Ordered domain size

TABLE 11.2 Line Broadening Results of Figure 11.15, Showing Ordered Domain Size, Using Equation 11.86 ... 

Degree Detector output (volts) B(2ff) (radian) Ordered domain size (pm)... 

Measurement of Ordered Domain Size by Light Diffraction... 

Diffraction line broadening has been adapted to light diffraction to measure ordered domain size by Chang and Ring [56]. The first treatment of diffraction line broadening was by Scherrer [57], who derived the equation... 

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. 

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 ternary mixtures of oil, water, and surfactant the ordering properties of the system follow from the vectorial character of the interactions of the surfactant molecules with both the oil and the water molecules. The typical size of the ordered domains, much larger than the molecular size, justifies the application of the mesoscopic Landau-Ginzburg approach to the ordering. In the simplest approach of Gompper and Schick [3,12], which we call here the basic Landau-Ginzburg model, the orientational degrees of free-... 

Figure 5. Arrhenius-plot of three relaxation times involved in total ordering process. ( ) Xi, ( ) X2, atomic jump processes within domains (o) xj, change in domain size.

Measurements of diffusion of tracer polymers in ordered block copolymer fluids is another potentially informative activity, since molecular diffusion is one of the most basic dynamic characteristics of a molecule. Balsara, et al. have measured the retardation of diffusion due to ordering in the diffusion of polystyrene tracer homopolymers in polystyrene-polyisoprene matrices of various domain sizes [167]. Measurement of the tracer diffusion of block copolymer molecules will also be important. Several interesting issues are directly addressable via measurements... 

Morphology of the anionically synthesized triblock copolymers of polyfp-methyl-styrene) and PDMS and their derivatives obtained by the selective chlorination of the hard segments were investigated by TEM 146). Samples with low PDMS content (12%) showed spherical domains of PDMS in a poly(p-methylstyrene) matrix. Samples with nearly equimolar composition showed a continuous lamellar morphology. In both cases the domain structure was very fine, indicating sharp interfaces. Domain sizes were estimated to be of the order of 50-300 A. 

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