Vapor - Liquid Phase Equilibria

Introduction

The investigation of liquid-vapor equilibria gives useful access to thermodynamic properties of solutions within the range of moderate to high polymer concentrations (40 to 90 wt.-% polymer). Any mixture containing components with detectable vapor pressures can be examined so that the corresponding activity coefficients and derived thermodynamic quantities become accessible.

So far vapor pressure measurements were extremely time consuming due to the necessity to free the system quantitatively from inert gases. For this reason we use a new method that combines a head-space sampler with a gas chromatograph; air needs not be pumped off and the measurements can easily be automated. To obtain the entire information concerning the composition dependent Flory-Huggins interaction parameters the following additional methods are usually applied: static light scattering and osmometry for small polymer concentrations (both of which are regulary used in our woking group) and inverse gas chromatography (IGC) for very high ones.

Experimental set-up

Fig. 1 shows the principle of the experimental set-up schematically. It consists of a head-space sampler, a gas chromatograph and an integrator. We have two apparatus in use, which differ in the GC detector; the first is a Flame Ionization Detector (FID) and second a Thermal Conductivity Detector (TCD). The FID registers ions produced when organic compounds are burnt in a hydrogen flame. The TCD works on the basis of the different thermal conductivity of different compounds. Normally the FID is to preferred because of its higher sensitivity, however, for non-combustible compounds, like water, TCD has to be used. The polymer solutions are usually prepared in crimp-top vials (5, 10 or 20 mL volume), sealed with air-tight septa. The attainment of equilibria is aided by means of a wobble mixer.

More technical details and results for various system can be obtained from the literature

Scheme of the HSGC

Fig. 1. Scheme of the apparatus used for vapor pressure measurements.

Results

The next figure shows the vapor pressures of cyclohexane (in arbitrary units, that is, the integrated areas of the GC peaks) as a function of the volume fraction of polystyrene for different temperatures.

CH/PS raw VLE data vs concentration

Fig. 2. Vapor pressure of cyclohexane as a function of the volume fraction of polystyrene for the indicated temperatures.

By means of the new method (in combination with traditional measurements) it was possible to observe some hitherto overlooked phenomena, like complicated concentration dependencies of the Flory-Huggins interaction parameter and - above all - molecular weight influences even in the range of high chain overlap. An example for these results is given in the next figure

CH/PVME chi vs conentration for different mol. weights

Fig. 3. Concentration dependence of the Flory-Huggins interaction parameter for the system cyclohexane/poly(vinyl methyl ether) at 65 °C; the molar masses of the polymer are indicated in the graph.

The HSGC method yields vapor pressure data (and thus χ) for polymer concentrations from 0.4 to 0.9. Additional data from light scattering or osmosis can be used to get information in the highly dilluted regime and IGC measurments for nearly pure polymer (but this is only applicable if the glass temperature of the polymer is quite low).

TL/PDMS chi vs conentration for different temperatures

Fig. 4. Concentration dependence of the Flory-Huggins interaction parameter for the system toluene/poly(dimethylsiloxane) at various temperatures (including data from osmotic pressure measurements)

Using the temperature dependence in Fig 4. it is possible to split the interaction pararmeter in its enthalpic and entropic part. These parts vary with the concentration of the polymer - in this case there are two distinct points where either the enthalpic part becomes zero (χH=0 athermic case) or the entropic part vanishes (χS=0 combinatoric mixture).

TL/PDMS chi_H and chi_S vs conentration

Fig. 5. The enpthalpic and entopic parts of the Flory-Huggins interaction parameter for the system TL/PDMS