Two-phase structure

According to the Porod law [28], the intensity in the tail of a scattering curve from an isotropic two-phase structure havmg sharp phase boundaries can be given by eqnation (B 1.9.81). In fact, this equation can also be derived from the deneral xpression of scattering (61.9.56). The derivation is as follows. If we assume qr= u and use the Taylor expansion at large q, we can rewrite (61.9.56) as... 

Our main interest here is concerned with patterns which can grow at constant speed even at low undercoolings A < 1, because if they exist they will dominate the system s behavior. A two-phase structure must then exist behind the growth front, filling the space uniformly on sufficiently... 

The aim is to predict, for given undercooling A and anisotropy e, the type of the two-phase structure and its characteristic length scales and velocity that is, to calculate the functions/ and v in the relation (80). The results will be summarized in the morphology diagram shown in Fig. 6. As it turns out. 

Multiblock polyethylene-polydimethylsiloxane copolymers were obtained by the reaction of silane terminated PDMS and hydroxyl terminated polyethylene oligomers in the presence of stannous octoate as the catalyst 254). The reactions were conducted in refluxing xylene for 24 hours. PDMS block size was kept constant at 3,200 g/mole, whereas polyethylene segment molecular weights were varied between 1,200 and 6,500 g/mole. Thermal analysis and dynamic mechanical studies of the copolymers showed the formation of two-phase structures with crystalline polyethylene segments. 

More usually, as has been described earlier, polyblends are made from incompatible polymers that give a two-phase structure. These polyblends show two TgS, one for each phase. The temperatures of these transitions correspond closely to the T s of the respective homopolymers. 

Figure 19.8 Two-phase structure of impact modified polypropylene...

Equations. For a ID two-phase structure Porod s law is easily deduced. Then the corresponding relations for 2D- and 3D-structures follow from the result. The ID structure is of practical relevance in the study of fibers [16,139], because it reflects size and correlation of domains in fiber direction . Therefore this basic relation is presented here. Let er be50 the direction of interest (e.g., the fiber direction), then the linear series expansion of the slice r7(r)]er of the corresponding correlation function is considered. After double derivation the ID Fourier transform converts the slice into a projection / Cr of the scattering intensity and Porod s law... 

Figure 8.19. Extraction of the scattering of an ideal two-phase structure from the raw scattering data of an isotropic UHMWPE material by means of spatial frequency filtering... 

D Structural Entities. In materials science, stmctural entities which can satisfactorily be represented by layer stacks are ubiquitous. In the field of polymers they have been known for a long time [156], Similar is the microfibrillar [157] structure. Compared to the microfibrils, the layer stacks are distinguished by the large lateral extension of their constituting domains. Both entities share the property that their two-phase structure is predominantly described by a ID density function, Ap (r3), which is varying along the principal axis, r3, of the structural entity. 

Figure 8.24. Demonstration of the edge-enhancement principle built into the chord length distribution, (a) Two-phase structure intersected by a straight line, (b) The density along the line, (c) The derivative of the density is a sequence of 5-functions which are marking the positions of the domain edges...

Figure 8.40. Computer-simulated IDFs gi (u) of ID two-phase structure formed by the iterated stochastic structure formation process. tt is the thickness of the transition layer at the phase boundary. o> is the standard deviation of a Gaussian crystallite thickness distribution... 

Polyester elastomers, 20 70-71, 74 Polyesterether elastomers chemical resistance of, 20 75t manufacture of, 20 75-76 market for, 20 77-78 models for two-phase structure in, 20 72-73... 

Figure 15. Left graph Quark star cooling by antineutrino and photon emission from the surface. Middle graph Two-phase structure developes due to the trapped antineutrinos a normal quark matter shell and a superconducting interior. Right graph Antineutrino untrapping and burst-type release of energy.

Copoly(ether ester)s consisting of short-chain crystalline segments of PBT and amorphous poly(ether ester) of poly(tetramethylene terephthalate) exhibit a two-phase structure and can be used for the production of high-impact-strength engineering plastics. These very interesting materials with their outstanding properties understandably require stabilization to heat and UV exposure [45],... 

Pearlite The two-phase structure (aFe,C + Fe3C) originating from the eutectoidal decomposition of austenite (that is the C solid solution in Fe) and having the overall composition of 0.76 mass % C (3.46 at.%C). The stable Fe-graphite eutectoid has a composition of 2.97 at.% C. 

These materials have two-phase structures based on hard segments of polystyrene and soft segments of butadiene for SBS, or isoprene for SIS, etc. 

In polymeric materials, the morphology development upon spinodal decomposition proceeds through various stages [92,93]. In the early stage of decomposition a co-continuous structure develops. A dispersed two-phase structure results only in the late stage of phase separation and the shape of the domains is not uniform. The morphology development upon spinodal decomposition is presented in Fig. 6. 

A different analysis of the scattering pattern uses the Debye correlation function (14), derived for a random two-phase structure with sharp interfaces ... 

The consequence of the positive interactions is that alloys which lie between xi and X2 can lower their Gibbs energy by forming two-phase structures. One phase which is y4-rich with composition Xi and the other which is B-rich with composition... 

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