The simple series model

The simple series model represents a composite with the two phases stacked in alternate layers lying parallel to the electrode surface. Average values for the dielectric constant 33 and the longitudinal strain coefficient 33 may be derived in the form 

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The early attempts to interpret the dynamic mechanical behaviour in structural terms include that of Smith et al. where the plateau modulus was correlated with the fraction of non-crystalline material f, determined by NMR. Plots of the plateau compliances at —60 °C and —160 °C as a function of f suggested a modified Takay-anagi series model, with a constant amount of non-crystalline material in parallel with the simple series model. The modd showed good internal consistency, with values for the compliances of the non-ciystalline regions which were acceptable in physical terms. 

A limit value for the yield strain Cy can be obtained using the simple series model of Nielsen. According to this model, perfect adhesion is assumed, and the actual strain of the polymer (cm) is higher than the strain of the composite (Cq) due to the fact that glass does not elongate the relationship is... 

Deviations from the simple ionie model are expeeted to inerease with inereasing formal eharge on the eation or anion and with inereasing size and ease of distortion of the anion. Again, deviations tend to be greater for smaller eations and for those (sueh as Cu+, Ag+, ete.) whieh do not have an inert-gas eonfiguration. The gradual transition from predominantly ionie to eovalent is illustrated by the isoeleetronie series ... 

Let us consider the real charge distribution in the vicinity of the tip, in contrast to the simple spherical model, where it was supposed that the overall charge is concentrated in the center of the spherical curvature of the tip apex. The charge qo = RU is generated in the center of the spherical curvature of the tip apex under an applied voltage U. Moreover, an infinite series of image charges qn is located at a distance r from the center of the sphere [70,71] ... 

In this section we first present a series of results (Sec. 3.1) which show that molecular dynamics simulations can be used to directly link atomic scale chemistry to the continuum theory of detonations. We then show (Secs. 3.2 and 3.3) that complex initiation behavior can arise even within the simple AB Model I system. Taken together, the results reviewed in this section demonstrate that simulations using REBO potentials provide a powerful probe of the interplay between the continuum properties of shockwaves and the atomic scale chemistry induced in the initiation and propagation of condensed phasn detonations. 

Finally, if the fast reactions are irreversible, further simplification is possible. In the simple series reactions, let the second reaction be fast and irreversible in Equation 5.41. We start with the slow time-scale model given in Table 5.4 and take the limit as Kz — oo giving... 

The simple MO model indicates that ligand a donation will give a negative QS (see Footnote) and r-acceptance a positive QS, so that these values are in rough agreement with the partial IS values and the spectrochemical series (Sections IV. A and V. C). Considering the many experimental and theoretical uncertainties this is probably all that may be expected. 

Deduce the equations corresponding to equations (11.16) and (11.17) for the Takayanagj models shown in figs 11.10(b) and (c). A polymer that is 75% crystalline by volume has amorphous and crystalline moduli E3 and equal to 1.0 x 10 and 1.0 x lO Pa, respectively, parallel to the draw direction. Calculate the modulus parallel to the draw direction for the simple series and simple parallel Takayanagi models and for the series-parallel and parallel-series models, assuming that in the last two models a = ft = 0.5. 

The modified series model shown in Fig. 21 has been extended to include the viscoelastic behaviour. To this end the simple assumption is made that the time-dependent part of the creep strain arises solely from the rotation of the chains towards the direction of the fibre axis as a result of the shear deformation of the crystallites. This yields for the fiber extension as a function of the time t during creep caused by a stress CTq... 

Figure 5 shows the outcome of a series of film thickness experiments ip indeed does scale as /d, su esting that the simple permeation model outlined in Sect. 5.1.3 is an appropriate description of the transport process. For the permeant concentrations used, it is beheved... 

Figure 2.18. Series circuit models for an electrochemical cell, K and X are the simple series resistance and reactance, respectively, in the elementary model. is the bulk solution resistance, Q is the double layer capacitance, Rp is the polarization resistance, and is the Warburg impedance.

Distinct NMR resonances were first observed for the enantiomers of 2,2,2-trifluoro-l-phenylethanol in the presence of (/ )-phenylethylamine. With (/ )-2-naphthylethylamine the magnitude of the non-equivalence was increased. A systematic study of a series of aryl alcohols in the presence of amines showed a consistent correlation between the sense of non-equivalence and the absolute configuration of the alcohol. From the simple solvation models proposed, the reciprocality of the CSA approach is evident, i.e. if chiral A can be used to assay racemic B then chiral B can be used to assay racemic A. With this in mind 1 -(9-anthryl)-2,2,2-trifluoroethanol (15a) was developed as a CSA for chiral amines. It is also effective with alcohols, lactones, a-amino acid esters, a-hydroxy acid esters and sulphoxides and is the most widely used chiral solvating agent. Other more specific solvating agents have been developed. Kagan has developed A -(3,5-dinitrobenzoyl)-l-phenylethylamine,forexample, as a CSA specifically for the assay of chiral sulphoxides prepared from sulphides by a modified Sharpless oxidation (section 6.3.2). 

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