Domain compression

In principle, compressing a monolayer should produce more domains of radius J eq. however McConnell shows that in practice, domains grow to exceed this radius. Once a domain grows to A = it becomes unstable toward... 

Fig. XV-8. Fluorescence micrographs of crystalline domains of an S-DPPC monolayer containing 2% cholesterol and compressed to the plateau region. [From H. McConnell, D. Keller, and H. Gaub, J. Phys. Chetn., 40, 1717 (I486) (Ref, 49). Copyright 1986, American Chemical Society.]...

Molecules are in continuous random motion, and as a result of this, small volume elements within the liquid continuously experience compression or rarefaction such that the local density deviates from the macroscopic average value. If we represent by 6p the difference in density between one such domain and the average, then it is apparent that, averaged over all such fluctuations, 6p = 0 Equal contributions of positive and negative 6 s occur. However, if we consider the average value of 6p, this quantity has a nonzero value. Of these domains of density fluctuation, the following statements can be made ... 

The particular type of thermoplastic elastomer (TPE) shown in Figure 3 exhibits excellent tensile strength of 20 MPa (2900 psi) and elongation at break of 800—900%, but high compression set because of distortion of the polystyrene domains under stress. These TPEs are generally transparent because of the small size of the polystyrene domains, but can be colored or pigmented with various fillers. As expected, this type of thermoplastic elastomer is not suitable for use at elevated temperatures (>60° C) or in a solvent environment. Since the advent of these styrenic thermoplastic elastomers, there has been a rapid development of TPEs based on other molecular stmctures, with a view to extending their use to more severe temperature and solvent environments. 

Figure IS. 7 The constant domains of immunoglobulins are folded into a compressed antiparallel p banel built up from one three-stranded p sheet packed against a four-stranded sheet (a). A topological diagram (b) shows the connected Greek key motifs of this fold.

Figure 15.24 Ribbon diagram (a) and topology diagram (b) of the fibronectin type III domain, which is composed of a three-stranded and a four-stranded p sheet packed together as a compressed barrel.

In spite of the presence of ECC, the sample exhibiting a domain structure remains unoriented on the macroscopic level. Figure 3 c shows a great difference in the structures obtained, if molecular orientation exists and if hydrostatic compression is applied. Although the method of hydrostatic compression of the melt is of paramount importance from the scientific view point just for samples crystallized under pressure it was possible to prove unequivocally the existence of ECC), it does not allow a direct preparation of oriented samples of high strength (they are brittle and readily crumble to powder under minimum strain). However, the material obtained in this way can probably serve as a semi-finished product for further technological treatment that would improve its mechanical properties. 

Fig. 5. Log-iog plot illustrating the hardness dependence of density for PE samples crystallized from the melt. The plot yields two straight sections which can be ascribed to two preferential deformation modes a crystal destruction and b compression of amorphous domains...

As will be outlined below, the computation of compressible flow is significantly more challenging than the corresponding problem for incompressible flow. In order to reduce the computational effort, within a CED model a fluid medium should be treated as incompressible whenever possible. A rule of thumb often found in the literature and used as a criterion for the incompressibility assumption to be valid is based on the Mach number of the flow. The Mach number is defined as the ratio of the local flow velocity and the speed of sound. The rule states that if the Mach number is below 0.3 in the whole flow domain, the flow may be treated as incompressible [84], In practice, this rule has to be supplemented by a few additional criteria [3], Especially for micro flows it is important to consider also the total pressure drop as a criterion for incompressibility. In a long micro channel the Mach number may be well below 0.3, but owing to the small hydraulic diameter of the channel a large pressure drop may be obtained. A pressure drop of a few atmospheres for a gas flow clearly indicates that compressibility effects should be taken into account. 

Figure 8.38. Structural parameters of an ensemble of needle-shaped soft domains in a poly(ether ester) as a function of elongation . D (open circles) is the average needle diameter, a/D (filled circles) is the relative standard deviation of the needle-diameter distribution. Square symbols demonstrate the lateral compressibility of the soft needles during elongation... 

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