162
Ind. Eng. Chem. Prod. Res. Dev. 1985, 2 4 , 162-166
Structure Solubility Correlations: Organic Compounds and Dense Carbon Dioxide Binary Systems Dlleep K. Dandge,’ John P. Heller, and Kennard V. Wilson New Mexico Petroleum Recovery Research Center, New Mexico Institute of Mining and Technology, Socorro. New Mexico 8780 1
The solubilities of several organic compounds in dense carbon dioxide (both liquid and supercritical) have been determined. Our data supplements earlier work by Francis. Based on these two sets of data,the structural features that either limit or enhance the solubility of different groups of compounds are identified. By use of this approach, some general structure-carbon dioxide solubility relationships have been developed and are illustrated by examples in the case of hydrocarbons, alcohols, phenols, aldehydes, ethers, esters, amines, and nitro compounds. These relationships can be used in qualitative predictions about the solubilities of substances in carbon dioxide; such information would be useful in enhanced oil recovery operations, supercritical fluid chromatography,and supercritical fluid extraction.
Introduction The use of dense (referred to in this paper for both liquid and supercritical states) carbon dioxide (C02)as a solvent is rapidly increasing in such important areas as enhanced oil recovery (EOR) (Orr et al., 1982; Holm and Josendal, 1982; Stalkup, 1983), supercritical fluid chromatography (SFC) (Giddings et al., 1968; Lauer et al., 1983; Wasen et al., 1980), and supercritical fluid extraction (SFE) (Paulaitis et al., 1983; Schneider et al., 1980). The critical temperature of COPis 31.04 OC and its critical pressure is 1070.6 psi. The solvent properties of supercritical C02 generally increase as a function of increasing density. It is the authors’ conviction, in fact, that the solubilities depend primarily on COz density, with the actual temperature above or below the critical value of 31.04 “C being irrelevant (to first order, at least, and except for solutes with a phase change near that temperature). Similarly, we expect the observed pressure dependence of solubility to be basically a density dependence. Therefore, it is important to employ the right conditions of temperature and pressure for the efficient extraction of a given substance. As EOR, SFC, and SFE processes work on this basic principle of effective extraction of the components, it is valuable to have prior knowledge of the solubilities of various chemicals in dense COP. Three decades ago, Francis (1954) reported the mutual solubilities of liquid carbon dioxide with each of 261 different substances. Despite the wealth of data obtained, Francis only briefly discussed the effect on solubility of the structure of a compound. Based both on Francis’ data on binary systems and additional data obtained in this laboratory, we have developed certain structure-solubility correlations in organic compounddense COPsystems. Our findings are reported here. Experimental Section Materials. Most of the chemicals used in this work were obtained from Aldrich Chemical Co. and were tested for solubility in COz without further purification. The C02 used was 99.99% pure. Solubility Measurements. The details of the design and function of the apparatus used in these experiments have been described in a paper (Heller et al., 1983) which explored the possible use of COP-soluble polymers as “direct thickeners” for mobility control in the displacement of oil from porous rock in reservoirs. For the convenience of the reader, a schematic of the apparatus is shown in 0196-4321/85/1224-0162$01.50/0
Figure 1, and a brief description is included below of the procedures followed to measure the solubilities of organic compounds in dense COP. The apparatus consists of three parts which correspond to the steps of the measurement procedure. The three parts are a mixing chamber, a means for transferring a known volume of solution to an assay chamber without appreciably lowering its pressure, and the assay chamber itself. The sample is initially placed in the mixing chamber which consists of a thick-walled, single-crystal sapphire tube (manufactured by Tyco Saphikon Division, Milford, NH) that also contains a Teflon-covered magnetic stirring bar. The sapphire tube is connected at each end by demountable seals to a high-pressure stainless steel tubing flow system. After initial evacuation or purging of this system to remove air, pure COP is condensed and then forced into the mixing chamber by a syringe pump. After this chamber containing the sample and COz has been isolated by valves, stirring is accomplished by mechanically moving an external magnet system up and down around the vertically oriented sapphire tube. The entire apparatus is operated inside a temperature-controlled water bath. After a time sufficient to achieve saturation, a known amount of the solution is transferred to an assay chamber that consists of a test tube of 100-mesh glass beads enclosed in a separate pressure chamber. Prior to the transfer, the assay