Environ. Sci. Technol. 1999, 33, 1274-1279
Correlating Solubility of Chemicals and Mixtures with Strength of Exposed High-Density Polyethylene Geomembrane WILLIAM MARTIN BARRETT, JR., PH.D., P. E.† AND RICHARD IAN STESSEL, P H . D . , P . E . , D . E . E . * ,‡ HSA Engineers, 4019 East Fowler Avenue, Tampa, Florida and Henry Krumb School of Mines, Columbia University, New York, New York 10027
Geomembranes in use as liners of landfills and other waste containment structures are subject to both chemical and mechanical attacks. The ability of the geomembrane to maintain its integrity in the face of these attacks is of major concern in the prevention of discharges from the waste disposal facility. In this work, geomembranes were subjected to simultaneous chemical exposure and mechanical loads using the comprehensive testing system (CTS). The chemicals selected were gasoline and surrogates selected on the basis of either health-based environmental concern related to the chemical’s release, or their use in ASTM (American Society of Testing and Materials) testing of rubbers exposed to gasoline. The thermodynamics of polymer-solvent interaction, expressed as cohesive energy density, was extended to binary-component mixtures and used to model the change in the mechanical performance of the geomembrane as measured by the CTS test parameter, ∆E, ∆E. It was found that a volume-fraction based thermodynamic mixing rule for the binary mixtures, consistent with regular solution theory, explained changes in the ∆E of the geomembrane. A nonlinear model provided the ability to predict ∆E as a function of the difference between the cohesive energy density of the solvent and the polymer.
Introduction Land disposal, in the form of landfills, has long been utilized for waste disposal: in recent years, the use of landfills has increased in the U.S. Groundwater contamination results from the release of leachate generated in the landfill into the underlying groundwater aquifer. Current guidance for lining municipal solid waste disposal systems suggests a double liner system with a permeability of less than 10-9 meters per second. A layer of polymeric sheet, called a geomembrane (GM), constitutes the least permeable liner layer. The ability of the liner system to provide a long-term barrier to the flow of leachate into the groundwater aquifer is currently an unresolved issue. There is evidence in the literature that exposure to other chemicals that may be present in the landfill’s leachate may increase the geomembrane’s permeability. * Corresponding author phone: (212) 854-8337; fax: (212) 8547081; e-mail:
[email protected]. † HSA Engineers. ‡ Henry Krumb School of Mines. 1274
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Under typical operating conditions, geosynthetic waste containment facility liners are exposed to a variety of chemical attacks and mechanical stresses. GMs are used to line landfills and lagoons and to underlay tanks, processing, and storage facilities to guard against environmental contamination in the event of spills or leaks. Homeowners and small-quantity generators can put hazardous waste into the municipal waste stream; container failure, matrix failure, or degradation processes may create or mobilize hazardous waste components that contact the geomembrane. As leachate can always be present on the bottom of a properly functioning landfill, the concern arises that light, or dense, immiscible fluids may be present in concentrated amounts floating on the water comprising the majority of the leachate (5). Mechanical stresses may result from placement of the geomembrane on slopes, loads applied by the wastes, machinery used in placing the wastes, and movement of the foundation materials underlying the geomembrane liner. The primary current method for testing geomembrane liners is the “Chemical Compatibility Testing of Wastes and Liner Materials, United States Environmental Protection Agency Method 9090”(1). This test is conducted by submerging the liner material in the chemical of interest for specified periods of time. At the end of the time required, a battery of standardized index tests is performed on the material. Concerns have been raised regarding the ability of these tests to simulate the actual conditions the geomembrane liners are exposed to in a landfill. The Comprehensive Testing System (CTS) was developed in response to specific criticisms of the index tests (2). The CTS allows a uniquely comprehensive approach to applying compressive load, displacement, and fluid head, all simultaneously and individually adjustable. CTS testing attempts mechanical simulation of landfill conditions combined with the introduction of fluids that may be present in landfill leachate, resulting in the ability to test the effects of chemical exposure with simultaneous loads (3). Previous geomembrane/chemical compatibility testing using the CTS showed that the CTS was greatly superior to traditional test methods, such as one-dimensional index tests and earlier multi-axial tests. The results of pure chemical testing have been correlated to polymer-solvent interaction parameters, such as cohesive energy density differences between the polymer and solvent, and solvent molar volume (4-6). This paper describes an exploration of the effects of chemical mixtures representing gasoline wastes on geomembranes. Because of its clear dominance in lining of landdisposal facilities, high-density polyethylene (HDPE) was chosen for evaluation.
