Asymmetric Binary Mixtures

However, in some special cases, the lost of information due to the thresholding procedure may cause a noticeable systematic error, because each lattice point such that < )(r) > < )0 contributes the same volume fraction 1/L3 regardless of the field magnitude. Consider an asymmetric binary mixture undergoing the phase separation. The local volume fraction distribution P(< >) has maxima at the equilibrium volume fractions, 1, and is asymmetric relatively to... 

Once synthesized several factors influence the particular leaflet of the membrane lipid bilayer where the lipids reside. One is static interactions with intrinsic and extrinsic membrane proteins which, by virtue of their mechanism of biosynthesis, are also asymmetric with respect to the membrane. The interaction of the cytoplasmic protein, spectrin with the erythrocye membrane has been the subject of a number of studies. Coupling of spectrin to the transmembrane proteins, band 3 and glycophorin 3 via ankyrin and protein 4.1, respectively, has been well documented (van Doit et al, 1998). Interaction of spectrin with membrane lipids is still somewhat conjectural but recent studies have characterized such interactions more precisely. O Toole et al. (2000) have used a fluorescine derivative of phosphatidylethanolamine to investigate the binding affinity of specttin to lipid bilayers comprised of phosphatidylcholine or a binary mixture of phosphatidylcholine and phosphatidylserine. They concluded on the basis... 

Figure 4.1-3 Proposed structure of the asymmetric [HCl2] ion bound to the [EMIM]" cation in a binary mixture of HCI/[EMIM]CI. The figure has been redrawn from reference 10 with permission.

The systems which are often involved in RESS and also in PGSS are highly asymmetrical binary mixtures which contain two substances with large differences in molecular size, structure, and intermolecular interactions. Two main features of the phase-behaviours for such systems are ... 

In this study we restrict our consideration by a class of ionic liquids that can be properly described based on the classical multicomponent models of charged and neutral particles. The simplest nontrivial example is a binary mixture of positive and negative particles disposed in a medium with dielectric constant e that is widely used for the description of molten salts [4-6], More complicated cases can be related to ionic solutions being neutral multicomponent systems formed by a solute of positive and negative ions immersed in a neutral solvent. This kind of systems widely varies in complexity [7], ranging from electrolyte solutions where cations and anions have a comparable size and charge, to highly asymmetric macromolecular ionic liquids in which macroions (polymers, micelles, proteins, etc) and microscopic counterions coexist. Thus, the importance of this system in many theoretical and applied fields is out of any doubt. 

When either of the semicrystalline forms of the asymmetric alkane are cooled, they transform to a double-layer and a triple-layer crystalline structure, respectively. These 1-d superlattices are described as ABAB... and ABAABA... stacks of crystalline layers as depicted in Figure 25, panels c and e. Note that the structure in Figure 25e is related to the mixed integer folded-extended structure in some pure n-alkanes (Figure 7c) and in binary mixtures of long n-alkanes (Section II.J, Figure 30b). 

Fig. 46. Schematic illustration of the interfacial brush formed by the binary mixture of short symmetric (S) and long asymmetric (L) copolymers with identical anchoring blocks. Depicted situation corresponds to Figs. 44 and 45. Short and long components of the mixed brush are characterized by mean inter-anchor spacings Xs1/2 and XL1/2 or equivalently by respective interfacial coverages os and oL...

Parameter will henceforth be referred to as the asymmetry of the model mixture, where xb > 1 characterizes a binary mixture in which the formation of B-B pairs is energetically favored, whereas for XB < L this is the case for A-A pairs. For the special case xb 1 the asymmetric mixture degenerates to the symmetric case previously studied in Refs. [84] and [85]. In addition, we define the selectivity of the solid surfaces by specifying Xs in Eq. (4.125d) in a fashion similar to xb in Eq. (4.125c). Hence, the parameter space of our model is spanned by the set , aBi s, Xb> X s -... 

McHugh, M. A. 1981. An experimental investigation of the high pressure fluid phase equilibrium of highly asymmetric binary mixtures. Ph.D. diss., Univ. of Delaware. 

One expression that has been suggested for the excess Gibbs energy of a binary mixture that is asymmetric in composition is... 

Figure 1.2-6 Class III phase diagram for an asymmetric binary mixture consisting of a solid and an SCF.

Figure 1.2-7 p-x diagram for an asymmetric binary mixture at a temperature which intersects the three-phase SLV line. 

Fig. 4.1-3 Structure proposed for the asymmetric [HCI2] ion bonded to the [EMIMJ+ cation in a binary mixture of HCl-[EMIM]Cl. The figure has been redrawn from Ref [10] with permission.

We caution that a binary mixture may obey the Porter equation (5.6.1) but still not be a quadratic mixture that is, may be parabolic in composition but and may not be. An example is the hexane-cydohexane mixture shown in Figure 5.2. Such behavior occurs because as)unmetries in and approximately cancel when they combine via the Legendre transform (5.2.18) to form g. Such cancellations are the norm rather than the exception. To say this another way, the Redlich-Kister expansion for (5.6.3) is usually dominated by the first term, which is symmetric in Xj and Xi-However, in the analogous expansions for and s, asymmetric terms are frequently important. 

Transport Properties of Binary Mixtures of Asymmetric Particles A Simulation Study... 

The preceding survey suggests that the binary mixture of GB fluid has not been studied so far by simulation or numerical methods although, as already mentioned, this is important because real systems are more likely to possess either size, shape, or interaction asymmetry, or any combination of them. The veriflcation of hydrodynamic relations is important for uncovering the nature of solute-solvent interactions in these more complex but model systems. This will certainly help to understand the composition dependence of the binary mixture of GB fluids. One expects in these studies a high degree of nonlinearity in composition dependence because asymmetric interaction-induced nonideal solution behavior has been observed for LJ mixtures of size-symmetric particles [22,23]. 

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