Ind. Eng. C h e m . R e s . 1989,28, 865-869 Doyle, C. D. J. Appl. Polym. Sci. 1961, 5 , 285. Ferziger, J. H. Numerical Methods for Engineering Application; Wiley & Sons: New York, 1981. Flynn, J. Thermochim. Acta 1980,37, 225. Hajaligol, M. R.; Howard, J. B.; Longwell, J. P.; Peters, W. A. Znd. Eng. Chem. Process Des. Dev. 1982, 21, 457. Hofmann, L.; Antal, M. J. Solar Energy 1984, 33(5), 427-440. Hopkins, M. W.; Antal, M. J.; Kay, J. G. J. Appl. Polym. Sei. 1984a, 29, 2163-2175. Hopkins, M. W.; DeJenga, C. I.; Antal, M. J. Solar Energy 1984b, 32(4), 547-551. Kothari, V. S.; Antal, M. J. Fuel 1985,64, 1487-1495. Lede, J.; Li, H. Z.; Villermaux, J. Fusion-Like Behavior of Biomass Pyrolysis; Preprints, Division of Fuel Chemistry 32(5); American Chemical Society: Washington, DC, 1987; pp 59-67. Mok, W. S.-L.; Antal, M. J. Thermochim. Acta 1983, 68, 165-186. Narayan, R.; Tabatabaie-Raissi, A.; Antal, M. J. A Study of Zinc Sulfate Decomposition at Low Heating Rates. Znd. Eng. Chem.
865
Res. 1988, 27, 1050. Sestak, J.; Satava, V.; Wendlandt, W. W. Thermochim. Acta 1973, 7, 333. Simmons, G. M. Particle Size Limitations Due to Heat Transfer in Determining Pyrolytic Kinetics of Biomass; Preprints, Division of Fuel Chemistry 2(29); American Chemical Society: Washington, DC, 1984; pp 58-64. Simmons, G. M.; Lee, W. H. Kinetics of Gas Formation from Cellulose and Wood Pyrolysis. In Fundamentals of Thermochemical Biomass Conversion; Overend, R. P., Milne, T. A., Mudge, L. K., Eds.; Elsevier: New York, 1985; pp 385-395. Tabatabaie-Raissi, A.; Antal, M. J. Solar Energy 1986, 36(5), 419-429. Varhegyi, G.; Antal, M. J.; Szekely, T.; Piroska, S. Energy Fuel 1989, in press. Received for review June 14, 1988 Accepted January 17, 1989
Methylene Chloride Migration in Polycarbonate Packages: Effect of Initial Concentration Profile Thomas J. Stanley* and Montgomery M. Alger K1-467CE, Polymer Physics and Engineering Laboratory, Corporate Research and Development, General Electric Company, Schenectady, N e w York 12301
T h e migration of small molecules out of polymeric food packages into food can be predicted if the important thermodynamic and transport parameters are known. These parameters can be measured in convenient extraction experiments. T h e surface region of a sample used in extraction testing can be substantially depleted of migrant. When extraction data for a depleted sample are interpreted with respect t o a mathematical model which assumes a flat initial migrant concentration profile, the thermodynamic and transport parameters are in error, resulting in a n inaccurate prediction of long-time migration behavior. The results presented here demonstrate that even freshly manufactured polymer samples can be substantially surface depleted because migrant diffusion is very rapid at the high temperatures the polymer sees during manufacture. Virtually all plastics contain trace quantities of small, mobile molecules such as plasticizer, residual monomer, or residual solvent. These mobile molecules can diffuse to the polymer surface and escape. As a result, there is a concern about the health effects of plastics that are used in food-packaging applications; plastic packages must be tested to show that no harm results from small molecules migrating from the package into the food with which it is in contact. Part of this testing process involves performing extractions to determine the quantity of migrant that accumulates in the food or in a “food-simulating liquid” (Fazio, 1979; Schwartz, 1983; Reid et al., 1983). Extraction testing usually involves contacting a polymer sample containing a known concentration of migrant with migrant-free food and then monitoring the accumulation of migrant in the food with time. A combination of experimental measurements and mathematical modeling proves useful in quantifying migration from packages. A convenient extraction experiment is carried out, and an appropriate mathematical model is used to determine the relevant transport and thermodynamic parameters through a fit to the experimental results (Rudolf, 1979,1980;Koros and Hopfenberg, 1979a,b; Reid et al., 1980; 1983; Till et al., 1982). Then the migration rates from different packages can be calculated with a model appropriate for a given set of conditions, which employs the measured thermodynamic and transport parameters. Besides minimizing the number of experimental measurements that must be made, migration modeling is powerful because it allows prediction of the