Background Polymer usefulness is dependent on the ability of the polymer to survive the environment in which it is placed. Diffusion of solvents into the polymer is related to the thermodynamics of dissolution and mobility of polymer and solvent molecules. This section discusses the thermodynamics of polymersolvent interactions. Thermodynamics of Polymer Solutions. The solubility of a solvent in a polymer can be determined from thermodynamic considerations. For a solvent to be miscible in a polymer, the Gibbs free energy of mixing must be negative, or:
∆Gmix ) ∆Hmix - T∆Smix < 0
(1)
where ∆Gmix is the free energy of mixing, ∆Hmix is the enthalpy 10.1021/es980616c CCC: $18.00
1999 American Chemical Society Published on Web 03/05/1999
of mixing, T is temperature in degrees Kelvin, and ∆Smix is the entropy of mixing. The enthalpy of mixing is based upon regular solution theory, which states that the mixing enthalpy is calculated from the interaction of contacting atoms. In the case where molecular interactions such as hydrogen bonding are present, ∆Hmix is proportional to the difference in the squares of the values of the Hildebrand solubility parameters for the solvent and polymer, δ1 and δ2, respectively. The value of (δ1 - δ2)2 or δ2 is the cohesive energy density (CED), which is the ratio of the molar energy of vaporization, ∆E, to the molar volume, V:
δ2 )
δ )
δ2d
∆E V
+
δ2p
(2)
+
δ2h
(3)
The values of δd, δp, and δh are the cohesive energy density components due to dispersive, polar, and hydrogen bond interactions, respectively. To determine the degree to which a liquid is a solvent, the distance from the solvent’s cohesive energy density to that of the polymer, RA, is calculated as follows:
RA2 ) (2δd,P - 2δd,S)2 + (dp,P - δp,S)2 + (δh,P - δh,S)2 (4) The subscripts P and S refer to the polymer and solvent, respectively (8). Thermodynamics of Multiple Component Systems. The simplest method to determine the effect of multiple components on the behavior of a fluid is to determine the properties of the fluid relative to a reference state and then the departure of the actual mixture’s properties from the properties of the reference state. The reference state is the state in which the thermodynamic properties are reasonably well-known, such as pure components. The thermodynamics of single-solvent adsorption are described above. In multiplesolvent systems, the chemical equilibrium between the solvent liquid and solvent sorbed into the polymer needs to be determined. The requirements for equilibrium between these two phases are (i) the pressure must be the same in both phases, (ii) the temperature must be the same in both phases, and (iii) the partial-molar Gibbs free energy of each component must be the same in each phase (9). The ideal-mixture model for the partial-molar Gibbs free energy for a mixture of chemicals states that the partialmolar Gibbs free energy is determined from the pure chemical’s molar Gibbs free energy (Gi) and the mole fraction of the material in the mixture (xi),
( ) ϑGi ϑNi
ideal
( ) ( ) ϑGi ϑNi
-
real
) Gi,pure + RT ln xi
(5)
where R is the ideal gas constant, Ni is the number of moles of solvent present, and T is the absolute temperature in Kelvin. The difference between the mixture’s actual partial-molar Gibbs free energy and the ideal mixture’s estimate of the partial-molar Gibbs energy is called excess partial-molar Gibbs energy, Giex
ϑGi ϑNi
(6)
ideal
Excess properties are typically complicated, nonlinear functions of composition, temperature, and pressure of the mixture, and are usually obtained experimentally (9). The excess partial-molar Gibbs free energy is typically expressed as an activity coefficient, γi. The activity coefficient is defined as:
ln γi )
The molar energy of vaporization is the energy that holds the molecules together and is therefore a measure of the intermolecular energy. Because the (δ1 - δ2) term is squared, the difference between δ1 and δ2 always contributes significantly to a positive ∆Hmix and must be balanced by a greater value in the entropy term. The CED is a measure of the strength of the secondary bonds in a polymer (8). Hansen (1967) recognized that several different interactions exist between the polymer (7): 2
Giex )
Giex RT
(7)
Regular solution theory assumes that the excess volume of mixing is zero, and the cohesive energy density is strictly that of the solvent components, whereupon the excess partialmolar Gibbs free energy of the mixture is given by:
Gex ) (x1V1 + x2V2) Φ1Φ2[δ1 - δ2]2
(8)
where Φi is the volume fraction of the ith species. When differentiated with respect to mole fraction one obtains:
