I n d . Eng. C h e m . Res. 1989, 28, 1494-1497
1494
SEPARATIONS Methylene Chloride Permeation in Polycarbonate Using a 14C Tracer Thomas J. Stanley,* William J. Ward, 111, and Montgomery M. Alger Polymer Physics and Engineering Laboratory, General Electric Research and Development Center, P.O. Box 8, Kl-467CE,Schenectady, New York 12301
The migration of small molecules from polymeric food packages into food can be predicted with mathematical models if the pertinent thermodynamic and transport parameters are known. These parameters can be measured using ‘*C-labeled solutes. For methylene chloride permeation through 0.5-mil polycarbonate films, steady state was reached in several hours. Adequate fluxes were realized with just 1-cm2diffusion area. The diffusion coefficient of methylene chloride in polycarbonate is 3.3 X lo-” cm2/s, and the solubility is 17 (cm3 (STP)/cm3)/cmHg, both measured a t 25 “C. No concentration dependence was noted over the range of conditions explored (200-3000 ppm methylene chloride in polycarbonate). These results are in good agreement with the results obtained in an independent experiment using unlabeled methylene chloride which was sorbed into solute-free polycarbonate films from dilute aqueous solutions. The migration of trace quantities of small molecules (residual solvent or monomer, reaction product, plasticizer, etc.) from plastic is of concern when these materials are used for packaging of food. Plastics used in such applications must be tested to show that harmful levels of these small molecules do not migrate from the polymer into the food with which it is in contact (Fazio, 1979; Schwartz, 1983). In this paper, we describe an experiment in which solute diffusivity and solubility can be determined quickly and at exceedingly low solute concentrations. The results can be used in conjunction with a mathematical model to predict the migration behavior of solutes in packages of different geometries (Koros and Hopfenberg, 1979; Reid et al., 1983; Stanley and Alger, 1989). By so doing, a maximum initial loading of solute in the polymer that satisfies the restrictions on solute levels in the food can be determined. In this work, we measured the solubility and diffusion coefficient of methylene chloride (a residual solvent) in polycarbonate using 14C-taggedmethylene chloride. Labeled CH2C12vapor was introduced on one side of the film at the start of an experiment; a Geiger counter was used to monitor the tracer accumulation on the opposite side of the film. The diffusion coefficient of methylene chloride in polycarbonate was determined from the dynamic response; the permeability, and hence solubility, was determined from the steady-state flux across the membrane. Because of the extreme sensitivity of the sensor used in this experiment, transport behavior with very low driving forces (and correspondingly low polymer-phase concentrations of methylene chloride) could be examined. In a companion paper (Stanley and Alger, 19891, we presented another technique for measuring the diffusion coefficient and solubility sorption of unlabeled solute from a dilute aqueous solution into initially solute-free films. Also, we discussed some potential problems with more “conventional” techniques for measuring the diffusion coefficient and solubility and illustrated how inaccurate measurements lead to poor predictions of package migration behavior.
Experimental Apparatus and Theory The permeation cell used in these experiments is diagrammed in Figure 1. This cell is a modification of the one employed previously for studies of COz transport (Alger and Ward, 1987; Alger et al., 1989). The cell was contained in a temperature-controlled enclosure. Most experiments were carried out at 25 “C. The membrane was mounted between the two half-cells, and nitrogen was swept past both sides of the membrane. To begin an experiment, the nitrogen sweep was stopped, and 14C-taggedmethylene chloride vapor was injected with a gas-tight syringe through a stopcock equipped with a septum into the “hot” chamber. The tagged methylene chloride having an activity of 25 mC/mmol was obtained from New England Nuclear Products in glass vials containing a small amount of liquid. Samples of saturated vapor were removed from the glass vial to start a measurement. As the tagged methylene chloride diffused through the membrane and accumulated on the “cold” side of the cell, its concentration was monitored with an Eberline Geiger-Mueller tube Model HP-230A. The GM tube was connected to an Eberline MS-2 miniscaler which summed the cumulative number of radioactive decays in the cold side of the cell. Because the detector efficiency is less than loo%, all of the decays were not counted; however, the calibration procedure used made it necessary to measure only a number proportional to the total decays. A small aluminum pan was placed over the Geiger counter to act as a radiation shield; this ensured that the counter measured only decays resulting from the tagged material that had permeated through the membrane. The Geiger counter response was recorded by a computer for later data analysis. The magnitude of experimental error from methylene chloride sorption into the O-rings used to seal the chambers or into exposed vacuum grease was a concern. To test for this effect, the cell was assembled without a membrane, and tagged methylene chloride was injected. Because only a 2% decrease in signal was noted on the time scale of an
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Figure 2. Typical experimental results. Geiger counter response in counts per minute versus time; 0.5-mil polycarbonate; 1 cm2; 25 "C; methylene chloride injected at 41 min.
