A general set of order parameters for molecular crystals

Crystallization is fundamental to many aspects of physics and chemistry in addition to being of technological relevance, for example, in the chemical, food, and pharmaceutical industries. However, the design of crystalline materials and crystallization processes is often challenging due to the many variables that can influence the process. As a part of an effort to gain a molecular-level understanding of the way molecules aggregate and organize themselves into crystal structures, in this work we present a new method to construct order parameters suitable for the study of crystallization and polymorph transformations in molecular systems. Our order parameters can be systematically defined for complex systems using information that can be obtained from simple molecular dynamics simulations of the crystals. We show how to construct the order parameters for the study of three different systems: the formation of α-glycine crystals in solution, the crystallization of benzene from the melt, and the polymorph transformation of terephthalic acid. Finally, we suggest how these order parameters could be used to study order-disorder transitions in molecular systems.     

Four levels of pattern recognition

Problems of pattern recognition in chemistry and other subjects can be divided conveniently into four different types depending on the level of scope of the problem.(1) Classification into one of a number of defined classes. As an example blood samples taken from persons known to be either controls or welders are considered. The problem is whether trace element concentrations in these samples contain information on whether or not a person is a welder.(2) Level 1 plus the possibility that an object is an outlier, i.e. does not belong to any of the defined classes. As an example, the üse of ¹³C-n.m.r. data to decide whether 2-substituted norbornanes have the exo or endo structure is discussed. (2A) Level 2, asymmetric. This situation occurs when one class does not have a systematic structure, but another class is homogeneous and can be described by a level 2 model. This occurs in the classification of materials or compounds as good or bad, active or inactive, and in binary classifications. As an example the use of trace element data to classify steel samples as having good or poor properties of strength is discussed.(3) Level 2 plus the ability to relate the variables measured to external properties of continuous character. As an example, the classification of a series of chemical compounds as β -receptor blockers, β -receptor stimulants, or neither, on the basis of their structural variables is discussed. In addition, relations between these structural variables and the measured biological activity are sought within each of the two classes.(4) Level 3 with the difference that several external property variables in the objects are measured. It may be desirable to use variables of the objects both for classification and for relations to several property variables: such examples are numerous in analytical chemistry.     

Air-coupled ultrasonic assessment of wood veneer

Air-coupled ultrasound (ACU) provides a tool to evaluate wood samples of small or moderate thickness (<30 mm) thereby avoiding direct contact or liquid coupling. Results of through-transmission ACU measurements on wood veneer samples and related products are reported with respect to a wide variety of quality aspects. Fluctuations in the averaged received signal levels appear to be correlated to the presence of natural or machine-induced thickness and density variations, flaws and grain damage, errors produced by the manufacturing process, insufficient bonding on a substrate, etc. In addition it is seen that the variability of the signal levels enables to distinguish between quarter and crown areas.     

Dissociative and molecular oxygen chemisorption channels on reduced rutile TiO2(110): An STM and TPD study

High-resolution scanning tunneling microscopy (STM) and temperature-programmed desorption (TPD) were used to study the interaction of O₂ with reduced TiO₂(110)–(1 × 1) crystals. STM is the technique of choice to unravel the relation between vacancy and non-vacancy assisted O₂ dissociation channels as a function of temperature. It is revealed that the vacancy-assisted, first O₂ dissociation channel is preferred at low temperature (~ 120 K), whereas the non-vacancy assisted, second O₂ dissociation channel operates at temperatures higher than 150 K–180 K. Based on the STM results on the two dissociative O₂ interaction channels and the TPD data, a new comprehensive model of the O₂ chemisorption on reduced TiO₂(110) is proposed. The model explains the relations between the two dissociative and the molecular O₂ interaction channels. The experimental data are interpreted by considering the available charge in the near-surface region of reduced TiO₂(110) crystals, the kinetics of the two O₂ dissociation channels as well as the kinetics of the diffusion and reaction of Ti interstitials.     

Exponential Dichotomy for Asymptotically Hyperbolic Two-Dimensional Linear Systems

We consider the problem of determining the existence of exponential dichotomy for a class of linear nonautonomous ODEs. An approach is explored that combines numerical techniques with rigorous perturbation theory. It is applicable to a given problem within the class we consider. Numerical results illustrate the utility of the approach.