Ind. Eng. Chem. Res. 1988,27, 586-593
586
for their support of this research. Registry No. Araldite MY720,31305-94-9; HT 976,80-08-0.
Literature Cited Alla, M.; Lippman, E. Chem. Phys. Lett. 1976, 37, 260. Bell, J. P. J. Polym. Sci. 1970, A-2(8), 417. Charlesworth, J. M. J. Polym. Sci. 1980, A-1(18), 621. Chin, I.-J.; Sung, C. S. P. Macromolecules 1984, 17, 2603. Cholli, A. Ph.D. Thesis, Case Western Reserve University, Cleveland, 1983, Chapters 3 and 4. Cholli, A.; Ritchey, W. M.; Koenig, J. L. Spectrosc. Lett. 1983, 17. Chu, H. S.; Seferis, J. C. The Role of the Polymeric Matrix in the Processing and Structural Properties of Composite Materials; Seferis, J. C., Nicolais, Luigi, Eds.; Plenum: New York, 1983. Delatycki, 0.;Shaw, J. C.; Williams, J. C. J. Polym. Sci. 1969, A-2(7), 753. Dusek, K.; Ilavsky, M.; Lunak, S. J. Polym. Sci., Symp. 1975,53, 29. Earl, W. L.; VanderHart, D. L. Macromolecules 1979, 12, 762. Flory, P. J. Principles of Polymer Chemistry; Cornel1 University Press: Ithaca, NY, 1953; Chapter 9. Garroway, A. N.; Moniz, W. B.; Resing, H. A. C-13 NMR in Polymer Science; Pasika, T., Ed.; ACS Symposium Series 103; American Chemical Society: Washington, D.C., 1979; p 67. Garroway, A. N.; Ritchey, W. M.; Moniz, W. B. Macromolecules 1982, i 5 , 1051. Good. I. J. ‘Contribution to the Discussion in a Symposium on 1949a, k l i , 271. Stdchastic Processes”. J . R. Statist. SOC. Good, I. J. T h e Number of Individuals in a Cascade Process”. Proc. Cambridge Philos. SOC. 1949g,45, 360. London, Ser. A 1962,268, 240. Gordon, M. Proc. R. SOC. Gupta, A.; Cizmelioglu, M.; Coulter, D.; Liang, R. H.; Yavrouian, A.; Tsay, F. D.; Moacanin, J. J. Appl. Polym. Sci. 1983,28(3), 1011. Heijboer, J. Znt. J. Polym. Mater. 1977, 6 , 11. Hester, R. K.; Ackerman, J. L.; Neff, B. L.; Waugh, J. S. Phys. Reo. Lett. 1976, 36, 1081. Kaelble, D. H. SPE J. 1959, 1071.
Keenan, J. D. Master’s Thesis, Department of Chemical Engineering, University of Washington, Seattle, 1979. Keenan, J. D.; Seferis, J. C.; Quinlivan, J. T. J . Appl. Polym. Sci. 1979, 24, 2375. Kenyon, A. S.; Nielsen, L. E. J. Macromol. Sci. Chem. 1969, A-3(2), 215. Leung, Y.-K.; Eichinger, B. E. J . Chem. Phys. 1984a, 80, 3877. Leung, Y.-K.; Eichinger, B. E. J . Chem. Phys. 1984b, 80, 3886. Macosko, C. W.; Miller, D. R. Macromolecules 1976a, 9, 199. Macosko, C. W.; Miller, D. R. Macromolecules 1976b, 9, 206. Macosko, C. W.; Miller, D. R. Macromolecules 1978, 11, 656. Mehring, M. High Resolution NMR Spectroscopy in Solids; Springer-Verlag: Berlin, 1976. Mertzel, E. A,; Ritchey, W. M.; Perchak, D.; Koenig, J. L. Znd. Eng. Chem. Res. 1988, following paper in this issue. Moacanin, J.; Cizmelioglu, M.; Tsay, F.; Gupta, A. Am. Chem. SOC., Coat. Appl. Polym. Sci. Proc. 1982, 47, 587. Morgan, R. J.; O’Neal, J. E. Po1ym.-Plast. Technol. Eng. 1978, 10(1), 49. Morgan, R. J.; Happe, J. A,; Mones, E. T. Proceedings of the 28th SAMPE Symposium, Los Angeles, April 12-14, 1983, pp 12-14. Murayama, T.; Bell, J. P. J . Polym. Sci. 1970, A-2(8), 437. Murphy, P. D.; Gerstein, B. C. Anal. Chem. 1982, 54, 522. Murphy, P. D.; Cassady, T. J.; Gerstein, B. C. Fuel 1981,61, 1233. Opella, S. J.; Frey, M. H. J. Am. Chem. SOC.1979, 101, 5854. Opella, S. J.; Waugh, J. S. J. Chem. Phys. 1977, 66, 919. 1979, 101, Opella, S. J.; Frey, M. H.; Cross, T. A. J . Am. Chem. SOC. 5856. Schroter, B.; Posern, A. Mukromol. Chem., Rapid Commun. 1982, 3, 623. Stockmayer, W. H. J . Chem. Phys. 1943, 11, 45. Stockmayer, W. H. J . Chem. Phys. 1944, 12, 125. Veeman, W. S.; Menger, E. M.; deMoer, H. C. Proc. IUPAC, 28th Macromolecules Symposium, Amherst, MA, 1982. Receiued for review October 20, 1986 Revised manuscript received May 28, 1987 Accepted December 1, 1987
Carbon-13 Nuclear Magnetic Resonance Characterization of Network Systems Elaine A. Mertzel,?Dennis R. Perchak, William M. Ritchey, and Jack L. Koenig* Department of Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106
