Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes. A large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker–Planck equation (Metzler R and Klafter J 2000a, Phys. Rep. 339 1–77). It therefore appears timely to put these new works in a cohesive perspective. In this review we cover both the theoretical modelling of sub- and superdiffusive processes, placing emphasis on superdiffusion, and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function. We also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems.

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The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

The field of viscous liquid and glassy solid dynamics is reviewed by a process of posing the key questions that need to be answered, and then providing the best answers available to the authors and their advisors at this time. The subject is divided into four parts, three of them dealing with behavior in different domains of temperature with respect to the glass transition temperature, Tg , and a fourth dealing with ‘‘short time processes.’’ The first part tackles the high temperature regime T.Tg ,i n which the system is ergodic and the evolution of the viscous liquid toward the condition at Tg is in focus. The second part deals with the regime T;Tg , where the system is nonergodic except for very long annealing times, hence has time-dependent properties ~aging and annealing!. The third part discusses behavior when the system is completely frozen with respect to the primary relaxation process but in which secondary processes, particularly those responsible for ‘‘superionic’’ conductivity, and dopart mobility in amorphous silicon, remain active. In the fourth part we focus on the behavior of the system at the crossover between the low frequency vibrational components of the molecular motion and its high frequency relaxational components, paying particular attention to very recent developments in the short time dielectric response and the high Q mechanical response. © 2000 American Institute of Physics.@S0021-8979~00!02213-1#

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1065&context=mse_pubs

Relaxation in glassforming liquids and amorphous solids

Drugs with low water solubility are predisposed to low and variable oral bioavailability and, therefore, to variability in clinical response. Despite significant efforts to "design in" acceptable developability properties (including aqueous solubility) during lead optimization, approximately 40% of currently marketed compounds and most current drug development candidates remain poorly water-soluble. The fact that so many drug candidates of this type are advanced into development and clinical assessment is testament to an increasingly sophisticated understanding of the approaches that can be taken to promote apparent solubility in the gastrointestinal tract and to support drug exposure after oral administration. Here we provide a detailed commentary on the major challenges to the progression of a poorly water-soluble lead or development candidate and review the approaches and strategies that can be taken to facilitate compound progression. In particular, we address the fundamental principles that underpin the use of strategies, including pH adjustment and salt-form selection, polymorphs, cocrystals, cosolvents, surfactants, cyclodextrins, particle size reduction, amorphous solid dispersions, and lipid-based formulations. In each case, the theoretical basis for utility is described along with a detailed review of recent advances in the field. The article provides an integrated and contemporary discussion of current approaches to solubility and dissolution enhancement but has been deliberately structured as a series of stand-alone sections to allow also directed access to a specific technology (e.g., solid dispersions, lipid-based formulations, or salt forms) where required.

Strategies to Address Low Drug Solubility in Discovery and Development

Basic characteristics of the liquid-glass transition are reviewed, emphasizing its universality and briefly summarizing the most popular phenomenological models. Discussion is focused on a number of alternative models which one way or the other connect the fast and slow degrees of freedom of viscous liquids. It is shown that all these ``elastic'' models are equivalent in the simplest approximation.

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Colloquium : The glass transition and elastic models of glass-forming liquids

Dynamic properties, derived from dielectric relaxation spectra of glass-formers at variable temperature and pressure, are used to characterize and classify any resolved or unresolved secondary relaxation based on their different behaviors. The dynamic properties of the secondary relaxation used include: (1) the pressure and temperature dependences; (2) the separation between its relaxation time τβ and the primary relaxation time τα at any chosen τα; (3) whether τβ is approximately equal to the independent (primitive) relaxation time τ0 of the coupling model; (4) whether both τβ and τ0 have the same pressure and temperature dependences; (5) whether it is responsible for the “excess wing” of the primary relaxation observed in some glass-formers; (6) how the excess wing changes on aging, blending with another miscible glass-former, or increasing the molecular weight of the glass-former; (7) the change of temperature dependence of its dielectric strength Δeβ and τβ across the glass transition temperature Tg; ...

Classification of secondary relaxation in glass-formers based on dynamic properties.

Dielectric loss spectra of glass-forming propylene carbonate and glycerol at temperatures above and below T(g) are presented. By performing aging experiments lasting up to five weeks, equilibrium spectra below T(g) have been obtained. During aging, the excess wing, showing up as a second power law at high frequencies, develops into a shoulder. The results strongly suggest that the excess wing, observed in a variety of glass formers, is the high-frequency flank of a beta relaxation.

https://arxiv.org/pdf/cond-mat/0001055.pdf

Excess Wing in the Dielectric Loss of Glass Formers: A Johari-Goldstein β Relaxation?

