Microstructure parameters

The coefficient of microheterogeneity has been introduced for the description of the microstructure of binary copolymers with symmetric units (Korshak et al., 1976). At larger number of types of units and/or when the structure isomerism is taken into account, the role of Km will be played by other analogous parameters. A general strategy of the choice of these latter is developed in detail (Korolev and Kuchanov, 1986), while their values are measured by the nuclear magnetic resonance (NMR) spectroscopy technique for a number of polycondensation polymers (Vasnev et al., 1997). 

It should be emphasized that for the Markovian copolymers, the knowledge of these structure parameters will suffice for finding the probabilities of any sequences LZ, i.e., for a comprehensive description of the structure of the chains of such copolymers at their given average composition. As for the CD of the Markovian copolymers, for any fraction of Z-mers it is described at Z 1 by the normal Gaussian distribution with covariance matrix, which is controlled along with Z only by the values of structure parameters (Lowry, 1970). The calculation of their dependence on time and on the kinetic parameters of a reaction system enables a complete statistical description of the chemical structure of a Markovian copolymer. It is obvious therewith to which extent a mathematical modeling of the processes of the synthesis of linear copolymers becomes simpler when the sequence of units in their macromolecules is known to obey Markov statistics. 

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The microstructure parameter increases from 0 to 0.6, along with a reduction in silicon density. The material in this region consists of two phases, one which contains only SiH bonds, and one with SiH2 bonds (chains) and voids. In the third region (Ch > 0.22) the material mainly consists of chains of SiHa bonds, and the material density is much lower. 

The gas flow rate is usually presented as a deposition parameter however, it is much more instructive to report the gas residence time [6], which is determined from the flow rate and the geometry of the system. The residence time is a measure of the probability of a molecule to be incorporated into the film. The gas depletion, which is determined by the residence time, is a critical parameter for deposition. At high flow rates, and thus low residence times and low depletion [303], the deposition rate is increased [357, 365] (see Figure 39) and better film quality is obtained, as is deduced from low microstructure parameter values [366],... 

FIG. 40. The influence of deposition temperature on (a) the hydrogen concentration, (b) the microstructure parameter, and (c) the Raman half width P/2. The labels A and P refer to the ASTER and the PASTA deposition system. Series A1 was prepared from a SiH4 H2 mixture at 0.12 mbar. Series A2 and A3 were deposited from undiluted SiHa at 0.08 and 0.12 mbar. respectively. Series PI was deposited from undiluted SiHa. (From A. J. M. Bemtsen. Ph.D. Thesis. Universiteit Utrecht. Utrecht, the Netherlands, 1998, with permission.)... 

FIG. 44. Plasma parameters as deduced from the lEDs and material properties as a function of power delivered to the SiHa-Ar discharge at an excitation frequency of 50 MHz and a pressure of 0.4 mbar (a) the plasma potential Vp (circles) and dc self bias (triangles), (b) the sheath thickness d, (c) the maximum ion flux r ax. (d) the growth rate r,/. (e) the microstructure parameter R. and (f) the refractive index ni ev- (Compiled from E. A. G. Hamers. Ph.D. Thesis, Universiteit Utrecht, Utrecht, the Netherlands. 1998.)... 

The microstructure parameter is low in the material deposited at the lowest power (Fig. 44e) it increases rapidly with increasing power up to 20 W, and then decreases again with further increasing power. The opposite holds for the refractive index (Fig. 44f), although that is less clear. A high value of the microstructure indicates a large fraction of Si—Ht bonds in the material, corresponding to an open material structure and a low refractive index. 

From a comparison between the behavior of the microstructure parameter R (Fig. 44e) and the ion kinetic energy per deposited atom, max (Fig- 45b), it can be concluded that a one-to-one relation appears to exist between the relative strength of the ion bombardment, expressed in terms of max, and the microstructure parameter. This has also been suggested by others [246,422]. 

In an attempt to relate ion bombardment to material structure it is very illustrative to correlate the refractive index ni ev and the microstructure parameter R with the kinetic ion energy per deposited atom. max- The data presented above... 