tube is filled with nitrogen gas at the pressure of the experiment. The annular space in the assay chamber is connected to a second syringe pump also containing nitrogen at high pressure. This pump is operated in reverse, as the transfer is accomplished by displacement of the solution from the sapphire tube with fresh C02from the first syringe pump. (The COPpath during transfer is indicated by a double arrow in Figure 1.) By this means, the total pressure within the system can be kept constant while the known volume of solution (of sample in dense COz) is introduced through a needle tube into the lower end of the test tube of glass beads. After the transfer of enough of this solution to bring the COP-nitrogen interface within a centimeter or so of the top of the beads, the transfer valve is closed, and the chamber is isolated from both the COPand N2systems. The assay chamber can now be depressurized through a valve connected to the annular space around the test tube. As first the nitrogen and then the COPleaves the chamber, the dissolved sample precipitates (or condenses) onto the glass beads in the test tube. After the pressure has been reduced to atmospheric, the 0 1985 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 1, 1985 163 TO ATMOSPHERE OR )VACUUM PUMP T HER MOSTATTE D WATER BATH
ASSAY
CHAMBER
NEEDLE TUBING T E S T TUBE F I L L E D w/GLASS BEADS
US1 RE
STIRRING MAGNET {o */EXTENSION ATMOSPHERE
PRESSURE TRANSDUCER
U
NITROGEN
BOTTLE
o-.
-3-
C 0 2 f l o w p o t h during initial loading
+-
COP
f l o w p o t h during t r a n s f e r
BOTTLE
Figure 1. Apparatus to measure solubility in dense COz. Table I. Approximate Operational Pressure-Temperature-Density Ranges for COz in Various Auulications pressure COz, density range, psi range, g/mL application temp range, "C EOR 24-95 1000-3500 0.5-0.95 SFC 35-70 2100-3200" 0.5-0.9 SFE 32+ 1200-7500 0.4-1.1 "The operational pressures are given here. Much higher pressures (up to 60000 psi) have been used (Giddings, 1968).
assay chamber is opened, and the test tube, glass beads, and needle tubing subsystem are weighed to determine the quantity of sample which had been carried over in the dense COP As in many laboratory procedures, proper attention must be given to safety considerations which are here made more stringent by the high pressures at which the experiments are performed. Because the compressibility of dense C 0 2 in the density range of the experiment is greater than that of water by a factor of about 10, the closed system utilized here is not so sensitive to small changes of volume (or of temperature) as might be expected. At the same time, the expansion ratio of the COz between 2500 psi and atmospheric pressure indicates a considerable explosion hazard. Thus, manipulations must be performed with care and with close attention to the pressure measurements. We have found, however, that a sudden and unpredictable fracture of the sapphire mixing chamber was the principal failure mechanism (in earlier work, when only thinnerwalled tubes were available). Even on those occasions, the cylindrical water bath made from thick polycarbonate material successfully contained the fragments from the tube, although a secondary shield constructed of sheet polycarbonate plastic surrounding the bath provides further reassurance. Results and Discussion Table I describes operational ranges of density, temperature, and pressure for COz in EOR, SFC, and SFE processes. Francis (1954) obtained the solubilities in C 0 2
Table 11. Solubilities of Organic Compounds in Dense C 0 2 solubility, w t 9b 25' C, 32 "C, compound 2500 psi 2500 psi benzoic acid 0.4 miscible miscible decanoic acid 0.03 2,6-dihydroxybenzoic acid 0.9 1.0 2,6-dinitrophenol 5.9 2,6-dinitrotoluene 17.9 di(o-xyly1)ethane miscible miscible ethyldodecanoate miscible miscible 2-fluorophenol 21.1 o-methoxyphenol insoluble insoluble 1,a-benzenediol 0.04 (Z)-butenedioic acid miscible miscible 2-methyl-3-hexanol miscible miscible 2,2-dimethylpropanoic acid 12.9 2-nitroacetophenone miscible miscible 2-nitrobenzaldehyde miscible miscible o-nitrophenol 0.2 p-nitrophenol miscible" miscible" pyrrole salted out pyrrolidine 2,6,10,14-tetramethylpentadecane miscible miscible miscible 2,4,4-trimethyl-l-pentanol miscible
" See text under "Amines". at 25 "C and 955 psi ( p = 0.71 g/mL). Table I1 describes the solubility data obtained in this laboratory at either 25 O C and 2500 psi ( p = 0.895 g/mL) or 32 O C and 2500 psi ( p = 0.86 g/mL). The solubilities are expressed in weight percent of a substance in COz at a given condition of temperature and pressure (density). An increase in C 0 2 density is only likely to increase the solubility of a compound, except perhaps under extreme pressure conditions, and hence the maximum limit on weight percent solubility of a given compound would vary with changes in CO, density. However, the trends in the relationship between structure and solubility would remain similar to those developed here. The effect of change in the temperature at constant density on the solubility