Physical Considerations

10 Dynamic Stress Softening Effect 5.1.10.1 Physical Considerations 

Various origins (i.e., physical interpretations) have been assigned to the DSS effect, all calling to local mechanisms involving interactions either between filler particles, or between filler particles and the polymer matrix. 

DSS is observed with nearly all filled systems and, accordingly, a number of mechanisms have been proposed in the literature that we have (somewhat arbitrarily) sorted out in two main categories  

From an engineering point of view, the most useful contribuhons from the literature are the ones that lead to quantitative workable models, i.e., mathematical relationships that can be used first to fit correctly experimental data, second to (tentatively) interpret fit parameters in view of the physical or physico-chemical processes considered. In discussing the physical interpretations of the DSS effect, quantitative workable models are therefore receiving hereafter privileged considerations. 

Commercial instruments have a reasonable balance between the recommended column size and the volume of the column and connecting tubing (XY). However, the theoretical plate number of a single column may give different values on different instruments, and even on replacement of the components and parts of a single instrument. Such discrepancies can be understood in terms of differences in the mechanics of the instruments and the design of their parts. 

Basic Concepts of High-performance Liquid Chromatography 

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The basic requirements for the Mephisto model was satisfactory accuracy, that means prediction of amplitude, position and phase relation between the various signals, and short computation times, typically a few minutes for the simulation of a whole Cscan, compatible with an intensive use. These a priori contradictory characteristics have been contented by means of appropriate approximations based on physical considerations. 

Orrell, W. H., Physical Considerations in Designing Vertical Thermosyphon Reboilers, Chemical Engineering, September 17, 1973. 

What are the environmental conditions in which the product must operate These are temperature range, ambient RF levels, dust, dirt, shock, vibration, and any other physical considerations. 

Apart from the design, complexity, age, and operating characteristics of the boiler plant itself, a checklist of various chemical and physical considerations includes the following ... 

By integrating this equation, and owing to the physical consideration that the velocity must be finite at r = 0,... 

Response We were not trying to use the chemometric techniques to create a physical model in the column. We also agree that physical models should be created in the traditional manner, based on the study of the physical considerations of a situation. Ideally you would start from a fundamental physical law and derive, through logic and mathematics, the behavior of a particular system this is how all other fields of science work. A chemometric technique then would be used only to ascertain the value (from a series of physical measurements) of an unknown parameter that the mathematical derivation created. 

In addition to thermal and viscosity changes, a third and perhaps the most important physical consideration in UHPLC is the influence of pressure on the solvent structure of the hydroorganic... 

The structure of the gap function (33) is then inspired by a physical consideration of a quark pair as in the usual BCS theory we consider here the quark pair on each Fermi surface with opposite momenta, p and —p so that they result in a linear combination of Jn = 0, 1 (see Fig. 3). 4... 

In the following section, it is shown that mathematical methods which have been used to interpret adsorption data bias the interpretation towards chemical and electrostatic properties which lead to a significantly sub-Nernstian response this bias arises out of the need for mathematical simplifications, not from physical considerations. 

An example of the use of this method with the constant capacitance model on the data for TiC>2 in 0.1 M KNO is illustrated in Figure 6. It appears from the figure that the problem is perfectly well determined, and that unique values of Ka and Ka2 can be determined. However, as is shown below, the values of Ka and Ka2 determined by this method are biased to fulfill the approximations made in processing the data (i) on the acidic branch, nx+, nx nx-, which yields a small value for Ka2, and (ii) on the basic branch, nx-, nx nx+, which yields a large value of Ka. Thus the approximation used to find values for Qa and Qa2 leads to values of Ka and Ka2 consistent with the approximation of a large domain of predominance of the XOH group. This constraint arose out of the need for mathematical simplicity, not out of any physical considerations. 

All the requisite structural information for a solid phase is contained (either explicitly or implicitly) in the description of its unit cell. A number of features, however, which are especially relevant for chemical-physical considerations, such as local coordination geometries, the existence of clusters of atoms or chains or layers, etc., are not self-evident in the aforementioned structural descriptions and can be deduced only by means of a more or less complicated series of calculations. 

Since the quantities df/d(Mj) are generally required during the solution of Eq. (2.69), the sensitivity equations are conveniently solved simultaneously with the species concentration equations. The initial conditions for Eq. (2.70) result from mathematical consideration versus physical consideration as with Eq. (2.69). Here, the initial condition [c M /da, ]f=0 is the zero vector, unless a, is the initial concentration of the /th species, in which case the initial condition is a vector whose components are all zero except the y th component, which has a value of unity. Various techniques have been developed to solve Eq. (2.70) [22, 23],... 

D = D° exp(-ac ), where D is the diffusion, D represents the zero-concentration limit, c is the concentration, a and v are parameters, fits the data from a wide variety of probes and matrix polymers ( ). Several theoretical justifications for this behavior have been presented (97-1011. but it is not possible to tell yet which, if any, is uniquely correct. The treatments range from simple physical considerations (98) to treatments of hydrodynsumical interaction of probe and matrix (97,991. Other more complex and general treatments (1001 do not explicitly arrive at the stretched exponential form, but do closely fit the available data. Much more work needs to be done on probe diffusion in such transient networks. Beyond enhancing the arsenal of gel characterization, the problem is quite fundamental to a number of other important processes. 

Conclusion drawn from physical considerations The steadily rising current density reaches a limiting current plateau in the 483 - 700 mV polarization range, prior to a further increase at higher polarization causing proton discharge at the cathode. 

The importance of the treatment lies in the physical considerations used for the choice of the valence and reference states as much as on the final results. 

There are situations when it can be difficult to obtain a sufficiently independent set of RDC measurements, such as in small molecules or in cases when poor chemical shift resolution limits the number of data points. As pointed out by Losonzci et al.,S9 in these cases it is still possible to restrict the possible solutions for the order tensor, with remaining ambiguities possibly lifted using additional experimental means or physical considerations. The procedure for dealing with this underdetermined case is to generate a unique solution for the existing data and then supplement this solution with vectors drawn randomly from the so-called null space. All solutions constructed in this manner are equally valid. The full set of solutions for the best fit order tensor in this underdetermined case is written,50... 

Generally, the atomic, outer, and interatomic sphere radii are chosen so as to minimize the volume between the spheres. Other physical considerations, such as empirical atomic or ionic radii, can also influence the initial choice of sphere sizes. It has also been recently shown that overlapping spheres may be used since the various expansion theorems are still valid (192). This technique has been used to calculate the molecular orbitals of Zeise s salt and ferrocene discussed later in this review (191, 193). 

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