Distributive mixing random

Temkin was the first to derive the ideal solution model for an ionic solution consisting of more than one sub-lattice [13]. An ionic solution, molten or solid, is considered as completely ionized and to consist of charged atoms anions and cations. These anions and cations are distributed on separate sub-lattices. There are strong Coulombic interactions between the ions, and in the solid state the positively charged cations are surrounded by negatively charged anions and vice versa. In the Temkin model, the local chemical order present in the solid state is assumed to be present also in the molten state, and an ionic liquid is considered using a quasi-lattice approach. If the different anions and the different cations have similar physical properties, it is assumed that the cations mix randomly at the cation sub-lattice and the anions randomly at the anion sub-lattice. 

Consider two liquid substances that are rather similar, such as benzene and toluene or water and ethylene glycol. When moles of the one are mixed with B moles of the other, the composition of the liquid mixture is given by specification of the mole fraction of one of them [e.g., Xa, according to Eq. (2.2)]. The energy or heat of the mutual interactions between the molecules of the components is similar to that of their self interactions, because of the similarity of the two liquids, and the molecules of A and B are distributed completely randomly in the mixture. In such mixtures, the entropy of mixing, which is a measure of the change in the molecular disorder of the system caused by the process of mixing the specified quantities of A and B, attains its maximal value ... 

Fig. 7.1 Schematic representation of random distributive mixing (e.g., a process that takes place in a V-blender).

Fig. 10.16 The evolution of the spatial distribution of 10,000 particles initially clustered in 10 randomly placed clusters in the C-shaped chamber. The fraction or number of pitches denotes the axial advance of the material in the chamber due to the counterrotation. [Reprinted by permission from T. Li and lea Manas-Zloczower, A Study of Distributive Mixing in Counterrotating TSEs, Int. Polym. Process., 10, 314 (1995).]...

Instead of the gamma single-passage distribution for the peripheral compartment, Wise [298] proposed the mixed random walk in series distribution,... 

According to Campbell (1992), the double perovskite, LaCaMnCoOf, was of interest as a cyclic mode methane coupling catalyst due to its structure and redox properties. This mixed oxide has an ordered perovskite structure showing multiple occupations of both A (La, Ca) and B (Mn, Co) sublattices. The crystalline material presented some ordered domains, while in other areas the cations were distributed at random. For the ordered domains, the most probable structural model was an AB03 perovskite-type structure in which Mn4 and Co3+ ions occupy B positions in adjacent AB03 units while La3+ and Ca2+ ions alternate in A positions. Two ions of this structure can be reduced ... 

These equations assume uniform distribution and random orientation of the particles. However, for nanoparticles good mixing can be difficult to achieve, and often chemical modification of the particles is used to enhance their dispersion in the polymer. Poor mixing causes the property changes for small concentrations of nanofillers to be rather modest (Valadares et al., 2006 Bokobza, 2007), much less than the orders of magnitude enhancement seen in Figure 6.26. 

For random reorientation the factor c= V2, which is often used in extrusion theory. The importance of rearrangements in distributing mixing is illustrated in Table 5.2. The generation of interfacial area is given as a function of the number of steps in the process between random orientations. 

E)istributive mixing is basically defined as an operation which is employed to increase the randomness of the spatial distribution of the minor constituent within the major base with no further change in size of that minor constituent. Distributive mixing is influenced by the strain... 

Three different mixing actions take place in the internal mixer [21] intensive or dispersive mixing around the tips of the rotor blade extensive mixing due to simple shear flow and extensional flow between the chamber walls and the cylindrical portions of the rotors and in the entrance region to the narrow gaps between rotor tip and distributive mixing due to random plug convection, as a result of ttie interaction between the two rotor tips. 

This value is the fictitious number of mixed pairs which would yield the correct value of the partition function if the molecules were distributed at random. Thus, if we take account of relation [2.48], this... 

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