of substances in CO, has not been taken into consideration in the following discussion. McHugh (1980) has shown that the temperature has a pronounced effect on the extraction of naphthalene only in the narrow region where the equilibrium shifts from solid-dense fluid to liquid-dense fluid. Thus, it is only in this region that the physical properties of a substance would be expected to have a substantial influence on the process of extraction. The organic compounds have been classified on the basis of their chemical nature and/or functional groups present. In each class, it is shown how changes in structure influence the solubility behavior in CO,. Examples follow in support of each such generalization. In the following discussion, "miscible" is used to represent the phrase "miscible in all proportions" in dense C 0 2 , and "soluble" to describe the percent solubility in dense COz. "Insoluble", on the other hand, means that the solubility in dense C 0 2was not detectable in our apparatus under the experimentalconditions used. This detectability limit is estimated at approximately 0.05 wt % . Hydrocarbons The knowledge of the miscibility of various hydrocarbons with C 0 2 has been of utmost importance in EOR with COP. A considerable amount of literature is available on both binary (Reamer, 1963) and ternary (Orr et al., 1982) (also pseudoternary) systems involving various hydrocarbons and carbon dioxide. In the case of normal alkanes, complete miscibility exists between carbon dioxide and alkanes with carbon number
164
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 1, 1985
12 and below. As the carbon number increases beyond 12, the miscibility continues to decrease rapidly. This is evident from the fact that n-dodecane is miscible while ntetradecane, n-hexadecane, and n-octadecane have solubilities of 16, 8, and 3%, respectively. Alkenes behave almost similarly except that unsaturation has some favorable effect. For a given carbon number, the solubility of an alkene seems noticeably higher than that of the n-alkane. 1-Octadeceneis 10% soluble while n-octadecane is 3% soluble. The iso- or branched alkanes are comparatively more soluble. The maximum limit of complete miscibility is between 19 and 30 carbon atoms as against 12 in normal alkanes. 2,6,10,14-Tetramethylpentadecane(CI9isoalkane) and other lower isoalkanes studied are miscible while squalane (C30isoalkane) is only partially miscible. An explanation for the increased solubility of isoalkanes over normal alkanes could be offered based on a paper by Hildebrand (1978). According to this, "A methyl group in a saturated hydrocarbon has three [SP3(C)-S(H)] bonds and one [SP3(C)-SP3(C)]bond, while a methylene group has two [SP3(C)-S(H)] bonds and two [SP3(C)-SP3(C)] bonds. Since electron density is considerably higher in C-C bond regions, intermolecular forces between molecules containing a number of exposed methylene groups will be correspondingly higher than those between molecules containing an equivalent number of exposed methyl groups". Thus, an increase in the number of methyl branches reduces the number of methylene groups along the hydrocarbon chain. This in turn diminishes the magnitude of intermolecular interactions in isoalkanes and imparts lower solubility parameter values. The end result, as seen, is increased solubility in dense C02,the solubility parameter of which is approximately 6 (Potter, 1982) under present experimental conditions. The generally observed lower melting and boiling points of the branched alkanes as compared to the normal alkanes are also reflective of the decreased intermolecular interactions due to branching. As has been pointed out by Francis (1954), dicyclic hydrocarbons are incompletely miscible whether they are naphthenic (cycloalkanes) or aromatic. The only dicyclic compound reported to be miscible is indene. We are still searching for more dicyclic compounds soluble in COP. In case of dicyclic compounds, increasing hydrogenation increases the solubility. Naphthalene (2%) < tetralin (12%) < decalin (22%). This is also evident from the solubilities of cyclohexylbenzene (8%) and biphenyl (2%1. The favorable effect of methyl substitution in dicyclic aromatic compounds can be seen by comparing the solubilities of diphenyl methane (4%) and [ 1,l-di(o-xyly1)ethane] (16%). Also, solubilities of a-methylnaphthalene (6%) and @-methylnaphthalene(9%) are higher compared to naphthalene (2%). An interesting comparison done by Francis (1954) takes into account the boiling points of the substances. He observed that carbon dioxide is incompletely miscible with both dicyclic naphthenic and aromatic hydrocarbons but mixes completely witth aliphatic or monocyclic hydrocarbons in the same boiling range as dicyclics. These latter include dodecane (bp 215-217 "C); p-di-tert-butylbenzene (bp 236 "C), 2,2,4,4,6,8,8-heptamethylnonane (bp 240 "C) which are miscible, while naphthalene (bp 218 "C), tetrahydronaphthalene (207 "C) and biphenyl (255 "C) are only partially soluble. We believe that chemical structure of a molecule rather than physical constants plays a larger role in such systems. As far as the solubility of monocyclic aromatic and naphthenic hydrocarbons is concerned, similar rules as ob-
