TOTAL Correlations

Source Dhulesia, H., New Correlations Predict FCC Feed Characterization Parameters, Oil iS Gas Journal, Jan. 13, 1986, pp. 51-54. 

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TOCSY Total correlation spectroscopy, in the homonuclear COSY format, e.g. HH TOCSY traces out all proton-proton coimectivities of a partial structure in addition to the coimectivities (V, V, V, J) as detected by HH COSY... 

Most integral equations are based on the Ornstein-Zernike (OZ) equation [3-5]. The idea behind the OZ equation is to divide the total correlation function h ri2) iiito a direct correlation function (DCF) c r 12) that describes the fact that molecules 1 and 2 can be directly correlated, and an indirect correlation function 7( 12), that describes the correlation of molecule 1 with the other molecules that are also correlated with molecule 2. At low densities, when only direct correlations are possible, 7(r) = 0. At higher densities, where only triplet correlations are possible, we can write... 

We apply the singlet theory for the density profile by using Eqs. (101) and (103) to describe the behavior of associating fluids close to a crystalline surface [120-122], First, we solve the multidensity OZ equation with the Percus-Yevick closure for the bulk partial correlation functions, and next calculate the total correlation function via Eq. (68) and the direct correlation function from Eq. (69). The bulk total direct correlation function is used next as an input to the singlet Percus-Yevick or singlet hypernetted chain equation, (6) or (7), to obtain the density profiles. The same approach can be used to study adsorption on crystalline surfaces as well as in pores with walls of crystalline symmetry. 

The TOTAL correlations calculate aromatic carbon content, hydrogen content, molecular weight, and refractive index using routine laboratory tests. The TOTAL correlations are listed below and are also in Appendix 3. Example 2-2 illustrates the use of TOTAL correlations. 

Comparison of TOTAL Correlations with Other Methods... 

ASTM D-2502 is one of the most accurate methods of determining molecular weight. The method uses viscosity measurements in the absence of viscosity data, molecular weight can be estimated using the TOTAL correlation. 

Step 2 Calculate refractive index 20°C from the TOTAL correlation. 

The findings from TOTAL, n-d-M, and API are summarized in Table 2-10. The comparison illustrates how sensitive the predicted feed composition is to the refractive index 20°C. For instance, using the TOTAL correlation, there is a 35% drop in the aromatic content in using RIpo) = 1.5000 instead of RI(2o> = L5105. When using these correlations, every effort should be made to obtain accurate and consistent values for the refractive index at 20°C. With the refractive... 

Note that the calculated RIjjo) closely matches that using the TOTAL correlation.)... 

The variation principle tells us that EHF is always larger than the exact energy, and this implies that the total correlation energy is always a negative quantity. From Eq. 11.70 it follows then that 7 corr is always positive, whereas VC0TT is negative according to the formulas ... 

Obviously, the bias limits on the temperature measurements are dominant in this specific case. When they are totally correlated, the last term in Eq. (2.9) cancels out the third and fourth terms, and Bq/Q equals 0.0056 instead if 0.036. 

A related experiment TOCSY (Total Correlation Spectroscopy) gives similar information and is relatively more sensitive than the REIAY. On the other hand, intensity of cross peak in a NOESY spectrum with a short mixing time is a measure of internuclear distance (less than 4A). It depends on the correlation time and varies as . It is positive for small molecules with short correlation time (o r <<1) and is negative for macromolecules with long correlation time (wr >>l) and goes through zero for molecules with 1 Relaxation effects should be taken into consideration for quantitative interpretation of NOE intensities, however. 

Homonuclear Hartmann-Hahn Spectroscopy or Total Correlation Spectroscopy 267... 

HOMONUCLEAR HARTMANN-HAHN SPECTROSCOPY (HOHAHA), OR TOTAL CORRELATION SPECTROSCOPY (TOCSY)... 

The HOHAHA spectrum (100 ms) of podophyllotoxin is presented. The HOHAHA, or TOCSY (total correlation spectroscopy), spectrum (100 ms) shows coupling interactions of all protons within a spin network, irrespective of whether they are directly coupled to one another or not. As in COSY spectra, peaks on the diagonal are ignored as they arise due to magnetization that is not modulated by coupling interactions. Podophyllotoxin has only one large spin system, extending from the C-1 proton to the C4 and 015 protons. Identify all homonuclear correlations of protons within this spin system based on the crosspeaks in the spectrum. 

HMQC-TOCSY Heteronuclear multiple quantum coherence-total correlation IAA Instrumental activation analysis... 

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