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 . fhys. 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. f n g . 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
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 1, 1985 167
kI or k,, see below) in what follows.
I)
Diglycidyl ether bisphenol A (DGEBA)
111
4,4'-diaminodiphenylmethane (DDMI R , - N H I t R2-CH-CH~
A
R,-NH-CHI-CH-Rt
'0' R,-NH-CH2-CH-RI
OH
111)
OH
+
Rt-CH-CH2 \ /
A
R,-N
f 1, CHZ-CH-R, bH
R e a c t i o n Pathways to Epoxy-Amine Cure
Figure 1. Epoxy-amine structures and curing reaction pathways.
Tirrel(l981) used reptation theory (De Gennes, 1971) in their model of the diffusion-affected kinetics of free-radical polymerization. De Gennes' own analysis (1982a,b) of systems composed of flexible chains in concentrated solutions was based on comparison of the reaction time with the reptation and Rouse times. The reaction theory of Rabinowitch (1937) is the foundation of the present model. The original Rabinowitch work was for small molecules, but the form of its correlation of intrinsic chemical kinetics and molecular diffusion, remarkably akin to the correlation of intrinsic chemical kinetics and external mass transfer in reactions involving catalyst particles (Carbeny, 1976),was appealing and hence was adopted. The development of the present model is accomplished as follows. We first described briefly some important aspects of epoxy-amine cure chemistry and kinetics. We then describe our use of the Rabinowitch conceptx, the diffusion coefficient suggested therein, and also its calculation in terms of free-volume theory. Finally, experimental results and their correlation in tem of the present model are presented. Background A commercially important class of epoxy resins is based on bisphenol A and epichlorohydrin. Their reaction yields the diglycidyl ether of bisphenol A (DGEBA),the structure of which is illustrated in Figure 1. For the pure DGEBA, n in Figure 1 is zero; standard grades of DGEBA prepolymer consist of mixtures of various chain lengths. We consider here the cure of DGEBA into a highly cross-linked structure (Murayama and Bell, 1970) by the aromatic amine 4,4'-diamindphenylmethane(DDM), also shown in Figure 1. The major curing reactions (Bell, 1970; Smith, 1961; Sourour and Kamal, 1976) are addition of primary and secondary amine groups with the less-substituted carbon of the epoxy ring to yield a hydroxyl group and a secondary and tertiary amine, respectively. These additions are illustrated in Figure 1. Side reactions, including amino addition with the more-substituted carbon (Isaacs and Parker, 1960) and etherification (Kakurai and Noguchi, 1960; Kwei, 1963) are often minor (Schechter et al., 1956; Kakurai and Noguchi, 1960; Dannenberg, 1963; O'Neil and Cole, 1956; Bell, 1970) and are not considered further here. Although the literature (Dusek et al., 1975; Dusek and Bleha, 1977; Harrod, 1962; Horie et al., 1970; Kakurai and Noguchi, 1961; Kvei, 1966) shows kl and kz of Figure 1to be, strictly, different, with k2/kl 0.5 (Huguenin, 1984), discrimination between the reactivities of primary and secondary amines is often unimportant (Sourour and Kamal, 1976; Prime and Sacher, 1972; Acitelli et al., 1971); k, and kz in Figure 1are thus considered to be equal (either
-