accumulation of migrant in food over very long time intervals that are not experimentally practical. The models most often used for the interpretation of extraction data are based upon a number of simplifying assumptions. The one under examination here is that of a flat initial concentration profile of migrant in the polymer. Test parts (molded plaques or pressed films) often are exposed to migrant-free air between the time they are prepared and the start of the extraction experiment. During this “aging” period, the surface region of the test part can become depleted of migrant because the migrant can escape into the surrounding air. The loss of migrant near the surface of the sample before the extraction experiment begins results in a slower rate of migration into the surrounding medium relative to that in an undepleted sample (Daniels and Proctor, 1975; Berens and Daniels, 1976; Ayres et al., 1983). The transport parameters determined from the depleted sample data by applying a model that assumes a flat migrant profile can be significantly in error (Ayres et al., 1983). This misinterpretation of transport parameters results in a poor prediction of the rate of accumulation of migrant in the package contents. Also, because migrant depletion occurs not only in test parts before extraction testing but also in packages before the package is filled and put on the market, it is necessary to account for surface depletion in package calculations to obtain accurate results (Ayres et al., 1983). In the first section of this paper, we show the results of our experiments to measure the partition coefficient of methylene chloride (MC) between water and polycarbonate
0888-5885/89/2628-0865~Q1.5Q/Q 0 1989 American Chemical Society
866 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
(PC) and the diffusion coefficient of methylene chloride in polycarbonate. We use very thin films of polycarbonate in these extractions. In "thin film" experiments, one has good control of the initial 'concentration profile in the polymer sample because thin films can be prepared by diffusing migrant into an initially "clean" film from migrant-spiked medium. When equilibrium is achieved, the spiked medium can be quickly replaced with clean medium and the desorption monitored. In the second section of this paper, we demonstrate with measurements on molded bottles the effect of surface depletion on the accumulation of migrant in water contained in the bottles. The most important finding is that even freshly manufactured samples can exhibit a significant degree of surface depletion. Because the rate of diffusion is much faster a t the high temperatures the polymer is exposed to during manufacture than under storage conditions, loss of migrant is greatly accelerated during fabrication. As a result, great care must be exercised in applying flat profile models to test parts and packages that are fabricated from the melt. Thin-Film Experiments In this section, we describe measurements of methylene chloride migration in polycarbonate using thin films. One-mil polycarbonate films, initially free of methylene chloride, were placed in clean vials, each equipped with a stopper and a stopcock to allow sampling of the water with time. At time zero, the vial was filled with water spiked with a known concentration of methylene chloride. The vials were maintained at 25 "C and agitation was provided by storing the samples in a constant-temperature shaking bath. By use of the criteria of Reid et al. (19831, only very mild agitation was required to ensure a wellmixed water phase. The concentration of methylene chloride in the water was followed with time by a gas chromatograph equipped with a Tenax-packed column and an electron capture detector. Two-microliter direct aqueous injections gave adequate sensitivity. Equilibrium between the water and the polycarbonate was assumed to have been attained when the concentration no longer changed with time (about 2 days). After equilibrium was reached, the spiked water was replaced with clean water, and the desorption of methylene chloride followed in the same manner. A control experiment in which an empty vial was filled with spiked water and the concentration monitored with time showed no loss of methylene chloride. A second control experiment in which clean polycarbonate was placed in clean water showed no detectable desorption. A sample plot is shown in Figure 1. In this measurement, 0.11 g of 1-mil polycarbonate film was placed in contact with 40 g of water initially spiked to 200 ppb with methylene chloride. Calculation of the partition coefficient is straightforward a mass balance at equilibrium gives the result directly for sorption of methylene chloride into the polycarbonate:
cw/co,w cw/co,w
K = a ( 1-
)
C, is the concentration of methylene chloride in the water at equilibrium, C0," is the initial water concentration, and a is the mass ratio of water to polycarbonate. For the measurement illustrated in Figure 1,we calculate a value of K of 220 (g of methylene chloridelg of polycarbonate)/(g of methylene chloride/g of water) on the sorption cycle. For desorption, using a slight modification of eq 1, we calculate a value of K of 240.
