Strength theory

Stephen W. Tsai, Strength Theories of Filamentary Structures, in Fundamental Aspects of Fiber Reinforced Plastic Conposites, Conference Proceedings, R. T. Schwartz and H. S. Schwartz (Editors), Dayton, Ohio, 24-26 May 1966, Wiley interscience. New York, 1966, pp. 3-11. 

R. NarayanaswamI and Howard M. Adelman, Evaluation of the Tensor Polynomial and Hoffman Strength Theories for Composite Materiais, Journal of Composite Materials, October 1977, pp. 366-377. 

The basis for linear solvent strength theory is the assertion that the logarithm of the capacity factor is linearly related to the solvent strength. This is expressed in the Equation 87 90... 

The practical consequence of linear solvent strength theory is that, in principle, it is possible to estimate the retention times of all peaks at any... 

The conceptual basis for understanding the connection between isocratic and gradient elution is well established and is called "linear solvent strength theory".22 27 Linear solvent strength theory proposes that, for a given solute, mobile phase, and column, if one measures the retention time of an analyte at two organic component concentrations, it will be possible to predict the retention time with any other mobile phase composition. The k value that would be observed in pure water, kw, is related to the actual k by the relationship... 

The regression coefficients of descriptors denote the system (combination of mobile and stationary phases) response to these interactions. These coefficients can be measured, however the procedure is time consuming and inappropriate for practical purposes. According to the linear solvent strength theory (LSST) the retention of the analyte depends on the volume fraction (cp) of the organic modifier in binary mobile phase systems ... 

A. Wang and P.W. Carr, Comparative study of the linear solvation energy relationship, linear solvent strength theory, and typical conditions model for retention prediction in reversed-phase liquid chromatography. J. Chromatogr.A 965 (2002) 3-23. 

Moreover, in various experiments it was found that at a constant total counterion concentration in the eluent the dependence of the retention factors on the organic modifier content tp largely follows the linear solvent strength theory (LSS) (Equation 1.5)... 

Brooks RA, Di Chiro G, Patronas N et al (1989) MR imaging of cerebral hematomas at different field strengths theory and applications. Comput Assist Tomogr 13 194-206 Brott T, Broderick JP, Kothari R et al (1997) Early hemorrhage growth in patients with intracerebral hemorrhage. Stroke 28 1-5... 

The physical cause in the first aspect is, most convincingly, associated with the back-bond strength theory. That is, atoms on the (111) surface have three bonds connected to the substrate lattice while those on the (100) surface have only two as shown in Fig. 7.39. Bonding of the surface silicon atoms to solution species such as Olf reduces the strength of the back bonds. The number of back bonds and the strength of surface bonds to the adsorbed species are then responsible for the different reactivity of different crystal surfaces. This can be regarded as the fundamental physical cause of anisotropic etching. 

The physical cause in the first aspect can be considered to be, most convincingly, associated with the backbond strength theory [18, 157, 158]. Because of the adsorption of OH, which has a large electronegativity, the backbond is polarized and weakened. The 111 plane has only one Si—OH surface bond, whereas 100 surface has two bonds as characteristically represented by the scheme shown in Fig. 28. The atoms on the (100) surface thus have weaker backbonds compared to those on the (111) surface due to the larger polarization. This is considered the fundamental cause for the higher dissolution rate of (100) surface than that of (111) surface. 

Crandall, P.G. and Wicker, L. 1986. Pectin internal gel strength theory, measurement, and methodology, in Chemistry and Function of Pectins, eds., M.L. Fishman and J J. Jen, Washington, DC American Chemical Society, pp. 88-102. 

Similarly, in gradient elution HP-RPC, resolution optimization can take advantage of the relationship between the gradient retention time of an analyte (expressed as the median retention factor k) and the median volume fraction of the organic solvent modifier, Ip, in regular HP-RPC systems based on the concepts of the linear solvent strength theory,1 31 such that... 

Cation selectivity data for monolayers (summarized in the introductory section) coincide with the predictions of the field strength theory. Fatty acids have high apparent pKa values, and completely ionized mono-layers (2,3, 4,5,6) select a strong field sequence (XI in Table II). Alkyl sulfates have low apparent pKa values, and completely ionized mono-... 

In previous studies (17, 35), we explained selectivity sequences for alkaline earth cations by specific binding sites, rather than by strong and weak fields. A re-examination of these data shows that selectivity data coincides with the field strength theory. The strong field sequence (VI in Table III) which was found at 10 dynes/cm and pH 9 (Figure 14)... 

Other properties of fatty acid monolayers such as the phase transition temperature are consistent with the field strength theory stearic acid monolayers formed rigid films on alkaline earth subphases (17, 35). The temperature of the phase transition from rigid to fluid monolayers, estimated by the Devaux talc test, was a function of pH and buffer composition (Figure 17). Thus transition temperature at pH 6 decreased in a weak field sequence (I in Table III) while transition temperatures at pH 8 decreased in an intermediate field sequence (III or IV in Table III). Since variables such as tt are not controlled in these experiments, it is surprising that transition temperature data followed these sequences. 

Pectin Internal Gel Strength Theory, Measurement, and Methodology... 

Equations (16.12) and (16.13) are very important, since they easily can be used to predict the influence of any operational parameter on the steepness factor, h, and therefore on the analysis time, efiSciency, and resolution. However, they are based on the validity of Equation (16.10). It has been shown that some deviations occur for some compounds and chromatographic systems (6), especially when retention is not governed solely by hydrophobic interaction. This is, for example, the case when the solutes are strongly basic and the stationary-phase acidity is high. Nevertheless, it is always possible to modify the form of the mobile-phase variation with time in order to maintain the applicability of the linear-solvent-strength theory [Equation (16.1)]. As we have seen above, this type of gradient offers a considerable help in the fundamental understanding of the retention behavior of the solutes and in the optimization of a separation. 

Traditionally, laminate strength theories are based on ply strengths and models that use them to predict when a laminate would fail. The complexities associated with failure of a single ply are compounded in this case by the fact that damage created in one ply can interact with damage in other plies and evolve very differently depending on the laminate. For example, matrix cracks may evolve to delaminations or may branch out to adjacent plies as shown in Figure 6.6. 

Tsai SW. Strength theories of filamentary structures. In Schwartz RT, Schwartz HS, editors. Fundamental aspects of fiber reinforced plastic composites. New York, USA Wiley Interscience 1968. pp. 3—11. 

Failure criterion is based on Coulomb Mohr Strength Theory. The results of the simulation is shown in Figure 5 and 6. As can be seen in Figure 5, just above the working face, the stress of igneousrock is -0.15 X10-6 0.0 Mpa, and the stress of coal measure strata is -5.5 x 10 —5.0 x 106 MPa. The simulation also shows that stress gradient changes suddenly at the interface of strata separate obviously. 

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