Composite relaxed

Figure 2 The composite "relaxed" potential energy surface for Man(al-3)Man3 calculated by using the molecular mechanics programme MM2(85).

The major advantage of this dramatic time reduction lies in the ability to scan the sample repeatedly, combine the relaxation-decay patterns collected from each scan, and then perform a Fourier transform upon the final composite relaxation-decay pattern. This technique, in essence, increases the spectral sensitivity by allowing the NMR signals acquired from each scan to be constructively added to each other while the noise cancels itself de-con structively. This approach greatly increases the sensitivity of the instrument and allows NMR experiments to be performed on samples that have low concentrations of the desired nucleus (i.e., for 31P, 20 mg of P/L is a feasible concentration with instrument time of hours to a few days). 

Fig. 3. Composite relaxation function obtained from six 96 point data sets plotted against log t for PEMA at 70 °C. Different symbols denote data obtained with different sampling intervals...

Because of the very low scattered intensity, the data at the shortest sampling interval is usually the poorest in quality. Arbitrary renormalization of the data followed by the graphical representation outlined above is most likely to amplify errors in the data analysis, focus attention on the inherent errors in the construction of the composite relaxation function, and give undue importance to the worst data. When the data is as limited in quality as it is for this problem, any method of analysis should be as numerically stable as possible and the maximum allowable smoothing of the data should be employed. This procedure may obscure subtle features, but only very high quality data could reliably demonstrate their presence anyway. At the present time a conservative approach seems more sensible. 

Fig. 7. Composite relaxation function for PMMA at 115 °C. The data is nearly linear over this range and has neither reached a value near the intercept at short times nor near the baseline at long times...

Since (1) and (2) will have different collisional efficiencies, the result will be a composite relaxation time for A, given by... 

In order to determine the extent of propagation of this correlated motion, the T s of hexadecanediol were obtained (Table VIII). The results indicate that the motional characteristics responsible for field dependent relaxation are present to C-16 at 75°. This behavior disappears between 80° and 95°. Although it is desirable to extend these measurements to longer alkyl chains, even for HDD, resolution of C-5 through Cn 3 is not possible, and only composite relaxation curves are obtained. 

Having established in this way that the relaxation of the protons is dipole-dipole in origin it is then appropriate to factor out from the composite relaxation rates, the magnitudes of the individual interproton relaxation contributions, the so-called p-values, or at least those p-values which are relevant to the study in hand. Thus in the case of a methyl glucoside we may wish to evaluate the relaxation contribution which the methyl protons make to the anomeric proton (pOCH3- H-l). 

Velocity dispersion and absorption observed at 20°C are shown in Fig.3. The solid lines are the single relaxation curves fitted under the assumption that the relaxation of furan and that of cyclohexane are effectively isolated in the mixtures and independent on each other. This assumption might be invalid in the intermediate region of composition. Relaxation frequency of furan is obtained at each concentration and summarized in Fig. 4, which shows rapid increase at small percentages of cyclohexane. This suggests that collision between furan and cyclohexane (F-C collision) is more effective in energy transfer of furan than collision between furan and furan (F-F collision). 

Numerous ESR studies of the nature, composition, relaxation, and dynamics of PC in cis- and trans-PA were carried out at convenient g>J2k < 10 GHz. Figure 1 exhibits the X-band ((oJ2n=9.7 GHz) ESR spectra of trans-PA as an example a single symmetric line with effective g=2.0026 and line width ABpp = 2.2 G. A small... 

When a sudden temperature increase is applied to a simple A B equihhrimn that is first order in each direction, we show in the following Justification that the composition relaxes exponentially to the new equilibrium composition ... 

AES Auger electron spectroscopy After the ejection of an electron by absorption of a photon, an atom stays behind as an unstable Ion, which relaxes by filling the hole with an electron from a higher shell. The energy released by this transition Is taken up by another electron, the Auger electron, which leaves the sample with an element-specific kinetic energy. Surface composition, depth profiles... 

Crimp. The tow is usually relaxed at this point. Relaxation is essential because it gready reduces the tendency for fibrillation and increases the dimensional stabiUty of the fiber. Relaxation also increases fiber elongation and improves dye diffusion rates. This relaxation can be done in-line on Superba equipment or in batches in an autoclave. Generally saturated steam is used because the moisture reduces the process temperatures required. Fiber shrinkage during relaxation ranges from 10 to 40% depending on the temperature used, the polymer composition used for the fiber, and the amount of prior orientation and relaxation. The amount of relaxation is also tailored to the intended apphcation of the fiber product. 

Measurements of stress relaxation on tempering indicate that, in a plain carbon steel, residual stresses are significantly lowered by heating to temperatures as low as 150°C, but that temperatures of 480°C and above are required to reduce these stresses to adequately low values. The times and temperatures required for stress reUef depend on the high temperature yield strength of the steel, because stress reUef results from the localized plastic flow that occurs when the steel is heated to a temperature where its yield strength is less than the internal stress. This phenomenon may be affected markedly by composition, and particularly by alloy additions. 

Typical properties of these alloys are shown in Table 25. In addition, these alloys exhibit notably excellent resistance to stress relaxation at high appHcation temperatures, for instance 200°C, and in this respect outperform beryUium—copper. However, the electrical conductivity of the strongest Cu—Ni—Sn composition (C729) is lower than that of C172. 

In photoluminescence one measures physical and chemical properties of materials by using photons to induce excited electronic states in the material system and analyzing the optical emission as these states relax. Typically, light is directed onto the sample for excitation, and the emitted luminescence is collected by a lens and passed through an optical spectrometer onto a photodetector. The spectral distribution and time dependence of the emission are related to electronic transition probabilities within the sample, and can be used to provide qualitative and, sometimes, quantitative information about chemical composition, structure (bonding, disorder, interfaces, quantum wells), impurities, kinetic processes, and energy transfer. 

As can be seen from Fig, 3.7, the pinch decomposes the synthesis problem into two regions a rich end and a lean end. The rich end comprises all streams or parts of streams richer than the pinch composition. Similarly, the lean end includes all the streams or parts of streams leaner than the pinch composition. Above the pinch, exchange between the rich and the lean process streams takes place. External MSAs are not required. Using an external MSA above the pinch will incur a penalty of eliminating an equivalent amount of process lean streams from service. On the other hand, below the pinch, both the process and the external lean streams should be used. Furthermore, Fig. 3.7 indicates that if any mass is transferred across the pinch, the composite lean stream will move upward and, consequently, external MSAs in excess of the minimum requirement will be used. Therefore, to minimize the cost of external MSAs, mass should not be transferred across the pinch. It is worth pointing out that these observations are valid only for the class of MEN problems covered in this chapter. When the assumptions employed in this chapter are relaxed, more general conclusions can be made. For instance, it will be shown later that the pinch analysis can still be undertaken even when there are no process MSAs in the plant. The pinch characteristics will be generalized in Chapters Five and Six. 

DavkJ Ford Sims, Viscoelastic Creep and Relaxation Behavior of Laminated Composite Plates, Ph.O. dissertation. Department of Mechanical Engineering and Solid Mechanics Center, Institute of Technology, Southern Methodist University, Dallas, Texas, 1972. (Also available from Xerox University Microfilms as Order 72-27,298.)... 

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