Affinely displaced

The Flory criterion requires that each crosslink between units which are already part of the gel must increase the number of active strands by 2. Examination of example structures shows that this number according to Scanlan s criterion is either 1, 2, or 3, depending on the structures involved. The difference between criteria is therefore a real one in physical terms. In the author s opinion, the Scanlan criterion is clearly the correct one. Any other choice would seem to depend ultimately on such questions as whether junctions with three anchors in the gel are equivalent to 4-anchor junctions insofar as the assumption of affine displacement is concerned. To the extent that the strands behave as linear... 

The dye HABA interacts with avidm yielding a complex with an absorption maximum at 500 nm. Biotin, because of its higher affinity, displaces HABA, causing a decrease in absorbance at 500 nm proportional to the amount of biotin present in the assay. 

In clinical research, Metribolone is used to determine receptor-site affinity / displacement. Let me explain that. Metribolone is a very powerful androgen receptor-site stimulator and antagonist. I doubt there is any AAS more powerful. Since it binds so strongly to the receptor-site, researchers use the drug to see if other drugs can dislocate it, or for comparison. Not even Deca can kick it out of receptor-sites ... 

Figure 15.5 Spectra simulated with a phantom network, in which each chain is elongated, and thus oriented, along its end-to-end vector. A gaussian distribution of the end-to-end vectors is assumed, a relaxed (isotropic) state b uniaxially elongated state (deformation ratio A, = 2.5). Affine displacement of junctions is assumed. No...

Jayaraman, G., Gadam, S. D., and Cramer, S. M. (1993). Ion-exchange displacement chromatography of proteins Dextran based polyelectrolytes as high affinity displacers.. Chromatogr. 630, 53-68. 

For a network of Gaussian chains having the same number n of links, uniaxially stretched by an amount L/Lo = A., the assumptions of affine displacement of jimction points and initial Gaussiein distribution of end-to-end vectors allows one to calculate the optical anisotropy of the network by integrating Eq.lO over the distribution of end-to-end vectors in the stretched state. By taking Treloar s expansion [11] for the inverse Langevin function, the orientation distribution function for the network can be put into the form of a power series of the number of Unks per chain ... 

Since the deformational forces are proportional to the cross section (A = d2) and the resistance to the lateral surface area (4dl), one would expect a larger displacement effect on fibrils than on microfibrils. The average length of both is practically the same, lf = lmfy but fibril thickness is about ten times that of microfibrils, df — 10dmf. If the mentioned difference in friction coefficient is also considered, one can conclude that most plastic deformation of fibrous structure is the consequence of the nearly affine displacement of fibrils and that only a small fraction is attributable to that of microfibrils. 

A closer analysis (19) of the stress field inside the fibril caused by the affine displacement reveals that the main forces on the microfibrils produce a shear displacement (Figure 5). It is relatively small, e.g. about 2000 A, for adjacent microfibrils of nylon 6 which may be 30,000-60,000 A long and 100-200 A thick. But it has a dramatic effect on interfibrillar tie molecules unfolded over the same length of 2000 A which corresponds to a molecular weight of about 20,000. In nylon 6 with a long period L = 100 A, such an unfolded chain crosses about 20 amorphous regions it is therefore counted 20 times as a taut tie molecule. Even a small fraction of interfibrillar tie molecules,... 

Absence of the rapid increase in load with mature neck indicates that the increase in frictional resistance to affine displacement of fibrils is smaller in polyethylene than in nylon 6. According to the model of fibrous structure, this means that there is less of a smoothing effect at the microfibril ends by unfolding of chains, less improvement in lateral contact between adjacent fibrils, and a smaller increase in the fraction of taut interfibrillar tie molecules. Such an effect is compatible with the model which predicts fibril length proportional to A and lateral dimensions proportional to A "1/2. In polyethylene with A — 9, the fibrils are more than three times longer than in nylon 6 with A = 2-3. Hence, with an equal number of microfibrils per fibril, the surface density of microfibrillar ends in polyethylene is at most one-third that in nylon 6. One would expect almost the same reduction in the effect of smoothing at such ends on the contact quality and frictional resistance of fibrils. 

Taking note of the mapping (34) as well, the affine displacement (37) corresponds to the displacement (14) of the five-dimensional space. 

The simplest case is that of high crosslink density or small coil interpenetration (Np 1). In this case, the restrictions on the configurations of network chains caused by the crosslinks dominate, and the constraints acting on the constraining chains may be omitted in the course of the calculation of the constraining potential. With the assumption of an affine displacement of the crosslink positions with the deformation of the sample, Eq. (12) was obtained with... 

An analytic expression for d has been derived in the case that effects of the constraints predominate over the crosslink contribution, i.e. in the melt case . The assumption of affine displacement of the tube axis of the constraining chains again gives Eq. (12) with... 

Of particular interest is the aforementioned interfacial partitioning technology. It has been demonstrated that small particles in a mixture partition differently to the interface of a suitable liquid-liquid system, such that (1) a particle-stabilised interfacial layer develops, and (2) that particles with a high-affinity displace those with lower affinities [34,35]. This opens possibilities for the development of a particle fractionation technology to produce essentially pure particles from a mixture, as is shown schematically in Fig. 9. 

Extinction angle. It is interesting to note that the assumption of affine displacement of the mean positions of the junctions lead always to a dependence on X and 0 of the type... 

Both H and h undergo concerted changes (a change in H from the reference state Ho directly affects the atomistic cell h and affinely displaces the inclusion boundary vertices according to xf = HHq xq,). The reference state, where H = Hq and h = ho, corresponds to Dh = 0. 

The early versions of the statistical theory of rubber elasticity assumed an affine displacement of the average positions of the network junctiOQs with the macroscopic strain This is tantamount to the assertion that the network Junctions are firmly embedded in the medium of which they are part. The elastic equation of state derived on this basis for simple extension at constant volume takes the familiar neo-Hookean form, i.e. Eq. (7), with... 

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