Vapour – Liquid Equilibria in the Polystyrene + Toluene System at Higher Concentrations of Solvent

This paper represents a continuation of the series concerning experimental determination of vapour–liquid equilibria (VLE) in diluted polymer + solvent systems. In the previous papers we dealt with the polymeric flow improvers + toluene, hexane, chloroform1,2, poly(acrylic acid) + water3, poly(methyl methacrylate) + acetone3, and poly(methyl methacrylate) + 2-butanone4 systems. The aim of this study is to provide new – and always welcome – experimental data on vapour–liquid equilibria (VLE) in the polystyrene (PS) + toluene system, determined under isothermal conditions at 363.15, 373.15, and 383.15 K using ebulliometric techniques infrequently exploited for the investigation of polymer solutions. Moreover, the three prediction models were tested against the new experimental data.


Introduction
This paper represents a continuation of the series concerning experimental determination of vapour-liquid equilibria (VLE) in diluted polymer + solvent systems.In the previous papers we dealt with the polymeric flow improvers + toluene, hexane, chloroform 1,2 , poly(acrylic acid) + water 3 , poly(methyl methacrylate) + acetone 3 , and poly(methyl methacrylate) + 2-butanone 4 systems.The aim of this study is to provide new -and always welcome -experimental data on vapour-liquid equilibria (VLE) in the polystyrene (PS) + toluene system, determined under isothermal conditions at 363.15, 373.15, and 383.15K using ebulliometric techniques infrequently exploited for the investigation of polymer solutions.Moreover, the three prediction models were tested against the new experimental data.

Experimental equipment and procedure
Experimental techniques are summarised and discussed in 5 .In our earlier study 1 , we designed a micro-ebulliometer for the quick measurement of the total pressure of systems containing a solvent and a polymer or a non-volatile component, for which only a little amount of material is required.Detailed testing and a discussion about the error caused by a little hold-up of solvent in the vapour phase part of the equilibrium still was published in 1 .
For this study, we exploited the improved original ebulliometer, which with simplified construction makes operation not only easier but more reliable.This ebulliometer was described in details recently 4 .The improved ebulliometer makes it possible to measure VLE with only a small amount of polymer available; 10 mL of liquid phase is required.As discussed in 2 , the experimental uncertainty u in the composition and pressure are estimated as u(w) = 0.0001, and u(P) = 0.001 kPa, respectively.

Results and data processing
The quality and the source of the individual compounds are summarized in Table 1.Table 2 presents the experimental vapour pressure data expressed in terms of toluene activity, a 1 = P 1 /P 1 o , in dependence on weight fraction of solvent w 1 , where P 1 is partial pressure and P 1 o is vapour pressure of pure solvent.For illustration, the experimental data are plotted in Figure 1.
The obtained experimental data were correlated using the UNIQUAC-FV model 6 , which includes the three contributions: combinatorial, residual, and free-volume.The first two contributions are identical to the original UNIQUAC model described in the DECHEMA Data Collection 5 .The free-volume contribution, which enables better description of polymer-solvent system, is calculated by means of the Flory expression 6 .The complete procedure is described in 4 .The calculation method requires as input data the densities of the solvent and of the polymer at the temperature of polymer solution, molecular weight of the repeating unit of component i, van der Waals volume parameters and the surface area parameters of the repeating unit of component i.The densities are estimated using the DIPPR data bank 7 for the solvent and the Tait equation parameters obtained by Rodgers 8 for polymer.The van der Waals volumes and the surface area parameters of the repeating units are calculated using the group contributions values by Bondi 9 , but normalized using the volume and external area of the CH 2 unit in the polyethylene 5 .The UNIQUAC-FV energy parameters A 12 and A 21 have been estimated by minimizing differences between experimental and calculated activities.In Table 3 are presented the estimated values within the temperature range 363.15-383.15K together with average absolute deviation in calculated activity.Additionally, these parameters were used to predict activities at the three particular isotherms and corresponding average absolute deviations in activities are summarised in Table 3, too.It can be seen that activities are well predicted; therefore, we can conclude that parameters are practically temperature independent.Figure 1 additionally illustrates successful prediction of data at 373.15 K with the UNIQUAC-FV model.
Note that the simple sorption method, often referred to as total pressure measurement, usually provides data only from the concentration range with a lower solvent content.Such type of data for the PS + toluene system are available in literature 4,10-12 but the dynamic total pressure method for boiling point measurement used in this work can provide data at high solvent concentrations.For further analyses of the obtained data, our data (M w = 250000 g mol -1 ) were compared with the experimental data 10 (M w = 275000 g mol -1 ) determined at 383.15 K as illustrated in Figure 2. It is obvious that data are well complementing each other.
We opted also for the prediction of phase behaviour using group-contribution predictive models developed earlier: the GC-Flory EoS model 13 the UNIFAC-vdw-FV model 14 , and the Entropic-FV model 15 .These models were used to predict the ac-tivities of toluene in mixtures with PS, because input values for all necessary group parameters for the models have already been published.Models are described in detail in [13][14][15] , where necessary equations, calculation procedure, and parameters are presented.
The reliability of all mentioned models is illustrated in Figure 2 for 383.15K.It can be seen that the predictions of activity versus concentration using the GC-Flory EoS, the UNIFAC-vdw-FV, and the Entropic-FV models are almost of the same quality.It is obvious that the models are mutually comparable and in good agreement.It should be pointed out that prediction procedures were used not for validation of the experimental data but rather to give an idea of the trend of activity as a function of concentration.

Conclusions
Total pressures over the PS + toluene system were determined ebulliometrically at three isotherms in the region of diluted concentrations of polymer and expressed in terms of solvent activity.These data complete existing literature data and were successfully correlated using the UNI-QUAC-FV model.Three known predictive models were tested against the obtained experimental data to see how applicable they may be for practical use.It was found that all three models can be used for prediction of VLE in the studied system.

F i g . 1 -
Activity a 1 of toluene in PS as a function of toluene weight fraction w 1 .Experimental data at () 363.15 K, () 373.15K and () 383.15 K. Solid line represents predicted activities at 373.15 K using the UNIQUAC-FV parameters estimated using all data within temperature range 363.15-383.15K. Ta b l e 1 -Description of compounds e 3 -A 12 and A 21 interaction parameters in the UNIQUAC-FV model for the toluene (1) + PS (2) system

L i s t
o f s y m b o l s a i -activity of component i A ij -UNIQUAC parameter for interaction i -j, K i, j -component M n -number average molecular weight, g mol -1 M w -weight average molecular weight, g mol -1 P -total pressure, kPa P i -pressure of component i, kPa P o -vapour pressure of pure solvent, kPa T -temperature, K u -uncertainty of measurements w i -weight fraction of component i