There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.

Supercooled liquids and the glass transition

Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods. † Correspondence: Chung-Ming Kuan, Institute of Economics, Academia Sinica, 128 Academia Road, Sec. 2, Taipei 115, Taiwan; ckuan@econ.sinica.edu.tw. †† I would like to express my sincere gratitude to the editor, Professor Steven Durlauf, for his patience and constructive comments on early drafts of this entry. I also thank Shih-Hsun Hsu and Yu-Lieh Huang for very helpful suggestions. The remaining errors are all mine.

Artificial neural networks

Although it has long been recognized that dynamics in supercooled liquids might be spatially heterogeneous, only in the past few years has clear evidence emerged to support this view. As a liquid is cooled far below its melting point, dynamics in some regions of the sample can be orders of magnitude faster than dynamics in other regions only a few nanometers away. In this review, the experimental work that characterizes this heterogeneity is described. In particular, the following questions are addressed: How large are the heterogeneities? How long do they last? How much do dynamics vary between the fastest and slowest regions? Why do these heterogeneities arise? The answers to these questions influence practical applications of glass-forming materials, including polymers, metallic glasses, and pharmaceuticals.

Spatially Heterogeneous Dynamics in Supercooled Liquids

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

A holographic fluorescence recovery after photobleaching technique has been used to measure translational diffusion coefficients DT for four probes in supercooled o‐terphenyl (OTP). DT values from 10−6 to 10−14 cm2/s were observed in the temperature range from Tg+8 K to Tg+90 K (Tg=243 K). In agreement with previous reports, the translational diffusion of probe molecules which are the same size as OTP molecules has a significantly weaker temperature dependence than T/η. However, as the size of the probe molecule is increased the temperature dependence of DT tracks T/η increasingly well. The transition between a weak temperature dependence to that of T/η occurs over only a factor of 3 in probe size. Previous work established that the rotational correlation times τc of these four probes in OTP tracks η/T. The product DTτc is independent of temperature for the largest probe but increases almost 2 orders of magnitude for the smaller probes as Tg is approached. A strong correlation is observed between this enhancement of translational diffusion and the KWW β values obtained from rotation measurements; probes with small β values show enhanced translation. These observations are qualitatively explained by spatially heterogeneous dynamics. The probes studied are rubrene, 9,10‐bis(phenylethynyl)anthracene, tetracene, and anthracene.

Enhanced translation of probe molecules in supercooled o‐terphenyl: Signature of spatially heterogeneous dynamics?

Coherent Raman imaging techniques have evolved to become powerful tools for biomedical imaging without the need for labelling.

Chemically sensitive bioimaging with coherent Raman scattering

An imaging platform based on broadband coherent anti-Stokes Raman scattering (BCARS) has been developed which provides an advantageous combination of speed, sensitivity and spectral breadth. The system utilizes a configuration of laser sources that probes the entire biologically-relevant Raman window (500 cm-1 to 3500 cm-1) with high resolution (< 10 cm-1). It strongly and efficiently stimulates Raman transitions within the typically weak "fingerprint" region using intrapulse 3-colour excitation, and utilizes the nonresonant background (NRB) to heterodyne amplify weak Raman signals. We demonstrate high-speed chemical imaging in two- and three-dimensional views of healthy murine liver and pancreas tissues and interfaces between xenograft brain tumours and the surrounding healthy brain matter.

High-Speed Coherent Raman Fingerprint Imaging of Biological Tissues.

Time resolved optical spectroscopy was used to observe molecular rotation over more than 14 decades in time for six probes in o‐terphenyl (OTP). In contrast to previous studies, probe rotation times are found to depend significantly upon probe size in the deeply supercooled regime. Systematic deviations from the temperature dependence of the Debye–Stokes–Einstein equation are observed, however, these deviations are relatively small. These observations are inconsistent with some models of cooperative molecular motion near Tg which invoke rigid aggregates or locally liquidlike regions. The width of the relaxation spectrum (characterized by the KWW β parameter) systematically decreases with increasing probe size. Near Tg, the largest probe (rubrene) rotates with nearly a single exponential correlation function. Based on the observed trend in β, it is estimated that OTP is homogeneous on length scales greater than 2.5 nm at Tg.

How do molecules move near Tg? Molecular rotation of six probes in o‐terphenyl across 14 decades in time

Coherent anti-Stokes Raman scattering (CARS) microscopy is emerging as a powerful method for imaging materials and biological systems, partly because of its noninvasiveness and selective chemical sensitivity. However, its full potential for species-selective imaging is limited by a restricted spectral bandwidth. Recent increases in bandwidth are promising but still are not sufficient for the level of robust component discrimination that would be needed in a chemically complex milieu found, for example, in intracellular and extracellular environments. We demonstrate a truly broadband CARS imaging instrument that we use to acquire hyperspectral images with vibrational spectra over a bandwidth of 2500 cm(-1) with a resolution of 13 cm(-1).

/pdf/simple-approach-to-one-laser-broadband-coherent-anti-stokes-23c638qtxb.pdf

Marcus T. Cicerone

Papers

Enhanced translation of probe molecules in supercooled o‐terphenyl: Signature of spatially heterogeneous dynamics?

Chemically sensitive bioimaging with coherent Raman scattering

High-Speed Coherent Raman Fingerprint Imaging of Biological Tissues.

How do molecules move near Tg? Molecular rotation of six probes in o‐terphenyl across 14 decades in time

Simple approach to one-laser, broadband coherent anti-Stokes Raman scattering microscopy.