Two-dimensional correlation plots

Noda has described an alternative approach that simplifies the comprehension of DIRLD spectra [4] and has subsequently generalized this approach [11] so that it 

SAMPLE MODULATION SPECTROMETRY WITH A STEP-SCAN INTERFEROMETER 

Noda showed that the wavenumber-dependent variations of the dynamic dichro-ism may be analyzed by a correlation t hnique. For a pair of DIRLD signals measured at two different wavenumbers, ZV4(vi, f) and AA(v2, t), the dynamic infrared cross-correlation function X(x) is defined as 

The dynamic dichroic difference signal takes the form 

The synchronous and asynchronous (i.e. quadrature) correlation intensities, V2) and (vi,V2), of the dynamic spectrum are given by 

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Goal Given a matrix of correlations, correlation creates the two-dimensional correlation plot. 

The PC loadings can be used to assess relationships between different variables in the model, as well as help explain the fundamental basis of the phenomena explained by the PCs. More specifically, if one looks at the loadings for the dominant PCs in the model, they can be used to detect general correlations between X-variables. For this purpose, they are often plotted as two-dimensional scatter plots, where each axis corresponds to a different PC number. An example of such a loading scatter plot for the polyethylene data... 

Figure 1 Two-dimensional contour plots of the log of the Raman-echo correlation function, In Cre(ti, T3), showing the effect of changing the rate of solvent-induced perturbations. All cases give a Raman line with the same FWHM (5 cm-1) and FIDs with similar decay times but give very different Raman echo results, (a) Fast modulation (b) intermediate modulation (A, = 3.32 cm-1, r( = 1.60 ps) (c) slow modulation. Calculations are based on a single Kubo-Anderson process [Equations (7)-(9)].

Several of the spectra in this workbook were obtained using techniques such as proton-detected C-H shift correlation and multiple-quantum-filtered phase-sensitive COSY which were not covered in detail in our main text because they have come into general use since it was written. This is a measure of the rate at which practical NMR is progressing but presents no problem in the interpretation of the spectra. Various field strengths and modes of presentation, ranging from continuous-wave traces to phase-sensitive two-dimensional contour plots, were used for the spectra. In part, this reflects the history of individual problems, but it is also intentional. It is important to be able to extract the essential message of a spectrum independently of the way it is presented. 

The pulse sequence which is used to record CH COSY Involves the H- C polarisation transfer which is the basis of the DEPT sequence and which Increases the sensitivity by a factor of up to four. Consequently, a CH COSY experiment does not require any more sample than a H broadband decoupled C NMR spectrum. The result is a two-dimensional CH correlation, in which the C shift is mapped on to the abscissa and the H shift is mapped on to the ordinate (or vice versa). The C and //shifts of the //and C nuclei which are bonded to one another are read as coordinates of the cross signal as shown in the CH COSY stacked plot (Fig. 2.14b) and the associated contour plots of the a-plnene (Fig. 2.14a and c). To evaluate them, one need only read off the coordinates of the correlation signals. In Fig. 2.14c, for example, the protons with shifts Sh= 1.16 (proton A) and 2.34 (proton B of an AB system) are bonded to the C atom at c = 31.5. Formula 1 shows all of the C//connectivities (C//bonds) of a-pinene which can be read from Fig. 2.14. 

These two-dimensional CH shift correlations indicate CH relationships through two and more bonds (predominantly Jch and Jch connectivities) in addition to more or less suppressed Jch relationships which are in any case established from the CH COSY contour diagram. Format and analysis of the CH COLOC or HMBC plots correspond to those of a C//COSY or HSQC experiment, as is shown for a-pinene (1) in Figs. 2.14 - 2.17. 

We introduced the technique for measuring the weak interaction forces acting between two particles using the photon force measurement method. Compared with the previous typically used methods, such as cross-correlation analysis, this technique makes it possible to evaluate the interaction forces without a priori information, such as media viscosity, particle mass and size. In this chapter, we focused especially on the hydrodynamic force as the interaction between particles and measured the interaction force by the potential analysis method when changing the distance between particles. As a result, when the particles were dose to each other, the two-dimensional plots of the kinetic potentials for each particle were distorted in the diagonal direction due to the increase in the interaction force. From the results, we evaluated the interaction coeffidents and confirmed that the dependence of the... 

A scatter plot provides a quick visual summary of where numerous data points exist in two-dimensional space. Scatter plots are commonly used to investigate positive or negative correlation between two variables plotted on the X and Y axes. 

In all cases we have used mean spectrum as reference spectrum (other references were tested no reference, first spectrum, last spectrum but the mean spectrum is the one giving the better results). All calculations were made under Matlab 6.5 with home made functions based on Noda s theories. The negative correlations are shaded in all the two-dimensional plots. 

Figures 13.7 and 13.8 are two examples of two-dimensional NMR spectroscopy applied to polymers. Figure 13.7 is the proton homonuclear correlated spectroscopy (COSY) contour plot of Allied 8207A poly(amide) 6 [29]. In this experiment, the normal NMR spectrum is along the diagonal. Whenever a cross peak occurs, it is indicative of protons that are three bonds apart. Consequently, the backbone methylenes of this particular polymer can be traced through their J-coupling. Figure 13.8 is the proton-carbon correlated (HETCOR) contour plot of Nylon 6 [29]. This experiment permits the mapping of the proton resonances into the carbon-13 resonances.

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