Solid-state (2-13NMR measurements are utilized t o characterize the tetrafunctional epoxy, tetraglycidyl(diaminodiphenyl)methane,and the tetrafunctional amine, diaminodiphenyl sulfone. Intermolecular effective ether cross-links, amine junction points, and extent of reaction of the amine and epoxy are measured for the polymerization. Chemical reactions in the epoxy-amine system are discussed, and the reactivity ratio of the epoxy-amine system is calculated. Junction point measurements are made by the use of the dipolar dephasing relaxation experiment. The experimental data collected with C-13 NMR are then compared with the calculated data from a model developed in this laboratory. T h e information obtained in this study is sufficient t o calculate the molecular weight between cross-links. The use of solid-state C-13 NMR to study cross-linked systems is a recent development. With the use of crosspolarization and magic angle spinning, it is now possible to obtain high-resolution spectra of rigid and insoluble networks (Garroway et al., 1979, 1982). The purpose of this present work is to illustrate the use of C-13 NMR cross-polarization spectra and data from the special dipolar dephasing pulse sequence (Alla and Lippman, 1976) to simplify the characterization of these insoluble networks. These experimental data, when compared with calculated t Present address: B.F. Goodrich, Technical Center, P.O. Box 122, Avon Lake, OH 44012.
0888-5885188 /262~-0586$0l.50/0
data from computer modeling (Mertzel et al., 1988), provide a means for better characterization of network systems. The samples characterized in this study are the networks formed by a tetrafunctional epoxy, tetraglycidyl(diaminodipheny1)methane (TGDDM), reacting with a tetrafunctional amine hardener, diaminodiphenyl sulfone (DDS). The structure of the monomers P(X0) and reactions of the functionalities forming dangling ends P(X1) connecting molecules P(X2), species which contribute one junction point to the network P(X3), and species which contribute two junction points to the network P(X4) can be seen in Figure 1 for TGDDM and Figure 2 for DDS. 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 587 A , Cross Polarization Pulse Sequence HIX
\9, 0
DECLUPLING
SPIN LOCK
OH
H-l
I
CONTACT
11,
B . DiDolar DeDhasing Pulse Sequence 9 4
Hlx
m
1
OH
DECOUPLING "IN
1
I IDECOUPLING
OH
DECAY
Figure 1. Chemically distinct species in the epoxy system characterized by C-13 NMR and modeling.
- CH2-
NH2
P (XI)
0
Figure 2. Chemically distinct species on the amine system characterized by C-13 NMR and modeling.
The dipolar dephasing pulse sequence is similiar to the cross-polarization pulse sequence. The cross-polarization and dipolar dephasing pulse sequences can be seen in Figure 3. The difference between the two pulse sequences is the insertion of a window in the proton decoupling in the dipolar dephasing pulse sequence, before the acquisition of the FID. Opella and Frey (1979) saw the importance of the dipolar dephasing experiment in the suppression of protonated carbon resonances in solid-state NMR. Opella and Frey (1979) and Opella et al. (1979) simplified the complicated spectra of amino acids and proteins by the use of dipolar dephasing, resolving quaternary aromatic carbons. Murphy and Gerstein (1982), with the use of this technique, were able to extract information on concentrations of aromatic quaternary and tertiary carbons as well as differentiating between aliphatic primarylquaternary and secondaryltertiary carbons in asphaltenes. In this experiment, the abundant spins appear to have enough homonuclear dipolar decoupling to behave as one spin bath (Murphy et al., 1981; Mehring, 1976). Thus, the C-13 magnetization, as a function of dephasing time Tdd, shows two decays. Secondary and tertiary carbons with proton nearest neighbors have short decays. The nonprotonated carbons have longer decays. Methyl groups, because of
OBSERVE
Figure 3. (A) Routine C-13 NMR cross-polarization pulse sequence. (B) C-13 NMR dipolar dephasing experiment with a window in the proton decoupling.
