J. MATER. CHEM., 1994, 4( 3), 385-388 Kinetic and Simulation Studies of Linear Epoxy Systems Ian P. Aspin,” John M. Barton,” Gabriel J. Buist,” Adrian S. Deazle,” Ian Hamerton,” Brendan J. Howlin*” and John R. Jonesa” Department of Chemistry, University of Surrey, Guildford, Surrey, UK GU2 5XH Materials and Structures Department, Defence Research Agency (Aerospace Division) RAE, Farnborough, Hampshire, UK GU74 6TD The kinetics and mechanism of the reaction between Bisphenol-A phenylglycidylether (BADGE) and 1,2-dianilinoethane (DAE) has been studied by a radiochemical method using tritium as the label and also by gel permeation chromatography (GPC). In parallel with these studies molecular simulation has been used to build models of the linear polymers formed, and their physical and mechanical properties have been calculated. Cast resin samples of the polymer have been produced for experimental determination of the physical and mechanical properties and the results of these determi- nations have been compared with the calculated values.These were found to be in reasonable agreement. Epoxy resins have a long history dating back to the 1950s’ and find widespread use in high-performance materials, adhesives, coatings and in the electronics industry. This in turn has led to an increasing appreciation of the need for fundamental research to be undertaken into resin synthesis, curing systems, properties of cured products, methods for their characterization and the mechanisms of epoxy resin cure.It is important to understand the factors influencing the cure and processing of epoxy resins, and to improve our predictive capability. A knowledge of the kinetics and mechanism of cure is accessible through the rate constants for the reaction and these in turn can be fed into cure processing schedules.2 Conventional high-performance liquid chromatography (HPLC) would seem to be an appropriate means for monitor- ing the appearance of oligomeric species during cure, but the effectiveness is reduced due to the non-quantitative nature of UV detection (unless the intermediates are synthesized and analysed in this manner). Radio-HPLC [a highly versatile method developed3 at the University of Surrey which allows one to measure, through the radioactivity, the concentrations of the reactants, intermediate(s) and product(s) as a function of time] provides a quantitative method for this detection, and the situation is further simplified by considering solely the amine (and subsequent amine-containing species).A kin- etic model has been developed4 which enables the consumption/production of species in the model systems to be monitored with respect to time. The rate constants for the individual steps are available from the fit of the experimental data to the calculated model. The use of this model should enable the use of better kinetic models in cure processing. A convenient starting point for the latter area is a study of amine-epoxide reactions and, in the case of the reaction of PGE and aniline to yield an aniline-(PGE), ‘trimer’, the experimental data have shown that the intermediate and product catalyse the reaction through involvement of the hydroxy group, which is produced upon opening the oxirane ring.Furthermore, the reaction was seen to be affected by trace amounts of water, and we have reported rate constants4 for the reaction of PGE catalysed by amines previously. The PGE-aniline model system is essentially half of a commercial epoxy system. Hence, the logical extension of this work was to study systems that can form linear polymers, but do not have the added complication of cross-linking. A further area of interest is the development of computer models to predict the physical and mechanical properties of the cured product. Hence, we report here our computational studies on the linear system and a comparison of this data with experimentally determined values.This serves as a vali- dation of the methods used and indicates their future potential in cross-linked systems. A full characterization of the system involves a number of complimentary characterization techniques’ both chemical (e.g. radio-labelling, GPC) and computational (e.g. kinetic, simulation studies). The results for this