Dispersion experimental data

Comparison of breakdown voltage (BDV) of polymer tantalum capacitors having polymer cathodes made by chemical in situ polymerization (typical range) and by polymer dispersions (experimental data points). Tantalum anodes were anodized at 100 V. 

Fig. 5.37 Comparison of the calculated phonon dispersion curve for Al with the experimental values measured using neutron diffraction. (Figure redrawn from Michin Y, D Farkas, M ] Mehl and D A Papaconstantopoulos 1999. Interatomic Potentials for Monomatomic Metals from Experimental Data and ab initio Calculations. Physical Review 359 3393-3407.)...

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

A number of HETP equations were developed other than that of Van Deemter. Giddings developed an alternative form that eliminated the condition predicted by the Van Deemter equation that there was a finite dispersion at zero velocity. However, the Giddings equation reduced to the Van Deemter equation at velocities approaching the optimum velocity. Due to extra-column dispersion, the magnitude of which was originally unknown, experimental data were found not to fit the Van Deemter... 

In the next chapter, experimental data supporting the Van Deemter equation will be described and discussed. Only data that has been acquired with equipment that has been specifically designed to eliminate, or reduce to an insignificant level, the dispersion sources described in this chapter can be used reliably for such a purpose. 

Unfortunately, any equation that does provide a good fit to a series of experimentally determined data sets, and meets the requirement that all constants were positive and real, would still not uniquely identify the correct expression for peak dispersion. After a satisfactory fit of the experimental data to a particular equation is obtained, the constants, (A), (B), (C) etc. must then be replaced by the explicit expressions derived from the respective theory. These expressions will contain constants that define certain physical properties of the solute, solvent and stationary phase. Consequently, if the pertinent physical properties of solute, solvent and stationary phase are varied in a systematic manner to change the magnitude of the constants (A), (B), (C) etc., the changes as predicted by the equation under examination must then be compared with those obtained experimentally. The equation that satisfies both requirements can then be considered to be the true equation that describes band dispersion in a packed column. 

In summary, it can be said that all the dispersion equations that have been developed will give a good fit to experimental data, but only the Van Deemter equation, the Giddings equation and the Knox equation give positive and real values for the constants in the respective equations. 

Experimental laboratory results and results from a full-scale modeb have shown the relation between the dispersed thermal power inside and the air temperature difference between the two sides of air curtain. The results shown in Fig. 10.67 are for different conditions. There are no other experimental data readily available, so caution is needed when applying these results to the design of an air curtain. 

For solvent models where the cavity/dispersion interaction is parameterized by fitting to experimental solvation energies, the use of a few explicit solvent molecules for the first solvation sphere is not recommended, as the parameterization represents a best fit to experimental data without any explicit solvent present. 

According to the criteria, the dispersed phase embedded in the matrix of sample 1 must have been deformed to a maximum aspect ratio and just began or have begun to break up. By observing the relative position of the experimental data to the critical curve, the deformational behavior of the other samples can be easily evaluated. Concerning the fibrillation behavior of the PC-TLCP composite studied, the Taylor-Cox criteria seems to be valid. 

Figure 7. Phonon dispersion including the electron-phonon interaction for bcc CuZn. Force constants have been obtained from ah initio calculations. Dashed line is the phonon dispersion without the V-i contribution. Diamonds mark experimental data. ...

The situation becomes most complicated in multicomponent systems, for example, if we speak about filling of plasticized polymers and solutions. The viscosity of a dispersion medium may vary here due to different reasons, namely a change in the nature of the solvent, concentration of the solution, molecular weight of the polymer. Naturally, here the interaction between the liquid and the filler changes, for one, a distinct adsorption layer, which modifies the surface and hence the activity (net-formation ability) of the filler, arises. Therefore in such multicomponent systems in the general case we can hardly expect universal values of yield stress, depending only on the concentration of the filler. Experimental data also confirm this conclusion [13],... 

Though experimental data on suspensions of fibers in Newtonian dispersion media give more or less regular picture, a transition to non-Newtonian viscoelastic liquids, as Metzner noted [21], makes the whole picture far or less clear. Probably, the possibility to make somewhat general conclusions on a longitudinal flow of suspensions in polymer melts requires first of all establishing clear rules of behavior of pure melts at uniaxial extension this problem by itself has no solution as yet. 

