Dynamic shape analysis

Galai CIS-1000 is an on-line particle size analyzer. A bypass from the process line feeds the sample into the sensor unit where it is sized and either drained off or fed back to the line. Full compatibility with the laboratory instrument is maintained since it uses the identical combination of laser-based time-of-transit particle sizing using the 1001 sensor and dynamic shape analysis using the 1002 sensor. The size range covered is from 2 pm to 3600 pm with measurement of size, area, volume, shape, concentration and estimated surface area with a cycling time of 300 s. 

For sake of simplicity in describing the essential ideas within this and the following sections, first we shall consider a simplified model of a formal, static nuclear arrangement for each molecule. This constraint on the model will be released when dynamic shape analysis is discussed. 

As it has been pointed out in Section 5.2, it is natural to formulate dynamic shape analysis aproaches in terms of the dynamic shape space D described earlier [158]. The reader may recall that the dynamic shape space D is a composition of the nuclear configuration space M, and the space of the parameters involved in the shape representation, for example, the two-dimensional parameter space defined by the possible values of the density threshold a, and the reference curvature parameter b of a given MIDCO surface. 

We shall distinguish two types of methods for dynamic shape analysis. The methods of the first type are used to determine which nuclear arrangements are associated with a given topological shape. The methods of the second type determine the available topological shapes compatible with some external conditions, for example, with an energy bound. 

Within the simplest formulation of a dynamic shape analysis method of the first type, the invariance of topological descriptors within domains of the dynamic shape... 

P.G. Mezey, "Dynamic Shape Analysis of Biomolecules Using Topological Shape Codes", in The Role of Computational Models and Theories in Biotechnology. J. Bertran (Ed.), pp. 83-104, Kluwer Academic Publishers, Dordrecht, 1992. 

Mezey, P.G. (1993a). Dynamic Shape Analysis of Molecules in Restricted Domains of a Configuration Space. J.Math.Chem., 13,59-70. 

Dynamic parameters for heterogeneous systems have been explored in the liquid, liquid like, solid like, and solid states, based on analyses of the longitudinal or transverse relaxation times, chemical exchange based on line-shape analysis and separated local field (SLF), time domain 1H NMR, etc., as summarized in Figure 3. It is therefore possible to utilize these most appropriate dynamic parameters, to explore the dynamic features of our concern, depending upon the systems we study. 

In the solid, dynamics occurring within the kHz frequency scale can be examined by line-shape analysis of 2H or 13C (or 15N) NMR spectra by respective quadrupolar and CSA interactions, isotropic peaks16,59-62 or dipolar couplings based on dipolar chemical shift correlation experiments.63-65 In the former, tyrosine or phenylalanine dynamics of Leu-enkephalin are examined at frequencies of 103-104 Hz by 2H NMR of deuterated samples and at 1.3 x 102 Hz by 13C CPMAS, respectively.60-62 In the latter, dipolar interactions between the 1H-1H and 1H-13C (or 3H-15N) pairs are determined by a 2D-MAS SLF technique such as wide-line separation (WISE)63 and dipolar chemical shift separation (DIP-SHIFT)64,65 or Lee-Goldburg CP (LGCP) NMR,66 respectively. In the WISE experiment, the XH wide-line spectrum of the blend polymers consists of a rather featureless superposition of components with different dipolar widths which can be separated in the second frequency dimension and related to structural units according to their 13C chemical shifts.63... 

The dynamic NMR (DNMR) spectroscopy has been used in studies of stereomutations of non-symmetrical di-Schiff bases [18].39 It was shown that the hindered Schiff bases exist in DMSO in two chiral conformations. The presence of a pair of conformers being in equilibrium was explained by the existence of two stereogenic axes a g (aligned to Cl—N8 bond) and a 7 (aligned to C6—N7 bond) due to restricted rotation around two Ar—N bonds. The trans to cis interconversion as well as enantio- or diastereoisomerisation barriers for the compounds studied have been established using line shape analysis. 

Binsch, G. Band-Shape Analysis." In Dynamic Nuclear Magnetic Resonance Spectroscopy Jackman, L. M. Cotton, F. A., Eds. Academic Press New York, 1975 pp. 45-81. See also Binsch, G. Top Stereochem., 1968, 3, 97-192. 

An appropriate cure cycle was established based on the results obtained from the thermal analysis and cure rheology studies of the resin and cured BCB bar and dogbone shaped samples were fabricated for testing. Bar shaped specimens had the dimensions of 3.5 x 0.5 X 0.125 and were used to stake compact tension specimens for fracture toughness studies and for dynamic mechanical analysis of a torsion bar. Dogbone shaped specimens for tensile tests had a gauge area of 1 x 0.15 and were approximately 0.040 thick. 

Thermal analysis, moisture uptake and dynamic mechanical analysis was also accomplished on cured specimens. Thermal analysis parameters used to study cured specimens are the same as those described earlier to test resins. The moisture uptake in cured specimens was monitored by immersing dogbone shaped specimens in 71 C distilled water until no further weight gain is observed. A dynamic mechanical scan of a torsion bar of cured resin was obtained using the Rheometrics spectrometer with a temperature scan rate of 2°C/minute in nitrogen at a frequency of 1.6Hz. The following sections describe the results obtained from tests run on the two different BCB resin systems. Unless otherwise noted all tests have been run as specified above. 

In solution, rate constants and activation parameters for dynamic processes can be estimated by direct analysis of the change of the NMR signal shape as a function of temperature. This technique is called line shape analysis (LSA) and it is best suited vhen the rate of exchange ranges from ca. 10 to 10 s" [142, 159]. 

The dynamic behavior of the model intermediate rhodium-phosphine 99, for the asymmetric hydrogenation of dimethyl itaconate by cationic rhodium complexes, has been studied by variable temperature NMR LSA [167]. The line shape analysis provides rates of exchange and activation parameters in favor of an intermo-lecular process, in agreement with the mechanism already described for bis(pho-sphinite) chelates by Brown and coworkers [168], These authors describe a dynamic behavior where two diastereoisomeric enamide complexes exchange via olefin dissociation, subsequent rotation about the N-C(olefinic) bond and recoordination. These studies provide insight into the electronic and steric factors that affect the activity and stereoselectivity for the asymmetric hydrogenation of amino acid precursors. 

Casey was able to prepare related zirconocene alkenyl complexes according to Scheme 8.18. Alkene coordination was established by a number of NMR techniques. While zwitterionic compounds 38 allowed the determination of the alkene dissociation energy, AG = 10.5 kcal mol , very similar to that of 35. Thermally more stable complexes were obtained by protonation of 37 with [HNMePh2][B(C5F5)4[. Dynamic NMR spectroscopy and line shape analysis allowed the measurement of the barriers of alkene dissociation (AG = 10.7 and 11.1 kcal mol ), as well as for the site epimerisation ( chain skipping ) at the zirconium center (AG = 14.4 kcal mol" ) (Scheme 8.19) [77]. 

The increase in time resolution of advanced sorption uptake methods and the joint use of sorption and radio-spectroscopic techniques allow for a more detailed analysis of the so-called "non-Fickian" behaviour of sorbing species in the intracrystalline bulk phase [18,28,29,76]. Correspondingly, information on molecular dynamics has been obtained for n-butane and 2-but ne in NFI zeolites by means of the single step frequency response method and C n.m.r. line-shape analysis [29]. As can be seen from Figures 4 and 5, the ad- / desorption for both sorbates proceeds very quickly, but with a... 

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