their substantial motion, have the capability of partially averaging the dipolar interactions and retain their magnetization for a relatively longer time. The nearestneighbor dipolar interactions were approximated by a Gaussian decay. The weaker dipolar interactions were well fitted to a Lorentzian decay (Mehring, 1976). Previously, this laboratory has used the dipolar dephasing sequence to separate the amorphous carbon resonances from the crystalline resonances in polyethylene (Cholli, 1983) and poly(oxymethy1ene)(Cholli et al., 1983). The separation of crystalline from amorphous resonances is possible because of the dependence of the dipolar interaction on molecular motion. The dipolar carbon proton interaction is weaker for amorphous carbons because of averaging due to the greater molecular motion at room temperature. During the delay in the proton decoupling, crystalline carbons dephase more rapidly than the amorphous carbons because of the greater proton-carbon interaction (Earl and VanderHart, 1979). Other studies have observed multiple components in relaxation studies (Veeman et al., 1982; Schroter and Posern, 1982). y-Irradiation effects on high-density polyethylene are studied with the dipolar dephasing pulse sequence (Cholli, 1983). Other applications include two-dimensional local field experiments (Hester et al., 1976) and multiple-contact cross-polarization (Opella and Waugh, 1977).
Experimental Section Instrumental Section. A modified C-13 solid-state Nicolet NT-150 spectrometer, with a Doty variable-temperature probe (Doty, 19851, was used. The Doty probe was stabilized a t 75 'C for the collection of all spectra. Cylindrical NMR sample spinners (Doty and Ellis, 1981) made of sapphire (A1,03) were rotated between 3.5 and 4.0 kHz for data collection. The spectra were collected at the magic angle of 54.7' (Andrew, 1959, 1971, 1981; Lowe, 1959; Kessemeier and Norberg, 1967) with a l-ms contact time and a delay between pulse sequence repetitions of 2 s. Cross-polarization spectra (Hartmann and Hahn, 1952) and dipolar dephasing spectra (Murphy et al., 1981) were the accumulation of 3000 transients for each spectrum for a good S I N . The cross-polarization and dipolar dephasing pulse sequences can be seen in Figure 3. The dipolar dephasing experiment is a combination of 24 spectra, for each of the 3 samples, with each spectrum having an in-
588 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988
crease in the window in the proton channel of the dipolar dephasing pulse sequence. Deconvolutions. The software RELAX,copyrighted by 3M (1985), was used for the deconvolution of the dipolar dephasing data. This program was written for the IBM personal computer and permita the graphical fit for several different relaxation behaviors in order to extract relaxation parameters. A single-exponential equation, with a Gaussian distribution, was used to separate rigid portions of the sample from more mobile portions. Sample Preparation. The tetrafunctional epoxy, TGDDM (Araldite MY720), and the tetrafunctional amine hardener, DDS (HT976), were obtained from Ciba-Geigy. The TGDDM was carefully heated to 125 O C . The DDS was slowly stirred into the TGDDM until a clear mixture was obtained. The mixture was degassed in a vacuum oven a t 125 "C for 20 min. The samples were cured at 125 O C for 5 days. Three samples were prepared with 20%,30%, and 40%, by weight, DDS to TGDDM. The ratios of functionalities of DDS to TGDDM are 0.341,0.51:1, and 0.68:1, respectively. A Perkin-Elmer DSC 7 was used to determine that the samples were completely cured.
Results and Discussion Chemical Structure and Kinetics. The chemical structures resulting from the polymerization of TGDDM with DDS are complex, with more than one reaction taking place during the cure. The reaction mechanism and network structures will be discussed briefly to enhance the understanding of this system. The following reactions for an epoxy cured by a secondary amine have been suggested (Schechter and Wynstra, 1956). The first reaction is that of an epoxy group with a primary amine to form a secondary amine:
The secondary amine can then react with another epoxy group to form a tertiary amine:
OH
The hydroxyl group can react further with an epoxy group to form an intermolecular ether cross-link: -CH-
I
I
OH
OH
Because the epoxy and amine are tetrafunctional, cyclization reactions can occur. The epoxy can have an intramolecular etherification reaction which forms an ineffective cross-link due to tetrafunctionality (Morgan et al., 1983): ?H
H
OH
H
I
t
A
' 0 25
0
Primary amine
E Secondary a"i
200
C Teriary amine
10
12
I
16
14
Change in Epoxy Concentrotion Initio1 Primary Amine Concentration Figure 4. Percentages of primary, secondary, and tertiary amines as a function of changes in epoxy concentrations for the reactivity ratio of 0.25.
