Heterogeneous multiphase systems

To a first approximation, the heat capacity in these heterogeneous, multiphase systems, Cp can be approximated by a weighted average of the component heat capacities ... 

Eor regular emulsion polymerization (or often referred to as macroemulsion, a heterogeneous multiphase system), a widely used expression for the rate is... 

Cellulosic polymers such as hypromellose (HPMC) and hypromellose acetate succinate (HPMCAS) have proven to be among the most effective concentrationenhancing polymers, yielding extensive and prolonged supersaturation from various ASD systems (Friesen et al. 2008 Miller et al. 2008 Curatolo et al. 2009). However, cellulosics are non-thermoplastic and as such are difficult to process thermally often leading to heterogeneous, multiphase systems (Six et al. 2003 Verreck et al. 2003). 

Heterogeneous multiphase systems (mixtures) lay claim to a special status, constituting the highest level in the hierarchical classification system. The prototype for this category is a rock granite. 

From a theoretical point of view, fillers, introduced into the matrix, must be characterized by numerous parameters (shape, dimension, size distribution, orientation in matrix, composition, etc.) the mean particle size of disperse phase is the most convenient parameter. Here we use the word phase only to describe the reinforcing component, not the thermodynamic meaning of the notion as a structure, a uniform part of a substance. Many reinforcing fillers may be composed of heterogeneous multiphase systems. For the convenience of comparison, the mean values of particle sizes (in m), introduced into a polymer ma-... 

Wang CY, Beckermann C (1993) Single- vs. dual-scale volume averaging for heterogeneous multiphase systems. Int J Multiphase Flow 19 397 07... 

It is worth mentioning that in heterogeneous multiphase systems, each phase retains its characteristics. The best method to check the presence of a phase separation in a system consists of the observation of two glass transition temperatures. Techniques of microscopy are also widely used to characterize heterogeneous systems (Figures 5.34 and 5.38) because they afford extremely precise information with respect to the phase dispersion and the structure of the interphase zones. 

Liquid multiphasic systems, where one of the phases is catalyst-philic, are attractive for organic transformation, as they provide built-in methods of catalyst separation and product recovery, as well as advantages of catalytic efficiency. The present chapter focuses on recent developments of catalyst-philic phases used in conjunction with heterogeneous catalysts. Interest in this field is fueled by the desire to combine the high catalytic efficiency typical of homogeneous catalysis with the easy product-catalyst separation features provided by heterogeneous catalysis and in situ phase separations. 

A multiphasic system for a chemical reaction can be constituted by any combination of gaseous, liquid, and solid phases. If a catalyst is present, it can be homogeneous or heterogeneous, thereby adding further phases—and degrees of freedom—to the system. Extra phases add new variables to a reaction, and it is therefore necessary that this be done for an advantage, such as an easier separation of the products, improved rates and selectivity, improved catalyst stability. 

This section describes catalytic systems made by a heterogeneous catalyst (e.g., a supported metal, dispersed metals, immobilized organometaUic complexes, supported acid-base catalysts, modified zeolites) that is immobilized in a hydrophilic or ionic liquid catalyst-philic phase, and in the presence of a second liquid phase—immiscible in the first phase—made, for example, by an organic solvent. The rationale for this multiphasic system is usually ease in product separation, since it can be removed with the organic phase, and ease in catalyst recovery and reuse because the latter remains immobilized in the catalyst-philic phase, it can be filtered away, and it does not contaminate the product. These systems often show improved rates as well as selectivities, along with catalyst stabilization. 

The scope of the multiphasic system was extended to coupling reactions—like the Heck reaction—using a heterogeneous supported catalyst, such as Pd/C. The rationale here lay in the observation that aryl halides were activated in the multiphasic system (as seen for hydrodehalogenation), and that therefore they should also be activated toward C-C coupling reactions. 

In general, block copolymers are heterogeneous (multiphase) polymer systems, because the different blocks from which they are built are incompatible with each other, as for example, in diene/styrene-block copolymers. This incompatibility, however, does not lead to a complete phase separation because the polystyrene segments can aggregate with each other to form hard domains that hold the polydiene segments together. As a result, block copolymers often combine the properties of the relevant homopolymers. This holds in particular for block copolymers of two monomers A and B. 

In multiphase systems, biological reactions are always carried out in the presence of water. This is true even if the presence of water is almost negligible. The biocatalyst maybe present as a solid phase, for example as immobilised enzymes or cells, or as an individual cell the substrate may also constitute a solid phase. When necessary, gas is sparged into reactors to supply oxygen or a gaseous substrate and to remove carbon dioxide. Thus, heterogeneous systems with four phases involved are very typical cases. 

We have previously emphasized (Section 2.10) the importance of considering only intensive properties Rt (rather than size-dependent extensive properties Xt) as the proper state descriptors of a thermodynamic system. In the present discussion of heterogeneous systems, this issue reappears in terms of the size dependence (if any) of individual phases on the overall state description. As stated in the caveat regarding the definition (7.7c), the formal thermodynamic state of the heterogeneous system is wholly / dependent of the quantity or size of each phase (so long as at least some nonvanishing quantity of each phase is present), so that the formal state descriptors of the multiphase system again consist of intensive properties only. We wish to see why this is so. 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

V.I. Dybkov. Reaction diffusion in heterogeneous binary systems. Part 3. Multiphase growth of the chemical compound layers at the interface between two mutually insoluble substances // J.Mater.Sci.- 1987.- V.22, No. 12.- P.4233-4239. 

In spite of their seeming variety, theoretical approaches of different authors to the consideration of solid-state heterogeneous kinetics can be divided into two distinct groups. The first group takes account of both the step of diffusional transport of reacting particles (atoms, ions or, in exceptional cases if at all, radicals) across the bulk of a growing layer to the reaction site (a phase interface) and the step of subsequent chemical transformations with the participation of these diffusing particles and the surface atoms (ions) of the other component (or molecules of the other chemical compound of a binary multiphase system). This is the physicochemical approach, the main concepts and consequences of which were presented in the most consistent form in the works by V.I. Arkharov.1,46,47... 

Ordinarily, the system may consist of several phases, whose interior in the state of equilibrium is homogeneous throughout its extent. The system, if composed for instance of only liquid water, is a single phase and if made up for instance of liquid water and water vapor, it is a two phase system. The single phase system is frequently called a homogeneous system, and a multiphase system is called heterogeneous. 

Multiphase system — An inhomogeneous system consists of two or more phases of one or more substances. In electrochemistry, where all processes occur at the interface thus all measurement systems must contain at least two - phases. In common understanding so-called multi-phase systems contain more than two phases. Good examples of such systems are -> electrode contacting a solid phase (immobilized at the electrode electroactive material or heterogeneous -> amalgams) and electrolyte solution, and an electrode that remains in contact with two immiscible liquids [i]. All phenomena appearing in such multi-phase systems are usually more complicated and additional effects as - interphase formation and -> mass transport often combined with - ion transfer must be taken into account [ii]. 

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