Evolution of the composition

At the initial stage of bulk copolymerization the reaction system represents the diluted solution of macromolecules in monomers. Every radical here is an individual microreactor with boundaries permeable to monomer molecules, whose concentrations in this microreactor are governed by the thermodynamic equilibrium whereas the polymer chain propagation is kinetically controlled. The evolution of the composition of a macroradical X under the increase of its length Z is described by the set of equations ... 

Here Jta(x) denotes the a-th component of the stationary vector x of the Markov chain with transition matrix Q whose elements depend on the monomer mixture composition in microreactor x according to formula (8). To have the set of Eq. (24) closed it is necessary to determine the dependence of x on X in the thermodynamic equilibrium, i.e. to solve the problem of equilibrium partitioning of monomers between microreactors and their environment. This thermodynamic problem has been solved within the framework of the mean-field Flory approximation [48] for copolymerization of any number of monomers and solvents. The dependencies xa=Fa(X)(a=l,...,m) found there in combination with Eqs. (24) constitute a closed set of dynamic equations whose solution permits the determination of the evolution of the composition of macroradical X(Z) with the growth of its length Z, as well as the corresponding change in the monomer mixture composition in the microreactor. 

Audibert, A., Roucache, J., "Evolution of the Composition of a Crude Oil During In-situ Combustion", Characterization of Heavy Crude Oils and Petroleum Residues. Ed. Technip, Paris, p 135-139, (1984). 

In contrast, let us analyze the same reaction system in a second case, namely considering that the reaction rate constants have the same value, k = Ay = 1 s 1. A comparison of the evolution of the compositions in the two cases is presented in Figure 2.5, and a phase plane of the second case is shown in Figure 2.6. 

Figures 7.9 and 7.10 show the evolution of the compositions and temperatures on representative column stages for a small step change in the feed flow rate. According to our theory, this disturbance influences the slow material-balance dynamics and has very little impact on the fast energy dynamics of the column. Indeed, while there are significant (albeit slow) changes in the stage compositions,...

The evolution of the composition i(p) in the course of the m-eomponent copolymerization can be presented as the movement of the point, which characterizes the system state, inside m-simplex along some trajectory, the location of the point along which is determined by conversion p. The behavior of such trajectories is of vital importance since it determines the values of all statistical characteristics of the copolymers produced at high conversions. 

Figure 14. Time evolution of the composition of the percolating water in the downstream part of the alteration profile of a pyrite-rich sandstone. = 10. The concentration of the dissolved species are given in mol/kg and the quantities of neoformed minerals are given in mol as a function of the parameter of advancement of the reaction t All data are represented as the logarithm of the molality (log m) vs. log. XU(a) corresponds to [U/Fe] = 5 X 10 (molar ratio) leached within the sandstone. U(l)) corresponds to the maximum possible dissolved uranium concentration. All the curves are direct Benson plots from the computer.

Figure IS. Time evolution of the composition of the percolating water in the alteration envelope upstream of the oxidation front (see Figure 13). = 10. ...

Fig. 18. Scheme of evolution of the composition of sedimentary rocks (after Ronov, 1964) I =jaspilites and their analogs 2 = evaporites 3 = limestones 4 = dolomites 5 = secondary quartzites 6 = clays and their metamorphic equivalents 7 = quartz sands 8 = arkoses 9 = graywackes 10= submarine volcanics, chiefly basic 11 = terrestrial volcanics. 

Fig. 20. Evolution of the composition of reducing fluid arriving from the mantle, as pressure drops under isothermal conditions (relative amounts are expressed in molar percentages). Dashed line shows partial pressure of incoming hydrogen.

From the diagrams that have been plotted, information can be obtained on the composition of the fluids in equilibrium with iron-ore minerals over wide ranges of temperature (200-850°C) and pressure (Pf =0.5-10 kbar), and the evolution of the composition of the fluids as a function of tempera-... 

The established regularities in the evolution of the composition of fluids also explains some particulars of the metamorphism of iron-formations of other t) es. In particular, the frequently observed disappearance of hematite in oxide rocks metamorphosed in amphibolite and granulite facies conditions can be caused by reduction by volatiles, especially by easily diffused hydrogen. Acceleration of diffusion with rise in temperature and increase in concentration gradients of volatiles leads to the appearance of more uniform mineral associations in place of formerly extremely variegated banded sequences. 

Ronov, A.B., 1964. General tendency in the evolution of the composition of the Earth s crust, ocean and atmosphere. Geokhimiya (Geochemistry), 8 715-743 (in Russian). 

A continuous CO2 laser-heating beam was directly passed axially through the NMR probe, which allowed to record NMR spectra from room temperature up to 1500°C. Experiments were carried out under argon atmosphere, so that the oxidation of the crucible and of the sample was excluded. The time, spent by the sample in the liquid state, has been minimized to avoid evolution of the composition during the experiment. 

