Winter Formal (Kirstys Krystal Book 1)
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Need more info? Call us on She has recently taught at Conti and Starmakerz, and currently works with Angelina Jandolo Dance and Stagecoach, with numerous teaching qualifications across the worlds of dance, music and gymnastics. During her studies she took extra courses about how to teach Dance Technique and Creative Dance to non-professional and professional dancers from the age of 3. Kirsty trained as a a professional musical theatre performer, and once graduated went on to work professionally as a singer and dancer on prestigious Cruise Ships, travelling the world and in multiple pantomimes nationwide.
Upon moving to London, she started teaching Dance at Stagecoach, where she is principal, and now lends her talents to ballet lessons at Angelina Jandolo Dance.
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Taylor trained at advanced levels of dance in Australia and the USA before moving to the UK, and has worked as a professional performer, coach and dance teacher since Nina has danced professionally across Europe and the UK in soloist roles, and has choreographed for professional productions alongside her teach work, which she has undertaken in venues including the Imperial Dance Society and SA Dance. Sarah began her dance training at the age of 4 in a small country town in Western Australia. She was inspired to pursue contemporary dance after taking part in Shawbrook Youth Dance at age Street Dance.
Angelina Jandolo. Nicky Wilson. Emily Reaney. An example of an additional frustrating factor is the combination of a centrosymmetric motif such as categories 1—5 with molecular chirality category 18 because two homochiral molecules cannot be related to one another by inversion symmetry. This simplistic case is an obvious example of where both molecules in the dimer should therefore be crystallographically independent. Other frustrated combinations also require an increase in the number of symmetry independent molecules to produce an optimum structure.
Aurophilic interactions in combination with most other factors also show a marked effect. The particular issue of the frustration between chirality and centrosymmetric dimer formation was examined closely in a related study for the centrosymmetric synthons A—E shown in Figure These data confirm an earlier study on chiral carboxylic acids by Sorensen and Larsen.
The answer is that all of these remaining structures fall into three distinct, easily understood groups. All of these structures are in space group C 2, and the dimer is situated on a crystallographic 2-fold rotation axis. Proper rotations do not invert chirality, but they do represent a relatively inefficient packing mode screw axes are generally preferred over rotations 7, , b, Exactly the same issues occur for the amide dimers, and hence we can predict that the occurrence of multiple independent molecules is a preferred option as compared to crystallographic symmetry such as 2-fold rotation that results in inefficient packing.
The racemic structure adopts a polar space group Pna 2 1 with segregated R and S tapes, while only the S tape is retained in the homochiral version, Figure The crystals were obtained both from solution and from the melt with no evidence of polymorphism.
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The packing of a series of closely related chiral palladium II amine complexes with a tendency to form centrosymmetric synthon 14 Figure 17 was examined by Calmuschi and Englert in , who crystal engineered a variety of quasiracemate cocrystals. Quasiracemate formation to give cocrystals with complexes bearing two different R groups gives the same packing pattern in the subgroup C 2 with one crystallographically independent molecule of each type. A study by Gavezzotti in compared the molecular and energetic properties of two thoroughly curated, error-free data sets for compounds containing only C, H, N, O, S, and F atoms retrieved from the CSD.
The data showed consistently that the molecules in the Z2 set were, on average, slightly smaller in terms of molecular volume than the Z1 set, although average density, packing coefficient, and lattice energy per atom proved to be identical. The Z2 sample contained a high percentage of alcohol groups, consistent with the earlier work of Brock. Perhaps the most interesting aspect of the study is that a comparison of the energetics of molecular pairs in the Z1 and Z2 sets showed that for the Z2 set the most strongly bound pair exhibits a higher interaction energy than in the Z1 set, and this pair is generally the asymmetric pair.
It was suggested that pairs representing a high total may represent cases where the pair arises from kinetic trapping, particularly in cases where one partner in the asymmetric unit pair is less stable in terms of both intermolecular and intramolecular interaction energy. In contrast, pairs contributing relatively little to the total were suggested to be legitimately stable structures.
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Because the molecules themselves are chemically identical and we know that donors tend to pair with acceptors or bumps with hollows in real crystals, it is difficult to imagine why the packing should be anything other than symmetrical, which, of course, is why the presence of multiple independent fragments in the asymmetric unit is such a tantalizing puzzle. This finding argues against the social bias suggestion and implies that the size difference is a real phenomenon.
