Activity coefficient , polymer

The development of active ceramic-polymer composites was undertaken for underwater hydrophones having hydrostatic piezoelectric coefficients larger than those of the commonly used lead zirconate titanate (PZT) ceramics (60—70). It has been demonstrated that certain composite hydrophone materials are two to three orders of magnitude more sensitive than PZT ceramics while satisfying such other requirements as pressure dependency of sensitivity. The idea of composite ferroelectrics has been extended to other appHcations such as ultrasonic transducers for acoustic imaging, thermistors having both negative and positive temperature coefficients of resistance, and active sound absorbers. 

Many other parepistemes were stimulated by the new habits of precision in theory. Two important ones are the entropic theory of rubberlike elasticity in polymers, which again reached a degree of maturity in the middle of the century (Treloar 1951), and the calculation of phase diagrams (CALPHAD) on the basis of measurements of thermochemical quantities (heats of reaction, activity coefficients, etc.) here the first serious attempt, for the Ni-Cr Cu system, was done in the Netherlands by Meijering (1957). The early history of CALPHAD has recently been... 

The difficulties engendered by a hypothetical liquid standard state can be eliminated by the use of unsymmetrically normalized activity coefficients. These have been used for many years in other areas of solution thermodynamics (e.g., for solutions of electrolytes or polymers in liquid solvents) but they have only recently been employed in high-pressure vapor-liquid equilibria (P7). 

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

Here, af, y, and x are the activity, activity coefficient, and mole fraction of the swelling agent. Making the assumption that a highly swollen network may be approximated by a dilute polymer solution,... 

The solubility of a gas is an integral part for the prediction of the permeation properties. Various models for the prediction of the solubility of gases in elastomeric polymers have been evaluated (57). Only a few models have been found to be suitable for predictive calculations. For this reason, a new model has been developed. This model is based on the entropic free volume activity coefficient model in combination with Hildebrand solubility parameters, which is commonly used for the theory of regular solutions. It has been demonstrated that mostly good results are obtained. An exception... 

The decrease in [M]e upon addition of monomer superficially seems to contradict the law of mass action. However, addition of monomer increases its activity in the equilibrated solution, although the increase becomes negligible as the activity approaches its limiting value. On the other hand, the resulting increase in polymer concentration raises the activity coefficient of the monomer, and this causes the observed decrease in the equilibrium concentration of the monomer. 

The activity coefficients of the polymers are much lower than those of the monomer. Theories predict, within their limits, a concentration, molar mass, and chemical structure independence of the counterion activity. As seen from Fig. 14, the experimental curvatures differ from the theoretical predictions. The concentration dependence and the absolute values of fa change with the molar mass. Further, the activity coefficient has been found to be reciprocally related to the molar mass [38]. To obtain reliable results a minimization of the salt out-... 

When the monomer phase is still present, the activity coefficient of the monomer dissolved in the gel phase is unity. Therefore, the volumetric fraction of polymer in the gel phase is calculated by solving, for the unknown cp2, the following equation ... 

In some cases it is more convenient to define a molal activity coefficient for the solute in the polymer phase and a molar activity coefficient for the liquid phase. Combining Eq. (4-33) and (4-43) one gets ... 

Using the above expressions for partition coefficients defined on the basis of weight fraction and volume fraction activity coefficients one avoids the difficulty of trying to define what exactly the molar volume of a polymer is. 

The partition coefficient describing solute partitioning between air and polymer is often referred to as a solubility coefficient, S. The solubility coefficient can be expressed in terms of the molal activity coefficient for polymers using Eq. (4-40) ... 

One of the central problems with estimating activity coefficients in polymer systems is that general observations made for low molecular weight component systems are no longer valid for polymers. It is observed that solution dependent properties are no longer directly proportional to the mole fraction of solute in the polymer at dilute concentrations. For example the solute partial pressure in a system containing a polymer is no longer directly proportional to its mole fraction, which is an apparent deviation from Raoult s law. 