served in normal and branched alkanes would be expected to apply. Branching on the side chain in such compounds promotes solubility. For example, p-di-tert-butylbenzene (C14)and 1,3,5-tri-tert-butylbenzene (C18)are miscible. However, a preliminary test in our laborabory has shown that 1-phenyldecane (C16)is only partially soluble in COz. The effect of halogen substitution in the a position in toluene is somewhat different. While (dichloromethy1)benzene is miscible, (trichloromethy1)benzenehas only 2 % solubility. Chlorine substitution on the aromatic ring has no effect on solubility in either direction. Both chlorobenzene and dichlorobenzenes are soluble.
Hydroxyl Compounds Alcohols. In primary alcohols, increasing the carbon chain length beyond 6 carbon atoms results in tremendous decrease in the solubility. n-Hexyl alcohol and other lower alcohols are miscible while n-heptyl alcohol and n-decyl alcohol have solubilities of only 6% and 1%. This is parallel to the solubility behavior of alcohols in water where n-propyl and lower alcohols are solubie, while n-butyl alcohol is soluble to the extent of 7.4%; n-pentyl, 1.96%; n-hexyl, 0.99% (Morrison and Boyd, 1980). As in the case of hydrocarbons, branching in primary alcohols helps to increase their solubility in dense C02. 2-Ethyl-1-hexanol (C,)has 17% solubility,and 2,4,4-trimethyl-l-pentanol (C,) is miscible. In the case of short-chain diols and triols, solubility is completely altered by either complete or partial etherification. In the case of partial etherification, all but one hydroxyl group per molecule need to be etherified to attain C 0 2 miscibility. Ethylene glycol and glycerol have solubility of 0.2% and 0.5%,respectively, while their di- and trimethyl ethers are miscible. Also, 0-methoxyethanol, 6-ethoxyethanol, and diethyleneglycol monomethyl ether are all soluble. Phenyl-substituted primary alcohols tend to dissolve less. Benzyl alcohol and 2-phenylethanol have 8% and 3 % solubility, respectively. Since branching helps to increase the solubility of primary alcohols, secondary and tertiary alcohols with a carbon number of 7 or above would be expected to be more soluble than n-heptyl alcohol. Indeed, this is evident from the fact that 2-methyl-3-hexanol is miscible. The data on cyclic alcohols are meager, although solubilities of cyclohexanol and 4-methylcyclohexanol have been reported to be only 4%. Phenols. As in alcohols, etherification of a phenolic-OH group markedly increases the solubility of a compound. Phenol is 3% soluble while anisole is miscible. The nature of a substituent group and its position have enormous effect in changing the solubility of phenolic compounds. Both chloro and nitro substituents in ortho to hydroxyl group give completely miscible substituted phenols. This is consistent with the fact that due to the presence of intramolecular hydrogen bonding, o-nitrophenol is soluble in nonpolar organic solvents. In contrast, chloro and nitro substitutions at para position in phenol produce very little improvement in the solubility of phenol. p-Chlorophenol is 8% soluble and p-nitrophenol has 1.8% solubility. 0Fluorophenol, although soluble in water, is also soluble in COP This suggests that an increase in the electronegativity of the halogen does not decrease the solubility of ortho halophenols. Methyl substitution a t any position in phenol, in general, increases its solubility. Ortho, meta, and para cresols have solubilities of 30,20, and 30%, respectively. The presence of a second chloro or nitro group in any position adversely affects the solubility of orthosubstituted phenols. The solubilities of 2,4-dichlorophenol and 2,6-dinitrophenol are 0.4% and 0.9%, respectively. Carboxylic Acids. In aliphatic carboxylic acids, the
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 1, 1985 165
length of the hydrocarbon chain should not exceed nine carbon atoms for miscibility. Decanoic acid and all other lower acids are soluble while dodecanoic acid has only 170 solubility. The miscibility of ethyl dodecanoate suggests that the solubility of dodecanoic and higher acids could be enhanced considerably by converting into esters of lower alcohols. The presence of halogens, hydroxyl groups, and aromaticity decreases the solubility of carboxylic acids. Chloroacetic acid and 2-hydroxypropanoicacid have 10% and 0.5% solubility, respectively, while phenyl acetic acid is insoluble. Aromatic acids are in general less soluble, but their acid chlorides are miscible with C02. Benzoic acid has 0.3% solubility while benzoyl chloride is soluble. The acid chlorides of miscible aliphatic carboxylic acid are also miscible with COz. Acetic acid and acetyl chloride are both miscible. However, solubility measurements of lauroyl chloride would shed some light on how differently acid chlorides of insoluble aliphatic carboxylic acids behave in
coz.