Hydroxylic molecules accelerate the ring-opening reaction through hydrogen-bonding in the transition state (Smith, 1961). These catalysts can be present either initially in the reaction mixture as trace impurities or, as illustrated in Figure 1,generated as the reaction proceeds. Following Sourour and Kamal (1976), the intrinsic rate expression is thus composed of two terms, the first representing catalysis by impurities (with rate constant k1) and the second autocatalytic term involving catalysis by the hydroxyl groups (with rate constant Itp) whose concentration equals the concentration of consumed epoxide groups. The foregoing permits description of the chemically controlled rate of consumption of epoxide rings as given in eq 1 (Sourour and Kamal, 1976) da/dt = kiCEO(1 - a)(R - LY)
+ kpa(1 - a)(R -
CY)
(1)
where ki and kp denote catalysis by impurity and product hydroxyls, respectively, R is the initial equivalent ratio amine to epoxide (amine hydrogens/epoxide rings), CEO is the initial ring concentration, and a is a fractional conversion based on epoxide rings, a = 1 - CE/Cm Reduction of eq 1to eq 2 (Sourour and Kamal, 1976),where kI = k{CEO,facilitates the analysis that follows. da,dt = ( d a / d t ) / [ l - a ] [ R- 0-1 = kI
+ kpa
(2)
Model Development The object of this section is the development of model equations capable of representing the control of the rate of curing reactions by either intrinsic kinetics or mass transport, as well as in the transition region between the two. Rabinowitch Model. Rabinowitch (1937) considered a densely packed medium in which molecules were surrounded by others in coordination spheres. When diffusion brought a readant molecule to within the first coordination sphere of the molecule with which it was to react, a state of encounter was reached. Comparison of the characteristic times for diffusion, encounters, and intrinsic chemical reaction led to the original Rabinowitch equation which is equivalent in form to eq 3
+ (Dl/D) exp(-E*/RT)I
k = ko exp(-E*/RT)/[l
(3)
In eq 3, Dl is a constant depending on the distance between two lattice points, on the packing mode, and on the frequency of collision; D is the diffusion coefficient of the reactant pair, E* is the intrinsic reaction activation energy. Equation 3 reduces to represent control by chemical reaction when D1exp(-E*/RT) > D. For the present purposes, eq 3 was used to calculate an apparent or global rate constant that could account for kinetic- and diffusion-controlled reactions and also the transition between the two. In the analysis that follows, experiments in diffusion-unaffected regions provided estimates of ko and E*. Estimation of D was accomplished in terms of free-volume theory. Diffusion and Free Volume. Free volume (Doolittle, 1951,1952,1957; Cohen and Turnbull, 1959) is somewhat nebulous but can be considered to be composed of the different terms illustrated in Figure 2 (Lipatov, 1977; Vrentas and Duda, 1979). If the space occupied by the molecules of an equilibrium liquid at 0 K describes the occupied volume vo, then the free volume uf is as given in eq 4 Uf
= v - vo
(4)
168
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 1, 1985
Table I. Typical Properties of the Uncured Epoxy Resin EPON 828" equiv epoxy content equiv hydroxy content equiv/L equiv/ kg equiv/L ref equiv/ kg Shell 5.2-5.4 Dannenberg (1963) 5.22 6.08 0.56 0.653
d:' 1.16 1.163
Y,
P (25 "C) 110-150
sp heat, cal/(g K) 0.5
This information was obtained from various technical bulletins provided by Shell Chemical Co. and from the literature (Dannenberg, 1963).
(Williams et al., 1955) suggest fg = 0.025 and af= 4.8 X K-' for amorphous polymers at TgC T < Tg+ 100 K; this corresponds to the first stage of the cure. Below Tg a value of af= 4.8 X K-' has been suggested as more appropriate (Bravenec, 1983). All of the foregoing permitted reduction of eq 6 as
W
3 -1 0
>
VOLUME
D = DOe x p W I
I
"f
i
INTERSTITIAL FREE VOLUME
OCCUPIED VOLUME
Tg TEMPERATURE Figure 2. Schematic division of the specific volume (after Vrentas and Duda, 1979).
