Frustrated crystal structure

Besides the identification of the local poljnnorphic structure of the crystallized polymer, it is possible in some cases to detect new (minority) crystal structures. For aramid fibers, previously not detected, but predicted, crystal structures have been identified based on SFM data obtained on cleaved fibers (137). Noteworthy are also the studies by Lotz and co-workers who elucidated the frustrated crystal structure of /3-PP with the help of SFM images with methyl group resolution (144). Finally, the mechanism of friction reduction on oriented PTFE films has been confirmed using SFM measurements with molecular resolution (145,146). 

The less symmetric model of the structure of sPS of Figure 2.19b is also an example of frustrated crystal structure of polymer [113]. The characteristic feature of frustrated structures is that two motifs maximize their interactions at the expense of the third motif. As a consequence, the third motif is frustrated since it is not in its ideal environment [114]. In the model of Figure 2.19b, the structural motif is the triplet of franx-planar chains. The different orientations of the three triplets of chains included in the unit cell are such that two triplets maximize their interactions at the expense of the third triplet [113]. 

Similar frustration has been evidenced for the crystal structure of isotactic poly(2-vinylpyridine)150 161 (Figure 2.28). Also in this case three independent threefold helices are included in the trigonal unit cell and the frustration is related to a different azimuthal orientation of the chains due to the different interactions between the chains.160 Two chains (chains A in Figure 2.28) maximize their interactions at the expense of the third one (chain B). 

The examples of polymer crystal structures shown in the previous sections are ideal structures, which can be described with the traditional concepts of the principles of equivalence and close packing or the new concepts of symmetry breaking146 and frustration.154 The models of perfect crystals are characterized by a long-range positional order for all the atoms (disregarding thermal motion). The X-ray diffraction patterns of such crystals, oriented with the chain axes along one direction (as in oriented fibers), present sharp reflections organized in layer lines. 

Figure 7 shows a plot of x as a function of cp. A rough correlation can be seen if cp is positive then x is positive and if cp is negative then x is negative. The crystal structure of XAGWUX contains two independent molecules with opposite conformations. One of the molecules is syn-syn the other is anti-anti. This occurrence frustrates any attempts to correlate the conformation of the cation with the acidic strength of the anion or other counter ion effects. 

Rather surprisingly, there is no literature report of a crystal structure for the carbonylation catalyst, [Rh(CO)2I2] . Previous attempts in our laboratory to characterise salts of the anion crystallographically have been frustrated by disorder in the solid state. 

With all the progress, however, it is still difficult to predict crystal structures. This frustration was powerfully expressed by Maddox [82] One of the continuing scandals in the physical sciences is that it remains in general impossible to predict the structure of even the simplest crystalline solids from a knowledge of their chemical composition. There is also considerable progress during the past few years in this respect, mainly due to the utilization of the wealth of information retrievable from the data banks, and especially the Cambridge files [88],... 

For some compounds, suitable crystals simply can not be obtained and all attempts are frustrated. The reasons are not well understood. In some cases, repeated attempts with varied conditions always produce multiple or twinned crystals. Trying a range of different solvents is the most obvious approach. It is not just that the crystal quality may vary with the solvent used incorporation of solvent in the crystal structure generates a different crystalline form (a solvate), which will probably have quite different crystal growth characteristics. In most cases the nature of the solvent is unimportant in the quest for a definitive crystal structure analysis. However, the study of different solvates (and different polymorphs) of the same compound can itself be of interest, with significant changes in molecular structure resulting from different intermolecular interactions. 

Uro gen III synthases from most sources are particularly unstable and can be totally inactivated by a brief heat-treatment which leaves HMBS fully active. This instability would frustrate any attempts to crystallise the enzyme. However, it has recently been reported that the UROS from B. subtilis is much more stable than from other sources [75] and this opens up the possibility of crystallisation and an X-ray crystal structure determination. 

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