Moreover, it is highly statistically significant not just in terms of mean value but as a distribution. This was interpreted to mean that small, rigid molecules are rather more likely to have difficulty packing with optimum 3D interactions, and this packing problem can be resolved by forming unsymmetrical interactions or including a second type of chemical residue. A detailed analysis of the relationship of crystal packing with molecular shape has recently been undertaken by Motherwell; however, this work addressed only structures with a single crystallographically independent molecule.
In general, the strongest intermolecular interactions are found between the largest faces of the independent molecules implying that molecules are fitting together to minimize surface area and emphasizing the importance of molecular shape. The smaller bridging groups in the other derivatives do not result in lowered symmetry on desolvation. The presence of symmetry-independent cages in the empty, porous structure results in unique stepped gas sorption behavior, never before observed for a molecular crystal.
The directional interactions between particular chemical functionalities in conjunction with molecular size and shape, and the requirement to form close-packed structure with optimal intermolecular interactions, are all intrinsic properties of the molecules that are assembled into a crystal structure.
Their influence or otherwise on the formation of structures with multiple symmetry-independent molecules should play a part no matter how the crystal is grown. In other words, they relate primarily to the thermodynamic stability of the final structure. In contrast, the circumstances under which a crystal is formed, the crystallization conditions, may also have a significant bearing on the crystallization outcome and hence the solid form obtained.
Crystallization is a self-assembly process that occurs in a variety of media solution, melt, gas-phase sublimation, or mechanochemically in the solid state under highly nonequilibrium conditions, with factors such as the degree of supersaturation stabilizing the unfavorable interface between growing crystal nucleus and fluid phase. It may be that under the prevailing crystal growth conditions the assembly or growth of the nucleus of a metastable polymorph is favored, resulting in a metastable solid form that can subsequently be transformed into the thermodynamic phase over time or by changes in temperature, pressure, etc.
This view has been suggested by Kuleshova et al. The structural arguments put forth for monoalcohols in section 4. This focus on conditions is effectively a consideration of nucleation and growth effects, as distinct from effects relating to the stability of the final crystal.
Nucleation is an extremely poorly understood phenomenon. Classical nucleation theory describes the association of a few molecules tens to hundreds to form an unstable precritical nucleus in which the unstable fluid interface is stabilized by a supersaturation gradient. Once this precritical nucleus grows to a certain critical size, growth becomes thermodynamically downhill in free energy terms as the stable molecules fully packed in the volume of the growing crystal begin to dominate over the unstable surface molecules.
This simplistic picture which can overestimate nucleation rate by up to 10 orders of magnitude neglects many features of real systems, and recent advances have modified this classical picture considerably.
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Two-step nucleation describes nucleation as occurring in a transient metastable, dense liquid phase bearing little resemblance to the final crystal structure. While there is some very interesting information on crystal growth and polymorphic transformation processes coming from high-resolution AFM, for example, the current understanding of nucleation phenomena is a long way from being able to predict structural characteristics such as the occurrence of symmetry independent molecules.
However, we can look empirically at the structural outcome of varying crystallization conditions. This compares to 1. Nangia and co-workers attributed this difference to the formation of gas-phase clusters upon condensation. The high effective concentration of the melt phase may also be a significant factor. A key question in considering whether fluid phase aggregation has any role to play in the polymorphic outcome of the crystallization process is whether intermolecular interactions in the liquid or gas precursor phase are sufficiently strong or long-lasting to result in meaningful concentrations of the aggregate species.
Techniques for measuring intermolecular interactions are well established, for example, using NMR spectroscopy, isothermal titration calorimetry, spectrophotometry, etc. Importantly, crystallization does not occur at equilibrium, however, but in a supersaturated regime or in the case of the melt, at very high effective concentration at the point of phase transition , and as a result there is a stabilization of any kind of intermolecular association by the supersaturation gradient.
Hence, even relatively weak intermolecular interactions may well be significant. In his entertaining perspective, Bernstein recounts the anecdote of his own initially unsuccessful attempts to isolate the low melting metastable polymorph of benzophenone. Periods of less than 10 days were insufficient. The implication is that it takes this very long period of time to break up seeds or aggregates of the competing stable form. Certainly work on isomorphic seeding of phenobarbital melts has shown that the melt phase is highly susceptible to the influence of pre-existing aggregates such as secondary or heteronuclei.
