Mass fractions from binary separation

Kassalainen and Williams [135] coupled thermal field flow fractionation (ThFFF) and matrix-assisted laser desorption/ionisation time-of-flight mass spectroscopy (MALDI-ToF-MS) to yield a powerful combination of techniques for the analysis of polydisperse PS. ThFFF high selectivity and sensitivity to chemical composition were used to separate polydisperse polymers and polymer mixtures into the narrow polydispersity and homogeneous chemical composition fractions essential for MAT.DT-ToF-MS analyses. On the other hand, because it is possible to measure directly using MALDI-ToF-MS, it alleviates the need for polymer standards for ThFFF. Kassalainen and Williams [135] address the coupling of ThFFF and MALDI-ToF-MS and identify compatibility issues. Optimum conditions were determined and developed to maximise the capabilities of the combined technique. Depending on the polymer and the method of matrix-assisted laser desorption/ionisation (MALDI) sample deposition, fractions from 1-10 ThFFF runs were combined for MALDI-ToF-MS analysis. Binary solvents are used to enhance ThFFF retention and resolution of low (<15 kDa) polymers, and methods developed to allow routine MALDI-ToF-MS analyses of PS polymers up to 575 kDa. Overall, the compatibility of the two techniques was extended from several kilodaltons to several hundred kDa. Polymer... 

As a second example, consider the partitioning of Cd(II) between two adsorbents—a-TiC and (am)Fe20j.H20. Figure 11 shows Cd(II) fractional adsorption as a function of pH for binary mixtures of these adsorbents under experimental conditions such that Cddl) and SOUp are constant only the surface site mole fraction varies from one end-member to the next. As the site mole fraction shifts between the end-members, the fractional adsorption edges for the binary adsorbent mixtures varies between the limits defined by end-members. In the absence of particle-particle interactions, the adsorbents should act as independent ligands competing for complexa-tion of Cd(II). If this is the case, then the distribution of Cd(II) in such binary mixtures can be described by a composite mass-action expression (13) which includes a separate term for the interaction of Cd(II) with each adsorbent. 

Here, we follow a later, simpler formulation that illustrates the power of optimal control for finite-time thermodynamic processes [11]. We take as the control variable the set of temperatures at a given number of equally spaced heat-exchange points along the length of the distillation column. The (assumed) binary mixtme comes in as a feed at rate F and is separated into the less volatile bottom at rate B and the distillate, at rate D, that collects at the top of the colmrm. Let x be the mole fraction of the more volatile component in the liquid and y, the corresponding mole fi action in the vapom, and their subscripts, the indications of the respective points of reference. Thus the total flow rates, for steady flow, must satisfy F = D + B, and xpF = x D + xbB. We index the trays from 0 at the top to N at the bottom. Mass balance requires that the rate V +i of vapour coming up from tray n + 1, less the rate of liquid dropping from tray n, L , must equal D for trays above the feed point at which F enters, and must equal —B below the feed point. Likewise the mole fractions must satisfy the condition that Vn+iVn+i —XnLn = xpD above the feed and —xpB below the feed. The heat required at each nth tray is... 

It is instructive to consider a binary mixture of polymers of different molar mass. Let us assume that they are linear polyethylene sharp fractions with significantly different chain lengths. Figure 8.29 illustrates the behaviour. The temperature Tj is the upper crystallization temperature for the high molar mass (H) polymer. Between temperatures Tj and T2 only H crystallizes. Temperature T2 is the upper crystallization temperature for the low molar mass (L) polymer. Temperatures Tj and T2 can be obtained from the graph of critical molar mass against upper crystallization temperature presented in Fig. 8.28. At temperatures below T2, both polymers crystallize but in separate crystal lamellae. Some limited cocrystallization (crystallization of both polymers in the same crystal lamella) occurs at very low crystallization temperatures. 

---