RT ln γ1 ) V1Φ22[δ1 - δ2]2
(9)
RT ln γ2 ) V2Φ12[δ1 - δ2]2
(10)
after substitution of eq 7. Regular solution theory provides a means to determine the activity coefficient and, therefore, the interactions between the solvents in the mixture. These are based on parameters already known, the solubility coefficient and molar volumes of each solvent, as well as the parameter varied in this experiment, concentration of each solvent in the mixture. To evaluate the effects of binarychemical exposure on an HDPE geomembrane, the values of each of the components of the CED of the mixture was determine using a volume-fraction weighted average of the individual components of the CED. This mixture CED was used to determine the value of the solubility of the chemical in the polymer, RA, using eq 4. Once these values of solubility were determined, they were used to model the effect of a mixture of chemicals on the geomembrane. Chemicals Tested. Motor vehicle fuels represent a major source of environmental contamination and, therefore, were the primary subject of this study. This work focused on gasoline, testing one commercial gasoline against surrogate mixtures. Surrogates were used to permit mixtures to be analyzed on the basis of known composition, where a gasoline’s composition is very complicated, including proprietary additives. Binary mixtures reduced the variables analyzed to allow different concentrations of the same chemicals. The surrogates chosen represented key constituents and echoed gasoline components that are of environmental concern. Under ideal-solution conditions, an appropriate measure of material strength should vary linearly with concentration from each of the two pure-component values. ASTM (American Society of Testing and Materials) tests rubbers used with gasoline-powered engines (ASTM D-471) using five standard reference fuels, listed in Table 1. These fuels are binary mixtures of 2,2,4 trimethyl pentane (isooctane) and toluene. Pure isooctane (fuel A) and pure toluene (fuel B) are included. In addition to their common use as a test for chemical compatibility, this test-fuel series inherently comprised a two-component mixture, allowing evaluation of the thermodynamic effects of a mixture on the geomembrane by varying relative concentrations. The U.S. EPA typically considers gasoline to be composed of volatile aromatics, primarily benzene, ethylbenzene, VOL. 33, NO. 8, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Composition of Test Fuel Mixtures composition (percent by vol) fuels
2,2,4 trimethyl pentane (isooctane)
toluene
xylenes
ASTM D-471 fuel A ASTM D-471 fuel B ASTM D-471 fuel C ASTM D-471 fuel D ASTM D-471 fuel E O-X A O-X B xylenes
100 70 50 40 0 70 30 0
0 30 50 60 100 0 0 0
0 0 0 0 0 30 70 100
FIGURE 2. Stress-strain plot for geomembrane subjected to cyclic loading by the CTS.
FIGURE 1. Comprehensive testing system. toluene, and xylenes (BTEX). This view of gasoline is based on health considerations, as these compounds are either known or suspected human carcinogens. As stated above, gasoline is significantly more chemically complex than this health-based view implies. Additionally, future gasoline blends will contain less of these aromatic compounds because of health effects. To further investigate the thermodynamic considerations, two additional mixtures of pure chemicals were tested, 30% xylenes with 70% isooctane (O-X A), and 70% xylenes with 30% isooctane (O-X B). Baseline data required also testing pure xylenes, simply shown as such in Table 1. Xylenes were selected on the basis of their past performance in pure chemical geomembrane testing using the CTS: xylenes had the least effect on the geomembrane (highest retention of strength) of the aromatic compounds tested (benzene, ethylbenzene, toluene, and xylenes) (4). The standard American Chemical Society reagent-grade mixture was employed in both tests, for several reasons: gasoline contains a mixture of xylenes; their structure would indicate similar behavior; quick calculation of CED2 (MPa) showed very similar results for all three isomers (95.09, 97.95, and 94.35 for m-, o-, and p- isomers, respectively) compared to the other materials (105.0 for toluene and 65.79 for isooctane) (10,11). Distilled, deionized water was used as a control. Water was selected because, as a liquid, it might have been hoped that it would provide fluid mechanical properties similar to the organic fluids, unlike use of a gas (air), which would provide negligible lubrication within the granular media.