The composites with the conducting fibers may also be considered as the structurized systems in their way. The fiber with diameter d and length 1 may be imagined as a chain of contacting spheres with diameter d and chain length 1. Thus, comparing the composites with dispersed and fiber fillers, we may say that N = 1/d particles of the dispersed filler are as if combined in a chain. From this qualitative analysis it follows that the lower the percolation threshold for the fiber composites the larger must be the value of 1/d. This conclusion is confirmed both by the calculations for model systems [27] and by the experimental data [8, 15]. So, for 1/d 103 the value of the threshold concentration can be reduced to between 0.1 and 0.3 per cent of the volume. 

The above correlation is valid for a bioreactor size of less than 3000 litres and a gassed power per unit volume of 0.5-10 kW. For non-coalescing (non-sticky) air-electrolyte dispersion, the exponent of the gassed power per unit volume in the correlation of mass transfer coefficient changes slightly. The empirical correlation with defined coefficients may come from the experimental data with a well-defined bioreactor with a working volume of less than 5000 litres and a gassed power per unit volume of 0.5-10 kW. The defined correlation is ... 

The industrial wastewater used in the experiment is considered as having non-coalescing air electrolyte dispersion. Thus the equations discussed above would be used as a theoretical model for the estimation of oxygen transfer rate in the liquid phase, and compared with the experimental data obtained. 

Hurst (19) discusses the similarity in action of the pyrethrins and of DDT as indicated by a dispersant action on the lipids of insect cuticle and internal tissue. He has developed an elaborate theory of contact insecticidal action but provides no experimental data. Hurst believes that the susceptibility to insecticides depends partially on the cuticular permeability, but more fundamentally on the effects on internal tissue receptors which control oxidative metabolism or oxidative enzyme systems. The access of pyrethrins to insects, for example, is facilitated by adsorption and storage in the lipophilic layers of the epicuticle. The epicuticle is to be regarded as a lipoprotein mosaic consisting of alternating patches of lipid and protein receptors which are sites of oxidase activity. Such a condition exists in both the hydrophilic type of cuticle found in larvae of Calliphora and Phormia and in the waxy cuticle of Tenebrio larvae. Hurst explains pyrethrinization as a preliminary narcosis or knockdown phase in which oxidase action is blocked by adsorption of the insecticide on the lipoprotein tissue components, followed by death when further dispersant action of the insecticide results in an irreversible increase in the phenoloxidase activity as a result of the displacement of protective lipids. This increase in phenoloxidase activity is accompanied by the accumulation of toxic quinoid metabolites in the blood and tissues—for example, O-quinones which would block substrate access to normal enzyme systems. The varying degrees of susceptibility shown by different insect species to an insecticide may be explainable not only in terms of differences in cuticle make-up but also as internal factors associated with the stability of oxidase systems. 

They defined an average contact time as the average residence time of a bubble per unit length of dispersion. Their experimental data were correlated by ... 

The values of the half-widths of the components of the rotational absorption spectrum of HC1, dissolved in various noble gases, are borrowed from [291]. In order to make this example obvious, a continuous curve is drawn through the calculated points. Comparison between experimental data and calculated results demonstrates, in line with the qualitative agreement, a good numerical coincidence of the observed. /-dependence of the half-widths of the rotational lines with the theoretical one in the case of HC1 dissolved in Kr and Xe. This allows one to estimate the model parameters for these systems dispersion of the potential... 

Figure 12.5. Ethylene oxidation on Pt finely dispersed on Au supported on YSZ.7 Effect of the current 1 on x 1, where x is the time constant measured during a galvanostatic transient experiment with I as the applied current x is obtained by fitting either r/r0=exp(-t/x) or l-exp(-t/x) to the experimental data depending on the sign of the current and whether the reaction is electrophilic or electrophobic, (a) Positive values of I for electrophilic (squares, T=371°C, pO2=18.0 kPa, Pc2H4=0-6 kPa) and electrophobic behavior (circle, T=421°C, p02=l 4.8 kPa, Pc2H4 CU kPa) (b) negative currents, electrophilic behavior (T=421°C, p02=14.8 kPa, pC2H4=0.1 kPa. Reprints with permission from Academic Press.

Our results indicate that dispersion coefficients obtained from fits of pointwise given frequency-dependent hyperpolarizabilities to low order polynomials can be strongly affected by the inclusion of high-order terms. A and B coefficients derived from a least square fit of experimental frequency-dependent hyperpolarizibility data to a quadratic function in ijf are therefore not strictly comparable to dispersion coefficients calculated by analytical differentiation or from fits to higher-order polynomials. Ab initio calculated dispersion curves should therefore be compared with the original frequency-dependent experimental data. 

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