Amine cyclization can occur through the reaction of an epoxide group with a secondary amine (Morgan et al., 1983): OH
I
/
OH
H
I
CH~CHCHZN-
-
RN\CH2CH-CH2
I
/ RN
CHzCHCH2
\
/N\CH*CHCH2
I
/0/
OH
An epoxide-epoxide reaction is also possible. In this system, it is acknowledged that curing a t high temperatures accelerates the etherification reaction, thus affecting the network structure (Schechter and Wynstra, 1956). This study will also show that both intermolecular and intramolecular etherification are dependent on relative concentrations of components. Because this high-performance epoxy-amine system is made up of bulky tetrafunctional amine, it has been shown that the cure does not go to completion for other than stoichiometric considerations (Keenan et al., 1979; Keenan, 1979). Steric and diffusional limitations must also be taken into consideration. The network model that is compared to the experimental data generated by (3-13 NMR is well suited to these limitations (Mertzel et al., 1988). The epoxy functionalities are all considered to have equal reactivities (Charlesworth, 1980; Flory, 1953; Keenan, 1979; Macosko and Miller, 1976). This model can take into consideration the substitution effect, that is, the reduced reactivity of the secondary amine resulting from the reaction of the primary amine in DDS (Charlesworth, 1980; Dusek et al., 1975; Morgan et al., 1983). There is still controversy concerning the relative reactivity rates of the primary and secondary amino hydrogens in DDS. Due to the fact that there are severe consequences on the physical properties of the network systems due to a decrease in cross-links from substitution effects as well as type of cross-links formed, motivation to study these systems is high. With considerable simplification, in order to view the basic kinetic behavior, the reaction of the DDS with TGDDM can be represented as follows (Levenspiel, 1962): epoxy + primary amine
ki
epoxy + secondary amine
secondary amine
k2
tertiary amine
This would be an irreversible, second-order, bimolecular reaction. The reaction would be parallel with respect to the epoxy and consecutive with respect to the primary,
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 589
I
A Primary amine
s
S Secondary amine
L
73 0
8
d H b RN-C-C-C / \ 0, Nd
0 C
c-c-c' I
VI
I
OH
10
18
I
C-C-C-R'
d
OH
I6
14
Change in Epoxy Concentration Initial Primary Amine Concentration
Figure 5. Percentages of primary, secondary, and tertiary amines as a function of changes in epoxy concentrations for the reactivity ratio of 0.50. 40% by weight DDS I
I O
12
16
14
I8
Change in Epoxy Concentration Initial Primary Amine Concentration
Figure 6. Percentages of primary, secondary, and tertiary amines as a function of changes in epoxy concentrations for the reactivity ratio of 1.00.
H iCH2N;0 HZCHCH2 OH
I
0 CH2CHI
OH
Figure 7. (A) Inefficient intramolecular (cyclic) ether cross-links. (B)Efficient intermolecular ether cross-links.
secondary, and tertiary amines. With the solving of the differential equations for this reaction, for reactivity ratios of 1.0,0.5, and 0.25, it can be seen in Figures 4, 5, and 6 that the reaction stops before all functionalities are reacted. These figures also show that concentration effects can increase the relative amount of tertiary to secondary amines in the sample, with the increase being due to the increase in the epoxy concentration (Levenspiel, 1962). Cross-Polarization C-13 NMR. The conventional cross-polarization experiment was used to distinguish between cyclic and noncyclic ethers (Figure 7). The cyclic ether is formed by intramolecular reaction of an epoxy functionality and hydroxyl group formed by an epoxyamine functional group reaction. The noncyclic ether is formed by an intermolecular reaction of an epoxy functionality with a hydroxyl group which was formed by an epoxy-amine functional group reaction. In the cross-polarization spectra of the epoxy-amine polymerization, carbons attached to hydroxyl groups, intramolecular ether linkages, and intermolecular linkages
I
I
1
are discernible. The peaks from the four different carbons involved with oxygen appear between 60 and 80 ppm in all spectra. The spectrum for a low concentration of DDS:TGDDM and a spectrum for a high concentration of DDS:TGDDM can be seen in Figure 8. The carbon attached to the hydroxyl grou p formed by the epoxyamine reaction, peak c, appears at 70 ppm. The peak for the two carbons involved in the intramolecular ether groups appears at 68 ppm. Both carbons in the CHOCH structure have the same environment; therefore, only one peak, with intensity contributions from both carbons, is seen. The carbons involved in the intermolecular ether linkage contribute two peaks. This is due to the fact that the carbons involved are in two different environments. The resonance due to a CH group occurs a t 75 ppm and the resonance of a CH2 group a t 63 ppm. At the top spectrum in Figure 8, where the concentration of DDS:TGDDM is less, there is a contribution from the intermolecular ether. The CH group a t 75 ppm, which is evident without deconvolution,decreases in intensity until it has a negligible contribution, in the higher concentration of DDS:TGDDM, in the bottom spectrum of Figure 8. This indicates that with an increase in the concentration of DDS more intramolecular cyclic ethers, which are ineffective cross-links, are formed. With the higher concentration of epoxy monomer, the hydroxyl group formed by the epoxy-amine reaction has more epoxy functionalities in its environment that compete with the intramolecular hydroxyl-epoxy reaction. There are more collisions in the same time unit, increasing the number of tertiary amines formed. Dipolar Dephasing Relaxation Data. We also desire to measure network junction points. These measurements are made possible by the dipolar dephasing experiment. It is possible to separate the carbons involved with rigid junction points from those carbons which are more mobile. A qualifying assumption is made that, at this point in the cure, all primary amines have reacted. The modified pulse sequence in Figure 3B, with the window in the dipolar decoupling between the contact pulse and the FID, is called the dipolar dephasing or
590 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 Dipaler Depharing Data 2 0 % Amine by Weigh1
Dipolar Depharmg Data 40 X amine by Weight
I Secondary amine 2 Tertiary amine
I 1
_ I
Delay Time (Microseconds)
Figure 11. Dipolar dephasing deconvolution curves as a function of delay time for sample with 40% by weight DDS.
