Pseudo-component

Table 1 is a file named "FLSHDAT" which contains the shown data for each component, pseudo or real components. Save it here if you make any changes or additions. 

In this work, polyurethane (PU) and epoxy (EP) mixtures were selected for investigation because they are known to form partially miscible IPNs with broad glass transition temperatures. These were first prepared by Frisch et al(6) using a simultaneous polymerization technique in bulk. These materials showed the effects of cross-linking only one polymer component (pseudo-IPN) and intentional grafting between the component polymers. Klempner et al (2) also studied PU/EP IPNs for vibration attenuation. The polyurethanes in this work were chain extended and crosslinked with a 4 1 equivalent ratio of butanediol (BD) and trimethylol propane (TMP). 

For the q - - 1-component pseudo-mixture we may modify the formulation of the Maxwell-Stefan equation given in the last line of (2.298) and the generalized diffusional driving force expression (2.283). The dusty gas model, for s = 1,2,..., q+l, yields ... 

This entry aims at describing the modeling of SVGM and its effects on structures. The total force is divided into two components pseudo-static and dynamic forces. After deriving a general formulation for the case of MDOF systems, two cases have been considered SDOF and MDOF systems. 

Flooding and Pseudo-First-Order Conditions For an example, consider a reaction that is independent of product concentrations and has three reagents. If a large excess of [BJ and [CJ are used, and the disappearance of a lesser amount of A is measured, such flooding of the system with all components butM permits the rate law to be integrated with the assumption that all concentrations are constant except A. Consequentiy, simple expressions are derived for the time variation of A. Under flooding conditions and using equation 8, if x happens to be 1, the time-dependent concentration... 

Most catalysts for solution processes are either completely soluble or pseudo-homogeneous all their catalyst components are introduced into the reactor as Hquids but produce soHd catalysts when combined. The early Du Pont process employed a three-component catalyst consisting of titanium tetrachloride, vanadium oxytrichloride, and triisobutjlalurninum (80,81), whereas Dow used a mixture of titanium tetrachloride and triisobutylalurninum modified with ammonia (86,87). Because processes are intrinsically suitable for the use of soluble catalysts, they were the first to accommodate highly active metallocene catalysts. Other suitable catalyst systems include heterogeneous catalysts (such as chromium-based catalysts) as well as supported and unsupported Ziegler catalysts (88—90). 

The second type of solution polymerization concept uses mixtures of supercritical ethylene and molten PE as the medium for ethylene polymerization. Some reactors previously used for free-radical ethylene polymerization in supercritical ethylene at high pressure (see Olefin POLYMERS,LOW DENSITY polyethylene) were converted for the catalytic synthesis of LLDPE. Both stirred and tubular autoclaves operating at 30—200 MPa (4,500—30,000 psig) and 170—350°C can also be used for this purpose. Residence times in these reactors are short, from 1 to 5 minutes. Three types of catalysts are used in these processes. The first type includes pseudo-homogeneous Ziegler catalysts. In this case, all catalyst components are introduced into a reactor as hquids or solutions but form soHd catalysts when combined in the reactor. Examples of such catalysts include titanium tetrachloride as well as its mixtures with vanadium oxytrichloride and a trialkyl aluminum compound (53,54). The second type of catalysts are soHd Ziegler catalysts (55). Both of these catalysts produce compositionaHy nonuniform LLDPE resins. Exxon Chemical Company uses a third type of catalysts, metallocene catalysts, in a similar solution process to produce uniformly branched ethylene copolymers with 1-butene and 1-hexene called Exact resins (56). 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

Residue curve maps exist for mixtures having more than three components but cannot be visualized when there are more than four components. However, many mixtures of industrial importance contain only three or four key components and can thus be treated as pseudo-temary or quaternary mixtures. Quaternary residue curve maps are more compHcated than thek ternary counterparts but it is stiU possible to understand these maps using the boiling point temperatures of the pure components and azeotropes (31). 

Drawing pseudo-binaryjy—x phase diagrams for the mixture to be separated is the easiest way to identify the distillate product component. A pseudo-binary phase diagram is one in which the VLE data for the azeotropic constituents (components 1 and 2) are plotted on a solvent-free basis. When no solvent is present, the pseudo-binaryjy—x diagram is the tme binaryjy—x diagram (Eig. 8a). At the azeotrope, where the VLE curve crosses the 45° line,... 

Fig. 8. Pseudo-binary (solvent-free)jy-x phase diagrams for determining which component is to be the distillate where (—) is the 45° line, (a) No solvent (b) and (c) sufficient solvent to eliminate the pseudo-a2eotiope where the distillate is component 1 and component 2, respectively (51) and (d) experimental VLE data for cyclohexane—ben2ene where A, B, C, and D represent 0, 30, 50, and 90 mol % aniline, respectively (52).

Feed analyses in terms of component concentrations are usually not available for complex hydrocarbon mixtures with a final normal boihng point above about 38°C (100°F) (/i-pentane). One method of haudhug such a feed is to break it down into pseudo components (narrow-boihng fractions) and then estimate the mole fraction and value for each such component. Edmister [2nd. Eng. Chem., 47,1685 (1955)] and Maxwell (Data Book on Hydrocarbons, Van Nostrand, Princeton, N.J., 1958) give charts that are useful for this estimation. Once values are available, the calculation proceeds as described above for multicomponent mixtures. Another approach to complex mixtures is to obtain an American Society for Testing and Materials (ASTM) or true-boihng point (TBP) cui ve for the mixture and then use empirical correlations to con-strucl the atmospheric-pressure eqiiihbrium-flash cui ve (EF 0, which can then be corrected to the desired operating pressure. A discussion of this method and the necessary charts are presented in a later subsection entitled Tetroleum and Complex-Mixture Distillation. ... 