Experimental Method, Materials, and Techniques of Analysis A simplified drawing of the configuration of the CTS test unit is shown in Figure 1. The CTS consisted of a test cell filled with granular media designed to apply loads to the geomembrane through pistons mounted on a compression tester 1276
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capable of applying cyclic loads. The granular media were intended to mimic soil, but glass beads were employed to minimize the physical damage caused by less-spherical natural soils, such as sand, which tend to impress points into the sample. A key objective of the CTS development was to enable evaluation of a sample’s behavior when exposed to a chemical in a manner similar to field conditions, but without causing physical damage to the sample due to shear or penetration. Details of its design, configuration, and breadth of application are available elsewhere (6,12). Geomembrane Test Samples. The geomembrane liner samples tested were 1.5 mm (60 mil) thick HDPE obtained from GSE Lining Technology, Inc., of Houston, TX. To reduce variation, test samples were obtained from the same roll of HDPE. For CTS testing, samples 40 cm × 40 cm (16 in. × 16 in.) were cut from this roll. Samples were inspected for surface imperfections that might lead to undesired modes of failure during testing. Test Chemicals. The chemicals used to evaluate the geomembranes in this project were obtained from Fischer Scientific, Inc. and met American Chemical Society certification. The gasoline used was Shell Oil Company super unleaded grade, 93 octane, obtained from a Shell Oil Company retail outlet. The ASTM reference fuels were created by mixing the appropriate quantities of pure isooctane with toluene to make four liters of reference fuel. CTS Testing. The CTS used an MTS Systems Corporation, Inc. (MTS) load frame and hydraulic ram. The cyclic displacement of the ram was controlled by MTS's function generator. Tests involved attainment of an initial displacement, to which was added cyclic displacements. The total manual initial displacement was 3.81 cm (1.50 in.), and the cyclic displacement was 2.54 cm (1 in.), resulting in a maximum total displacement of 6.35 cm (2.5 in.). The displacement and displacement rate chosen were developed in earlier range-finding testing (12). The displacement rate is the fastest of the increments tested below the rate at which catastrophic sample failure occurred during early time; below that rate, test results were substantially similar. The system was assembled as shown in Figure 1. Separately, 2 L of chemical were loaded into a pressure vessel under a fume hood. The vessel was then brought to the CTS, connected to the top of the cell and regulated air pressure. By opening a valve, the chemical flowed into the top of the CTS, stopping when it appeared in the outlet pipe. The test was then begun. Strain in the GM as a function of applied stress is shown in Figure 2. After a few cycles, the system reached steady state, where the loads (stresses) resulting from the displacement (strains) were relatively constant. Tests ran for 4000 seconds, or approximately 1 h; the sample was thus exposed to 48 cycles, or 43 cycles after the completion of ramping.
TABLE 2. Comprehensive Testing System Data by Chemical ∆E (MPa) chemical
trial 1
trial 2
trial 3
benzene ethylbenzene gasoline reference fuel A (iso-octane) reference fuel B reference fuel C reference fuel D reference fuel E (toluene) 70% isooctane + 30% xylenes 30% isooctane + 70% xylenes water xylene
32.77 21.96 26.81 50.47 45.77 46.69 44.60 30.26 49.19 45.35 35.20 47.35
27.18 24.73 23.09 53.38 49.91 48.26 45.03 30.07 43.39 45.99 37.09 49.82
31.62 19.16 30.80 54.43 47.45 42.33 39.54 35.62 53.15 47.80 30.41 45.77
The ∆E, ∆E, was defined to describe the mechanical response of the system:
∆E )
(σmax - σmin) (max - min)
(11)
where σ and are the stress and strain (5). The ∆E provides a single-parameter measure of the material’s elasticity/ plasticity and strength as revealed under cyclic loading. Analysis of variance (ANOVA) of the ∆E data was conducted to determine if statistically significant differences in geomembrane performance were present. These differences would be the result of the chemical exposure. The data were sorted by chemical, and post-hoc tests were conducted using the Tukey wholly significant differences (WSD) method, a single analysis sufficient to determine whether statistically significant differences between treatments existed for a balanced data set (13). Nonlinear regression techniques were used to model ∆E as a function of RA.
