Perspective pubs.acs.org/JPCL
Many-Body Nature of Relaxation Processes in Glass-Forming Systems S. Capaccioli,†,‡ M. Paluch,§ D. Prevosto,‡ Li-Min Wang,∥ and K. L. Ngai*,‡ †
Dipartimento di Fisica and ‡CNR-Institute for Chemical and Physical Processes, Dipartimento di Fisica, Università di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy § Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland ∥ State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, Hebei 066004, China ABSTRACT: Most glass-forming systems are composed of basic units interacting with each other with a nontrivial anharmonic potential. Naturally, relaxation and diffusion in glass formers is a many-body problem. Results from recent experimental studies are presented to show the effects of many-body relaxation and diffusion manifested on the dynamic properties of glass formers. Considering that the effects are general and critical, the problem of glass transition will not be solved until the many-body nature of the relaxation process has been incorporated fundamentally into any theory.
glass transition. Nevertheless, we present herein some recently discovered general and critical experimental facts not taken into account in conventional as well as current theories of glass transition. Collectively, the facts presented below show the manybody nature of the primary structural α-relaxation through its own properties and the nontrivial relation it has with the faster secondary β-relaxation acting as the precursor. Glass transition occurs upon lowering the temperature or elevating the pressure in a liquid when the relaxation time of molecular motions responsible for structural rearrangements becomes longer than the time scale of the experiment. As a result, structural relaxation toward equilibrium is arrested below some temperature, Tg, and the system is in the glassy state. The structural α-relaxation rate is dependent on specific volume and entropy, and hence, the glass transition is necessarily partly caused by the densification as well as reduction in entropy, the basis of free volume and configurational entropy theories for glass transition. However, interacting with each other via the intermolecular potential, the motions of molecules in the glass former are not independent of each other. The complex motions, appropriately described as many-body relaxation, may have an effect on the structural relaxation rate not accountable by volume and entropy. In the absence of intermolecular interaction, relaxation in noninteracting systems has exponential time dependence for its correlation function. Thus, the deviation from exponential time dependence or the broadening of frequency dispersion beyond Debye relaxation found in neat glass formers indicates many-body relaxation. The parameter n
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esearch on the glass transition problem nowadays is taking place in different disciplines including physical chemistry, chemical physics, material science, polymer science, and condensed matter physics. More researchers are joining in the search for the solution of the problem due to the hype that it is a long-standing unsolved problem. The key to solving the glass transition problem is ultimately the full understanding of the physics governing the structural relaxation and its dynamic properties. The problem differs from others by the great variety of substances, materials, and systems involved in glass transition and the immense spectral range (10−14−106 s in the time domain corresponding to 1013−10−7 Hz in the frequency domain) in which the dynamics of the processes leading to glass transition have been probed by available experimental techniques. A plethora of general properties and phenomena, together with changes upon varying the chemical/physical structure or parameters defining the system, that are critical for glass transition, await consideration and require explanation. Only by considering all of them can the physics be totally identified. However, realistically, it is not easy for anyone to have access to and command of all of the critical experimental facts. Naturally, attempts to solve the glass transition problem invariably have selected a few popular or preferred experimental facts for consideration. Even if successful in explaining these limited experimental facts, the glass transition problem has not been solved. This is because other critical experimental facts have not been dealt with and, even worse, may have already contradicted or invalidated the theory. For the same reason, commonly, a researcher in glass transition also is not aware of all the critical experimental facts, and unfortunately, acceptance of a theory is solely based how well it can explain a subset of experimental facts. This Perspective is not the medium for reviewing the totality of critical experimental facts on the dynamics of relaxation leading to © 2012 American Chemical Society
Received: December 12, 2011 Accepted: February 23, 2012 Published: February 23, 2012 735
dx.doi.org/10.1021/jz201634p | J. Phys. Chem. Lett. 2012, 3, 735−743
The Journal of Physical Chemistry Letters
Perspective
Figure 1. Dielectric loss data (loss normalized to the value of the maximum of the α-loss peak) at various combinations of temperature and pressure as indicated to demonstrate the invariance of the dispersion of the α-relaxation at constant α-loss peak frequency fα or equivalently at constant α-relaxation time τα for (a) dipropyleneglycol dibenzoate (DPGDB), (b) propylene carbonate (PC), (c) benzoyn isobutylether (BIBE), and (d) polychlorinated biphenyl (PCB62). Black and red symbols are data taken at atmospheric and elevated pressures, respectively.
the same at elevated pressure P up to a few GPa by raising the temperature T. One general property has emerged from these studies at elevated pressure.3,4 For any fixed value of τα, the frequency dispersion or n in the Kohlrausch correlation function of the structural α-relaxation is constant, independent of changes in thermodynamic conditions imposed by different combinations of T, P, and their conjugate variables, which are entropy S and volume V. By now, this property has been found in more than 50 glass formers of different classes including small-molecule van der Waals liquids and mixtures, amorphous polymers, components of polymer blends, room-temperature ionic liquids, and pharmaceuticals.2 Examples taken from the small molecular glass formers3,4 are shown in Figure 1. Lack of superposition can occur at frequencies sufficiently high above fα. Such deviation is due to the contribution from resolved or unresolved secondary β-relaxation at higher frequencies or shorter times, whose relaxation strength may not have the same P and T dependence as the α-relaxation. Class of Secondary Relaxations of Fundamental Importance to Glass Transition. In addition to structural α-relaxation, there are secondary relaxation processes that have transpired at earlier times. Most theories focus their attention on the α-relaxation and do not consider any secondary relaxation to be important for glass transition. It turns out that secondary relaxation belonging to a special class has various properties indicating that it bears strong connection to the α-relaxation, and consideration of the two combined is necessary for a full account of the many-body relaxation in glass formers and glass transition. Moreover, secondary relaxation of this special class is universal and found in all kinds of glass formers,2,5 organic, molecular, polymeric, metallic, inorganic, ionic, colloidal, and plastic crystalline. Most remarkable is the finding of the secondary relaxation in metallic glasses,6−8 which are atomic particles devoid of rotational degrees of freedom, and in plastic crystals, which have no translational degree of freedom.9
appearing in the Kohlrausch stretched exponential correlation function1 for the α-relaxation ϕ(t ) = exp[−(t /τ)1 − n ]
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