Interaction parameter from vapor pressure

Gee ° has applied this method to the determination of the interaction parameters xi for natural rubber in various solvents. Several rubber vulcanizates were used. The effective value of VelV for each was determined by measuring its extension under a fixed load when swollen in petroleum ether. Samples were then swollen to equilibrium in other solvents, and xi was calculated from the swelling ratio in each. The mean values of xi for the several vulcanizates in each solvent are presented in Table XXXVI, where they are compared with the xi s calculated (Eq. XII-30) from vapor pressure measurements on solutions of unvulcanized rubber in some of the same solvents. The agreement is by no means spectacular, though perhaps no worse than the experimental error in the vapor pressure method. 

Most commonly used are further developments of the cubic van der Waals EOS. This EOS for the first time allowed the description of different phenomena, such as condensation, vaporization, occurrence of the two-phase region and critical phenomena, using only two parameters a and b which take into account the interaction forces between the molecules and the volume of the molecules. The introduction of a further parameter, the acentric factor m, which can be derived from vapor pressure data, leads to a more reliable description of the saturation vapor pressures. 

For rubbery phases, the models are used in their original equilibrium formulations, which requires knowledge of the pure component parameters and the binary interaction parameters entering the mixing rules associated with the models. The former can be retrieved from pure component volumetric data at different temperatures and pressures and, when applicable, from vapor pressure data for each pair of substances the binary parameter is either retrieved from volumetric data or adjusted to the solubility data. In several cases, the default value offers a reasonable estimation of the solubility isotherms. 

The solvent-polymer interaction parameters were calculated from vapor pressure data of aqueous homopolymer solutions [25], using the Flory-Huggins expression [26] x//=6 ln/)//) —ln(l — 0) —(1 — l/N)0, where p is the vapor pressure and 6 is the polymer volume fraction. The chain length N was determined using 13/3 (EO) or 30/9 (PO) monomers per bead. This gives for the interaction parameters X s=l-4, Xi>s=l-7 (here S denotes solvent). For the EO-PO interaction parameter from group contribution methods [27] we estimated xep = 3.0. 

Without taking polymeric species into account, they could model the vapor pressure curves up to a concentration of 100 wt%. They regressed the necessary binary interaction parameters from experimental data of Kablukov and Zagwosdkin [185] and MacDonald and Boyack [166]. Messnaoui and Bounahmidi... 

The power of a solvent can be determined from the Huggins interaction parameter, xi> which represents the polymer solvent interactions. The parameter can be calculated experimentally from vapor pressure or osmotic measurements using Eq. (16) ... 

Traditionally, the binary interaction parameters such as the ka, kb, k, ki in the Trebble-Bishnoi EoS have been estimated from the regression of binary vapor-liquid equilibrium (VLE) data. It is assumed that a set of N experiments have been performed and that at each of these experiments, four state variables were measured. These variables are the temperature (T), pressure (P), liquid (x) and vapor (y) phase mole fractions of one of the components. The measurements of these variables are related to the "true" but unknown values of the state variables by the equations given next... 

Thus, if the saturated vapor pressure is known at the azeotropic composition, the activity coefficient can be calculated. If the composition of the azeotrope is known, then the compositions and activity of the coefficients at the azeotrope can be substituted into the Wilson equation to determine the interaction parameters. For the 2-propanol-water system, the azeotropic composition of 2-propanol can be assumed to be at a mole fraction of 0.69 and temperature of 353.4 K at 1 atm. By combining Equation 4.93 with the Wilson equation for a binary system, set up two simultaneous equations and solve Au and A21. Vapor pressure data can be taken from Table 4.11 and the universal gas constant can be taken to be 8.3145 kJ-kmol 1-K 1. Then, using the values of molar volume in Table 4.12, calculate the interaction parameters for the Wilson equation and compare with the values in Table 4.12. 

Example 11.2 Using the Underwood Equations, determine the best distillation sequence, in terms of overall vapor load, to separate the mixture of alkanes in Table 11.2 into relatively pure products. The recoveries are to be assumed to be 100%. Assume the ratio of actual to minimum reflux ratio to be 1.1 and all columns are fed with a saturated liquid. Neglect pressure drop across each column. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters assumed to be zero (see Chapter 4). Determine the rank order of the distillation sequences on the basis of total vapor load for ... 

This introduces two "interaction parameters" per binary pair. The pure component coefficients, a and b i, are evaluated from critical data and the acentricity, as proposed by Soave in his original paper (1). The pure component aii varies with reduced temperature so as to match vapor pressure. (Soave s recently revised expression for a (17) has not been used.)... 

We are at a loss to explain the discrepancy in the BF3 enthalpies of interaction with the sulfur donors. Steric effects may be operative, but this is far from the whole story for the BCI3 interaction is much larger than BF3 with these donors. Furthermore, using the tentative ( 113)3 parameters to estimate those of ( 2115)3 , we calculate an enthalpy from E and of 11.1 k.cal mole- for the BF3-P( 2H6)3 adduct compared to a measured value of 9.5 k.cal mole i. The authors report much difficulty with the sulfur donor system, but their error estimates could not possibly account for the difference between our calculated and the observed result. The behavior of ( 2115)35 compared to ( 2115)3 is clearly inconsistent with the behavior of these two donors toward ( 2H5)sAl where both enthalpies are correctly predicted with our parameters. It may be that the BF3-( 2115)25 system has an even lower equilibrium constant than reported and is completely dissociated over the temperature range studied. (This would require a very different entropy if the — AH predicted by E and were correct.) A slight impurity (reported to be less than 0.1%) or decomposition product could interact appreciably with BF3 and changing pressure contributions from this adduct with temperature could be attributed incorrectly to the sulfur donor adduct. The actual BF3-sulfur donor adduct would then be a very common example of an adduct which cannot be studied by the vapor pressure technique because it is completely dissociated at the temperatures at which one of the components has appreciable vapor pressure. We have examined the reaction of BF3 ( 2Hs) 2O with large excess of ( H2) 4S in dichloroethane solution at 25 ° and have found the equilibrium constant to be too low to be measured calorimetrically. 

The solvent activity in a solution of polybutadiene in benzene was determined by measuring the vapor pressure / , of benzene over solutions containing various concentrations of poly-mer.f A plot of ln(p,// ) — In 4>, — (1 — /ri) 2 versus — in which/ is the vapor pressure of the pure benzene —yields a straight line having an intercept of zero and a slope equal to 0.33. Evaluate the interaction parameter x from this result. Is the 0 temperature above or below the experimental temperature Explain. 

Temperature control may also be required to control the sensitivity of the coating to the analyte. Apart from the aforementioned temperature sensitivity of coating physical parameters, the partition coefficient between analyte in the ambient gas or liquid phase and that sorbed by the coating is typically exponentially dependent on absolute temperature. For simple physical interactions, such as an organic solvent being sorbed by a polymer film, the largest contribution to this effect is the strong temperature dependence of the solvent s vapor pressure. The sensitivity of the coated device is thus temperature dependent [34]. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

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