The influence of the molecular crystalline arrangement upon the state of a Jahn-Teller-active center has been investigated in crystals of the complex Cu(mtz)(6)(BF(4))(2), where mtz = 1-methyltetrazole. Crystal structures at 293, 123, and 93 K were determined by X-ray diffraction for the copper complex and at 293 and 100 K also for the analogous zinc complex, Zn(mtz)(6)(BF(4))(2). The respective lattice parameters for the copper complex at 293, 123, and 93 K are as follows: a = 18.137(4), 17.597(4), 17.575(4) Å; b = 10.247(4), 10.131(4), 10.133(4); c = 18.446(5), 18.531(4), 18.535(4) Å; beta = 112.62(2), 113.55(2), 113.61(2) degrees. Those for the zinc complexes at 293 and 100 K, respectively, are as follows: a = 18.153(2), 17.663(2) Å; b = 10.289(1), 10.159(2) Å; c = 18.506(3), 18.578(3) Å; beta = 113.21(1), 114.15(2) degrees. The crystal system is monoclinic, space group P2(1)/n (Z = 4), for all crystals with two crystallographically inequivalent pairs of centrosymmetric molecules, M(mtz)(6)(BF(4))(2), in the unit cell. The two inequivalent Cu(mtz)(6)(2+) complexes, Cu(A) and Cu(B), both exhibit Jahn-Teller distortions, but in different ways, the Cu-N distances for the unit on site A being 2.015(4), 2.031(5), and 2.384(5) Å at 93 K, while those for the unit on site B are 2.053(5), 2.126(5), and 2.204(5) Å. However, the Jahn-Teller radii of the two complexes, as calculated from the metal-ligand distances and the U tensors of the two CuN(6) units, were both found to be 0.41(3) Å. EPR experiments at room temperature on polycrystalline samples of the pure copper compound and of the copper-doped zinc compound confirm the presence of two different Jahn-Teller centers; both complexes are rapidly pulsating, but the CuN(6) units on site A are confined predominantly to one potential well of the warped Mexican hat potential, whereas the CuN(6) units on site B have density in all three wells. At 78 K, however, the spectrum of the polycrystalline material is consistent with a single site having an axial g tensor with maximum anisotropy (g( parallel) = 2.300(5), g( perpendicular) = 2.068(5)). While the low-temperature X-ray results also indicate a structure in which the Cu(A) center is exclusively populated in one potential well, the U tensor and potential well population data for the Cu(B) centers indicate that at 93 K a nonpulsating averaged structure based on tetragonally elongated CuN(6) units is being observed. The more pronounced preference for the CuN(6) octahedron on site A to show elongation in one specific direction, in contrast to that on the B site, appears to be due to the differing impacts of the local-site strains at the two distinct centers of symmetry, and a simple model for evaluating a crystal "packing" strain from the bond length data for the isomorphous zinc complex is described.

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Summary: The description of polymerization reactors by means of fundamental mathematical models is a challenging problem. At the same time, these models offer a very powerful tool for process control, monitoring, optimization, scale‐up, and operator training and often allow for a better understanding of underlying mechanisms. Some approaches and tools used in industry to meet these challenges are illustrated. The scope and complexity of polymerization models developed and applied to industrial processes are shown. In addition to kinetic aspects of the model development some emphasis is given to the thermodynamic description of phase behavior and phase partitioning in polymerization reactors. Also, the important task of a careful and thorough parameter evaluation is briefly discussed as this is a prerequisite of predictive modeling. Finally, some typical model predictions are illustrated with experimental data.