system are reported here as part of our continuing research effort to understand the mechanism of epoxy cure. Experimental Sample Preparation The DAE (Aldrich) and BADGE (Shell as Epon 828) were both recrystallized from chloroform before use. Radio-labelling of Amine Samples The DAE was labelled using catalytic hydrogen exchange based on the method of Jones and co-workers.6 Purity and location of labels was assessed using 3H NMR. Samples prepared in this way were then diluted with unlabelled DAE and used without further purification.Apparatus ‘H and 3H NMR spectra were obtained in CDCl, at 25°C using a Bruker AC-300 NMR spectrometer operating at 300 and 320 MHz, respectively. Radio-HPLC was performed on DAE-BADGE reaction samples made up as acetone solutions using a tetrahydrofuran (THF)-water (containing 1YOtrifluoroacetic acid, TFA) gradi- ent elution (varying between 40:60 and 70:30 in order to effect separation, depending on the length of the oligomsr). The system comprised a Spectraphysics SP-8700 solvent gradient pump, Nuclear Enterprises Isoflo 1 radio-detector and a Spherisorb ODs5 12.5 cm reversed-phase column.Data were collected and analysed by an Apple IIe computer operating an NE radiochromatography program (ISOMESS 2000). All experiments were conducted at room temperature at a flow rate of 1 ml min-’. Kinetic fits were performed on the data using the in-house program KINET version 3.1.4 GPC was performed using a Waters system comprising a 510 pump, 490 UV detector operating at 254nm and two columns: Polymer Laboratories PLgel 3p mixed-E ,,and a Waters p-STYRAGEL column with pore size lo4A. The eluent was dichloromethane-methanol(95:5)at a flow rate of 1ml min-’. The data were collected and analysed using a Waters Data Module.The GPC was first calibrated using BADGE NH-NH I I DAE linear epoxy repeat unil (dimer) Fig. 1 Structures of species studied in the course of this work narrow weight range polystyrene samples, and later using known epoxy standards. Conformational Analysis Conformational analysis of DAE-BADGE oligomers was performed on a Silicon Graphics 4D20 using the program POLYGRAF version 3 (Molecular Simulations, Inc.). Mechanical properties were also determined using the mechanical properties module in POLYGRAF. An atomistic model where n=2 (Fig. 1) was used for the mechanical simulation. A periodic boundary condition was used to simulate the bulk properties of the oligomer. Determination of Mechanical Properties Samples of DAE-BADGE oligomers were cast as thin sheets and cured using the following schedule: degassed at 50 "C for 30 min in a vacuum oven, a further 30 min at 100"C and then the liquid was syringed into a mould and placed in an oven at 100 "C for 12 h. The mechanical properties (e.g.Young's, bulk and shear moduli) of the machined samples were deter- mined using an Instron universal testing apparatus at room temperature (crosshead speed 0.1 mm min-'). Results Conformational Analysis The flexibility of the chain was investigated by carrying out conformational searches around the dihedral angles q51 and 42(Fig. 1)using a soft search in 10" steps. The plot of and b2 against energy appears in Fig. 2 and a two-dimensional projection of this is represented in Fig.3. Radio-HPLC A typical chromatogram showing the separation of the peaks is shown in Fig. 4. The plot clearly shows peaks for each of the amine-containing species produced during the course of the reaction. A computer fit of the data, produced from this experiment, is given in Fig. 5 and the rate constants determined for the reaction are k, =0.07 l2 mol -2 h -', k, =0.15 l2 rnolp2 h-' and k2=0.13 l2 mol-2 h-', k,=0.125 l2 mol-2 h-l and k4=0.25 l2 rnolp2h-' where k, refers to the amine-catalysed initiation step, k, refers to the formation of the J. MATER. CHEM., 1994, VOL. 4 Fig. 2 Conformational plot of us. 4, (the ether linkage) of the linear epoxy chain Fig. 3 Two-dimensional conformational projection of dl us.#, (the ether linkage) of the linear epoxy chain tlmin Fig. 4 A typical radio-HPLC chromatogram showing optimal peak separation (THF-H,O, containing 1YOTFA, gradient elution varying between 40:60 and 70:30, flow rate 1ml min-l). 