I\
Dipolar Dophasing Data
30? Amino b y Weight Secondary amme 2 Tertiary amine
1
-
C
0
Y
60
0
u C
_J
7
400 Y
I
I
Delay Time (Microseconds)
C
Y
0, a
200
Figure 10. Dipolar dephasing deconvolution curves as a function of delay time for sample with 30% by weight DDS.
nonquaternary carbon suppression experiment. Because of the l / p 3 dependence, where r is the internuclear distance, the coupling between protons bonded to carbons is stronger than the coupling between carbons and nearestneighbor protons. During the delay in the proton decoupling, there is rapid loss of the C-13 magnetization of carbons bonded directly to protons, whereas quaternary carbons with nonprotonated protons only as nearest neighbors retain their magnetization. Opella et al. (1979) were one of the first to identify the significance in being able to separate the quaternary from the nonquaternary carbons in solid-state NMR. This technique is now routine in many laboratories. By choosing an aromatic quaternary carbon to characterize, by the dipolar dephasing experiment, we have chosen a carbon which retains magnetization for a much longer time compared to that of other carbons in the system. This aromatic quaternary carbon is the aromatic carbon attached to the primary, secondary, or tertiary amine of the hardener. With the long decay time (up to 700 ps) of the intensities, due to the fact that this carbon is not protonated, it is possible to separate rigid junction points from more mobile secondary amino hydrogens taking full advantage of the dipolar dephasing experiment. This is due to the tighter coupling between junction point carbons in a rigid environment and nearest-neighbor protons versus the more mobile secondary amines with much less coupling. Twenty-four spectra, with delay times between 5 and 700 p s , were collected for each sample. The intensities, of the quaternary aromatic carbon of the amine hardener involved in the junction points, were plotted versus the size of the window in the proton decoupling. These plots can be seen in Figures 9-11. The resulting curves were then deconvoluted into two components by use of a computer program (RELAX, 1985), which uses a single-exponental equation with a Gaussian distribution, specially designed for extracting relaxation parameters from relaxation experiments. The component with the more rapid decay is assigned to the carbon of the more rigid tertiary amine involved in the junction point. The slow decaying com-
10
Functionalities Reacted/Total Functtonalities
Figure 12. Percentage of junction points as a function of extent of reaction calculated by the (2-13NMR experiment. Table I. C-13 NMR Dipolar Dephasing Intensities for t h e Secondary a n d Tertiary Amines in the DDS System as a Function of Concentration intensity DDS:TGDDM ratio secondary amine tertiary amine 0.34:l 180 550 0.55:l 220 260 0.68:l 570 430
'(2-13measurements have a 15% experimental error. ponent is assigned to the carbon attached to the more mobile secondary amine. Table I shows the intensities of the two components, as a function of concentration. If the experimental data from the dipolar dephasing experiment are compared with calculated data from the proposed model previously presented (Mertzel et al., 1988), the trend in the concentration dependence of junction points can be seen (Figure 12). The calculated data from the proposed model, on the r axis, can be compared to the experimental data on the y axis. As the concentration in amine hardener is decreased in the sample, the percent of secondary amines reacting to form tertiary amines increases. In the system under investigation, this varies from 70% tertiary amines for the lowest concentration of amine hardener to only 42 % tertiary amines in the highest concentration of amine hardener. This in turn can be compared to only 0.72 extent of reaction of amine hardener for the higher concentration to 0.85 extent of reaction of amine hardener for the lowest concentration. These data exhibit the same behavior as data from concentration effects calculated from kinetics (Figures 4-6) (Levenspiel, 1962) as previously mentioned. Calculations for t h e TGDDM:DDS System The experimental data from the NMR dipolar decoupling experiment were used to calculate the percentage of junction points in the DDS system for each DDS:TGDDM
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 591 Table 11. Percentage DDS Junction Points in the Amine System and Contribution to the Amine-Epoxy System as a Function of Concentration % amine junction pt contribution DDS:TGDDM ratio from DDS from DDS:TGDDM 0.34:l 76 26 0.51:l 54 30 0.68:l 43 30
Table IV. Number of DDS, TGDDM, Ether, and Total Junction Points for the DDS:TGDDM System as a Function of Concentration DDS: junction points TGDDM % DDS % TGDDM % ether % total ratio 0.34:l 26 4 2 32 0.55:l 30 10 1 41 0.68:l 30 17 0 47
Table 111. Secondary and Tertiary Amine Contributions to the Epoxy-Amine System and the Extent of Reaction of DDS and TGDDM as a Function of Concentration fraction of extent of DDS: secondBY ' tertiary reaction reaction TGDDM ratio amines amines DDS TGDDM 0.76 0.88 0.30 0.34:l 0.24 0.77 0.42 0.46 0.54 0.55:l 0.49 0.43 0.72 0.68:l 0.57
Table V. Calculated and Experimental Amine Junction Points in the Epoxy-Amine System as a Function of Concentration % DDS" junction points calcd DDS:TGDDM ratio by NMR by model 0.34:l 26 f 1 26 31 0.55:l 30 f 1 33 0.68:l 30 f 3
'
L
F
4001
/
a The error introduced by the experimental calculation of junction points by C-13 NMR is 15%.