The UNIFAC (Unified quasi chemical theory of liquid mixtures Functional-group Activity Coefficients) group-contribution method for the prediction of activity coefficients in non-electrolyte liquid mixtures was first introduced by Fredenslund et al. (1975). It is based on the Unified Quasi Chemical theory of liquid mixtures (UNIQUAC) (Abrams and Prausnitz, 1975), which is a statistical mechanical treatment derived from the quasi chemical lattice model (Guggenheim, 1952). UNIFAC has been extended to polymer solutions by Oishi and Prausnitz (1978) who added a free volume contribution term (UNIFAC-FV) taken from the polymer equation-of-state of Flory (1970). 

Mixtures of hydrocarbons are assumed to be athermal by UNIFAC, meaning there is no residual contribution to the activity coefficient. The free volume contribution is considered significant only for mixtures containing polymers and is equal to zero for liquid mixtures. The combinatorial activity coefficient contribution is calculated from the volume and surface area fractions of the molecule or polymer segment. The molecule structural parameters needed to do this are the van der Waals or hard core volumes and surface areas of the molecule relative to those of a standardized polyethylene methylene CH2 segment. UNIFAC for polymers (UNIFAC-FV) calculates in terms of activity (a,-) instead of the activity coefficient and uses weight fractions... 

The weight fraction activity coefficient of a solute i in a polymer is then calculated from the activity by dividing by its weight fraction in a manner analogous to mole fraction activity coefficients ... 

The liquid phase and polymer phase activity coefficients were combined from different methods to see if better estimation accuracy could be obtained, since some estimation methods were developed for estimation of activity coefficients in polymers (e.g. GCFLORY, ELBRO-FV) and others have their origins in liquid phase activity coefficient estimation (e.g. UNIFAC). The UNIFAC liquid phase activity coefficient combined with GCFLORY (1990 and 1994 versions) and ELBRO-FV polymer activity coefficients were shown to be the combinations giving the best estimations out of all possible combinations of the different methods. Also included in Table 4-3 are estimations of partition coefficients made using the semi-empirical group contribution method referred to as the Retention Indices Method covered in the next section. 

Calculated using polymer density = 0.85., (L) = liquid phase activity coefficient, (P) = polymer phase activity coefficient, - not possible to calculate a result AAR = average absolute ratio for calculated (calc.) > experimental (exp.) = calc./exp. for calc. < exp. = exp./calc. 

ELBRO-FV cannot model water as a solvent, otherwise it was often better than UNIFAC-FV in accuracy. For water-containing systems UNIFAC liquid activity coefficient estimations should be used with ELBRO-FV polymer activity coefficients. 

Estimate the polymer/liquid partition coefficient for cis-3-hexenol between a package with a LDPE material food contact layer. The package contains a food system whose partitioning characteristics can be simulated using 100 % ethanol at 25 °C. Use the UNIFAC activity coefficient estimation method and assume a dilute solution (x, = w, 0.00001). 

With the necessary contributions calculated then the activities and activity coefficients can be calculated. For solutions with polymers Eq. (4-63) is used ... 

In the case of polar liquids and polymers an estimation of the activity coefficients for z and z + 1 in L or P can be tried using another method, e.g. the UNIFAC method. If this is not possible then both the partition coefficient for z and z + 1 in the gas/liquid or gas/polymer system must be experimentally determined. For the relatively volatile alkanes this is possible without a great amount of work. 

Kontogeorgis, G.M., Fredenslund, A., Tassios, D.P. Simple activity coefficient model for the prediction of solvent activities in polymer solutions. Ind. Eng. Chem. Res., 1993,32 362-372. 

Traditional approaches for the calculation of the phase equilibria and sorption of penetrant molecules in polymers are based on equation-of-state models [27,28,29], which take into account the PVT properties of both gas and polymer, and the activity coefficient models [30], which take into account the specific interactions between... 

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