We report dielectric data on six different plastic crystalline materials, namely 1-cyanoadamantane, adamantanone, pentachloronitrobenzene, cyclo-hexanol, ethanol, and meta-carborane, covering a frequency range of up to 14 decades and up to 20 GHz. Information on phase transitions, the α-relaxation, and relaxation processes beyond the α-relaxation are provided. The α-relaxation shows clear non-Debye behavior and varying degrees of deviation from thermally activated behavior. Our results reveal a generally rather low fragility of plastic crystals. In some of the investigated materials evidence for Johari–Goldstein type β-relaxations is obtained. In addition, the question of the so-called excess wing of the α-relaxation peak is addressed in detail. In all cases, it is either absent or can be ascribed to a β-relaxation submerged under the α-peak. Overall, the present work provides a broad database on the dielectric behavior of plastic crystals, and may be taken as a review of the dynamic phenomena occurring in these materials, many of them being observed also in structural glass formers.

/pdf/relaxation-dynamics-in-plastic-crystals-25cd30vxfw.pdf

Relaxation dynamics in plastic crystals

Previous dielectric relaxation measurements of glycerol and propylene carbonate and new results on propylene glycol performed below the conventional glass transition temperatures T_(g) after long periods of aging all show that the excess wing (a second power law at higher frequencies) in the isothermal dielectric loss spectrum, develops into a shoulder. These results suggest that the excess wing, a characteristic feature of a variety of glass-formers, is the high frequency flank of a Johari–Goldstein β-relaxation loss peak submerged under the α-relaxation loss peak. With this interpretation of the excess wing assured, the dielectric spectra of all three glass-formers measured at temperatures above T_(g) are analyzed as a sum of a α-relaxation modeled by the Fourier transform of a Kohlrausch–Williams–Watts function and a β-relaxation modeled by a Cole–Cole function. Good fits to the experimental data have been achieved. In addition to the newly resolved β-relaxation on propylene glycol, the important results of this work are the properties of the β-relaxation in this class of glass-formers in the equilibrium liquid state obtained over broad frequency and temperature ranges.

/pdf/nature-and-properties-of-the-johari-goldstein-b-relaxation-1n2jiod4f5.pdf

Nature and properties of the Johari–Goldstein β-relaxation in the equilibrium liquid state of a class of glass-formers

Dielectric spectroscopy covering more than 18 decades of frequency has been performed on propylene carbonate in its liquid and supercooled-liquid state. Using quasioptic submillimeter and far-infrared spectroscopy, the dielectric response was investigated up to frequencies well into the microscopic regime. We discuss the alpha process whose characteristic time scale is observed over 14 decades of frequency and the excess wing showing up at frequencies some three decades above the peak frequency. Special attention is given to the high-frequency response of the dielectric loss in the crossover regime between alpha peak and boson peak. Similar to our previous results in other glass-forming materials, we find evidence for additional processes in the crossover regime. However, significant differences concerning the spectral form at high frequencies are found. We compare our results to the susceptibilities obtained from light scattering and to the predictions of various models of the glass transition.

https://arxiv.org/pdf/cond-mat/9812179.pdf

Broadband dielectric spectroscopy on glass-forming propylene carbonate.

Broadband dielectric spectroscopy has been performed on supercooled glycerol for temperatures between 184 and 413 K. The measurements cover 18 decades of frequency and extend into the far infrared regime. The timescale of the α-process is observed over 14 decades of frequency as a function of temperature. In the THz range an additional loss peak was observed which is identified as the boson peak known from neutron and light scattering experiments. Between the α and boson peak the loss minimum has been observed as a function of temperature down to the glass temperature. It is very broad and cannot be ascribed to a simple superposition of α and boson peak. The data are compared to the susceptibilities obtained from neutron and light scattering.

R. Brand

Papers

Excess Wing in the Dielectric Loss of Glass Formers: A Johari-Goldstein β Relaxation?

Relaxation dynamics in plastic crystals

Nature and properties of the Johari–Goldstein β-relaxation in the equilibrium liquid state of a class of glass-formers

Broadband dielectric spectroscopy on glass-forming propylene carbonate.

Dielectric and far-infrared spectroscopy of glycerol