GEIGER COUNTER
DATA OUTPUT TO DATA LOGGER
Figure 1. Schematic diagram of "C diffusion cell.
experiment, it was concluded that methylene chloride sorption was not a significant source of error. Also, it was important that the amount of the exposed film be small so that the methylene chloride pressure in the hot chamber not be affected by sorption in the membrane. By use of 0.5-mil-thick films with just 1-cm2 exposed area, this condition was satisfied.
Calculation of 14CHzC1z Permeability In the analysis that follows, it is assumed that the driving force for permeation is unchanged during the course of an experiment. This assumption, satisfied when only a small fraction of the initial charge to the hot chamber passes through the membrane during an experiment, greatly facilitates the analysis. The experimental variable measured was the cumulative number of 14Cdecays, X*(t), as a function of time, which was recorded with the Eberline system. The amount of 14CH2C12that had permeated through to the low-pressure side, Q* [cm3(STP)],and the flux, N * [cm3(STP)/(s.cm2)], can be expressed in terms of the time derivatives of the counts as follows: dX* Q*(t) = dt (1) 1 d2X* 60A dt2 where y [cm3(STP)of 14CH2C12/cpm]is the cell constant, A [cm2] is the film area, and the factor of 60 is added to convert the flux to time units of seconds. To simplify notation, the term "cpm" is used interchangeably with counts/minute, dX*/dt. Thus, the flux can be expressed as
N * ( t ) = y-
(3)
The cell constant y is the conversion factor required to relate the detector response to the tagged gas volume. In previous experiments with 14C02(Alger and Ward, 1987, Alger et al., 1989), y was determined at the end of each experiment, after a steady-state flux had been established across the f i i , by transferring a known volume of gas from the hot chamber to the cold chamber and dividing this volume by the resulting increase in cpm. The standard practice was to use a syringe to remove a small quantity of gas from the hot side and then to inject it into the cold
side. We found the sensitivity of this procedure inadequate for these experiments. Instead, we ruptured the membrane to allow the tagged vapor to distribute uniformly throughtout the cell. Following breaking the membrane, the count rate increased rapidly to a fixed value. The difference in the rate of counts before injection and after membrane rupture is given by (4) AX*'ceu = cpmlrUp+ - cpmIinjThe net effect of rupturing the membrane was to transfer a fraction of the initial charge of tagged methylene chloride from the hot to the cold chamber. The number of moles in the hot chamber immediately after injection N is given by
where p2* is the partial pressure of tagged 14CH2C12and V2is the volume of the hot chamber. The fraction of initial charge transferred by breaking the membrane is given by the ratio of the volume of the cold chamber, V,, to the total cell volume, V l + V2. The moles of tagged gas effectively transferred from the hot to the cold side of the cell can be converted to a standard volume V t :
where a is the ratio of the volume of the cold side to the total cell volume, 273 is the standard temperature in K, and 76 is the standard pressure in cmHg. The volume ratio, a,was most conveniently determined by assembling the cell with an impermeable aluminum film separating the two chambers, injecting a sample of tagged vapor into the cold chamber, and finally rupturing the foil to release the tagged gas to distribute throughout the cell. The ratio of count rates after to before rupturing the foil gave the necessary volume ratio (0.44). The geometry of the hot side was such that its volume could be easily calculated. Finally, the cell constant, y, was evaluated by dividing the amount of tagged gas transferred in the calibration step by the change in cell count rate: 1 273v$2* y=a (7) AX*lceu 76T An example plot of cpm versus time during a typical run is illustrated in Figure 2. After the initial dynamic response, a "steady state" is reached. As indicated earlier, this steady state is maintained only as long as the driving force for transport across the membrane remains essentially constant; that is, the amount of methylene chloride
1496 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 lo 4
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14 1.8 22 (THOUSANDS) AVERAGE FILM CONCENTRATION (PPM)
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Figure 3. Same experimental results as in Figure 2. The calibration step is shown also.
