Fractionator principle

If these considerations are assumed to be justifiable, this fractionation principle must have a universal character. It is of interest, then, to ascertain whether, relative to starch, classical non-solvents can show the same phenomena as are met with in the salt solutions. As is well known, such... 

Crystallization analysis fractionation (Crystaf) fractionates polymer chains according to differences in crystallizability. Crystaf can be used to fractionate polymers due to differences in chemical composition, comonomer sequence length, and tacticity. It may also respond to long-chain branching, provided that the polymer is branched enough to affect its crystallinity. The fractionation principle operative in Crystaf was discussed in the section on batch fractionation for the case of slowly cooling (or warming) solutions of semicrystalline polymers. 

Since delocalised electrons in a band cannot be treated by classical statistics, we abandon the site fraction principle, and express all activities simply as concentrations, and denote the new equilibrium constant with a prime" ... 

Using the principle of corresponding states requires knowledge of pseudo-critical constants of petroleum fractions these should be estimated starting from characteristic properties which are the normal boiling temperature and the standard specific gravity. 

As the temperature of the liquid phase is increased, the system ultimately reaches a phase boundary, the bubble point at which the gas phase (vapour) begins to appear, with the composition shown at the left end of the horizontal two-phase tie-line . As the temperature rises more gas appears and the relative amounts of the two phases are detemiined by applying a lever-ami principle to the tie-line the ratio of the fractionof molecules in the gas phase to that hn the liquid phase is given by the inverse of the ratio of the distances from the phase boundary to the position of the overall mole fraction Xq of the system. 

Measurements of pressure driven fluxes may also be performed on mixtures, and here care must be exercised in interpretation, since the fluxes of the two substances are not in proportion to their mole fractions in the mixture. Consequently the fluxes and must, in principle, be measured... 

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

The equations derived in Sec. 6.7 are based on the assumption that termination occurs exclusively by either disproportionation or combination. This is usually not the case Some proportion of each is the more common case. If A equals the fraction of termination occurring by disproportionation, we can write n = A[ 1/1 - p] + (1 - A)[2/(l - p)] and n /n = A(1 + p) + (1 - A)[(2 + p)/2]. From measurements of n and n /n it is possible in principle to evaluate A and p. May and Smith have done this for a number of polystyrene samples. A selection of their data for which this approach seems feasible is presented ... 

For preparative purposes batch fractionation is often employed. Although fractional crystallization may be included in a list of batch fractionation methods, we shall consider only those methods based on the phase separation of polymer solutions fractional precipitation and coacervate extraction. The general principles for these methods were presented in the last section. In this section we shall develop these ideas more fully with the objective of obtaining a more narrow distribution of molecular weights from a polydisperse system. Note that the final product of fractionation still contains a distribution of chain lengths however, the ratio M /M is smaller than for the unfractionated sample. 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

Most synthetic latices contain 5—10 wt % of nonelastomeric components, of which more than half is an emulsifier or mixture of emulsifiers. One reason for this relatively high emulsifier concentration as compared with natural latex is that emulsifier micelles containing solubiHzed monomer play a principle role in the polymerization process. A high emulsifier concentration is usually necessary to achieve a sufficiently rapid rate of polymerization. Secondly, a considerable fraction of the surface of the polymer particles must be covered by adsorbed soap or equivalent stabilizer to prevent flocculation... 

Fig. 9. Principles of field-flow fractionation (a) sample equilibrium position before flow is initiated, (b) fractionated sample after flow initiation, and (c) a...

In principle, the catalytic converter is a fixed-bed reactor operating at 500—620°C to which is fed 200—3500 Hters per minute of auto engine exhaust containing relatively low concentrations of hydrocarbons, carbon monoxide, and nitrogen oxides that must be reduced significantly. Because the auto emission catalyst must operate in an environment with profound diffusion or mass-transfer limitations (51), it is apparent that only a small fraction of the catalyst s surface area can be used and that a system with the highest possible surface area is required. 

The same procedure may be applied in principle to design of forced-recirculation reboilers with shell-side vapor generation. Little is known about two-phase flow on the shell side, out a reasonable estimate of the fric tion pressure drop can be made from the data of Diehl and Unruh [Pet Refiner, 36(10), 147 (1957) 37(10), 124 (1958)]. No void-fraction data are available to permit accurate estimation of the hydrostatic or acceleration terms. Tnese may be roughly estimated by assuming homogeneous flow. 

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