Table VI. Percentage of Sol, Network, and Dangling Ends in the Epoxy System as Calculated from the Model, as a Function of Concentration epoxy system DDS:TGDDM ratio % sol % network % dangling ends 0.34:l 24 76 41 0.55:l 11 89 33 0.68:l 7 93 26
200
a"
Functionalities ReactedITotal Functionalities
Figure 13. Model predictions for the concentration dependence of junction points as a function of extent of reaction for (A) 20% by weight DDS, (B)30% by weight DDS, and (C) 40% by weight DDS.
concentration (Figures 9-11). This was done by dividing the number of tertiary amines plus the number of secondary amines into the number of tertiary amines. This percentage was then converted to percent of amine junction points in the system. The contribution of amine junction points to the system is the amine junction point contribution times the starting moles of amine monomer. In this case, the assumption was made that no amine monomer was present when the reaction stopped. The error introduced by the C-13 NMR experiment, in measuring junction points, is 15%. The junction point contribution in both cases can be seen in Table 11. The extent of reaction of DDS was calculated by the determination of the junction points (tertiary amines) and the number of secondary amines from the NMR dipolar decoupling experiment. The number of tertiary amines plus half of the secondary amines was divided by the total number of functionalities available for reaction. By multiplying the extent of reaction of the amines by the starting moles of amine monomer, the extent of reaction of TGDDM, from the DDS:TGDDM ratio, can be calculated. Table I11 shows the extent of reaction for both DDS and TGDDM. With the extent of reaction for TGDDM, the number of total epoxy junction points, for each concentration, can be theoretically estimated from the random epoxy model. The curve for change in junction points with change in extent of reaction can be seen in Figure 13. The number of effective ether junction points can be calculated from NMR cross-polarization data. Table IV gives the number of DDS, TGDDM, ether cross-links, and total cross-links
Table VII. Percentage of Sol, Network, and Dangling Ends in the Amine System, Calculated from the Model, as a Function of Concentration amine system DDS:TGDDM ratio % sol % network % dangling ends 0.349 0 100 0 0.551 1 99 5 0.681 2 98 8
for each DDS:TGDDM concentration. The error in the difference between the percent of amine junction points calculated from the NMR data versus amine junction points calculated from the model was small. As the concentration of amine increased, the error between the calculated and experimental junction points increased as well. This increase in error with concentration may be due to the increased mobility of the system. Table V shows the difference between the experimental and calculated data. With a low concentration of DDS:TGDDM, the reactivity ratio can be more accurately predicted. I n the 0.341 DDS:TGDDM, the reaction stopped at 0.88 extent of reaction. This indicates that the reactivity ratio is 0.75. The model predictions for P(XO), P(Xl), P(X2), P(X3), and P(X4) are shown in Figure 14. The reaction does not proceed to the 0.88 extent of reaction for the samples with higher concentrations of DDS. This may be due to concentration effects and steric restrictions during polymerization. Other studies have shown the reactivity of this system to be between 0.1 and 0.2. However, these studies looked a t equal concentrations of DDS:TGDDM. The reactivity ratio of secondary to primary amine was for a specific gel. The experimental data from NMR made it possible to calculate amine junction points, extent of reaction of the DDS, and percent of effective ether junction points. The extent of reaction of the TGDDM was calculated from the DDS data. To calculate the number-average molecular weight between cross-links, additional information from
592 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 PRIMARY AMINE REACTION \OH
~ d +e
RNHz 600
H RN
- c - 7 -C
H
PH - c - c -c,
lzzzsJ
H RN-,C
040
050 P(X0) 060
070
080
090
,NR'
A RN
NR'
7-c-c
P(XI)
030
OH
- C -C,
7
P(X-2)
'
NR'
CYCLIZATION
P(X3)
E
R -AMINE R'- EPOXY
OH
0 0 + 'NRI-RN
0
2
koH , N A'
OH
10
SECONDARY AMINE REACTION OH
Functional i t ies Reacted/ Total Funct ionali t ies
Figure 14. Model predictions for five different chemical species in the amine system for reactivity ratio of 0.88. RN
Table VIII. Number-Average Molecular Weight as a Function of Concentration DDS:TGDDM ratio no.-av. molec. wt' 675 0.34:l 914 0.55:l 1041 0.681 *The error introduced by the experimental calculation of junction points, with C-13 NMR, is 15%.