200 190
,
~
/
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/
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,
1
/
,
,
SORPTION CYCLE
DESORPTION CYCLE
30 20
0
40
80
120
160
200
240
TIME (HOURS)
Figure 1. Methylene chloride concentration in the water phase versus time for sorption and desorption cycles of thin-film experiments. 0.11 g of 1-mil polycarbonate film placed in 40 g of water initially containing 200 ppb of methylene chloride a t 25 "C.
The diffusion coefficient must be determined from a fit of a mathematical model to the dynamic response of the sorption/desorption curves. The governing equation is Fick's second law:
where C(x,t) is the migrant concentration in the polymer and D is the diffusion coefficient. The first boundary condition imposes phase equilibrium at the outside surfaces of the film: C(0,t) = K*C"(t)
(3)
K * is the distribution coefficient described above but corrected with specific gravities to express concentrations in units of mass per volume, and C " ( t )is the methylene chloride concentration in the water. We assume the water phase is well-mixed, and therefore, there are no spatial variatons. However, because the water volume is finite, C " varies with time, and it is necessary to specify that the methylene chloride leaving one phase accumulates in the other: (4)
V" is the volume of water, and A is the polymer surface area. The second boundary condition is a symmetry condition:
where 6 is the film thickness. Finally, it is necessary to supply the appropriate initial condition. If the initial concentration profile in the polymer sample is assumed to be flat, which is appropriate for both the sorption and desorption cycles of these experiments, then the initial condition is given by C(x,O) = c w
(6)
An analytical solution to eq 2 subject to conditions 3-6 is given by Crank (1975). Our solutions were found by numerical integration with the IMSL routine DPDES ( I M s L Library Manual, 1979) and verified by using the analytical solution. We used the numerical routine because we were interested in solutions for nonuniform initial profiles for which the analytical solutions are particularly cumbersome to use (March and Weaver, 1928; Schumann, 1931).
Ind. Eng. Chem. Res., Vol. 28,No. 6, 1989 867
:
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MEASURED VALUES -MODEL (D=3.5X16”cm2/s)
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Figure 2. Data of sorption cycle of Figure 1 replotted as the mass of methylene chloride sorbed by polycarbonate normalized to the mass sorbed a t equilibrium versus square root of time. Model predictions using K = 230 (g of MC/g of PC)/(g of MC/g of water) and D = 3.5 X lo-” cm2/s are shown for comparison.
To fit the model to the data, we employed a technique originally described by Carman and Haul (1954). First, the values of fractional uptake, defined as the mass of migrant sorbed by the polymer normalized with the mass sorbed at equilibrium, are determined from the measurements. Next, the values of fractional uptake as a function of dimensionless time are calculated from the mathematical model presented above (but cast in dimensionless form). The dimensionless time is given by 7=-
4Dt
(7)
62
Third, the values of the real time t corresponding to the experimentally measured values of fractional uptake are plotted against the calculated values of dimensionless time T at the same fractional uptakes. From eq 7,we expect a linear relationship; the value of D is found from the slope. The experimental results of the sorption cycle of the measurement from Figure 1 are shown in Figure 2 as fractional uptake versus the square root of time. The calculated fractional uptake curve using a diffusion coefficient of 3.5 X cm2/s (determined by using the Carman and Haul technique described above) has been added to this figure for comparison. The fit to the data is very good. Both the diffusion coefficient and the partition constant were determined from sorption and desorption experiments at several different concentrations. Within experimental uncertainty, the same results were found for sorption as for desorption, and no discernible concentration dependence was noted. The diffusion coefficient is 3 x 10-l’cm2/s (fl x l0-l1), and the partition coefficient is 230 (g of CH,Cl,/g of polycarbonate)/(g of CH2C12/gof water) (*30),both a t 25 OC. These results are consistent with those of an independent technique, a transient membrane transport study employing 14CHzC12(Stanley et al., 1989). Bottle Extractions To test for the effect of surface depletion on short-time extractions, small bottles were molded from polycarbonate specifically manufactured to contain an abnormally high concentration of methylene chloride (75 ppm), and the migration of this residual solvent into clean water was monitored with time. The freshly made bottles were divided into two groups. The bottles of the first group were filled with distilled water as soon as they were cool to the
Table I. Physical Parameters of Small Bottles Used in Extraction Testing inside surface area 24.5 volume 140 cm2 32 mil wall thickness diffusion coeff 3 X lo-” cm2/s partition constant 230 (g CHZC12/g PC)/(g CH2C12/g H20)