Ethers. It has been shown in the discussion of alcohols that etherification of hydroxyl groups generally improves the solubility of a compound. The primary reason for this might be a considerable decrease in the polarity of the parent compound and also loss of intermolecular hydrogen bonding. Another example of this is the miscibility of 1,4-dimethoxybenzene when compared to the insolubility of 1,4-benzenediol. Etherification does not improve very much the solubility of multinuclear aromatic hydroxy compounds. 2-Methoxybiphenyl and cu-methoxynaphthalene have solubilities of only 5 % and 1%,respectively. The presence of nitro and amino groups in aromatic ether compounds decreases their solubility. p-Anisidine and o-nitroanisole have less than 2 % solubility. Unlike the situation in alcohols and acids, halogen-substituted aliphatic ethers are soluble. Both l,l'-oxybis[2chloroethane] and 2,2'-oxybis[ 2-chloropropane] are miscible. Esters. Like etherification, esterification generally enhances the solubility of both aliphatic and aromatic carboxylic acids. Ethyl ester of 2-hydroxypropanoic acid is miscible, whereas 2-hydroxypropanoic acid has only 0.5%solubility. Similarly, the ethyl ester of phenylacetic acid is miscible; however, the parent acid is insoluble. Also, the fact that methylbenzoate and methyl ester of 2hydroxybenzoic acid are soluble while their parent acids are not shows that the conversion of polar acid groups into nonpolar ester groups completely changes the solubility of carboxylic acids. Aldehydes. Simple aliphatic aldehydes such as ethanal, pentanal, and heptanal are miscible. Unsaturation in aliphatic aldehydes has no apparent adverse effect on the solubility, since compounds such as 2-propenal and trans-2-butenal are miscible. Phenyl substitution, however, decreases the solubility of unsaturated aldehydes. 3-Phenyl-2-propenal has 4% solubility while 3-phenylpropanal has 12% solubility. Benzaldehyde and 2hydroxybenzaldehydeare insoluble. However, no data are available on the solubility of any other aromatic aldehydes. Nitrogen-Containing Compounds Amides. N-Alkyl substitution completely alters the solubility of amides as can be seen from miscibility of both N,N-dialkyl (both methyl and ethyl) formamides and acetamides as compared to almost insoluble formamide and acetamide. No data were available on the solubility of aromatic amides. However, similar trends observed in case of formamide and acetamide can be predicted although N-alkyl
substitution in these amides may not give miscible products. Amines. Francis (1954) has addressed the effect of basicity of organic compounds on their solubility in C02. He has concluded that weakly acidic C 0 2has no noticeable affinity for moderately basic aniline (Kb = 4.2 X pyridine (Kb = 2.3 x IO-lO), and 2-picoline (Kb = 9.38 x However, COz does form salts with stronger bases such as ainmonia (Kb = 10") and aliphatic amines (Kb = He found p-phenetidine (Kb = to be the borderline case, permitting observations on metastable liquid-liquid solubilities before solid salt appears. Pyridine and 2-picoline, both nitrogen-containing heterocyclic compounds, are miscible while aniline, a primary amine, has solubility of only 3%. All are, however, moderately basic. This observation prompted us to investigate the effect of basicity on the solubility of nitrogen heterocycles. We chose pyrrolidine (Kb = lo+) and pyrrole (Kb = due to the wide difference in their basicities. Pyrrolidine formed white solid salt immediately on contact with dense COP Pyrrole instantly became miscible, giving a homogeneous solution. This turned out to be a somewhat unstable solution as a small amount of yellowish solid salt separated a few minutes after mixing. Apparently, a major portion of pyrrole was still in solution with C02since (a) the quantity of solid separated (approximately0.2 mL) was much smaller compared to the sample (2 mL), and (b) only a single liquid phase was observed when solid was allowed to settle at the bottom of the mixing chamber. These data indicate that