the model was used. This additional information consisted of the number of epoxy junction points and the number of dangling ends from TGDDM and DDS. It is assumed that the sol consists of monomer only. A summary of the percent of sol, network, and dangling ends for DDS and TGDDM is shown in Tables VI and VII. The number of chains between effective cross-links were calculated. There are three chains radiating from each junction point and two junction points a t the end of each chain; therefore, the number of nondangling chains radiating from each junction point is equal to three-havles of the number of three-way effective junction points. The average molecular weight between junction points was calculated by first calculating the total weight of the system: Wt =
(Wa
-Da)ma
+ (We -De)me
where W, = weight of amine, D, = weight of dangling ends of amine, We = weight of epoxy, De = weight of dangling ends of epoxy, and m = moles. The number of total junction points, JP, was calculated as follows: JP, = JP, + JP, + JPether The total number of junction points was then multiplied by three-halves to determine the number of chains, C. The formula for calculating the average molecular weight between cross-links is ATc = (MWt)/C where M = average molecular weight of monomer. The results are shown in Table VIII. The average molecular weight between cross-linksshould go down with the increase in DDS:TGDDM. In this case, a t lower concentrations of amine, there is an increase in ether cross-links as well as an increase in amine cross-links with decreases in amine concentration, which give the reverse effect. The reason that the junction points, in this case, are not inversely proportional to the number-average molecular weight between cross-links is due to concentration effects. With decreases in concentration, there is an increase in the junction points due to both increases in the number of secondary amines reacting and the
EPOXY
- HYDROXYL
OH
REACTION R'
0
C -C- C - R' OH
Figure 15. Summary of reactions in the epoxy-amine system.
number of effective ether cross-links. The increase in amine and ether junction points decreases the number of interconnecting species between junction points. This increase outweighs the additional epoxy junction points from increased amine concentrations.
Summary of Reactions in the Epoxy-Amine System The above experimental data, from cross-polarization and dipolar dephasing experiments compared to calculated data from modeling (Mertzel et al., 1988),give insight into the different chemical species in the TGDDM and DDS polymerization. Figure 15 outlines the reactions that take place in this system. The reaction of the primary amine in Figure 15, top, proceeds by two channels. The primary amine can react with an epoxy where one epoxy functionality on the epoxy molecule has already reacted. This reaction forms a secondary amine and a junction point contribution from the epoxy molecule. At this point, no cyclization can occur and two OH groups are available for intermolecular ether linkages. These intermolecular ether linkages can react to form effective cross-links. The same primary amine can react with an epoxy functionality where neither epoxy functionality on the epoxy molecule has reacted. This reaction forms a secondary amine and an epoxy with another functionality free for reaction. The intramolecular ether linkages can be separated from the intermolecular linkages by C-13 NMR. When the area under the curve is calculated, a semiquantative calculation can be made to determine the ratio of cyclized ether linkages to ethers contributing effective junction points. The modeling contributes the number of junction points formed by the epoxy. The junction points for a random reaction, where all functionalities have equal reactivity, are represented by the curve in Figure 13, which goes to 100%junction points when all functionalitieshave reacted. In the latter reaction, where there is an epoxy functionality free for reaction and a secondary amine, in the same molecule, there is a possibility of the reaction going
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 593 further to form two types of cyclizations (Figure 15, upper middle). These cyclization reactions subtract from the effectivejunction points that could have been formed. The first cyclization species formed is an ether cyclization. In this case, the OH group, from the primary amine and epoxy functionality reaction, goes on to react with its neighboring epoxy functionality. The second cyclization possible is an amine cyclization formed by the secondary amine reacting with the available epoxy functionality. This cyclization leaves two OH groups available for intermolecular ether linkages but neither are effective cross-links. These cyclization reactions are dependent on concentration. The cross-polarization data show that the ratio of ether cyclization to the effective ether junction points decreases with a decrease in amine concentration. This is due to an increase in epoxy functionalities available to react with the hydroxyl groups. As the amine concentration decreases, the dipolar dephasing data showed that the ratio of tertiary amines to secondary amines is higher. This, in turn, will decrease amine cyclization because of the reduction in secondary amines which accelerate this reaction. Thus, cyclization, as a whole, decreases with a decrease in the concentration of amine. In Figure 15, bottom middle, it can be seen that there are two secondary amine reactions possible. The secondary amine can react with one of two epoxy functionalities to form a tertiary amine (effective cross-link), leaving a hydroxyl group and an epoxy still able to react. The secondary amine can also react with an epoxy molecule, where one epoxy functionality has already reacted, forming a tertiary amine which is an effective junction point and another effective junction point contributed by the epoxy molecule. This reaction leaves two effective cross-links and two hydroxyl groups available for intermolecular ether linkages. There are more epoxy functional groups to react with the hydroxyl groups to form intermolecular ether cross-links. The hydroxyl reaction is shown in Figure 15, bottom. The OH group, from a reactior, between an amine and an epoxy functionality, can go on to form an intermolecular ether linkage which has effective cross-linking. Another reaction in this polymerization is a reaction between epoxy functionalities. This reaction has, as yet, been difficult to treat. Conclusions This study has shown that solid-state C-13 NMR is useful in characterizing network systems. The cross-polarization experiment can distinguish between the ether species in the system, separating effective cross-linking from ether cyclization. The dipolar dephasing experiment determines the extent of amine junction points in the system and gives insight into the manner in which junction points change with concentration of amine hardener. This characterization was made more obvious by comparing the experimental data from NMR to the data derived from modeling. Due to the fact that epoxy functionalities on a molecule all have equal reactivity, it is possible to indirectly investigate the epoxy molecule from a modeling point of view to deduce cross-link information.
