Ideal chemical network

Let us assume that the ideal chemical network has no physical interactions. Such a network instantly fails when some critical strain is reached. In the correspondence with the theory of elasticity, the work of strain, Ag, per unit of its volume can be represented by... 

The Flory principle is one of two assumptions underlying an ideal kinetic model of any process of the synthesis or chemical modification of polymers. The second assumption is associated with ignoring any reactions between reactive centers belonging to one and the same molecule. Clearly, in the absence of such intramolecular reactions, molecular graphs of all the components of a reaction system will contain no cycles. The last affirmation concerns sol molecules only. As for the gel the cyclization reaction between reactive centers of a polymer network is quite admissible in the framework of an ideal model. 

A knowledge of v can give an indication of the transit time of a plug of chemical or an ensemble of cells through a microfluidic channel network and thus to assess whether there is enough time for complete mixing or chemical reaction. Both Eq. (11) and Eq. (12) are strictly only valid under idealized conditions (i.e. incompressible and non-viscous fluids and steady flow), but can still be helpful for overall estimation and assessment. 

This is a theoretical study on the entanglement architecture and mechanical properties of an ideal two-component interpenetrating polymer network (IPN) composed of flexible chains (Fig. la). In this system molecular interaction between different polymer species is accomplished by the simultaneous or sequential polymerization of the polymeric precursors [1 ]. Chains which are thermodynamically incompatible are permanently interlocked in a composite network due to the presence of chemical crosslinks. The network structure is thus reinforced by chain entanglements trapped between permanent junctions [2,3]. It is evident that, entanglements between identical chains lie further apart in an IPN than in a one-component network (Fig. lb) and entanglements associating heterogeneous polymers are formed in between homopolymer junctions. In the present study the density of the various interchain associations in the composite network is evaluated as a function of the properties of the pure network components. This information is used to estimate the equilibrium rubber elasticity modulus of the IPN. 

The cure of thermoset resins involves the transformation of a liquid resin, first with an increase in viscosity to a gel state (rubber consistency), and finally to a hard solid. In chemical terms, the liquid is a mixture of molecules that reacts and successively forms a solid network polymer. In practice the resin is catalyzed and mixed before it is injected into the mold thus, the curing process will be initialized at this point. The resin cure must therefore proceed in such a way that the curing reaction is slow or inhibited in a time period that is dictated by the mold fill time plus a safety factor otherwise, the increase in viscosity will reduce the resin flow rate and prevent a successful mold fill. On completion of the mold filling the rate of cure should ideally accelerate and reach a complete cure in a short time period. There are limitations, however, on how fast the curing can proceed set by the resin itself, and by heat transfer rates to and from the composite part. 

Even for systems with highly complex fluid dynamics, where the flow cannot adequately be approximated by a single chemical reactor, a network of ideal reactors may form the basis of a useful approximation. Because of the computational difficulties of handling mixing and chemical reaction in the complex flow patterns encountered in industrial applications,... 

Since complex systems may involve up to several hundreds (and even thousands) of chemical species and reactions, simple reaction pathways cannot always be recognized. In these cases, the true reaction mechanism remains an ideal matter of principle, which can be only approximated by reduced reaction networks. Also in simpler cases, reduced networks are more suitable for most practical purposes. Moreover, the relevant kinetic parameters are mostly unknown or, at best, very uncertain, so that they must be evaluated by exploiting adequate experimental campaigns. With the aim of presenting an example of the problems related to chemical kinetics, a case study is introduced and discussed in detail in the next subsection. 

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. 

The network of chemical bonds within molecules only partially determines the chemical and physical properties. Intermolecular interactions cause gases to deviate from the ideal gas law (as we will discuss in Chapter 7) or condense into liquids. Interactions between nonbonded atoms in the same molecule cause proteins to fold into specific configurations, which catalyze chemical reactions critical to life. 

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