basicity has tremendous influence on the solubility of nitrogen-containing heterocyclic compounds as in the case of amines. The upper limit on the basicity for such compounds to be soluble in C 0 2 is approximately Kb = lo4. In amines, the solubility generally decreases in the order of tertiary > secondary > primary. This is reflected in the following examples: N,N-dimethylaniline (miscible) > N-methylaniline (20%) > N,N-diethylaniline (17%) > N-ethylaniline (13%) > aniline (3%). The effect of various N-alkyl Substituents is also clearly evident from miscibility of N,N-dimethylaniline and only 17% solubility of N,Ndiethylaniline. Also, N-methyl substitution may be preferable to N-ethyl to improve the solubility of amines. Increasing the number of aromatic substituents on nitrogen decreases the solubility as exemplified by the 4 % solubility of N-ethyl, N-benzylaniline. In general, substituents with either electron donating (Cl, OR, etc.) or electron withdrawing (-COOH,-COOR) resonance effect would have no substantial influence on the solubility of an aromatic amine. Dicyclic amines, as would be expected, are much less soluble. Nitro Compounds. As in the case of amino groups, solubility is diminished by nitro groups, especially if more than one are present. In case of aliphatic nitro compounds, the effect of hydrocarbon chain length on the solubility of a compound has not yet been determined. Nitropropane and lower homologues are miscible. Although higher homologues of l-nitropropane have not been studied, one can, at the most, expect complete miscibility only up to l-nitrododecane as increasing the normal hydrocarbon chain beyond C12results in a considerable drop in solubility. (See section on hydrocarbons.) Aromatic nitro compounds widely differ in their solubility. Nitrobenzene is miscible while dicyclic nitro compounds are very sparingly soluble. The type and position of a substituent in relation to a nitro group in an aromatic compound has profound in-
166
Ind. Eng. Chem. Prod. Res. Dev. 1985, 24, 166-171
fluence on the solubility. For example, o-nitrotoluene is miscible while p-nitrotoluene has solubility of only 20%. Similarly, as seen before, o-nitrophenol is soluble while p-nitrophenol has solubility of less than 2%. Any other substituent has an adverse effect on the solubility of nitrobenzene.
Summary The solubility of a number of organic compounds in dense C 0 2 has been examined including both those reported in Francis' (1954) classic work and recent experiments performed for this compilation. The compounds are classified as hydrocarbons, hydroxyl compounds (alcohols and phenols), carboxylic acids, ethers, esters, aldehydes, and nitrogen-containing compounds (amides, amines, and nitro compounds). Among structural features which greatly influence the solubilities in dense COz are: chain length, branching, number of rings, and position and type of substituents on the rings in case of hydrocarbons; chain length, branching, and nature (primary, secondary, or tertiary) in alcohols; type and position of substituents in phenols; chain length, aromaticity, and type of substituent in carboxylic acids; aromaticity and nitrogen containing functional groups in ethers; extent of N-alkyl substitution and type of alkyl group in amides and aromatic amines, basicity, and nature (primary, secondary, and tertiary) in case of amines; and type and position of substituent, number of nitro groups and aromatic nuclei in nitro compounds. These results may be of immediate interest in the fields of EOR, SFC, and SFE. Acknowledgment Part of this work was performed with support from the U.S. Department of Energy, the New Mexico Energy Re-
