2714
Macromolecules 1994,27, 2714-2718
Concentration-Dependent Thermodynamic Interaction Parameters for Polymer Solutions: Quick and Reliable Determination via Normal Gas Chromatography Hans-Michael Petri and B. A. Wolf' Institut fur Physikalische Chemie, Johannes Gutenberg Universitat, 0-55099 Mainz, Germany Received November 2, 1993; Revised Manuscript Received February 28, 1994'
ABSTRACT: Equilibrium vapor pressures were determined by combining a head-space sampler with a gas chromatograph for the system cyclohexane/polystyrene in the temperature range from 35 to 65 "C. From these measurements the Flory-Huggins interaction parameter x,its variation with a,the volume fraction of the polymer, and its enthalpy part were calculated; x(pJ was represented by an analytical expression given by Koningsveld and Kleintjens and compared with different experimental findings reported in the literature. All measurements agree reasonably well at 35 "C(in the vicinity of the 8 temperature of the system). Differences develop as T is raised; at 65 OC x and its concentration dependence are found to be less pronounced than reported. Under these conditions there also exists a discrepancy between the values calculated from x((a) for vanishing polymer concentration and those directly measured. The reasons for that observation are discussed. The Dresent work demonstrates that the new method yields quick and reliable information on
Introduction For many theoretical considerations as well as for numerous practical applications the knowledge of the Gibbs energy of mixing as a function of composition is of utmost importance. Despite this need there is only a little experimental information due to the fact that considerable labor is required to obtain these data. Normally it is necessary to combine different kinds of measurements, among them that of vapor pressure as a function of polymer concentration, and these-when performed in the usual way-are rather time consuming. For the above reasons it was checked whether a normal gas chromatograph in combination with a head-space sampler could be used to obtain the equilibrium vapor pressures of polymer solutions. This procedure would-in contrast to the traditional measurements-not require the removal of air; furthermore, it could be easily automatized. The system cyclohexane/polystyrene (CH/PS)was chosen to test out the new method, since it is probably the one studied in greatest detail.
Experimental Section Apparatus. The different instruments and their setup can be seen in Figure 1. A pneumatically driven thermostated head-space sampler (Dani HSS 3950, Milano, Italy) takes 20 p L of the gas phases in equilibrium with the polymer solutions and injects it into a gas chromatograph (Shimadzu GC 14A, Kyoto, Japan). A glass column packed with 10% Apiezon M on Chromosorb W was used. A flame ionization detector (Hzof 99.9% purity and dried pressurized air) served to measure the amount of solvent contained in the injected gas volume. The signalswere integrated and registeredby means of an integrator (Shimadzu Chromatopac C-RGA). Procedures. Polymer solutions (3 mL), contained in crimptop vials (capacity 5 mL) sealed with air-tight septa, were rotated at the equilibrium temperature for typically 5 days on a wobble mixer (IDL, TRM-V, Nidderau-Heldenbergen, Germany) to guarantee the establishment of the correct vapor pressure. Then the vials were transferred into the head-space sampler and conditioned for 1.5h. Typically one injection was performed per minute. 0
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Head Space Sampler
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Recorder Figure 1. Scheme of the experimental setup for the determination of vapor pressures by means of gas chromatography. The transfer line was kept at a temperature ca. 10 "C higher than the sampler in order to avoid condensation. The injector and the detector temperatureswere 140"C,and that of the column was 120 "C. The flow rates of Nz (carrier gas, 0.8 bar), of Hz,and of the pressurized air were 500,60, and 500 mL/min, respectively. After each series of measurements the vials were weighted to check their tightness. Although it is possible to obtain absolute values for the vapor pressures p1 of the solvent via calibration, these figures were not calculated since it is only the ratio p 1 / p f (the index o standing for the pure solvent) that is required for the calculation of the thermodynamic data and p1/plo is directly accessible from the ratio of the corresponding integrated detector signals. Materials. Cyclohexane (p.a., Merck, Darmstadt, Germany) was kept over a molecular sieve of 3 A. The weight-average molecular mass of the polystyrene sample PS 233 (PSS; Mainz, Germany) is 233 kg/mol; its molecular nonuniformity (M,/M.) - 1 is
