Ethylene diffusion coefficients

Surprisingly, the temperature does not have a great effect on the equilibrium constant for the reaction of Ag and ethylene. All of the equilibrium constants shown in Tables V and VI are of the same magnitude. In contrast, a temperature increase from 5 to 35 "C enhances the ethylene diffusion coefficients by a factor of 3 to 4. Diffusion coefficients for the Ag -ethylene complex also increase by a factor of 2 to 3 over the same temperature range. This implies that the transport mechanism at low partial pressure of gas is controlled by gas solubility. More likely, a low concentration of gas at the gas-membrane interface limits the amount of gas adsorbed into a membrane. 

Permeation in the vinyUdene chloride copolymer and the polyolefins is not affected by humidity the permeability and diffusion coefficient in the ethylene—vinyl alcohol copolymer can be as much as 1000 times greater with high humidity (14—17). 

Here Ceq is the ethylene concentration equilibrium to the concentration in a gaseous phase, Kp the propagation rate constant, N the concentration of the propagation centers on the catalyst surface, Dpe the diffusion coefficient of ethylene through the polymer film, G the yield of polymer weight unit per unit of the catalyst and y0at, ype are the specific gravity of the catalyst and polyethylene. 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

The mobilities of alkylpyridines were modeled and predicted in capillary zone electrophoresis.35 The model predicted that compounds adopt a preferred orientation, and additionally predicted mobilities of structural isomers to within 4%, a higher degree of accuracy than can be obtained from simple considerations of van der Waal s radius. Quantitative prediction of the mobilities of some pyridines, such as alkenylpyridines, was not possible. Mobilities of small solutes in capillaries filled with oligomers of ethylene glycol were related to solution viscosity and the diffusion coefficient.36... 

The solubility of ethylene in freshly prepared polyethylene, and its diffusion out of the latter were studied in relation to the formation of explosive ethylene-air mixtures in storage. Explosive mixtures may be formed, because the solubility of ethylene in its polymer (e.g. 1130 ppm w/w at 30°C) considerably exceeds the concentration (30 ppm at 30°C) necessary to exceed the lower explosive limit above the gas-containing polymer in closed storage, and the diffusion coefficient is also 30% higher than for aged polymer samples. 

The self-diffusion coefficients in supercritical ethylene were measured using the pulsed NMR spectrometer described elsewhere (9,10), automated for the measurement of diffusion coefficients by the Hahn spin echo method (11). The measurements were made at the proton resonance frequency of 60 MHz using a 1 1.2 kG electromagnet. 

Some measurements have been made of self diffusion in pure ethylene and in ethylene-sulfur hexafluoride mixtures (22), but these measurements were made very close to the critical temperature and up to pressures of only about 100 bar. Proton spin-lattice relaxation times (T.) of ethylene have been measured at temperatures from 0°C to 50°C and pressures up to about 2300 bar (13). The relaxation time values were -M0—50 sec for much of the region studied. Several relaxation mechanisms contribute to this long relaxation time and make both the measurement and analysis of the relaxation times very difficult. For these reasons, we decided to limit our study to the measurement of the self-diffusion coefficient in supercritical ethylene (60. 

The temperatures chosen correspond to those for which density data (19-21) for ethylene and ethylene-C02 are available. The experimental self-diffusion coefficients of ethylene as a function of temperature and density are presented in Figure 2. The pressures corresponding to the chosen densities were determined from the compressibility data of Michels and Geldermans (20). 

Figure 2. Density and temperature dependence of the experimental self-diffusion coefficients of compressed supercritical ethylene.

The hard sphere diameters were then used to calculate the theoretical Enskog coefficients at each density and temperature. The results are shown in Figure 3 as plots of the ratio of the experimental to calculated coefficients vs. the packing fraction, along with the molecular dynamics results (24) for comparison. The agreement between the calculated ratios and the molecular dynamics results is excellent at the intermediate densities, especially for those ratios calculated with diameters determined from PVT data. Discrepancies at the intermediate densities can be easily accounted for by errors in measured diffusion coefficients and calculated diameters. The corrected Enskog theory of hard spheres gives an accurate description of the self-diffusion in dense supercritical ethylene. 

Figure 3.32. A change in the initial distribution of electron transfer distances Y(r) = cmo(r) with the encounter diffusion coefficient D. Ions are produced in 9,10-dicyanoanthracene (DCA, fluorescer) + p-anisidine (ANS, quencher) encounters at c = [ANS] = 0.3 M. The value of D is 4.6 x 10-5 cm2/s in acetonitrile and 0.094 x 10 5cm2/s in ethylene glycol. The parameters of Wi(r) were determined experimentally [90] and used in Ref. 27 to obtain these distributions.

Th-FFF can be applied to almost all kinds of synthetic polymers, like polystyrene, polyolefins, polybutadiene, poly(methyl methacrylate), polyisoprene, polysulfone, polycarbonate, nitrocelluloses and even block copolymers [114,194,220]. For some polymers like polyolefins, with a small thermal diffusion coefficient, high temperature Th-FFF has to be applied [221]. Similarly, hydrophilic polymers in water are rarely characterized by Th-FFF, due to the lack of a significant thermal diffusion (exceptions so far poly(ethylene oxide), poly(vi-nyl pyrrolidone) and poly(styrene sulfonate)) [222]. Thus Th-FFF has evolved as a technique for separating synthetic polymers in organic solvents [194]. More recently, both aqueous and non-aqueous particle suspensions, along with mixtures of polymers and particles, have been shown to be separable [215]. 

Fl-FFF is most attractive for water-soluble polymers [59] and can directly deliver the diffusion coefficient distribution and also a molar mass distribution via the relationship D=AM b. This was exploited for poly(ethylene oxide), poly(styrene sulfonate) and poly(vinyl pyrrolidone) and other polymers using published Mark-Houwink constants [361 ]. Many papers just report on the fractionation of polymers or the determination of the hydrodynamic size distribution of polymers. Examples include poly(styrene sulfonates) [59,165,243],poly(acrylic acid) [243] and poly(2-vinylpyridine) [59]. 

Table 7.2 shows the viscosity, mutual diffusion coefficient, and thermodynamic factor for aqueous solutions of ethylene glycol and polyethylene glycol (PEG) at 25°C the diffusivity decreases considerably with increasing molecular weight, while the viscosity increases. Table 7.2 shows the thermal diffusion ratios for liquids and gases at low density and pressure the thermal diffusion ratios are relatively larger in liquids. 

Table 7.2a. Viscosities, mutual diffusion coefficients, and thermodynamic factors for aqueous solutions of ethylene glycol and PEG at 25°Ca...

Table 7.2b. Thermal diffusion ratio, KJt thermal diffusion coefficients Dj, and heats of transport Q for aqueous ethylene glycol and polyethylene glycol (PEG) solutions at 25°Ca...

Diffusional motion. Many rotational and translational diffusion processes for hydrocarbons within zeolites fall within the time scale that is measurable by quasielastic neutron scattering (QENS). Measurements of methane in zeolite 5A (24) yielded a diffusion coefficient, D= 6 x lO" cm at 300K, in agreement with measurements by pulsed-field gradient nmr. Measurements of the EISF are reported to be consistent with fast reorientations about the unique axis for benzene in ZSM-5 (54) and mordenite (26). and with 180 rotations of ethylene about the normal to the molecular plane in sodium zeolite X (55). Similar measurements on methanol in ZSM-5 were interpreted as consistent with two types of methanol species (56). 

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