This study has given insight to the fact that there is a delicate balance between concentration of amine hardener and the temperature of cure (Morgan et al., 1983),which must be maintained to optimize the mechanical properties from these epoxy-amine systems. Acknowledgment The authors express their gratitude to the Materials Research Laboratory of the National Science Foundation for their support of this research. Registry No. (TGDDM)(DDS)(copolymer), 63804-34-2; Araldite MY720, 31305-94-9; HT 976, 80-08-0. Literature Cited Alla, M.; Lippman, E. Chem. Phys. Lett. 1976, 37, 260. Andrew, E. R. Arch. Sci. 1959,12, 103. Andrew, E. R. Prog. NMR Spectrosc. 1971,8, 1. Andrew, E. R. Phil. Trans. R. SOC.London, Ser. A 1981, A299, 29. Charlesworth, J. J. Polym. Sci., Polym. Chem. Ed. 1980, 18, 621. Cholli, A. Ph.D. Thesis, Case Western Reserve University, 1983, Chapters 3 and 4. Cholli, A.; Ritchey, W. M.; Koenig, J. L. Spectrosc. Lett. 1983, 17. Doty, F. D. Manual for Variable Temperature Probe; Doty Scientific: Columbia, SC, 1985. Doty, F. D.; Ellis, P. D. Reo. Sci. Instrum. 1981, 52(12), 1869. Dusek, K.; Ilavsky, M.; Lunak, S. J. Polym. Sci., Symp. 1975,53,29. Earl, W. L.; VanderHart, D. L. Macromolecules 1979, 12, 762. Flory, P. J. Principles of Polymer Chemistry; Cornel1 University Press: Ithaca, NY, 1953; Chapter 9. Garroway, A. N.; Moniz, W. B.; Resing, H. A. C-13NMR in Polymer Science; Pasika, T., Ed.; ACS Symposium Series 103; American Chemical Society: Washington, D.C., 1979; p 67. Garroway, A. N.; Ritchey, W. M.; Moniz, W. B. Macromolecules 1982,15, 1051. Hartmann, S. R.; Hahn, E. L. Phys. Reu. 1952, 128, 3042. Keenan, J. D. Master’s Thesis, Department of Chemical Engineering, University of Washington, Seattle, 1979. Keenan, J. D.; Seferis, J. C.; Quinlivan, J. T. J. Appl. Polym. Sei. 1979,23, 2375. Kessemeier, H.; Norberg, R. E. Phys. Reu. 1967, 155, 321. Levenspiel, 0. In Chemical Reaction Engineering, Illinois Institute of Technology, Ed.; Wiley: New York, 1962. Lowe, I. J. Phys. Reu. Lett. 1959, 2, 288. Macosko, C. W.; Miller, D. R. Macromolecules 1976,9, 206. Mehring, M. High Resolution NMR Spectroscopy in Solids; Springer-Verlag: Berlin, 1976. Mertzel, E. A.; Ritchey, W. M.; Perchak, D.; Koenig, J. L. Ind. Eng. Chem. Res. 1988, preceding paper in this issue. Morgan, R. J.; Happe, J. A.; Mones, E. T. Proceeding of the 28th SAMPE Symposium, April 12-14, 1983. Murphy, P. D.; Gerstein, B. C. Anal. Chem. 1982, 54, 522. Murphy, P. D.; Cassady, T. J.; Gerstein, B. C. Fuel 1981, 61, 1233. Opella, S. J.; Frey, M. H. J . Am. Chem. SOC.1979, 101, 5854. Opella, S. J.; Waugh, J. S. J. Chem. Phys. 1977, 66, 4919. Opella, S. J.; Frey, M. H.; Cross, T. A. J . Am. Chem. SOC.1979,101, 5856. RELAX(ation), Version 1.0, Copyright by Minnesota Mining and Manufacturing Co., Minneapolis, MN, 1985. Schechter, L.; Wynstra, J. J. Ind. Eng. Chem. 1956,48, 86. Schroter, B.; Posern, A. Makromol. Chem., Rapid Commun. 1982, 3, 623. Veeman, W. S.; Menger, E. M.; deMoer, H. H. C. Proceedings of IUPAC, 28th Macromolecules Symposium, Amherst, CA, 1982.
Receiued for review October 20, 1986 Reuised manuscript received May 28, 1987 Accepted December 1, 1987