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A simple illustration of the role of solution speciation comes from the polymorphism of 2,6-dihydroxybenzoic acid, which crystallizes as a hydrogen-bonded dimer containing form from the relatively nonpolar solvent toluene, and as a catemer from chloroform. It is suggested that the relatively polar chloroform inhibits dimer formation, and indeed toluene solutions are found to be dimer rich. The analogy between solution-phase association and crystal structure has been probed by Hunter and co-workers who used 1 H NMR contact induced shifts over a wide concentration range to derive the solution structure of amides 21 and 22 and their self-association constants.
The solution structures matched the hydrogen-bonded dimers observed in the solid state with rmsd values of 0. More recently, a detailed study on the solution association of tolfenamic acid has shown that conformational change in solution of the tolfenamic acid molecules is a prerequisite for their dimerization to strengthen intermolecular interactions, and this factor has a bearing on the polymorphic outcome. In conditions slightly closer to real crystallization, Davey and co-workers have used small-angle neutron scattering coupled with empirical potential structure refinement EPSR to examine the structure of supersaturated methanolic solutions of benzoic acid.
The neutron data in solution suggest that the carboxylate group interacts with a total of two methanol molecules and one other benzoic acid group in a chain-like fashion. In total, each molecule is surrounded by nine methanol molecules and five benzoic acid molecules in a micelle-like structure, although the hydrogen-bonded dimer motif is absent.
Clearly the progression from this solvated cluster to a crystal requires considerable rearrangement accompanied by desolvation. Such a process is somewhat reminiscent of two-step nucleation theory. Davy and co-workers have also used synchrotron in situ SAXS and WAXS to study the formation of prenucleation aggregates in sunflower seed oil, benzamide melts, p -azoxyanisole melts, and supersaturated aqueous solutions of urea, sucrose, and citric acid.
In contrast, the single component melts provided evidence for the appearance of short-lived metastable crystalline and liquid crystalline states indicating precrystalline molecular assembly. This allowed the characterization of a new highly metastable form of benzamide and also showed that liquid crystal ordering for p -azoxyanisole is an essential precursor to the formation of a metastable crystal structure. Work in our own group has resulted in the isolation of crystals of three DMSO solvates of the imaging agent diatrizoic acid The strongest interaction to solvent that from the carboxylic acid is retained in all of the solvates.
This leads to speculation that intermolecular association may be guided initially by weaker interactions, while more strongly interacting functional groups remain solvated until a relatively late stage in the desolvation process. However, a seeding role or formation of a solid solution with the aniline cannot be ruled out and complicates the interpretation of this unusual structure. Work on the relationship between solution speciation and nucleation, and its relevance to crystal structure remains highly challenging and is beyond the scope of the present work to review in detail.
The current state of the art has been recently reviewed by Davey et al. In a very elegant paper, Johnstone et al. The PV term implies that changes in pressure may affect the volume of the system and hence the molecular volume and packing coefficient, while change in temperature will affect the relative importance of the entropic contribution.
Compound 26 adopts a range of slightly different conformations at K within 6 kJ mol —1 of one another in energy. Raising the pressure to 4. Overall, however, the high pressure solid form is quite different.
click The molecular conformational energy in the new form is considerably less stable than the ambient pressure form; however, the phase is more efficiently packed even allowing for the effect of increased pressure. The pressure-induced phase change is thus fully reversible. In an elegant comparison, Ridout and Probert have recently used in situ crystallization to obtain both low temperature and high pressure polymorphs of the secondary monoalcohol isopropanol, a common laboratory solvent.
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The work of Taylor and Macrae showed that hydrogen-bonded chains and rings are more or less equally likely for secondary alcohols, and this trend is certainly represented in the two structures. The low temperature form adopts a rather low density of 0. The effect of pressure would seem to favor the more efficiently packed polymorph with less optimal hydrogen bonds.
The effect of changing temperature on a crystal is studied far more frequently than changing pressure for practical experimental reasons. Increasing temperature may also provide sufficient thermal energy to irreversibly transform a metastable polymorph in a monotropic system into the most thermodynamically stable polymorph.
Such strong kinetic trapping is one possible factor in the formation of metastable polymorphs, which might show strong directional intermolecular interactions without being as burdened by the increasing importance of close packing as the nucleus, and ultimately crystal, grows larger.
It has been pointed out that because little is known about the structure of the crystallization nucleus, this kind of term is almost impossible to confirm or refute, 22a a view we have considerable sympathy with.