Density dimerization

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

Figure Bl.17.11. Reconstructed density of an a,p-tiibulin protein dimer as obtained from electron crystallography (Nogales etal 1997). Note the appearance of the p-sheets ((a), marked B) and the a-helices ((b), marked H) in the density. In particular the right-handed a-helix H6 is very clear. Pictures by courtesy of E Nogales and Academic Press.

The vapor density of acetic acid suggests a molecular weight much higher than the formula weight, 60.06. Indeed, the acid normally exists as a dimer (4), both in the vapor phase (5) and in solution (6). This vapor density anomaly has important consequences in engineering computations, particularly in distillations. 

Bismuth Penta.fIuoride, Bismuth(V) fluoride consists of long white needles that have been shown to have the same stmcture as the body-centered, tetragonal a-polymorph of uranium hexafluoride. The density of the soHd is 5.4 g/mL at 25°C. The soHd consists of infinite chains of trans-bridged BiF polyhedra dimers and trimers are present in the vapor phase (22). Bismuth pentafluoride may be prepared by the fluorination of BiF or... 

In the Institut Fransais du Petrc le process (62), ethylene is dimerized into polymer-grade 1-butene (99.5% purity) suitable for the manufacture of linear low density polyethylene. It uses a homogeneous catalyst system that eliminates some of the drawbacks of heterogeneous catalysts. It also inhibits the isomerization of 1-butene to 2-butene, thus eliminating the need for superfractionation of the product (63,64). The process also uses low operating temperatures, 50—60°C, and pressures (65). 

Substituents on the methine chain can stabilize the dye radical cation if the substituent (like methyl) is located on the high electron density carbons. However, no significant stabilization occurs when alkyl groups are on the alternate positions (like 9, 11 for the dication in Fig. 9). Current results for several dyes including die arbo cyanines and carbocyanines indicate that electronic stabilization of the dication radical lengthens the radical lifetime and also enhances the reversibiUty of the dimerization process (37). 

The inaccuracy seems not to prohibit study of the structural properties of associating fluids, at least at low values of the association energy. However, what is most important is that this difficulty results in the violation of the mass action law, see Refs. 62-64 for detailed discussion. To overcome the problem, one can apply thermodynamical correspondence between a dimerizing fluid and a mixture of free monomers of density p o = P/30 = Po/2 and dimer species [12]. The equation of state of the corresponding mixture... 

Let us begin our discussion from the model of Cummings and Stell for heterogeneous dimerization a + P ap described in some detail above. In the case of singlet-level equations, HNCl or PYl, the direct correlation function of the bulk fluid c (r) represents the only input necessary to obtain the density profiles from the HNCl and PYl equations see Eqs. (6) and (7) in Sec. II A. It is worth noting that the transformation of a square-well, short-range attraction, see Eq. (36), into a 6-type associative interaction, see Eq. (39), is unnecessary unless one seeks an analytic solution. The 6-type term must be treated analytically while solving the HNCl... 

The behavior of assoeiating fluid near the hard wall was extensively studied in the framework of the theory diseussed above. The model of Cummings and Stell was applied to relatively dense fluids at a high degree of dimerization [33,36]. Fig. 1 presents the density profiles ealeulated within the framework of the eombined PYl/EMSA theory (i.e., the density profiles were evaluated from the PY 1 equation, whereas the bulk direet eorrelation fune-tions follow from the EMSA equation) and HNCl/EMSA approximations [33]. The ealeulations were performed for L = 0.42[Pg.181]

The density profiles are presented for the model of Cummings and Stell [25-27]. The fluid is in eontaet with the (100) plane of the faee-eentered eubie lattiee, the bulk fluid partieles and the solid atoms are assumed of the same size, ai = a2 = infinite dilution (Kq /ksT) [25]. The ealeulations have been done by using PYl... 

Aeeording to Wertheim [8-11], the fluid density at a point 1 of the bulk assoeiating fluid is split into two terms, namely the density of unbonded speeies, po(l)> and the density of (singly) bonded speeies, Pi(l), sueh that the total density is p(l) = po(l) + Pi(l)- We set the matrix of densities for a dimerizing fluid... 

A dimerizing Lennard-Jones fluid has been studied for the bulk density p = 0.75, and at temperature T — 1.35, for different values of the assoeia-tion energy, namely = 2, 6, 10, and 11.5 [118]. The results for... 

The density profiles are shown in Fig. 7(a). Fig. 7(b), however, illustrates the dependenee of the degree of dimerization, x( ) = P i )lon the distance from the wall. It ean be seen that, at a suffieiently low degree of dimerization (s /ksT = 6), the profile exhibits oseillations quite similar to those for a Lennard-Jones fluid and for a hard sphere fluid near a hard wall. For a high degree of dimerization, i.e., for e /ksT = 10 and 11.5, we observe a substantial deerease of the eontaet value of the profile in a wide layer adjacent to a hard wall. In the ease of the highest assoeiation energy,... 

The a-s-a and sp-s-sp cuts of the density profiles (Figs. 9(c) and 9(d)) clearly demonstrate that for a highly dimerized fluid the nonassociatively adsorbed dimers have a tendency to orient perpendicularly or slightly tilted... 

Fig. 17 shows the adsorption isotherms of all (undimerized and dimerized) particles. Except for a very fast increase of adsorption connected with filling of the first adlayer, the adsorption isotherm for the system A3 is quite smooth. The step at p/k T 0.28 corresponds to building up of the multilayer structure. The most significant change in the shape of the adsorption isotherm for the system 10, in comparison with the system A3, is the presence of a jump discontinuity at p/k T = 0.0099. Inspection of the density profiles attributes this jump to the prewetting transition in the... 

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