Results The calculated values of ∆E are listed in Table 2. Box plots of the ∆E data are shown in Figure 3. The highest ∆E observed was for isooctane (reference fuel A), followed by xylenes. As shown in Figure 3, gasoline’s mean ∆E was lower than all but ethylbenzene. Water, the control, had a ∆E that was in the middle of the range of values observed (34.23 MPa). The fact that the control had a ∆E below some test chemicals indicated that water may affect the granular media differently than the organic compounds. Water’s polarity and ability to form hydrogen bonds is known to increase the friction angle of soils, that is, it increases the load-bearing capacity of soils. Thus, an additional area for investigation would be the effect of a liquid on the particle mechanics and friction of a multiaxial test system. ANOVA showed that differences between ∆E for 36 of the 60 pairs of chemicals were significant at a confidence level of 95%. The ∆E of mixtures of isooctane with toluene and isooctane with xylenes were between the ∆E of the pure components. Performance Modelling. A nonlinear model was employed to fit the ∆E data from all of the test chemicals except water to the value of RA2. The model selected assumed that the ∆E was a maximum when the chemical was not soluble in HDPE (RA2 f ∞), decreasing to 0 MPa when the chemical’s RA2 ) 0 (when the chemical’s cohesive energy density was equal to that of polyethylene). Water was excluded from the analysis because of the suspicion that its usefulness as a control may have been compromised, as discussed above. The value of RA2 for each chemical was calculated from the volume fraction weighted averages of the components of the CED, listed in Table 3 (8,14), using eq 4. This model allowed
FIGURE 3. Box plot of ∆E by chemical tested.
TABLE 3. Cohesive Energy Densities and Solubility (RA2) for High Density Polyethylene and Tested Chemicals (8) δd (MPa)1/2 δp (MPa)1/2 δh (MPa)1/2 RA2 (MPa)
compound HDPE benzene ethylbenzene toluene xylenes reference fuel A reference fuel B reference fuel C reference fuel D reference fuel E 70% isooctane + 30% xylenes 30% isooctane + 70% xylenes gasoline (14) water
17.6 18.4 17.8 18.0 17.8 14.3 15.4 16.2 16.5 18.0 15.35
0.0 0.0 0.6 1.4 1.0 0.0 0.4 0.7 0.8 1.4 0.3
0.0 2.0 1.4 2.0 3.1 0.0 0.6 1 1.2 2.0 0.9
6.6 2.5 6.6 10.77 43.56 19.7 9.9 6.8 6.6 21.2
16.75
0.7
2.2
8.1
16.80 15.6
0.59 16.0
1.11 42.3
4.2 1239
∆E to approach a steady value for the insoluble chemicals tested, decreasing in an exponential manner as the solubility of the solvent in the polymer increased, as shown in Figure 4. The resulting equation, using data from the pure and binary mixtures tested, was:
∆E(RA2) ) ∆Emax(1 - exp-kRA2)
(12)
where ∆E(RA2) is the value of ∆E as a function of solubility, ∆Emax is the maximum value approached as the solubility decreases, and k is a constant. The value of ∆Emax was 51.02 MPa and k was 0.203 MPa-1. The correlation coefficient was 0.989, indicating that a chemical’s solubility and the resulting ∆E for that chemical were strongly related. The more soluble the chemical was in the polymer, the lower the resulting ∆E value observed from testing that chemical. This showed that a geomembrane’s performance could be explained in terms of the interactions between polymer and solvents present in the landfill, as measured by RA2. VOL. 33, NO. 8, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Plot of ∆E as a function of solvent solubility in polyethylene.
Discussion Chemical interactions occur when the effect of a mixture of chemicals is found to differ from the effects of the individual chemicals. The analyses of ∆E as a function of solubility included both the pure components and the mixtures of chemicals. This analysis showed that mixtures of isooctane with xylenes and mixtures of isooctane with toluene behaved in a way that could be predicted on the basis of the volume fraction of the pure component in the mixture. The mixtures of toluene and isooctane had ∆E having intermediate values between those of the two pure components. Further, as the volume fraction of isooctane increased in the mixture, so did the ∆E. This trend was apparent for mixtures of xylenes and isooctane as well. These effects could be correlated to the value of RA2 for the polymer-solvent system, regardless of whether a pure solvent or a mixture of chemicals was used. The correlation coefficient for the relationship was 0.989. The value of the correlation coefficient confirms the suitability of the relationship between the solubility of the chemical in the polymer to the effect of the chemical on the mechanical properties of the geomembrane as measured by ∆E. It was expected that gasoline might bear little relationship to the component materials tested; only ethylbenzene had a greater effect on HDPE than any other component tested. Using the composition techniques to determine RA2 for gasoline, the result was 29 MPa, compared to the test result of 27. The gasoline components in the test fuels comprised only approximately 31% of gasoline, so the correspondence with the result shown in Figure 3 is surprising. However, the conclusion would be that the compounds used to represent gasoline are somewhat relevant to the risk of release into the environment, using the technique presented. Straying further afield, a similar calculation with motor oil, having given a test result of 45, produced a calculated result of 51; motor oil’s components are still more different from those tested. Other materials that have CEDs greatly different from those evaluated in this work fall outside the limits set for this model; different parameters would have to be determined. In particular, it has been noted in other work that chlorinated solvents act differently, with mechanisms yet to be determined. The use of a simple mixing rule, the volume fraction of pure organic chemicals in the mixture, that allows a rapid 1278
