Domain sizes

The time-dependent structure factor S k,t), which is proportional to the intensity I k,t) measured in an elastic scattering experiment, is a measure of the strength of the spatial correlations in the ordering system with wavenumber k at time t. It exliibits a peak whose position is inversely proportional to the average domain size. As the system phase separates (orders) the peak moves towards increasingly smaller wavenumbers (see figure A3.3.3. 

Due to the conservation law, the diffiision field 5 j/ relaxes in a time much shorter than tlie time taken by significant interface motion. If the domain size is R(x), the difhision field relaxes over a time scale R Flowever a typical interface velocity is shown below to be R. Thus in time Tq, interfaces move a distanc of about one, much smaller compared to R. This implies that the difhision field 6vj is essentially always in equilibrium with tlie interfaces and, thus, obeys Laplace s equation... 

Surface reconstructions have been observed by STM in many systems, and the teclmique has, indeed, been used to confmn the missing row structure in the 1 x 2 reconstruction of Au(l 10) [28]. As the temperature was increased within 10 K of the transition to the disordered 1 1 phase (700 K), a drastic reduction in domain size to -20-40 A (i.e. less than the coherence width of LEED) was observed. In this way, the STM has been used to help explain and extend many observations previously made by diffraction methods. 

Adechanical stahility. ChemisoriDtion to tire surface, intennolecular interactions and crosslinking between adjacent compounds—if possible—all contribute to tire resulting stability of tire monolayer film. Lateral force microscopy investigations revealed tliat tire mechanical stability towards lateral forces on tire nanometre scale is likely to be detennined by tire defect density and tire domain size on a nano- to micrometre scale [163, 1731. 

The breadth of the peaks in an x-ray diffractogram provide a detennination of the average crystallite domain size, assuming no lattice strain or defects, tlirough the Debye-Scherr fonnula ... 

Figure C2.17.9. Size-dependent changes in PXRD linewidtlis. PXRD can be used to evaluate tire average size of a sample. In tliese cases, different samples of nanocrystalline titania were analysed for tlieir grain size using tire Debye-Scherr fonnula. As tire domain size increases, tire widtlis of tire diffraction peaks decrease.

Kolubayev T, Geacintov N E, Paillotin G and Breton J 1985 Domain sizes in chloroplasts and chlorophyll-protein complexes probed by fluorescence yield quenching induced by singlet-triplet exciton annihilation Biochimica Biophys. Acta 808 66-76... 

Cobalt—chromium films (20 at. % Cr) exhibiting strong perpendicular anisotropy, ie, hexagonal i -axis normal to the substrate surface, have been studied (53). Fifty nanometer films are composed of columnar crystaUites and the domain size was found to be a few stmctural columns in diameter. Magnetization reversal was shown to occur by domain rotation in thick films. Thinner (ca 10-nm thick) films do not show the columnar crystaUite... 

AppHcations of soHd-state nmr include measuring degrees of crystallinity, estimates of domain sizes and compatibiHty in mixed systems from relaxation time studies in the rotating frame, preferred orientation in Hquid crystalline domains, as weU as the opportunity to characterize samples for which suitable solvents are not available. This method is a primary tool in the study of high polymers, zeoHtes (see Molecular sieves), and other insoluble materials. 

In the suspension polymerization of PVC, droplets of monomer 30—150 p.m in diameter are dispersed in water by agitation. A thin membrane is formed at the water—monomer interface by dispersants such as poly(vinyl alcohol) or methyl cellulose. This membrane, isolated by dissolving the PVC in tetrahydrofuran and measured at 0.01—0.02-p.m thick, has been found to be a graft copolymer of polyvinyl chloride and poly(vinyl alcohol) (4,5). Early in the polymerization, particles of PVC deposit onto the membrane from both the monomer and the water sides, forming a skin 0.5—5-p.m thick that can be observed on grains sectioned after polymerization (4,6). Primary particles, 1 p.m in diameter, deposit onto the membrane from the monomer side (Pig. 1), whereas water-phase polymer, 0.1 p.m in diameter, deposits onto the skin from the water side of the membrane (Pig. 2) (4). These domain-sized water-phase particles may be one source of the observed domain stmcture (7). 

These primary particles also contain smaller internal stmctures. Electron microscopy reveals a domain stmcture at about 0.1-p.m dia (8,15,16). The origin and consequences of this stmcture is not weU understood. PVC polymerized in the water phase and deposited on the skin may be the source of some of the domain-sized stmctures. Also, domain-sized flow units may be generated by certain unusual and severe processing conditions, such as high temperature melting at 205°C followed by lower temperature mechanical work at 140—150°C (17), which break down the primary particles further. 

The phase separation process at late times t is usually governed by a law of the type R t) oc f, where R t) is the characteristic domain size at time t, and n an exponent which depends on the universality class of the model and on the conservation laws in the dynamics. At the presence of amphiphiles, however, the situation is somewhat complicated by the fact that the amphiphiles aggregate at the interfaces and reduce the interfacial tension during the coarsening process, i.e., the interfacial tension depends on the time. This leads to a pronounced slowing down at late times. In order to quantify this effect, Laradji et al. [217,222] have proposed the scaling ansatz... 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

In the standard approaches to the systems in which monolayers or bilayers are formed, one assumes that the width of the film is much smaller than the length characterizing the structure (oil or water domain size, for example). In such a case it is justified to represent the film by a mathematical surface and the structure can be described by the local invariants of the surface, i.e., the mean H and the Gaussian K curvatures and by the global (topological)... 

The above results show that the structure of the system with the molecules self-assembled into the internal films is determined by their correlation functions. In contrast to simple fluids, the four-point correlation functions are as important as the two-point correlation functions for the description of the structure in this case. The oil or water domain size is related to the period of oscillations A of the two-point functions. The connectivity of the oil and water domains, related to the sign of K, is determined by the way four moleeules at distanees eomparable to their sizes are eorrelated. For > 0 surfactant molecules are correlated in such a way that preferred orientations... 

Chu et al. [24] correlated viscosity-morphology and compatibility of PS-PB blends. The effect of styrene-butadiene triblock copolymer in PS-PB was studied, and it was found that the domain size decreases with an increase of compatibilizer loading. The blending methods influenced the morphology due to the difference in the extent of mixing. 

Els and McGill [48] reported the action of maleic anhydride on polypropylene-polyisoprene blends. A graft copolymer was found in situ through the modifier, which later enhanced the overall performance of the blend. Scott and Macosko [49] studied the reactive and nonreactive compatibilization of nylon-ethylene-propylene rubber blends. The nonreactive polyamide-ethylene propylene blends showed poor interfacial adhesion between the phases. The reactive polyamide-ethylene propylene-maleic anhydride modified blends showed excellent adhesion and much smaller dispersed phase domain size. 

The reactive extrusion of polypropylene-natural rubber blends in the presence of a peroxide (1,3-bis(/-butyl per-oxy benzene) and a coagent (trimethylol propane triacrylate) was reported by Yoon et al. [64]. The effect of the concentration of the peroxide and the coagent was evaiuated in terms of thermal, morphological, melt, and mechanical properties. The low shear viscosity of the blends increased with the increase in peroxide content initially, and beyond 0.02 phr the viscosity decreased with peroxide content (Fig. 9). The melt viscosity increased with coagent concentration at a fixed peroxide content. The morphology of the samples indicated a decrease in domain size of the dispersed NR phase with a lower content of the peroxide, while at a higher content the domain size increases. The reduction in domain size... 

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