Nonideal networks

Incompletely cured networks constitute an important case of nonideal networks. They can be considered homogeneous if they result from step polycondensation. The following factors are expected to have an influence on Tg (beyond the gel point) ... 

A nonideal network may be obtained as in the previous case but using different nonstoichiometric molar ratios or arresting the polymerization at different conversions, to modify the structure. In these cases, the presence of a sol fraction and dangling chains will introduce an additional plasticization effect, surimposed on the new architecture (Vallo et al., 1993). 

The yielding of networks will be described first, beginning with the analysis of deformation mechanisms and the influence of physical aging. The effect of hydrostatic pressure will be treated with yielding criteria. The influence of physical (T, e) and structural parameters on yielding will then be described for ideal and nonideal networks. 

Series of nonideal networks obtained using off-stoichiometric epoxyamine formulations have also been employed for yielding studies. As the highest Tg corresponds to the stoichiometric formulation, it is expected that <7y, measured at a constant temperature, should also be a maximum for the same formulation. This was the trend reported in some of these studies (Morgan et al., 1984 Vallo et al., 1993). 

DMSO and water form a solution with nonideal behavior, meaning that the properties of the solution are not predicted from the properties of the individual components adjusted for the molar ratios of the components. The strong H-bonding interaction between water and DMSO is nonideal and is the primary driver for the very hygroscopic behavior of DMSO. Even short exposure of DMSO to humid air results in significant water uptake. Water and DMSO nonideal behavior results in an increase in viscosity on mixing due to the extensive H-bond network. 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

The network structure at any conversion may be obtained by joining the different fragments at random, with a probability given by the concentration of every fragment in the mixture. This is a mean-field approach and is not valid when nonidealities are present. Unequal reactivities, substitution effects, and intramolecular cycles give place to preferred nonrandom combinations. 

Homogeneous nonideal, e.g. open networks, obtained from the same chemistry as the previous ones. These networks contain dangling chains as a result of incomplete cure, nonstoichiometric composition, or presence of monofunctional monomers. 

In principle, these relationships open the way to a determination of fg which is found to decrease with crosslink density as well in ideal epoxy networks (Gerard et al., 1991), as in nonideal polyesters (Shibayama and Suzuki, 1965). However, it must be recognized that, in both series of data, it is impossible to have consistent values of, Cf, Cf, a, and fg except if BD varies with the structure, which can be considered as a serious argument against the free volume interpretation of WLF parameters. 

We can distinguish first between homogeneous and inhomogeneous networks (Chapter 7). In homogeneous networks a distinction between ideal and nonideal structures may be performed. This concept is presented in Chapters 10 and 11. 

There is a vast amount of literature dealing with the influence of network structure (essentially crosslink density) on yielding. Key structural parameters related to yielding will be considered separately for ideal, nonideal, and inhomogeneous networks. 

In Chaps. 5 and 6 model-based control and early diagnosis of faults for ideal batch reactors have been considered. A detailed kinetic network and a correspondingly complex rate of heat production have been included in the mathematical model, in order to simulate a realistic application however, the reactor was described by simple ideal mathematical models, as developed in Chap. 2. In fact, real chemical reactors differ from ideal ones because of two main causes of nonideal behavior, namely the nonideal mixing of the reactor contents and the presence of multiphase systems. 

It is generally accepted that the stratum comeum represents the primary electrical barrier in skin. Though impedance results vary from subject to subject and from site to site on the same individual, the electrical response of skin can be modeled as a simple RC network. Nonideal behavior is associated with environmental conditions, the hydration of the skin, and the integrity of the stratum comeum. 

Kim, S.B., G.J. Ruiz, and A.A. Linninger, Rigorous separation design. 1. Multicomponent mixtures, nonideal mixtures, and prefractionating column networks. Industrial and Engineering Chemistry Research, 2010, 49(14) 6499 6513. 

In the present section we indicate how tracer residence time data may be used to predict the conversion levels that will be obtained in reactors with nonideal flow patterns. As indicated earlier, there are two types of limiting processes that can lead to a distribution of residence times within a reactor network. 

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