In Fig. 31, the evolution of the composition of the surface as a function of ion fluence is shown for CF+ impact (normal incidence) at 50, 100, and 200 eV. Note that the C and F content increases continuously, representing steady deposition. A small amount of Si is lost at the early stages for the... 

We also know that the Earth reservoirs have changed in composition over time. Such changes have been documented in this book. See for example - the isotopic evolution of the mantle (Chapter 3, Section 3.2.3), the secular evolution of the continental crust (Chapter 5, Section 5.3), the evolution of the composition of the atmosphere (Chapter 5, Section 5.3) and oceans (Table 5.5). Secular change in the biosphere, a process which we otherwise call evolution, is discussed in Chapter 6. Charting these changes and identifying the precise character of the systems of the early Earth is a task which is well underway. 

In view of the renewed interest for a high-density r-process, a simple steady flow model, referred to in the following as HIDER, may be developed. Irrespective of the specific details of a given astrophysical scenario, it allows to follow in a very simple and approximate way the evolution of the composition of an initial cold (say T = 0) highly neutronized matter under the combined effect of /3-decays and of the captures of free neutrons that are an important initial component of the considered material. These are the only two types of transformations that have to be considered if fissions are disregarded, and if... 

This condition assumes that the time evolution of the composition PDF is of interest. If only the stationary PDF is required, local time stepping can be employed as discussed below. 

In this work, nanocomposite supports formed by nanometric domains of alumina dispersed on a-Al203 beads were synthesized by a modified incipient wetness impregnation method in order to improve specific surface area and surface reactivily of a-Al203 large porosity precursor. The obtained composites were characterized by conventional physical methods like N2 adsorption-desorption, mercury porosimetry, TEM and SEM, in order to describe the evolution of the composite textural properties with the impregnated phase morphology. 

As the metathesis reaction proceeds it is necessary to take account of the secondary reactions of the products in order to understand the evolution of the composition of the reaction mixture with time. There will then be another eight reactions involving fra i-pent-2-ene, and four each for cis- and lrans-but-2-ene and cis- and frans-hex-3-ene, making 32 propagation reactions in all. By assuming that the concentrations of [Mt]=CHMe and [Mt]=CHEt are the same, and by equating various ratios of rate constants, it is possible to show that a linear relationship of the type shown in Fig. 6.2 is to be expected (Leconte 1979b). 

Fig.l. Sketches of time-evolution of the composition (concentration) fluctuations in the (a) early, (b) intermediate, and (c) late stages of spinodal... 

Also crucial is the following observation relative to the elements of a pointer basis (which is also an eigenbasis of As) are robust [15,16]. Physically, it means that, once effected, the decoherence will keep the states of a pointer basis effectively intact in the course of the unitary evolution of the composite system S + E. This robustness of certain system s states is crucial for the macroscopic context of the decoherence theory. Particularly, it means that the decoherence effect gives rise to both, existence and maintenance of states of a pointer basis — that is, the relevance of the superselection rules — of an open system in the course of the unitary evolution of the combined system S + E. In other words, the decoherence effect tends to freeze the open system s dynamics as defined by the decomposition (9.11). The decoherence time To is usually very short, including the mesoscopic systems such as certain macromolecules [12]. It is therefore not for surprise that the decoherence effect has been observed in the quite controlled circumstances only recently [12,17,18]. 

Concerning the modulus evaluatirai of the fillers is always problematic. The modulus has been evaluated. Different composites had been processed with increasing LCFo i content. The fillers modulus has been estimated by fitting a semiempiri-cal Halpin-Tsai model on the evolution of the composites Young s modulus as a function of fillers volume fraction. By extrapolation at 100% of fillers, we obtain the filler modulus which is estimated at 6.7 GPa. This value is coherent with wheat straw data given in the literature (Hornsby et al. 1997 KrtMibergs 2000). 

A Mass Spectrometer (MS) (Balzers QMS200) was used for species analysis. This instrument can provide the qualitative and quantitative temporal evolution of the composition of the outlet gas mixture. The following m/e ratios were monitored in order to follow the transient behavior of the most relevant species 15 (NHj), 18 (H2O), 28 (N2), 30 (NO), 32 (O2), 40 (Ar), 44 (NjO), and 46 (NO2). The MS data were elaborated taking into account the species cross-sensitivities and the response factors periodically estimated by means of specific calibration runs in a blank reactor, thus obtaining the outlet concentrations of reactants and products. A UV analyzer (ABB Limas IIHW), which provided accurate continuous simultaneous measurements of ammonia, NO, and NO2, was also coupled in parallel to the MS [10]. 

FIGURE 2.22 The evolution of the composition profiles across the interface for the l-propanol(l)—n-hexane (2) mixture at 298.15 K. The liquid phase composition, Xj, increases from top left to bottom right. 

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