Fluctuations of composition

As mentioned in my report, in addition to large coexisting domains of solid and fluid phase lipids, there may be fluctuations of composition and density in the fluid-lipid phase that are not seen in the electron microscope but that may affect nuclear magnetic resonance spectra. 

Consider a small fluctuation of composition (or any other order parameter that is conserved for a system), SXb = XB — XB. Expanding F Xb) in SXB yields... 

It is not an easy task to define inhomogeneities in the structure of a polymer network. Every system will exhibit the presence of defects and fluctuations of composition in space when the scale of observation becomes smaller and smaller. A hierarchy of structures exists, from atomic dimensions to the macroscopic material. A scheme of different scale levels used to describe linear and crosslinked polymer structures is shown in Fig. 7.2. Inhomogeneities described in the literature for polymer networks are ascribed to permanent fluctuations of crosslink density and composition, with sizes varying from 10 nm up to 200 nm. This means that their size lies in the range of the macromolecular scale. 

Figure 4. Inhomogeneity of silica-aluminas prepared by various methods. A series of 17 commercial samples of silica-aluminas from seven different producers was submitted to microanalysis. All of them showed considerable fluctuations of composition at the scale of several tens of nanometers to several micrometers. These samples were prepared by coprecipitation or by the sol-gel method. It is not known whether some of these samples were prepared from alkoxides. Smaller but significant fluctuations at the micrometer scale were also observed for two laboratory samples prepared from alkoxides. The samples were dispersed in water with an ultrasonic vibrator. A drop of the resulting suspension was deposited on a thin carbon film supported on a standard copper grid. After drying, the samples were observed and analyzed by transmission electron microscopy (TEM) on a JEOL-JEM 100C TEMSCAN equiped with a KEVEX energy dispersive spectrometer for electron probe microanalysis (EPM A). The accelerating potential used was 100 kV.

Structural chemical zoning in this gallosilicate zeolite, i.e. an alternation of Ga-rich MAZ and Ga-poor MOR layers in its framework, probably due to the local fluctuation of composition of the mother liquor caused by the crystallisation of the previous layer. 

It follows from the construction in fig. 12.1(b) that for any composition between one end of the curve of fig. 12.1(a) and the nearest point B, partition of the mixture into two phases of different compositions would lead to an increase in the total value of AG ix. Compositions in the two corresponding regions are therefore stable against fluctuations of composition. In contrast, for any composition between the two points B where the common tangent... 

Suppose that the configurative point liM been moved from outside the binodal into the region between the binodal (2 2/) and spinodal x2api) with the concentration X2 = X2,o (the point D). The system is composed of r i moles of component 1 and of i2 moles of component 2, so that nj + n2 = n and X2.0 = n2/n. Further, assume that a fluctuation of composition spontaneously occurred in a certain local region and the concentration of component 2 became Xj there (Figure 1.7 and 1.8). Then, this concentration in the rest of the system is Xj. In terms of mole numbers, there are n moles in the local region (n = n l -I- n 2 n 2 = Xjw ) and n" moles in the rest of the system (n" = (n — n )x2). As a result of such a fluctuation, the Gibbs potential varies by... 

Alternatively, it can be argued that possibly the most important factor in determining what macroscopic phase relationships will be observed for extended-defect systems is the way in which the components are distributed initially, since local fluctuations of composition will profoundly affect microdomain texture. Further discussion of this point is taken up in the section on fluorite-related phases. 

To analy2e premixed turbulent flames theoretically, two processes should be considered (/) the effects of combustion on the turbulence, and (2) the effects of turbulence on the average chemical reaction rates. In a turbulent flame, the peak time-averaged reaction rate can be orders of magnitude smaller than the corresponding rates in a laminar flame. The reason for this is the existence of turbulence-induced fluctuations in composition, temperature, density, and heat release rate within the flame, which are caused by large eddy stmctures and wrinkled laminar flame fronts. 

It is generally preferable to meter each of the individual components of a two-phase mixture separately prior to mixing, since it is difficult to meter such mixtures accurately. Problems arise because of fluctuations in composition with time and variations in composition over the cross section of the channel. Information on metering of such mixtures can be obtained from the following sources. 

TTie polydispersity of the blocks is quite narrow if the above conditions are satisfied. Consequently, the fluctuations in composition within a sample are small115). Accurate... 

Ishibashi, J., Grimaud, D., Nojiri, Y. Auzende, J.M. and Urabe, T. (1994a) Fluctuation of chemical compositions of the phase-separated hydrothermal fluid from the North Fuji Basin Ridge. Marine GeoL, 116, 215-226. 

River inputs. The riverine endmember is most often highly variable. Fluctuations of the chemical signature of river water discharging into an estuary are clearly critical to determine the effects of estuarine mixing. The characteristics of U- and Th-series nuclides in rivers are reviewed most recently by Chabaux et al. (2003). Important factors include the major element composition, the characteristics and concentrations of particular constituents that can complex or adsorb U- and Th-series nuclides, such as organic ligands, particles or colloids. River flow rates clearly will also have an effect on the rates and patterns of mixing in the estuary (Ponter et al. 1990 Shiller and Boyle 1991). 

The general experimental approach used in 2D correlation spectroscopy is based on the detection of dynamic variations of spectroscopic signals induced by an external perturbation (Figure 7.43). Various molecular-level excitations may be induced by electrical, thermal, magnetic, chemical, acoustic, or mechanical stimulations. The effect of perturbation-induced changes in the local molecular environment may be manifested by time-dependent fluctuations of various spectra representing the system. Such transient fluctuations of spectra are referred to as dynamic spectra of the system. Apart from time, other physical variables in a generalised 2D correlation analysis may be temperature, pressure, age, composition, or even concentration. 

Structural Imperfections. In many respects HREM has had a greater impact upon our knowledge of the nature of the atomic reorganization at crystalline imperfections than any other single technique. One of the very first contributions of HREM as a new analytical and structural tool was described in the paper by Iijimia (42) in 1971 on 2 10 29 v -ewe< down to its b - axis. Structural faults, arising from subtle fluctuations in composition, could be clearly seen in the block-structure (based on NbO octahedra) which is a feature of this ternary oxide system. More than a decade later similar materials are yielding to active scrutiny by HREM, and Horiuchi (43), for example, has shown how point defects may be directly viewed... 

Phases may also become unstable with regard to compositional fluctuations, and the effect of compositional fluctuations on the stability of a solution is considered in Section 5.2. This is a theme of considerable practical interest that is closely connected to spinodal decomposition, a diffusion-free decomposition not hindered by activation energy. 

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