search and Development Institute, various oil companies, and the American Cyanamid Co. The authors are grateful to them for their support. Appreciation is expressed to Paula Bradley for her assistance in the preparation of the manuscript. Registry No. Benzoic acid, 65-85-0;2,&dihydroxybenzoicacid, 303-07-1;2,6-dinitrophenol,573-56-8;2,6-dinitrotoluene,606-20-2; di(o-xylyl)ethane,952-80-7; o-methoxyphenol,90-05-1; 2-butenedioic acid, 6915-18-0;2-nitroacetophenone,614-21-1; p-nitrophenol, 100-02-7. Literature Cited Francis, A. W. J . phvs. Chem. 1954, 58, 1099-1114. W i n g s , J. C.; Myers, M. N.; McLaren, L.; Keiler, R. A. Science 1988, 162, 67-72. Heller, J. P.; Dandge, D. K.; Card, R. J.; Donaruma, L. 0.International SympOSlUm on Oilfield and Geothermal Chemistly, Denver, CO, June 1983; Society of Petroieum Englneering, Dallas, TX, 1983 SPE Paper No. 11789. Hildebrand, J. H. Ind. Eng. Chem. Fundem. 1878, 17, 365-366. Holm, L. W.; Josendal, V. A. Soc. Pet. fng. J . 1982, 22, 87-98. Lauer, H. H.; McManigili, 0.; Board, R. D. Anal. Chem. 1983, 55, 1370-1375. McHugh, M.; Paulaitis, M. J. Chem. Eng. Data 1980, 25, 326-329. Morrison, R. T.; Boyd, R. N. "Organic Chemistry", 3rd ed.; Allyn and Bacon, Inc.: Boston. 1980; p 497. Orr, F. M., Jr.; Silva, M. K.; Lien, C. L. Soc. Pet. fng. J . 1982, 22, 28 1-291. Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R . T.; Reid, R. C. Rev. Chem. Eng. 1903, I , 179-250. Potter, R. L. American CyanamM Co., Stamford, Ct. 06904, personal communication, 1982. Reamer, H. H.; Sage, 6. H.; J . Chem. Eng. Data 1983, 8 , 508-513. Schnelder. G. M.; Stahi, E.; Wike, G., Eds. "Extraction with Supercritical Gases"; Verlag Chemie: Florlda, 1980. Stakup, F. I. "Mlscibie Displacement"; Society of Petroleum Engineers Monograph 8, 1983. Wasen, U. van; Swaid, I.; Schneider, G. M. Angew. Chem. Int. Ed. fngl. 1980, 19, 575-587.
Received for review August 13, 1984 Accepted November 9, 1984
Intrinsic and Transport-Limited Epoxy-Amine Cure Kinetics Frederlc 0. A. E. Huguenln and Mlchael 1.Klein' Department of Chemical Englneering and the Center for Composite Meterials, Universm of Delaware, Newark, Delaware 19716
A mathematical-modelfor the kinetics of the polymerization and cure of an epoxy-amine resin was developed. The initial rates of pdymerization were controlled by intrinsic thlrd-order kinetics that accounted for the auto&ta@ic effect of the hydroxyl groups generated during the reaction. The polymer cure was controlled by may transport, which was characterized by an average diffusion coefficient for reacting spedip. A single rate expression was used for all stages of polymerization. A global rate constant therein was calculafed in terms of the invariant chemically intrinsic rate constants and a cure-dependent diffusion coefficient, The functionality of the latter was deduced from free-volume theory,and its estimation required determination of the glass-transition temperature and two other measurable parameters. Dlfferentlal scanning calorimetry (DSC) pr;pvkled experimental kinetics that were correlated better by the diffusion-corrected model than by a similar model with a truly Invariant global rate constant.
Introduction Epoxy-amine resins can exhibit a wide range of desirable chemical, mechanical, and electrical properties. The prediction, optimization, and control of these properties during resin fabrication would be facilitated by a quantitative kinetics model that is valid over the entire range of the polymerization. This would be especially useful at the final stages of cure where the ultimate properties of the fully cured piece are realized. Unfortunately, the ma& transport limitations on high molecular weight species that form as the reaction nears completion can obscure intrinsic 0196-432 118511224-0166$01.50/0
chemical reactivities and, hence, render quantitative kinetics analysis difficult. The object of the present communication is to describe a modeling approach that couples separate intrinsic chemical kinetics and diffusion models into a single mathematical description of the polymerization and cure of epoxy-amine resins. The importance of diffusional intrusions on observable polymerization kinetics has been recognized previously (Sourour and Kamal, 1976; Horie et al., 1968). North and Reed (1963) related changes in alkyl methacrylate rate constants to the diffusion of macroradicals. Tullig and 0 1985 American Chemical Society