crossing the membrane by diffusion must represent only a small fraction of the initial charge to the hot chamber. This condition can be verified during calibration. The data in Figure 2 have been replotted with the calibration response included in Figure 3. The count rate just before breaking the membrane is proportional to the total amount of tagged gas that had diffused through the membrane. The count rate after breaking the membrane is proportional to 01 times the initial charge. From Figure 3, we can calculate that the driving force had changed by only a few percent when the experiment was ended. The permeability of 14CH2C12is given by the expression
p,* =
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3
Figure 4. Methylene chloride diffusion coefficient in polycarbonate at 25 "C as a function of the average film concentration. - 2 6
1
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PZ* where 1 [cm] is the film thickness. Combination of eq 3, 7, and 8 then gives the following for evaluating the permeability in terms of the experimentally measured values:
It is important to note that the 14CH2C12pressure, p2*, driving the diffusion process cancels out in the calculation of the permeability when using the calibration procedure. A final point is that we have neglected mass-transfer resistances outside of the membrane in the above analysis. This is reasonable because the characteristic diffusion time in the gas space of the chamber was several minutes and the characteristic diffusion time in the membrane was over 100 min. The experimental time lag, %*[SI, is found by extrapolating the steady-state portion of the cpm versus time curve back to the x axis. A steady state is established after about 2.5 time lags. Typically,we waited about 4 time lags before terminating an experiment to ensure a linear response. The diffusion coefficient is calculated from the time lag with the well-known relationship (Crank, 1975) 12
L D* = -
6%*
Finally, the solubility can be calculated once both the diffusion coefficient and permeability are known (Crank, 1975): K * = P,*/D* (11)
Experimental Results Values of the diffusion coefficient and solubility at 25 "C as a function of the average loading of methylene chloride in the film are shown in Figures 4 and 5. The
(THOUSANDS) AVERAGE FILM CONCENTRATION (PPM)
Figure 5. Methylene chloride solubility in polycarbonate at 25 "C as a function of the average film concentration.
concentrations reflect the total methylene chloride concentration in the film (only 40% of the methylene chloride was tagged). There was no discernible concentration dependent within the range of several hundred to several thousand ppm. The motivation behind this work was to understand migration of methylene chloride in polycarbonate food packages, and we restricted our attention to the pertinent concentration range. It is not surprising that we saw no concentration dependence within this very dilute range. Two runs were made at 35 "C to examine the temperature dependence of the diffusion coefficient and solubility. The activation energy for diffusion is 15 kcal/mol, and the activation energy of the solubility (heat of sorption) is -11 kcal/mol. Finally, because in many packaging applications the inside of the package is exposed to high humidity, we looked at the effect of humidity on K and D. Two runs were made at 25 "C in which nitrogen saturated with water was used to sweep out the cell prior to injecting the methylene chloride. Within experimental error, the transport parameters are the same in water-saturated polycarbonate as in dry polycarbonate.
Concluding Remarks Because of the increasing use of plastics in food and beverage packaging, there is concern about the migration of potentially harmful substances present in trace quantities in the polymer from the polymer into the food. Measurement of thermodynamic and transport parameters and then application of mathematical models allow pre-
1497
Znd. E n g . C h e m . Res. 1989,28, 1497-1503
diction of the extent and rate of migration. In this paper, we have described the measurement of the solubility and diffusion coefficient of methylene chloride in polycarbonate using 14C-tagged methylene chloride. Extremely small partial pressures of tagged material could be used, resulting in measurements at very low concentrations of methylene chloride in the polymer. We have determined values of K and D with an independent experiment in which methylene chloride was sorbed from a dilute aqueous solution into clean polycarbonate (Stanley and Alger, 1989). Sorption was monitored through measurements of the aqueous-phase concentration of methylene chloride. The results of the sorption technique are in close agreement with the results of the 14Cexperiment we report here. We conclude with a few brief comments about the relative merits and general applicability of the two techniques. First, the 14Cexperiment is the more flexible. It can be used with any carbon containing gas or vapor, and a very broad range of permeabilities and diffusion coefficients can be measured by varying the film thickness, diffusion area, and tagged gas charge. The sorption experiment is less universally applicable; good sensitivity is realized only for systems in which the partition coefficient is sufficiently large that the liquid-phase concentration changes appreciably. Also, very low polymer-phase concentrations can be explored only when very sensitive detectors are available. A GC equipped with an electroncapture detector allowed us to equal the sensitivity of the 14C experiment for methylene chloride, but we are restricted to halogenated solutes with this detector. Second, the sorption experiment gives the parameters of direct interest in packaging applications-the diffusion coefficient and the partition coefficient of the solute between the polymer and the external liquid phase. The 14Cexperi-
ment, on the other hand, yields a Henry’s law constant from which the partition coefficient must be calculated (using a liquid-phase activity coefficient). Third, tagged solutes used in the 14Cexperiment are expensive compared to untagged ones used in the sorption experiment. Finally, the 14Cexperiment was relatively difficult to establish; the sorption experiment was easy. Both experiments require a great deal of care to set up and run to ensure accurate measurements. Registry No. CHZClz,75-09-2.