1, Amine; 2, amine-epoxide dimer; 3, epoxy-ended trimer J. MATER. CHEM., 1994, VOL. 4 10 20 30 40 50 60 t/h Fig. 5 Typical computer fit (KTNET version 3.1) of the radio-HPLC data produced from the BADGE-DAE (16:l molar ratio) reaction. k/12 mol-2 s-l: k,, 4.167; k,, 3.611; k,, 1.944; k3, 3.472; k4, 6.944 dimer, k, refers to the formation of the epoxy-ended trimer, k, refers to the water-catalysed formation of the dimer and k, to the water-catalysed formation of the trimer. Gel Permeation Chromatography Fig.6 depicts a stacked plot of the GPC profiles of BADGE-DAE reaction samples taken over a timescale of 4 h. The formation of higher oligomers and consumption of mon- omers can be clearly seen. The observed broadening in the latter chromatograms (polydispersity increased from 1.46 at t=O to 5.03 at t=96 h) is obviously due to formation of polymeric material. Simulation of Mechanical Properties The computed elastic constants of the system are given in Table 1 and these are compared with the experimental deter- minations of the actual Young's modulus, bulk modulus, shear modulus, Poisson's ratio and the Lam6 constant, 1.Estimated standard deviations for these values are given where possible. A further comparison is apparent from this table with the QSPR (quantitative structure-property relationship) results for these constants calculated by the method of van Kre~elen.~ Discussion Conformational Analysis The full investigation of the conformational flexibility has been submitted for publication separately,8 but it is appro- priate to observe that the conformational minima of these plots indicate that the preferred dihedral angles for 4, and 42 are+90" and+ 180".This has importance for the confor- mations adopted by the atomistic models used for the calcu- lation of the mechanical properties as shown in Tablc 1. Radio-HPLC The use of conventional kinetic treatments to provide the rate constants is not feasible in these systems because of the autocatalytic nature of the reactions.Consequently the rate equations cannot be manually integrated and it is necessary to use computer methods to perform this task. The profile of the peaks in the initial stages of reaction is very similar to that of the PGE-aniline system, vindicating its use as a suitable model of polymer formation. It is reasonable therefore to assume that similar chemical reactions are taking place in the initial stages of the reaction. Using this assumprion the data can be fitted to the current rate model program to derive comparative rate constants for the reactions. Obviousiy, how- ever, at later stages of cure there are many more species being formed and this is indicated in Fig. 7. A complete treatment of these data depends on the full characterization of these higher species and modification of the rate equations and software, and work is currently underway to address this.It is interesting to note that from the derived rate constants the k,/k, ratio for this system is close to unity. In other studies this ratio has been found to be closer to 0.5.9 Indeed, in our previous study of the aniline-PGE system the ratio was found to be 0.43.6The separation of the reactive nitrogen aloms by the ethane bridge effectively removes any influence that the first BADGE moiety to have been added may have on the addition of the second. Hence there is no electronic or steric effect on the reactivity at either nitrogen atom and the addition Fig. 6 GPC profiles [dichloromethane-methanol (95:5) at a flow rate of 1ml min-', UV 254 nm] of BADGE-DAE (1:l molar ratio) reaction samples taken over a timescale of 4 h J.MATER. CHEM., 1994, VOL. 4 Table 1 Comparison of computed and actual measured elastic constants of the BADGE-DAE polymer system" Young's modulus bulk modulus, shear modulus, Poisson ratio, Lame constant, E/GPa BIGPa G/GPa 1' I/GPa calc.' 5.84 (2.4) 5.36 (2.68) 2.05 (0.91) 0.37 (0.09) 6.19 (2.94) expt.' 3.84 (0.34) 4.61 (0.12) 1.41 (0.17) 0.36 (0.01) 3.667 (0.004) QSPR~ 4.15 4.32 1.36 0.36 3.29 ~~~ a Standard deviations in parentheses. bCalculated from POLYGRAF mechanical simulation. 