Further details are available (Lipatov, 1977; Vrentas and Duda, 1979; Huguenin, 1984). It will be convenient to consider a nondimensional fractional free volume, f (Williams et al., 1955), such that
f = V f / ( V o + Vf) = V f / V
(5)
Inspection of Figure 2 suggests that variations off with temperature correspond reasonably with variations of u since u, is essentially temperature dependent. Transport properties including the self-diffusion coefficient have been phrased in terms of free volume by Cohen and Turnbull (1959), Bueche (1962), Macedo and Litovitz (1965), Chung (1966), and others. In the simple approximation used here, these analyses were expressed conveniently by eq 6, which is similar to the originally empirical Doolittle (1951) equation
D = Doexp(-yu*/uf)
(6)
In eq 6, Do is a constant, y accounts for the overlap of free volume (usually 1/2 < y < l ) , and u* is a critical volume. Since u* is of the order uo (Macedo and Litovitz, 19651, eq 6 reduces conveniently to
D
= Doexp(-B uo/uf)
= Do exp(-B((l/f) - 1)) (7)
It was further useful to allow the fractional free volume to be linearly dependent on temperature (Williams et al., 1955), such that af/aT
G
af
(8)
and
f
= fg
+ Qf(T- Tg)
(9)
In eq 9, f g is the fractional free volume at Tgand cyf is the thermal expansion coefficient of the free volume; we approximated both to be constant. Theory and experiment
- l/(fg +
4 T - Tg))ll
(10)
where in our simple approximation the parameters fg,cyf, B, and Do were considered constant throughout the cure. Substitution of eq 10 into the Rabinowitch model allowed correlation of the experimental cure kinetics as follows. First, at low conversion, intrinsic kinetics parameters were deduced by assuming the reaction rate to be diffusion-unaffected. Second, and at high conversions, the diffusion model parameters (e.g., B and Doin eq 10) were deduced by fitting the Rabinowitch asymptote to experimental DSC results. The latter calculation was facilitated by recognizing that since the rate constants kI and kp respectively vary from 1.4 X to 2.3 X 10-1min-' and 1.2 X lo-' to 2.9 min-' over the temperature range studied (Huguenin, 1984), the more important reaction governed by the latter was also more likely to be diffusion-limited than the less important reaction governed by the former. We thus accounted for the influence of diffusion on only the autocatalyzed reaction, which also becomes more important as the cure progresses into the diffusion-limited regime. This permitted eq 2,3, and 10 to be combined as
1 --In 6
B
+ -1 In B
([
kPa - l]/exp[-Ep*/RT] iu, - kI
where 6 = D1/Do,T i s the curing temperature, kI,kp, and Ep* are the intrinsic (constant) kinetics parameters, and fg and afare the estimated free-volume parameters. In eq 11only Tgand a (or iu,) varied during an isothermal cure. We thus interrupted several otherwise identical isothermal cures in order to determine experimentally the dependence of T8 on a for a simulated cure. The slope and intercept obtamed from plotting these data in the manner suggested by eq 11 provided values of B and 6. Experimental Section Differential scanning calorimetry (DSC) was used to monitor the extent and rate of reaction over the range of cure studied. We report here the details of materials, procedure, and methods of analysis. A DGEBA diepoxy resin and DDM diamine system was studied. The EPON 828 resin was supplied by the Shell Chemical Co. and was used as received. Typical properties of the uncured resin are listed in Table I. The average degree of polymerization of the EPON 828 was approximately n = 0.2 (see Figure l),and an equivalent epoxy weight of 188, suggested by the manufacturer, was used in the calculation and analyses that follow. The resin was cured with 4,4'-diaminodiphenylmethane (DDM), a diamine (functionality g = 4) whose equivalent weight is 20.2. Dynamic DSC trials showed the DDM
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 1, 1985 169
i;
IOdr
0.4
0 O 000 0
5 0o
100
150 2
200
2 5L0
300
350 :
400
4: 5 0
-
kl (min?
E
10-2€
tlme (min)
Figure 3. ExperimentalDSC analysis of the rate and extent of the DGEBA-DDM cure reaction vs. time at 130 O C and R = 0.99.
