Understanding stress-induced disorder and breakage in organic crystals: beyond crystal structure anisotropy

Crystal engineering has advanced the strategies for design and synthesis of organic solids with the main focus being on customising the properties of the materials. Research in this area has a significant impact on large-scale manufacturing, as industrial processes may lead to the deterioration of such properties due to stress-induced transformations and breakage. In this work, we investigate the mechanical properties of structurally related labile multicomponent solids of carbamazepine (CBZ), namely the dihydrate (CBZ·2H2O), a cocrystal of CBZ with 1,4-benzoquinone (2CBZ·BZQ) and the solvates with formamide and 1,4-dioxane (CBZ·FORM and 2CBZ·DIOX, respectively). The effect of factors that are external (e.g. impact stressing) and/or internal (e.g. phase transformations and thermal motion) to the crystals are evaluated. In comparison to the other CBZ multicomponent crystal forms, CBZ·2H2O crystals tolerate less stress and are more susceptible to breakage. It is shown that this poor resistance to fracture may be a consequence of the packing of CBZ molecules and the orientation of the principal molecular axes in the structure relative to the cleavage plane. It is concluded, however, that the CBZ lattice alone is not accountable for the formation of cracks in the crystals of CBZ·2H2O. The strength and the temperature-dependence of electrostatic interactions, such as hydrogen bonds between CBZ and coformer, appear to influence the levels of stress to which the crystals are subjected that lead to fracture. Our findings show that the appropriate selection of coformer in multicomponent crystal forms, targetting superior mechanical properties, needs to account for the intrinsic stress generated by molecular vibrations and not solely by crystal anisotropy. Structural defects within the crystal lattice, although highly influenced by the crystallisation conditions and which are especially difficult to control in organic solids, may also affect breakage

Influence of Snowmelt Timing on the Diet Quality of Pyrenean Rock Ptarmigan (Lagopus muta pyrenaica): Implications for Reproductive Success

The Pyrenean rock ptarmigan (Lagopus muta pyrenaica) is the southernmost subspecies of the species in Europe and is considered threatened as a consequence of changes in landscape, human pressure, climate change, and low genetic diversity. Previous studies have shown a relationship between the date of snowmelt and reproductive success in the Pyrenean ptarmigan. It is well established that birds laying early in the breeding season have higher reproductive success, but the specific mechanism for this relationship is debated. We present an explicative model of the relationship between snowmelt date and breeding success mediated by food quality for grouse in alpine environments. From microhistological analyses of 121 faecal samples collected during three years in the Canigou Massif (Eastern Pyrenees), and the assessment of the chemical composition of the main dietary components, we estimated the potential quality of individual diets. Potential dietary quality was correlated with free-urate faecal N, a proxy of the digestible protein content ingested by ptarmigan, and both were correlated with phenological stage of consumed plants, which in turn depends on snowmelt date. Our findings suggest that the average snowmelt date is subject to a strong interannual variability influencing laying date. In years of early snowmelt, hens benefit from a longer period of high quality food resources potentially leading to a higher breeding success. On the contrary, in years of late snowmelt, hens begin their breeding period in poorer nutrient condition because the peaks of protein content of their main food items are delayed with respect to laying date, hence reducing breeding performance. We discuss the possible mismatch between breeding and snowmelt timing

Effect of internals on the flow pattern and mixing in stirred tanks

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Solving the inverse problem for aggregation in activated sludge flocculation using a population balance framework

Many systems contain populations of individuals. Often, they are regarded as a lumped phase, which might, for some applications, lead to inadequate model predictive power. An alternative framework, Population Balance Models, has been used here to describe such a system, activated sludge flocculation in which particle size is the property one wants to model. An important problem to solve in population balance modelling is to determine the model structure that adequately describes experimentally obtained data on for instance, the time evolution of the floc size distribution. In this contribution, an alternative method based on solving the inverse problem is used to recover the model structure from the data. In this respect, the presence of similarity in the data simplifies the problem significantly. Similarity was found and the inverse problem could be solved. A forward simulation then confirmed the quality of the model structure to describe the experimental data

Modeling the Manipulation of Crystal Morphology Distributions

In the chemical industries in general and in the specialty and fine chemical industries, in particular, the crystal shape and its distribution are of considerable interest because it can remarkably influence the product downstream processing and usability. Also bioavailability and dissolution behavior of active pharmaceutical ingredient is governed by the nature of prevailing crystal faces. Consequently it is important to predict, optimize and control shape distributions for industrial applications. The shape of a convex crystal can be completely defined by a set of surfaces (planes) along with their normal distances from the crystal center (Zhang et al., 2006). One can then obtain boundaries in the shape space, which stand for the appearance/ disappearance of distinct morphological properties of a crystal (Borchert et al., 2008). An evolutionary crystal shape reaching such a boundary looses a face (or faces of similar kind) on the crystal surface in the sense that it grows out of the crystal. Therefore its dynamics is dimensionally smaller by one than it was before because only the real faces on the crystal surface determine the evolution in shape space. This imparts the system a hybrid character with varying degrees of freedom. This makes computations of single crystal shape evolution trajectories more complex than for purely continuous processes. Based on the systematic procedure of Borchert et al. (2008), we identify morphological subspaces and define corresponding crystal number densities. In order to describe the dynamics of crystal population in these subspaces the identification of multidimensional population balance equations for each of the subspaces is required. Clearly, since a crystal can evolve from one shape to another, meaning transitions of number densities from one sub-space to another and vice versa, the dynamics of these number densities is coupled. This aspect requires the specification of clear boundary conditions and exchange terms, which will be the significant part of discussion. There are two different cases of how the crystals can be exchanged between morphological domains one by continuous influx into a lower or equally dimensional domain and second by discontinuous (instantaneous) jump from a lower to a higher dimensional domain. Due to this peculiarity one obtains a varying set of partial di fferential equations that describes the evolution of crystal populations. Clearly the dynamics is governed by the supersaturation which is the result of the joint crystal growth. The dependency of boundary conditions and exchange terms on supersaturation is an interesting aspect. Since supersaturation determines the growth behavior of the individual faces one can manipulate the crystal shape towards a desired direction in shape space by changing supersaturation. Hence a thorough analysis of the joint state space, which consists of the shape space and the supersaturation coordinate, is necessary to keep track of possible discrete morphological changes, which will be a key part of presentation. We also present an interesting model case study that illustrates the proposed methodology. References Zhang, Y., Sizemore J. P. & Doherty M. F. (2006). Shape Evolution of 3-Dimensional Faceted Crystals. AIChE Journal, 52, 1906-1915. Borchert, C. B., Nere, N. K., Ramkrishna, D., Voigt, A., and Sundmacher, K. On the Prediction of Crystal Shape Distributions in a Steady State Continuous Crystallizer. Chemical Engineering Science, under revision, 2008. Borchert ,C. B., Nere, N. K., Ramkrishna, D., Voigt, A., and Sundmacher, K. Evolution of Crystal Shape Distributions and Morphology Classification. ISIC17, Maastricht, 2008