'Experimentally determined. Quantitative structure property relationships (calculated from group contributions).of the second BADGE molecule is as equally favourable as the first. In the aniline-PGE system mentioned earlier the second PGE unit has to add to a nitrogen atom that already has one PGE molecule attached to it. Preliminary molecular orbital calculations performed under COSMIC" indicate that electronically there is little reason why the addition of a second PGE unit should not be as fast as the first. This raises the likelihood that steric hindrance is the factor affecting reactivity in this system. GPC In Fig. 6 it can be seen that after only approximately 4 h of reaction peaks are discernible for degrees of polymerization up to n =4 (polymer repeat units). Minor peaks can also be detected for both the amine-terminated and epoxy-terminated linear trimers. Simulation of Mechanical Properties The version of POLYGRAF used for this simulation is limited to 1000 atoms in a periodic system.For a fully atomistic model where n =40, then it would be necessary to model 3240 atoms and this would be beyond the scope of the program. Therefore, the mechanical properties were calculated using the Weber et al." method to give an 'infinite' chain (e.g. n =a).As M, for the polymer is directly related to the mech- anical properties in which we are interested, there is likely to be some discrepancy between the results determined from the simulation and the actual experimental determination. This is reflected in the larger standard deviations given on the model data.The predicted discrepancy between simulation and experimental data arises from: (i) the small number of atoms present in the periodic boundary box (hence the model displays a slight anisotropy when mechanical properties are determined); (ii) the lengths of polymer chains built in the model are infinite rather than the distribution of finite chain lengths found in the real system; (iii) finally, the model makes no allowance for defects present in the sample. However, it can be seen from Table 1 that the results are actually in reasonable agreement, indicating that it is possible to obtain comparative information from limited models such as these. Conclusions This work indicates that the use of kinetic and computer modelling of epoxy cure reactions can yield complementary information on the structure, mechanisms and expected bulk properties.This is encouraging for it highlights the possible future use of computer simulation to design novel materials with specified, desirable properties. It also provides a funda- mental understanding of the cure reactions involved with epoxy resin systems and may have implications for the industrial processing/use of commercial polymers. 3100, 80 i w1 I1 tlrn in Fig. 7 Typical radio-HPLC chromatogram depicting from the later stages of a BADGE-DAE reaction involving a higher amine concen- tration showing a number of reaction intermediates (conditions as for Fig.4). 1, Amine, A; 2, amine-epoxide dimer, AE; 3, epoxy-ended trimer, EAE; the remaining assignments are yet to be confirmed; 4, AEA or cyclic (AE),?; 5, (AE),; 6, cyclic (AE),?; 7.E(AE),; 8, (AE),; 9, E(AE),; 10, (AE), The work of Mr. Adrian Deazle and Dr. Ian Aspin was generously supported by The Procurement Agency, Ministry of Defence (grant 2064/102/A) and SERC (grant GR/H27786), respectively. The authors thank the Materials and Structures Department, Defence Research Agency (Aerospace Division) RAE, Farnborough for the kind use of their thermal analysis facilities and Dr. Martin Clegg (DRA) for GPC measurements. We would also like to thank Dr. S. Ramdas (BP Research Centre, Sunbury) for access to computing facilities. References 1 Chemistry and Technology of Epoxy Resins, ed. B. Ellis, Blackie Academic and Professional, London, 1993,and references therein.2 J. M. Vergnaud and J. Bouzon, Cure of Thermosetting Resins: Modelling and Experiments, Springer-Verlag, London, 1992, and references therein. 3 G. J. Buist, A. J. Hagger, J. R. Jones, J. M. Barton and W. W. Wright, Polym. Commun., 1988,29, 5. 4 G. J. Buist, A. J. Hagger, B. J. Howlin, J. R. Jones, M. J. Parker, J. M. Barton and W. W. Wright, Comput. Chem., 1993,17,257. 5 Polymer Characterization, ed. B. J. Hunt and M. I. James, Blackie Academic and Professional, London, 1993,and references therein. 6 G. J. Buist, A. J. 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