Random mixing

Figure A2.5.14. Quasi-lattice representation of an equimolar binary mixture of A and B (a) randomly mixed at high temperature, and (b) phase separated at low temperature.

Any of the four monomer residues can be arranged in a polymer chain in either head-to-head, head-to-tail, or tail-to-tail configurations. Each of the two head-to-tail vinyl forms can exist as syndiotactic or isotactic stmctures because of the presence of an asymmetric carbon atom (marked with an asterisk) in the monomer unit. Of course, the random mix of syndiotactic and isotactic, ie, atactic stmctures also exists. Of these possible stmctures, only... 

When there is a large difference between ys(A) and ys(B) in the equation above, there must be signihcant deparmres from dre assumption of random mixing of the solvent atoms around tire solute. In this case tire quasi-chemical approach may be used as a next level of approximation. This assumes that the co-ordination shell of the solute atoms is hlled following a weighting factor for each of tire solute species, such that... 

On the other hand, upon closer examination even the copper-gold solid solutions evince serious discrepancies with the quasichemical theory. There is a composition range where the entropy of solution is larger than that for random mixing (see Fig. 1) where... 

The configurational entropy of the mobile guest ions, assuming random mixing and a concentration x, residing in x° lattice sites of equal energy, is... 

The simplest situation is the symmetrical one (NA = NB), with the solvent equally good for both blocks. We imagine that the excluded volume interactions of A and B are stronger than the A-B repulsive interactions so that the overall structure of the layer is like that of a single component in other words, both components are equally stretched. The issue is whether or not they are homogeneously mixed with one another in the monolayer. This is essentially a two-dimensional random mixing process. In that spirit, we write the free energy... 

By using the liquid lattice approach to treat the random mixing of a disoriented polymer and a solvent, the so-called Flory-Huggins theory is often used to correlate the penetrant activity and the composition of the solution ... 

An alternative approach aimed at reducing the segregation tendencies of medicaments and excipients involves milling the former to a small particle size and then physically absorbing it uniformly onto the surface of the larger particles of an excipient substrate. By these means ordered, as opposed to random, mixing is realized and dissolution is enhanced as a result of the fine dispersion [7]. 

The calculation of Zconf makes use of the random mixing approximation for the fully disordered state. Several authors [23-27] have reported improved estimates of Zconf that take into account the effect of local ordering at low temperatures however, the resulting improvement in the prediction of the... 

As a simple approximation we will ignore any deviations from random mixing that are caused by the interactions this procedure is also known as the mean field approximation. 

While the mole fraction is a natural measure of composition for solutions of metallic elements or alloys, the mole fraction of each molecule is chosen as the measure of composition in the case of solid or liquid mixtures of molecules.1 In ionic solutions cations and anions are not randomly mixed but occupy different sub-lattices. The mole fractions of the atoms are thus an inconvenient measure of composition for ionic substances. Since cations are mixed with cations and anions are mixed with anions, it is convenient for such materials to define composition in terms of ionic fractions rather than mole fractions. In a mixture of the salts AB and AC, where A is a cation and B and C are anions, the ionic fractions of B and C are defined through... 

The average interactions and 3X6 evaluated under the assumption of a random distribution of the A and B molecules in space (random mixing). This point has been discussed by Rice13 using the quasi-chemical approximation the corrections to the various excess functions appear to be of the order of 5-10%. 

This conclusion implies that the excess entropy of mixing is non-zero and that the mixed micelles presumably acquire more internal order than they would by random mixing. An examination of the magnitude of the deviations from the regular solution approximation shows that there must be a large TS contribution to the excess free energy of mixing. 

Let us consider a multisite mixture of type (A, B, C,. . . ) (M, N, O,. . . ) Z, where cations of types A, B, C and M, N, O, respectively, occupy energetically distinct sites present in one mole of substance in the stoichiometric amounts Vj and V2, and Z is the common anionic group. Applying the permutability concept to each distinct site and assuming random mixing and the absence of interactions on sites, the activity of component A M Z in the mixture may be expressed as... 

If we replace half the Al with Si on a tetrahedral plane, we have random mixing over jNj- sites. This sort of mixing does not contradict the Al avoidance principle. Let us now... 

Figure 3.5. Schematic representation of random mixing of atom/molecule of B...

Recent studies suggest that small NPs are far more fluid than initially thought. Lower melting points [9] and the dominance of surface energies [10] in small NPs suggest that these systems may be quite dynamic, which can be used to make new nanomaterials. By exploiting the differences in adsorbate bond enthalpies to different metals in small bimetallic NPs [8, 11], randomly mixed alloys can be... 

Turbulent diffusion is not reaUy diffusion but the mixing of chemicals through turbulent eddies created by convection. Turbulent diffusion is thus a form of convection. Although it has the appearance of diffusion in the end (i.e., random mixing similar to diffusion), the causes of diffusion and turbulent diffusion are very different. Since the end products are similar, diffusion coefficients and turbulent diffusion coefficients are often simply added together. This process will be discussed in this chapter. 

The segregation of the different molecules according to their polarity is just the opposite of random mixing and is thus a clear sign of uncollective behavior characteristic of non-ideal mixing. 

The random mixing theory and mixing processes have been extensively explored (2). Randomization requires equally sized and weighted particles, with little or no surface effects, showing no cohesion or interparticle interaction, to achieve the best results it cannot be applied to all practical mixing situations, especially where cohesive or interacting particles are mixed. 

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