touch after molding (about 15 min). These are referred to as “fresh” bottles. The bottles of the second group were placed in a constant-temperature box through which circulating nitrogen was passed for 20 days before they were filled with water to begin the extraction. These are referred to as “depleted” bottles. The role of the nitrogen sweep was to remove all methylene chloride that escaped from this group of bottles; we assume that the concentration at the inside and outside surfaces of each bottle was zero while in the nitrogen sweep. To maintain temperature and to provide agitation, the filled bottles were stored in a shaker bath. As with the thin-fiim experiments, this mild agitation ensured a well-mixed liquid phase (Reid et al., 1983). Tops for the bottles containing a stopcock were fabricated so that repeated samplings of the water in a single bottle could be made with a syringe. The methylene chloride level in the water was measured using the technique described previously. By using polycarbonate containing an abnormally high residual of methylene chloride, adequate sensitivity was achieved with the small injections; as a result, the volume of water in the bottles was essentially unchanged over the lifetime of the experiment. The results for one fresh bottle and one depleted bottle, each representative of the several on which measurements were made, are presented in Figure 3. The pertinent physical characteristics of the bottles are summarized in Table I. The migration rate from the depleted bottle was slower than from the fresh bottle. These results are replotted in Figure 4 with model predictions added for comparison. In these calculations, we use the values of K and D determined in the thin-film experiments and reported earlier. The model presented earlier is valid here because the duration of these experiments is relatively short (6 weeks); on this time scale, the bottle wall is essentially an infinite slab, and therefore, what happens at the outside surface does not influence what happens at the inside surface. For longer predictions, the equations are easily modified to account for the loss of methylene chloride to the surroundings through the outside surface. Surface depletion was simulated by nu-
868 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
0
TIME (HOURS)
”’
Figure 4. Extraction results of Figure 3 with theoretical predictions added for comparison.
merical integration of eq 2 using a flat initial profile and a zero concentration outside boundary condition (ensured in this case through the use of the nitrogen sweep). The migrant concentration profile after the specified period of time for depletion was saved and then used as the initial condition for the water extraction calculation. From Figure 4,the depleted bottle results are fit nicely by the calculations. The fresh bottle migration data, however, fall below the prediction. This poor fit to the fresh bottle data can be explained in the following way. Surface depletion began in all of the bottles as soon as the well-mixed polymer was extruded, and because diffusion in polymers is strongly temperature dependent, surface depletion was very rapid at the high temperatures the polymer saw during bottle manufacture. As a result, it proved necessary to account for this accelerated aging to accurately predict migration in the bottles. In the injection blow-molding process, a “balloon” of polycarbonate called a parison was extruded a t a temperature well above the glass transition. A mold was then clamped around the parison, and the hot polymer was blown out into the mold. The mold was opened, and the bottle, then at a temperature near its glass transition, fell onto a conveyer. Some 15 min later, the bottle was cool to the touch. (It was at this point that “fresh” bottle extractions were begun, and the bottles of second group were placed in the nitrogen sweep for aging.) It was impossible to quantify the surface depletion experienced by the bottles during the complex parison blowing portion of this process. However, a reasonable estimate was made for the cooling off period of the molded bottle. A characteristic time for conduction in a 32-mil polycarbonate slab in a few seconds. (The thermal diffusivity is about 1X cm2/s.) Because the actual cool time was orders of magnitude slower than the characteristic conduction time, heat transfer from the bottles was externally controlled; therefore, the bottle wall temperature, while time dependent, was position independent. As a result of this condition, the extent of surface depletion could be readily calculated by supplying the temperature dependence of the diffusion coefficient and a bottle wall temperature history to the model. One can visualize the accelerated surface depletion in the following way. The dimensionless time increases rapidly with respect to real time when the bottle is hot and decelerates as the bottle cools due to the influence of D on the dimensionless time. After the bottle has cooled, the final dimensionless time can be used to calculate an equivalent depletion time at room temperature which
51 101 151 201 251 301 351 401 451 501 551 601 651 701 751 801 851 REAL TIME (SEC)
Figure 5. Equivalent room-temperature age of bottles as they cool from Tgto room temperature versus real time. Activation energy of diffusion is 15 kcal/mol, and bottle cool rate is exponential with 5-min time constant.
