Dimer coefficients calculations

Cm, Xd> Xm arc concentrations and mole fractions, respectively, of dimer and monomer em° is the absorption coefficient of the monomer (found by extrapolating em to C=0 and Kx KC for Cd4. We found values of K for each of the alcohols at a series of temperatures from —10° to +45°C. A plot of log10 K vs. IjT is given in Fig. 4. There is considerable scatter, but the trend in each case is roughly linear, within the limits of error. From the slopes of the lines the heats of formation of the alcohol dimers were calculated and are listed in Table 1. 

Table VII. HDEHP Dimer Activity Coefficients Calculations...

Fernandez et al.121 have applied CCS and CCSD to calculations of the frequency-dependent interaction induced hyperpolarizability of the A2 dimer. The calculated virial coefficients are compared with available experimental data. 

In equation (2) c, is the liquid mole fraction, the vapor pressure, Y,- the liquid activity coefficient, F, a correction factor for pure components, 2, the true vapor mole fraction, and p is the system pressure. F. and the relation between 2 and y., the vapor mole fraction without dimerization, are calculated according to Marek, Standart, 1954. The temperature and pressure dependent mole fraction based equilibrium constant for the dimerization can be found in Fredenslund et al. 1977. With a heat of reaction of about -6lkJ I mole, the vapor phase dimerization affects the enthalpy calculations as well. 

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

Ozin et al. 107,108) performed matrix, optical experiments that resulted in the identification of the dimers of these first-row, transition metals. For Sc and Ti (4s 3d and 4s 3d, respectively), a facile dimerization process was observed in argon. It was found that, for Sc, the atomic absorptions were blue-shifted 500-1000 cm with respect to gas-phase data, whereas the extinction coefficients for both Sc and Scj were of the same order of magnitude, a feature also deduced for Ti and Ti2. The optical transitions and tentative assignments (based on EHMO calculations) are summarized in Table I. 

From spectrophotometric measurements (at 425 mfi) on the appearance and disappearance of dimer, values for the rate coefficients ki and k were found to be (at 0 °C and ionic strength 1.0 M) 6.7x10 and 3.3x10 l.mole . sec , respectively. Under the same conditions k, was calculated to be 3.9x10 1. mole . sec. ... 

An effective thickness of the layer where the fluorescence is observed is assumed to be the depth where the excitation light intensity is 1/e of the initial value. The thickness was calculated to be 1.4 im from an absorption coefficient of the film at 295 nm (excitation wavelength). Therefore, the observed fluorescence spectral change is due to that of aggregate states of EPy in the depth region of 1.4 fin from the ablated surface. Actually, it is well known in a PMMA matrix that the excimer band is due to the ground state dimer of the dopant (23). 

Employing experimental supersaturated solution diffusion coefficient data and the cluster di sion theory of Cussler (22), Myerson and Lo (27 attempted to estimate the average cluster size in supersaturated glycine solutions. They estimated an average cluster size on the order of two molecules. Their calculations indicated that while the average cluster size was small, large clusters of hundreds of molecules existed, only there were very few of them. Most of the molecular association was in the form of dimers and trimers. 

The characteristic ratio of atactic polylferf.-butyl vinyl ketone) is determined from light scattering and viscosimetry measurements, and at 300 K in benzene the dipole moment ratio and its temperature coefficient are measured. Calculations of Ca and Da based on a two-state RIS model, with parameters independently derived from a previously developed semiempirical potential energy surface and from epimerization equilibrium measurements for dimeric and trimeric oligomers, are in excellent agreement with the experimental results. The predicted temperature coefficient is positive but lower in magnitude than that observed. 

A full quantum mechanical calculation of the simplest dimer ion is a formidible task (—e.g., [F—H... H—F] with 21 electrons). We are forced to examine the matter using various approximations. Using a molecular orbital approach we can view the problem as one of five electrons associated with the several atomic cores. For [F—H... H—F], the amplest MO could be built from 2 P orbitals on F and Is orbitals on H, as in Table I. By symmetry, the orbital coefficients for the two F atomic orbitals will be identical in magnitude as will those of the two H atomic orbitals. The orbital coefficients, cit, can thus be chosen to be positive definite if the sign convention in Table I is used. The MO s should be... 

If the nucleus senses another metal ion with a different Am value, then the total shift will be given by the sum of two terms of the type of Eq. (6.9), each containing its own Am and C, values. Ami and Ami can be estimated from the monomeric analogs. The C, i and C,-2 values can be calculated once and for all for each system with (he help of Hamiltonian Eq. (6.3). Their values are reported in Table 6.1 for dimers involving 5, and 52 values from xh to 1k [3], These coefficients can be calculated from the following equations ... 

Some of the initial work dealt with the formation of proton-bound dimers in simple amines. Those systems were chosen because the only reaction that occurs is clustering. A simple energy transfer mechanism was proposed by Moet-Ner and Field (1975), and RRKM calculations performed by Olmstead et al. (1977) and Jasinski et al. (1979) seemed to fit the data well. Later, phase space theory was applied (Bass et al. 1979). In applying phase space theory, it is usually assumed that the energy transfer mechanism of reaction (2 ) is valid and that the collisional rate coefficients kx and fc can be calculated from Langevin or ADO theory and equilibrium constants. 

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