Kauzmann paradox interpreted via the theory of frustration- limited-domains

The entropy, Sliq(T), of many supercooled liquids decreases strongly and the structural relaxation time increases dramatically as the temperature T is lowered below the melting point, Tm. Below the glass transition temperature, Tg, the system relaxes too slowly for supercooled liquids to equilibrate in the experimental times; however, if the data above Tg are extrapolated to lower T, one finds that the extrapolated Sliq(T)→Sxtal(T) as T→TK, Sxtal(T) being the entropy of the crystal. This phenomenon is known as the “Kauzmann paradox.” If the extrapolation is extended below TK, it may be that the extrapolated Sliq(T)→0 as T→TKc>0; we call this apparent violation of the third law, the “Kauzmann catastrophe.” We discuss these phenomena, as well as the general problem of the entropy of supercooled liquids, in terms of the theory of frustration-limited domains. The apparent vanishing of [Sliq(T)−Sxtal(T)] and the apparent violation of the third law that results from extrapolation to T’s below Tg are consistent with extension of the scaling result predicted by the theory to inappropriately low T’s.

Observed anomalies in supercooled liquids described by frustration-limited domain theory

The properties of supercooled liquids are particularly interesting because they cannot be understood simply as an extension of liquid properties at temperatures above the melting point, and in this sense they are anomalous. These anomalies include apparent divergences and thermodynamic contradictions. We give a general description of a select set of anomalies and discuss how they can be understood within the theory of frustration-limited domains.

Observed anomalies in supercooled liquids described by frustration-limited domain theory

Observed anomalies in supercooled liquids described by frustration-limited domain theory