The role of the substrate temperature can be inferred from a plot of /J2 ev and R versus max at the three temperatures mentioned 200, 250, and 300°C (see Figure 49). At a substrate temperature of 200°C the refractive index is lower at every max than at a substrate temperature of 250°C. Further, the threshold at which dense material is obtained is observed to be a few electron volts higher than at 250°C. The refractive index at 300°C is high and independent of max-The microstructure parameter R as a function of max behaves similarly for material deposited at 200 and at 250°C. At 300°C the value of R is less than 0.1 and independent of max- It is noteworthy to show the relation between the internal stress and max as a function of temperature (Fig. 50). The stress is linearly... 

The increase in the deposition rate rj (Fig. 63d) corresponds to the increase in the ion flux (Fig. 63c) the fraction of arriving ions per deposited atom, / ,, is constant at about 0.25. Such observations have also been reported by Heintze and Zedlitz [236], who furthermore suggested that the deposition rate may well be controlled by tbe ion flux. The kinetic ion energy per deposited atom, max, is also constant and amounts to about 5 eV. As was shown in Section 1.6.2.3, the material quality as reflected in the refractive index 2 eV (Fig. 63e) and the microstructure parameter R (Fig. 63f) is good 2 cv is around 4.25, and R is low (<0.1). The depletion of the silane stays constant at a value of 4.0 0.4 seem in this frequency range. The partial pressures of silane, hydrogen, disilane (1.3 x 10 - mbar), and trisilane (2 x 10 mbar) in the plasma are also independent of frequency. Similar... 

The deposition rate increases upon increasing the pressure. This is explained by noting that the impingement rate per unit area, r,, of molecules on the filament is linearly dependent on the pressure as r, = pj 2nksT, with the gas temperature. However, as the pressure becomes higher, the collisional mean free path of the silane becomes smaller, and the silane supply to the filaments becomes restricted. Moreover, the transport of deposition precursors to the substrate is restricted as well. The mean free path of silane was estimated to be 2.5 cm at a pressure of 0.02 mbar [531]. i.e.. the mean free path about equals the distance between filament and substrate. Indeed, a maximum in deposition rate is observed at this pressure. This corresponds to a value of pdk of 0.06 (cf. [530]). The microstructure parameter plotted as a function of pd has a minimum around Ms = 0.06 0.02 [530]. 

Figure 13. A few microstructural parameters for Nafion and sulfonated poly(arylene ether ketone)s,i as a function of the solvent (water and/or methanol) volume fraction Xy. (a) the internal hydrophobic/hydrophilic interface, and (b) the average hydrophobic/hydrophilic separation and the diameter of the solvated hydrophilic channels (pores).

Workers have shown theoretically that this effect can be caused both at the microstructural level (due to tunneling of the current near the TPB) as well as on a macroscopic level when the electrode is not perfectly electronically conductive and the current collector makes only intermittent contact. ° Fleig and Maier further showed that current constriction can have a distortional effect on the frequency response (impedance), which is sensitive to the relative importance of the surface vs bulk path. In particular, they showed that unlike the bulk electrolyte resistance, the constriction resistance can appear at frequencies overlapping the interfacial impedance. Thus, the effect can be hard to separate experimentally from interfacial electrochemical-kinetic resistances, particularly when one considers that many of the same microstructural parameters influencing the electrochemical kinetics (TPB area, contact area) also influence the current constriction. 

The dimensionless microstructural parameter a. accounts for the penetration of the thermal layer into the catalytic one, caused by the progressive reaction of the soot, which is in contact with the catalyst. Results are presented for different values of a. (see appendix) in Fig. 21. The two layers remain separate for values of a. close to 1. As a decreases the degree of penetration between the layers... 

Fig. 21. Normalized soot mass evolution for different values of the microstructural parameter a.

In inert atmospheres the mechanical properties of RBSN are constant up to 1200-1400 °C because of the absence of a glassy grain boundary phase, which is also the reason for the excellent thermal shock and creep behaviour. The thermal shock resistance, hardness and elastic constants depend on the microstructural parameters but are much lower than for dense Si3N4 ceramics [539]. 

The measurement of residual stresses is usually associated with the analysis of mechanical properties, and not microstructure. However, residual stress fields in nanocomposites depend directly on microstructural parameters (particle size, position and spacing), as well as bulk material properties, such as differences in the coefficient of thermal expansion. 

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