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determination of which chemicals were expected to have the greatest impact on the properties of a geomembrane has the potential to streamline the testing needed to evaluate a waste for compatibility with a proposed geomembrane. For example, when a new waste is to be introduced into a landfill, use of a linear mixing rule to determine the additional effect that the new component would have on the geomembrane would greatly streamline the determination of the overall effect of placing that waste into the landfill on the geomembrane liner. The average ∆E of gasoline was statistically significantly below all chemicals except benzene and ethylbenzene. All of the mixtures of toluene and isooctane used by ASTM to simulate the effects of gasoline had ∆E greater than gasoline. Gasoline is a complex mixture of a variety of organic chemicals, including the aromatic and aliphatic hydrocarbons that were tested in this project, as well as olefins and polynuclear aromatic hydrocarbons. For the hydrocarbons present in gasoline, the effects of chemical exposure should be additive as was the case for the binary mixtures explored in this work. The gap of over 2 MPa indicated that chemicals were present in gasoline that had a greater effect on the performance of the geomembrane than the chemicals traditionally considered based upon health effects. Nevertheless, the chemicals tested were the largest constituents of gasoline. The implication is that chemicals present in quantities of less than 5% might have an effect on the performance of the geomembrane containment structure. Furthermore, examination of RA2, given the relationship to geomembrane strength shown here, shows that the chemicals viewed as most deleterious to health, such as the known carcinogen benzene, may not be the most responsible for the escape of that known carcinogen. The chemicals responsible for release of toxic chemicals may not be the same as the chemicals with adverse health effects. A key conclusion, however, is that this model was developed with a limited set of compounds used to represent one multicompound material of concern in land disposal: gasoline. There are many other compounds of concern, and other constituents of concern. For this model to evolve, there must be both additional testing and chemical effects parameter development for materials that may act in different manners; chlorinated solvents are a key example. Finally, although HDPE dominates the liner industry, there are other suitable materials that remain to be tested; without their evaluation, it cannot be determined at this time if this model is suitable to other polymers.
Literature Cited (1) (1) “Compatibility Test For Waste and Membrane Liners, Method 9090”; SW-846. In Test Methods for Evaluating Solid Waste, 3rd ed.; U.S. Environmental Protection Agency; U.S. Government Printing Office: Washington, DC, 1992. (2) Stessel, R. I.; Goldsmith, P. J. Air Waste Manage. Assoc. 1992, 42 (9), 1178. (3) Barrett, W. M. Ph.D. Dissertation, University of South Florida, Tampa, FL, 1998. (4) Barrett, W. M.; Stessel, R. I.; Fetterly, F. A. J. Air Waste Manage. Assoc., Submitted for publication. (5) Stessel, R. I.; Hodge, J. H. J. Hazard. Mater. 1995, 42 (3), 265. (6) Stessel, R. I.; Barrett, W. M.; Li, X. J. of Appl. Polym. Sci. 1998, 70 (11), 2097. (7) Hansen, C. M. Ph.D. Dissertation, Danish Technical Press: Copenhagen, 1967. In Gedde, U. W. Polymer Physics; Chapman and Hall: London, 1995. (8) Gedde, U. W. Polymer Physics, Chapman and Hall: London, 1995. (9) Sandler, S. I. Chemical and Engineering Thermodynamics; John Wiley and Sons: New York, 1997. (10) Majer, V.; Svoboda, V. Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation; Blackwell Scientific Publications: Oxford, 1985. In http://webbook.nist.gov/chemistry.
(11) Tsonopoulos, C.; Ambrose, D. J. Chem. Eng. Data 1995, 40, 547. In http://webbook.nist.gov/chemistry. (12) Stessel, R. I. Paper 97-MP25.03. In Proceedings of the Annual Meeting of the Air & Waste Management Association; Air and Waste Management Association: Pittsburgh, PA, 1997. (13) Miller, R. In Encyclopedia of Statistical Sciences; Kotz, S., Johnson, N. L., Eds.; John Wiley and Sons: New York, 1982; Vol. 5, pp 679-689.
(14) Cline, P. V.; Delfino, J. J.; Rao, P. S. C. Environ. Sci. Technol. 1991, 25, 914.
Received for review June 16, 1998. Revised manuscript received January 22, 1999. Accepted January 26, 1999. ES980616C
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