TABLE 13-28 Pseudo-Component Representation of Feed for the Atmospheric Crude Tower of Fig. 13-94... 

The equations that have been developed for design using these pseudo constants are based on steady-state mass balances of the biomass and the waste components around both the reactor of the system and the device used to separate and recycle microorganisms. Thus, the equations that can be derived will be dependent upon the characteristics of the reactor and the separator. It is impossible here to... 

The actual Russian standards allow presentation of hydrocarbon components of UGC as individual compounds only for C -C hydrocai bons. The rest is described as pseudo-compound C,, although its content may reach 60 % m/m. Apparently, the detailed determination of composition of hydrocarbons C, in UGC allows essentially to raise quality of both its processing and its record. The best method for the determination of heavy hydrocai bons is capillary gas chromatography. Typical approach is based on preliminary sepai ation of UGC samples to gaseous and liquid phases. 

In crude distillation, there are thousands of different compounds present having a virtually continuous spectrum of boiling points. It would be impractical to consider each of these compounds in describing the crude or designing the equipment to process it. Instead the crude is treated as if it were composed of a manageable number (< 50) of pseudo components. These are defined by dividing the crude distillation curve into a series of adjacent boiling cuts. 

Usually, product specifications for a crude distillation unit are expressed in terms of the products 15/5 or ASTM distillation curves. The prediction of a product 15/5 distillation is accomplished simply by blending the quantities of the pseudo components in the stream so as to form a true boiling point, 15/5 equivalent, distillation curve. This curve can then be converted to an ASTM type distillation using an empirical method. Figure 5 illustrates how a typical ASTM curve compares to the 15/5 curve for the same material. 

Appearance of the metallic structure of CNT is based on the crossing of the highest occupied (HO) and the lowest unoccupied (LU) bands (see, e.g.. Fig. 3), each accompanying pseudo rt-type crystal orbital. Note that pseudo n-type orbital, particularly when all the valence atomic orbitals (AO) are taken into consideration, implies that its main AO component is normal to the cylindrical CNT surface. The band crossing mentioned above is possible when these two... 

The gas pseudo critical pressures and temperatures can be approximated from Figure 2-16 or they can be calculated as weighted averages of the critical temperatures and pressures of the various components on a... 

Recently Gadamer s view > has been widely accepted. He postulates for these compounds a tautomeric system of three components, in which the quaternary ammonium hydroxide, the pseudo base (or... 

A chiral titanium complex with 3-cinnamoyl-l,3-oxazolidin-2-one was isolated by Jagensen et al. from a mixture of TiCl 2(0-i-Pr)2 with (2R,31 )-2,3-0-isopropyli-dene-l,l,4,4-tetraphenyl-l,2,3,4-butanetetrol, which is an isopropylidene acetal analog of Narasaka s TADDOL [48]. The structure of this complex was determined by X-ray structure analysis. It has the isopropylidene diol and the cinnamoyloxazolidi-none in the equatorial plane, with the two chloride ligands in apical (trans) position as depicted in the structure A, It seems from this structure that a pseudo-axial phenyl group of the chiral ligand seems to block one face of the coordinated cinnamoyloxazolidinone. On the other hand, after an NMR study of the complex in solution, Di Mare et al, and Seebach et al, reported that the above trans di-chloro complex A is a major component in the solution but went on to propose another minor complex B, with the two chlorides cis to each other, as the most reactive intermediate in this chiral titanium-catalyzed reaction [41b, 49], It has not yet been clearly confirmed whether or not the trans and/or the cis complex are real reactive intermediates (Scheme 1.60). 

Step 3. Calculate the weight average critical temperature and critical pressure for the remaining heavier components to form a pseudo binary system. (A shortcut approach good for most hydrocarbon systems is to calculate the weight average T only.)... 

Step 4. Trace the critical locus of the binary consisting of the light component and psuedo heavy component. When the averaged pseudo heavy component is between two real hydrocarbons, an interpolation of the two critical loci must be made. 

Step 8. Repeat Steps 2 through 7 until the assumed and calculated convergence pressures check within an acceptable tolerance, or until the two successive calculations for the same light and pseudo heavy components agree within an acceptable tolerance. 

The use of the K-factor charts represents pure components and pseudo binary systems of a light hydrocarbon plus a calculated pseudo heavy component in a mixture, when several components are present. It is necessary to determine the average molecular weight of the system on a methane-free basis, and then interpolate the K-value between the two binarys whose heavy component lies on either side of the pseudo-components. If nitrogen is present by more than 3-5 mol%, the accuracy becomes poor. See Reference 79 to obtain more detailed explanation and a more complete set of charts. 

The second method can be applied to mixtures as well as pure components. In this method the procedure is to find the final temperature by trial, assuming a final temperature and checking by entropy balance (correct when ASp t, = 0). As reduced conditions are required for reading the tables or charts of generalized thermodynamic properties, the pseudo critical temperature and pressure are used for the mixture. Entropy is computed by the relation. See reference 61 for details. ... 

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