would result in the same degree of surface depletion. The final dimensionless time is given by T
=
It;
dt
D(t) is given by D = Do exp(-E/RT) (9) where T , the bottle wall temperature, is a function of time: T = T’ + (T” - T’) exp(-t/t*) (10) We assume the bottle cools exponentially from the mold temperature, T m ,to room temperature, T’, with a time constant t*. Finally the equivalent room-temperature age is found from
Here T is found from eq 8, and D is the room-temperature diffusion coefficient. For the bottles under consideration here, we assumed the mold temperature was Tg(120 O C ) and the time constant was 5 min. The diffusion activation energy is 15 kcal/mol. (We describe the experiments in which the activation energy is measured elsewhere (Stanley et al., 1989). However, this is a typical activation energy for small molecule diffusion in glassy polymers (Berens and Hopfenberg, 1982).) The equivalent room-temperature depletion time versus real time is plotted in Figure 5. It is revealing to see that depletion rate when the bottles were very hot was so great that the degree of surface depletion during the very short cool down period was equivalent to about day of depletion at room temperature. This calculation corresponds only to a portion of the manufacturing process but suggests that the effective roomtemperature depletion time of manufacture is of the order of days. Because we can quantify the surface depletion of any temperature history as an equivalent room-temperature depletion time, it seemed reasonable to fit the fresh bottle data in this way. The results for various degrees of room-temperature depletion time are shown in Figure 6. The 5-day calculations fit the data very well, and based on the above arguments, it seems very reasonable to conclude that the surface depletion experienced by these bottles during manufacture is equivalent to about 5 days at room temperature. The bottles exposed to nitrogen for 20 days before extraction testing have experienced the equivalent of 25 days of room-temperature exposure; the data for fresh and depleted bottles are shown in Figure 7
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 869 depletion effect can be considerable even for freshly fabricated parts due to accelerated migrant loss a t high temperature. Also, it is necessary to account for surface depletion in the walls of plastic packages to accurately predict the migration rate from that package. Due to rapid diffusion of migrant during manufacture, surface depletion is likely to be a significant concern.
0
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Acknowledgment
’I2 Figure 6. “Fresh” bottle data from Figure 3 with model predictions assuming 0, 0.5, 5, and 25 days of aging. TIME (HOURS)
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Literature Cited
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FREW BOTTLES X AGED EOTrLES 5 DAYS AGING
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Lorraine Rogers did most of the experimental measurements described in this paper. We appreciate her careful and diligent work. Dr. William Ward offered many helpful suggestions concerning the experimental procedures employed in this work. Also, he was kind enough to review a preliminary version of the manuscript. We are grateful for all of his help. Registry No. MC, 75-09-2; H,O, 7732-18-5.
32
’I2
Figure 7. Extraction data from Figure 6 with model predictions modified to account for effect of aging during bottle manufacture.
