Shape analysis

Shape regeneration can be performed by Fourier transformation techniques. First the particle s center of gravity is found from its outline. Then a polar coordinate system is set up. Schwarcz and Shane 

A plot of log A versus log n gives a straight line with a slope of -s, wWch is the shape signature of the particle, (generalizations of this method to three-dimensional particles are also possible. Particle shapes can be analyzed and reproduced using this Fourier transform method. 

All of the interactions discussed above have a strong dependency on motion, (or lack of motion) in solids. It is not surprising then that the motions that are present in a solid can be detected by motion-sensitive NMR methods. The methods used in this volume can be divided into two catagories line-shape analysis and relaxation studies. 

Schaefer and coworkers, in another chapter in this text, used dipole-dipole line shapes obtained in a very clever way to investigate rotational motion of the aromatic rings in polystyrene. The method used a WAHUHA pulse sequence to decouple proton-proton dipolar interactions, cross polarization to enhance signal acquisition and an overall sampling technique synchronous with the sample rotation. The dipole- 

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Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

The representation of molecules by molecular surface properties was introduced in Section 2.10. Different properties such as the electrostatic potential, hydrogen bonding potential, or hydrophobicity potential can be mapped to this surface and seiwe for shape analysis [44] or the calculation of surface autocorrelation vectors (refer to Section 8.4.2). 

Hopfinger et al. [53, 54] have constructed 3D-QSAR models with the 4D-QSAR analysis formahsm. This formalism allows both conformational flexibility and freedom of alignment by ensemble averaging, i.e., the fourth dimension is the dimension of ensemble sampling. The 4D-QSAR analysis can be seen as the evolution of Molecular Shape Analysis [55, 56]. 

Rhyn K-B, H C Patel and A J Hopfinger 1995. A 3D-QSAR Study of Anticoccidal Triazlnes Usir Molecular Shape Analysis. Journal of Chemical Information and Computer Science 35 771-778. 

Electron impact fragmentation studies on 1,2-benzisoxazoles and benzoxazole indicate that isomerization takes place before degradation. Shape analysis and metastable ion abundances in the mass spectra indicate that isomerization to o-cyanophenols occurred prior to degradation by loss of CO or NCH (75BSB207). 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

AJ Hopfinger. A QSAR investigation of dihydrofolate reductase inhibition by Baker triazmes based upon molecular shape analysis. I Am Chem Soc 102 7196-7206, 1980. 

Figure 2 Spectral parameters typically used in band shape analysis of an FTIR spectrum peak position, integrated peak area, and FWHM.

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

Chemical shift anisotropy 5.5,5 xxr yy zz Line-shape analysis MAS-sidebands Coordination symmetry... 

Nuclear electric quadrupole QCC (quadrupole coupling constant), (asymmetry parameter) Line-shape analysis, nutation NMR Coordination symmetry... 

Another example is the proton exchange between H2O and HDO at low water concentrations in organic solvents. t values were obtained by line shape analysis ... 

Weis [85AHC(38)1, pp. 70-73] has also studied the kinetics of 1,4-dihydro to 1,6-dihydro transformation quantitatively using H NMR line-shape analysis. The results indicated that two mechanisms (monomolecular and bimolecular reactions) are involved in the process, for which all the kinetic parameters were calculated. 

After the completion of this manuscript a paper concerning conformational analyses of 1,1, 3,3 -tetra-r< H-alkylmctallocene of iron and ruthenium including 6 based on thorough NMR spectroscopic measurements (line-shape analysis) has appeared in which the nature of the transition states has conclusively been discussed in detail [164]. 

NMR line shape analysis, 260-263 Negative activation enthalpy, 162 Noncompetitive inhibitor, 93 Nucleophilic catalysis, 237-238 Numerical simulations, 112-119... 

Solid state materials have been studied by nuclear magnetic resonance methods over 30 years. In 1953 Wilson and Pake ) carried out a line shape analysis of a partially crystalline polymer. They noted a spectrum consisting of superimposed broad and narrow lines which they ascribed to rigid crystalline and amorphous material respectively. More recently several books and large articles have reviewed the tremendous developments in this field, particularly including those of McBrierty and Douglas 2) and the Faraday Symposium (1978)3) —on which this introduction is largely based. 

In Fig. 7 actual numbers for the correlation times of the motion are included that apply for 2H NMR of deuterons in C—H bonds. It is evident that the line shape analysis of deuteron spectra should, in principle, provide a means to determine accurate values for the correlation times in a range of at least three orders of magnitude, the limits... 

Fig. 10. Correlation times for the tetrahedral jump motion in solid HMT obtained from 2H line shape analysis and 2H spin alignment...

Although long-time Debye relaxation proceeds exponentially, short-time deviations are detectable which represent inertial effects (free rotation between collisions) as well as interparticle interaction during collisions. In Debye s limit the spectra have already collapsed and their Lorentzian centre has a width proportional to the rotational diffusion coefficient. In fact this result is model-independent. Only shape analysis of the far wings can discriminate between different models of molecular reorientation and explain the high-frequency pecularities of IR and FIR spectra (like Poley absorption). In the conclusion of Chapter 2 we attract the readers attention to the solution of the inverse problem which is the extraction of the angular momentum correlation function from optical spectra of liquids. 

Bodor, G. X-ray Line Shape Analysis. A. Means for the Characterization of Crystalline Polymers. Vol. 67, pp. 165-194. 

Polysaccharide Polydispersity and Simple Shape Analysis by Sedimentation Velocity... 

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