melting point to be 90 "C, which was considered close enough to the handbook standards (92-93 "C) to allow the diamine to be used as received from Aldrich. A Du Pont 910 DSC connected to a Du Pont 990 programmer-recorder system was used to monitor the cure and also in the measurement of glass transition temperatures. The operation of these instruments has been described in detail elsewhere (Huguenin, 1984). Before each series of experiments, the DDM was dissolved in either chloroform or dichloromethane, and the resulting solution was then mixed with the resin. This mixture was quickly chilled in an ice-water bath where the solvent could be evaporated under vacuum (-90 kPa). Typically, sample weights of 10 to 20 mg were poured into an aluminum pan which was placed into the DSC cell. As suggested by Fava (1968), an empty pan was used as a reference. The DSC cell was operated in a nitrogen atmosphere. A slight loss of material, estimated to amount to 5% to 10% of the total weight, occurred during the heating of the sample and was attributed to the evaporation of residual solvent since control experiments on resin-DMM systems prepared without solvent were in material balance. Both isothermal and temperature-programmed scans were exploited. The former was used to infer the rate of reaction as a function of cure time. Temperature programming was always at a constant rate that ranged from 5 to 20 "C/min. These experiments enabled determination of the total heat of reaction as -20.0 kcal/mol and the glass transition temperature of partially cured samples. Further details concerning the operation and calibration of the instruments are available (Huguenin, 1984). Results Stoichiometric ( R = 0.99) DGEBA-DDM systems were partially cured for times up to 180 min and at isothermal temperatures of 90 to 180 "C. Typical results obtained from DCS analysis of the cures are illustrated in Figure 3, where both the rate and extent of cure are plotted vs. time of isothermal reaction at 130 "C and R = 0.99. Linear regression of the first stages of cure, e.g., t < 5 min in Figure 3, allowed determination of the intrinsic rate constants kI and kp as 0.028 m i d and 0.57 min-', respectively, at 130 "C. Analyses reported elsewhere (Huguenin, 1984) showed that no determining improvement on kinetics was gained by considering the unequal reactivities of the amine hydrogens. Similar estimation of rate constants at each isothermal cure temperature enabled determination of associated Arrhenius parameters. This is summarized in the Arrhenius diagram of Figure 4, which indicates parameters of [log A(min-l), E*(kcal/mol)] = 17.6, 17.01 and [6.1, 11.81 for kI and kp, respectively. The temporal variation of the glass-transition temperature was estimated for each isothermal cure as follows. Upon interruption of each cure, the sample was cooled and then immediately scanned at 20 "C/min to measure TB' The evolution of Tgas a function of time (Le., as a function of extent of cure) is shown in Figure 5 for isothermal cures
0)
16'
21
22
I
I
I
t
23
24
25
26
27
2E
29
IOOO/T (K-')
Figure 4. Arrhenius diagrams for (a) kI and (b) kp.
I
cD150
DGEBA/DDM Samples
.
Tc' 9O0C Tc=115"C
-
-
Time (min)
Figure 5. Estimated variation of the glass transition temperature with extent of cure at T,. Table 11. Values of B and 8 Determined from Isothermal Cures at T = 115 "C param set fg CY^, K-' B 6 1 2
0.025 0.025
1.67 0.78
5X 5X
"WLF value (Williams et al.,
1955).
1.35 X 2.90 X
lod
*Typical of polymers in
glassy state (Bravenec, 1983).
of 90 and 115 "C. The data points thus represents interrupted cures of otherwise identical DGEBA-DDM samples that were quenched and subsequently subjected to a DSC scan for determination of Tg.The reproducibility of the indicated glass transition temperature at a given time was determined to be about 2-3 "C. Fitting the data shown in Figure 5 to a spline function allowed calculation of Tgat any cure time, and, hence, the three curing variables a,iu,, and Tgcould all be determined at a given cure time. Having already deduced kI and kp, determination of the parameters B and 6 amounted to calculation of the slope and intercept of the appropriate plot of eq 11. Results are summarized in Table I1 for a constant value of fg = 0.025 and for values of af= 5 X K-l and 5 X 10+ K-I, respectively, the Williams et al. (1955)
170
Ind. Eng, Chem. Prod.
Res. Dev., Vol.
-
___
.