with calculations for 5 and 25 days of room-temperature depletion time, respectively. The agreement is outstanding. The 25-day calculations fit the depleted bottle results about as well as the 20-day calculations; the explanation is that, by 20 days, the surface is already significantly depleted, and 5 more days makes little difference. All of the “actionn occurs in the first few days. When there is uncertainty about the initial migrant profile in a polymer sample, good short-time extraction results provide a clue. If the migrant profile at the beginning of the extraction is flat, the migrant accumulation versus the square root of time is linear at short time and later decays toward an equilibrium value. If the sample was depleted, however, the migration curve exhibits an “S” shape. This short-time induction period can be indicative of surface depletion (Ayres et al., 1983). In Figure 7 , the calculations show this induction period, and the effect is more pronounced for the longer depletion time. Also, while there is a good deal of scatter in the data, both the fresh and aged bottles appear to exhibit this S shape, which is indicative of aging. Conclusions The migration rate from polymer samples exposed to air before testing so that migrant can escape from the surface region is substantially attenuated relative to that from a sample having an initially flat migrant profile. To interpret transport parameters based on a model assuming a flat initial concentration profile of migrant, great care must be exercised to ensure that a uniform profile does in fact exist in the polymer sample at the beginning of the extraction experiment. For melt-processed samples, the
Ayres, J. L.; Osborne, J. L.; Hopfenberg, H. B.; Koros, W. J. Effect of Variable Storage Time on the Calculation of Diffusion Coefficient Characterizing Small Molecule Migration in Polymers. Ind. Eng. Chem. Prod. Res. Dev. 1983,22, 86. Berens, A. R.; Daniels, C. A. Prediction of Vinyl Chloride Monomer Migration from Rigid PVC Pipe. Polym. Eng. Sci. 1976,16,552. Berens, A. R.; Hopfenberg, H. B. Diffusion of Organic Vapors at Low Concentration in Glassy PVC, Polystyrene, and PMMA. J. Membr. Sci. 1982, 10, 283. Carman, P. C.; Haul, R. A. W. Measurement of Diffusion CoeffiLondon 1954, A222,109. cients. Proc. R. SOC. Crank, J. The Mathematics of Diffusion; Oxford University Press: London, 1975. Daniels, G. A.; Proctor, D. E. VCM Extraction from PVC Bottles. Mod. Packag. 1975, April, 45. Fazio, T. FAD’s View of Extraction Testing Methods for Evaluation of Food Packaging Materials. Food Technol. 1979, April, 61. IMSL Library Manual; International Mathematical and Statistical Libraries: Houston, TX, 1979. Koros, W. J.; Hopfenberg, H. B. Small Molecule Migration in Products Derived from Glassy Polymers. Ind. Eng. Chem. Prod. Res. Dev. 1979a, 18, 353. Koros, W. J.; Hopfenberg, H. B. Scientific Aspects of Migration of Indirect Additives from Plastic to Food. Food Technol. 19798, April, 56. March, H. W.; Weaver, W. The Diffusion Problem for a Solid in Contact with a Stirred Liquid. Phys. Rev. 1928, 31, 1072. Reid, R. C.; Sidman, K. R.; Schwope, A. D.; Till, D. E. Loss of Adjuvants from Polymer Films to Food or Food Simulants. Effect of the External Phase. Ind. Eng. Chem. Prod. Res. Dev. 1980,19, 590. Reid, R. C.; Schwope, A. D.; Sidman, K. R. Modelling the Migration of Additives from Polymer Films to Food and Food Simulating Liauids. Fourth International Symposium on Migration, Ham- buig, Germany, 1983. Rudolf. F. B. Diffusion in MulticomDonent Inhomoeeneous Svstem with Moving Boundary. I. Swilling a t Const& Volume. J. Polym. Sci., Polym. Phys. 1979, 17, 1709. Rudolf, F. B. Diffusion in Multicomponent Inhomogeneous System with Moving Boundary. 11. Increasing or Decreasing Volume. J. Polym. Sci., Polym. Phys. 1980, 18, 2323. Schumann, T. E. W. The Diffusion Problem for a Solid in Contact with a Stirred Liquid. Phys. Rev. 1931, 37, 1508. 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.; Ward, W. J., 111. Measurement of Methylene Chloride Transport Parameters in Polycarbonate using a 14CTracer. Submitted for publication in Ind. Eng. Chem. Res. 1989. Till, D. E.; Ehntholt, D. J.; Reid, R. C.; Schwartz, P. S.; Schwope, A. D.; Sidman, K. R.; Whelan, R. H. Migration of Styrene Monomer from Crystal Polystyrene to Foods and Food Simulating Liquids. Ind. Eng. Chem. Fundam. 1982,21,161. Received for review July 18, 1988 Revised manuscript received January 24, 1989 Accepted February 16, 1989