Literature Cited Alger, M. M.; Ward, W. J. Measurement of COz Diffusion in Polymer Films. J. Plas. Film Sheet 1987, 3, 33. Alger, M. M.; Ward, W. J.; Stanley, T. J. 14C02and COz Transport in Polycarbonate: Measurement of the Time Lag and Permeability. J . Polym. Sci., Polym. Phys. 1989, 27, 97. Crank, J. The Mathematics of Diffusion; Oxford University Press: London, 1975. Fazio, T. FDA’s View of Extraction Testing Methods for Evaluation of Food Packaging Materials. Food Technol. 1979, April, 61. Koros, W. J.; Hopfenberg, H. B. Small Molecule Migration in Products Derived from Glassy Polymers. Znd. Eng. Chem. Prod. Res. Dev. 1979,18, 353. Reid, R. C.; Schwope, A. D.; Sidman, K. R. Modelling the Migration of Additives from Polymer Films to Food and Food Simulating Liquids. Fourth International Symposium on Migration, Hamburg, Germany, 1983. Schwartz, P. S. Migration and the Regulation of Indirect Food Additives: A Reassessment. Fourth International Symposium on Migration, Hamburg, Germany, 1983. Stanley, T. J.; Alger, M. M. Methylene Chloride Migration in Polycarbonate Packages: Effect of Initial Concentration Profile. Znd. Eng. Chem. Res. 1989,28, 865.
Received for review January 26, 1989 Accepted July 10, 1989
Effect of Retrograde Solubility on the Design Optimization of Supercritical Extraction Processes Miriam L. Cygnarowiczf and Warren D. Seider* Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 192 04
A general strategy to design cost-efficient supercritical extraction processes is applied to a process to dehydrate acetone with supercritical carbon dioxide. The extractor, distillation column, heat exchangers, and compressors in the process flow sheet are simulated, and a nonlinear program is used to locate the optimal designs with respect to both the utility and annualized costs. As the design variables are varied, the strategy overcomes the difficulties in maintaining the proper phase distribution in the near-critical distillation tower. When the cost of utilities only is minimized, local and global minima are identified. The local minima arise due to the retrograde solubility effect associated with supercritical fluids. Minimization of the annualized cost is shown to be preferred for the design of SCE processes, since the equipment costs are an appreciable fraction of the total cost. Furthermore, the annualized cost appears to possess a unique (global) optimum. Supercritical extraction (SCE) is an increasingly important technology in the food and pharmaceutical industries because it allows the substitution of nontoxic, environmentally safe solvents, like COz, for traditional liquid solvents like methylene chloride and hexane. At the present time, this is most applicable in the food and
* Author to whom correspondence should be addressed. Employed by the U.S. Department of Agriculture, Eastern Regional Research Center, Philadelphia, PA, while completing a doctoral program at the University of Pennsylvania, Department of Chemical Engineering.
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pharmaceutical industries where the use of toxic solvents is regulated. However, more stringent regulations regarding toxic waste disposal may, in the future, broaden the significance of this technology to include many segments of the chemical process industry. In Europe and, on a more limited scale, in the United States, SCE is used commercially to decaffeinate coffee and tea and to extract hops and spices. These commercial successes indicate that SCE is a viable alternative for the preparation of some food products. Its feasibility is determined by the scale of the process, the value of the product, the need for a nontoxic solvent, etc. Design 0 1989 American Chemical Society