--
24, No. 1, 1985
Exper mental Pred cted lntr nsic K netics ~
-
8
16
24
32
40
-
-
48
/
I
56
64
,
72
80
T m e (minl
Figure 6. Experimental and model DSC curves for epoxy-amine cure a t 115 "C and R = 1.0
prediction of cyf and the value considered to be more typical of polymers in a glassy state (Bravenec, 1983). Table I1 shows B represent be of order unity in both cases, whereas 6 = 1.35 X 10 for cyf = 5 X 10" and 6 = 2.9 X lo+ for the value of af= 5 X corresponding to glassy polymers. Having deduced the parameters of the general model, a DSC curve could be generated by numerically integrating eq 11 forward in time. The program logic involved evaluation of the rate constant in successive steps in order to account for the influence of mass transport limitations. The computer program is available (Huguenin, 1984). The experimental and two predicted DSC signals are illustrated in Figure 6 for isothermal cure a t 115 "C and R = 1.002. The first predicted DSC signal in Figure 6 was generated by assuming the rate constants to be diffusion-unaffected; i.e., the intrinsic rate constants kI and k p were considered to be governing and truly constant over the entire range of cure. The second predicted curve in Figure 6 represents the numerical integration of the Rabinowitch model described above, with [fg, cyf, B , 61 = [0.225,5 X 0.78, 2.9 X lo4]. The agreement between predicted and experimental DSC signals is clearly better when the rate constants are adjusted for the influence of diffusion. The discrepancy observed at low times in Figure 6 is due to nonequilibration of the system after introduction of the sample in the DSC cell. Discussion Several approximations were required in our derivation of the present model equations. These and the overall utility of the present approach are discussed in the following. Our calculation of the parameters B and 6 was achieved by permitting k p to be diffusion-affected and by considering kIto be truly constant and chemically intrinsic. This is qualitatively reasonable and quantitatively useful for two reasons. First, the autocatalytic term is always larger than the impurity-catalyzed term in the overall rate expression except at very low reaction conversions. At low conversions both terms should be chemically intrinsic. Second, at higher conversions the autocatalytic term is much more important than the impurity-catalyzed term since kp/k1 10-20. Further, the time constants for diffusion to reaction (and hence the severity of diffusional limitations) should be larger for the autocatalytic term than the impurity-catalyzed term. This is because of the relative values of the intrinsic rate constants and also because the impurities are small, mobile molecules while the autocatalytic hydroxyl groups are attached to a polymer backbone. Both the fractional free volume a t the glass transition temperature, fg, and the coefficient of thermal expansion, ah were assumed to remain constant over the entire range of cure. It should be noted that these parameters might actually vary, especially as T nears the glass transition
-
temperature. The present correlation was evidently insensitive to this issue since two parameters (B and 6) were measured. WLF theory (Williams et al., 1955) indicates that the value of cyf = 5 X K-' introduced into eq 11is typical. However, we have overextended this theory in certain instances near the completion of the reaction where the temperature of the system was lower than Tg. It has been suggested that eq 9 can be extrapolated about 10 to 20° below Tg, but in this condition the use of the universal constants (Williams et al., 1955) is not strictly justified and a value of cyf about an order of magnitudes lower may be more appropriate (Bravenec, 1983). Thus two values for afwere considered: cyf = 5 X K-l and cyf = 5 X K-l. The latter was used in the the generation of the DSC signal described above. Clearly any profound errors incurred in using af= 5 X could be compensated for in the measurement of B (and 6 ) , but it is reassuring that B was found to be nearly unity (Williams et al., 1955) for either assumed value of a p The present mathematical description is clearly not an a priori prediction, in its present form, but rather a useful correlation of experimental data. The structure of the model is appealing, however, in that it accounts for cure controlled both by intrinsic chemical kinetics and also transport of reacting species. The model's parameters are predictable in principle, and a truly a priori model could result from an improved understanding of the dependence of the glass transition temperature on cure conversion. Summary and Conclusions A model of the kinetics of the cure of epoxy-amine resins was developed. The early stages of cure were controlled by intrinsic chemical kinetics and the final stages of cure were controlled by the mobility of the reacting species; free volume theory provided an estimate of the latter. Introduction of experimentally determined intrinsic chemical rate constants and an estimated diffusion coefficient into the Rabinowitch (1937) equation allowed calculation of an overall rate constant and hence global reaction rates. The agreement between experimental and model DSC traces was encouraging. Free-volume theory was an appealing basis for the diffusion model since a residual diffusivity of polymeric species through a network was permitted toward the end of the cure. This predicted continuation rather than cessation of the reaction as the glass transition temperature reached the cure temperature. DSC was a convenient probe into both the early and final stages of the epoxy-amine cure. Isothermal experiments provided intrinsic rate constants, and dynamic experiments permitted estimation of T g for several interrupted cures. The present model should be a useful start to a more fundamental a priori prediction of the kinetics of diffusion-affected cure reactions. Acknowledgment
We acknowledge the financial support of the Center for Composite Materials as well as useful discussions with Professors M. M. Denn, R. L. McCullough, R. B. Pipes, and Dr. L. D. Bravenec. Nomenclature B = constant in free volume model of order unity CA = concentration of amino hydrogens, equiv/L CE = concentration of e oxide rings, equiv/L
D = self-diffusivity,cm B/ s D1 = constant in Rabinowitch equation, cmz/s
Ind. Eng. Chem. Prod. Res. Dev. 1985, 24, 171-175
Do= constant in Doolittle equation, cmz/s f = fractional free volume, v f / v fg = fractional free volume at Tg kI = impurity-catalyzed rate constant, s-l kp = autocatalytic rate constant, s-l R = equivalents ratio, CAO/CEO T, = cure temperature, K Tg= glass-transition temperature, K
Greek Letters CY = fractional conversion of epoxide rings, 1 - CE/C~O CY^ = thermal expansion coefficient of free volume, K-' iu, = da,/dt = reduced rate (da/dt)/(l . . - a)(R- CY) 6'= Dl/Do v = molar volume, cm3/mol vf = free volume, cm3/mol vo = occupied volume, cm3/mol Superscripts 0 = global, observable m = ultimate, asymptotic Subscripts E = epoxide A = amine 0 = initial (except for yo, see above) Registry No. (Bisphenol A).(epichlorohydrin)(copolymer), 25068-38-6; 4,4'-diaminodiphenylmethane, 101-77-9.
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Received for review July 5, 1984 Accepted November 8, 1984
Evaluation of Aromatic Extracts as Antioxidants for Mineral Oils Dhoalb A. AI-Sammerral' and Mahmood M. Barbootl Petroleum Research Centre, Jadiriyah, Baghdad, Iraq
Two aromatic extracts separated from light (grade 40) and heavy (grade 60) oil distillates by a selective solvent (furfural) were evaluated as oxidation inhibitors for sulfur-free and sulfur-containing refined mineral oils. The effectiveness of various concentrations of these extracts in preventing oxldation of the oil samples under oxidizing conditions was studied statically by differential scanning calorimetery (DSC) and dynamically by a catalytic oxidation test procedure. The results obtained from these two methods of evaluation correlated well. The grade 40 and 60 extracts Imparted good antioxidant protection to the sulfurcontaining mineral oil. The grade 60 extract exhibited a similar behavior In the sulfur-free oil, while the grade 40 extract could not be regarded as an efficient antioxidant for the same oil. W h the aid of aromatic extracts it is possible to improve substantially lubricants of various types, particularly with regard to their resistance to oxidative attacks.
Introduction The quality of lubricating oil distillates is improved by solvent extraction processes, which remove the polyaromatic fractions and those more polar species that impart instability. The distillate is usually contacted with a selective solvent such as furfural or phenol to provide a higher viscosity index raffinate and an aromatic extract from both of which the solvent is recovered (Berridge, 1975). The aromatic extracts are dark oils containing asphaltic residues. The composition of the extract is dependent on the extractive power of the solvent, operating parameters, and the type of distillate being extracted, but in normal refinery operation the extract would be expected to contain a196-4321/85/1224-0171801.5afa
about 70 wt 90 and upward of aromatic compounds (Biske, 1975). Sulfur, nitrogen, and oxygen compounds concentrated in the extract are mainly in heterocyclic ring structures. Owing to their high aromatic character, the extracts have a useful solvent power (Nejak, 1968). This led to their utilization as extenders in rubber and plastic compositions and as a partial replacement for linseed oil in paints and varnishes. A variety of organic chemical compounds have been used as oxidation inhibitors in lubricating oils (Molyneux, 1967). These include sulfur compounds, amines, and phenolic derivatives. Polyaromatic fractions separated chromatographically from refined mineral oils (AI-Sammerrai et al., 0 1985 American Chemical Society
