~~~~~ ~ Molecular modelling of the physical and mechanical properties of two polycyanurate network polymers? Ian Hamerton, C. Richard Heald and Brendan J. Howlin" Department of Chemistry, University of Surrey, Guildford, Surrey, UK GU2 5XH Elastic moduli and glass transition temperatures (T,s) of two polycyanurates, based on the dicyanates of bisphenol A and an oligomeric poly(ary1ene ether sulfone), have been predicted from molecular simulation. The simulated mechanical and physical parameters offer reasonable agreement with the experimental values. This is one of the first preliminary reports of the prediction of properties of a network polymer. The development of commercial cyanate (-0-CEN) chemis-try followed the discovery by Grigat and Putter in 1964 of a convenient and reliable preparation involving treatment of alkoxide or phenolate with cyanogen halide.' Several other methods of preparation are known, but are less widely appli- cable.' Alkyl cyanates readily isomerize to the corresponding isocyanate (-N=C=O), but aryl cyanates (1) do not rearrange and their chemistry is dominated by attack of nucleophiles on the cyanato ~arbon.~ A particularly important reaction is the cyclotrimerization to yield 1,3,5-triazines (or sym-triazines)(2), Scheme 1; the reaction is promoted by heat and a range of catalysts including protic acids, Lewis acids, bases and metal ions.4 The cyclotrimerization of a dicyanate gives rise to a network structure, and cyanate ester resins formed by homo- or co-polymerization of the dicyanate of bisphenol A, or closely related compounds, are an increasingly important class of high-performance polymers.2 The resins possess high glass transition temperatures ( 190-260 "C),show low dielectric loss behaviour and low moisture absorption, are tough, and show good peel strength; they are seen as potential replacements for epoxy resins and bismaleimides.2 In their range of applications as high performance materials the value of the cured resin < is extremely important as it largely governs the use temperature.Hence, an ability to predict this parameter would be of major importance in designing new materials. Previous work has demonstrated the feasibility of building molecular models of poly(ary1ene ether sulfone) s, poly(ary1ene ether ketone)s5-* and linear epoxy polymer^.^^'^ The results of this study have indicated that modelling of thermoset polymers in the bulk should give insights into the factors governing the observed physico-mechanical properties.The aim of the current study is to calculate physical and translion metal 0 catalyst-nonylphenol, heat * NAN cyclotrirnerization 044& X D Qx 1 2 Scheme 1 Polymerization reaction for the polycyclotrimerization reac- tion and monomer structures for the compounds studied. Bisphenol A dicyanate: X =4-NCO-C6H4-C(CH3)2-. Six ring poly(ary1ene ether sulfone) dicyanate: X =4-NCO-C,H4-C( CH3)2-C6H4-O-C6H,-S02- C,H,-O-C,H,-C( CH3)2-. +Presented at the Second International Conference on Materials Chemistry, MC2, University of Kent at Canterbury, 17-21 July 1995.mechanical properties from simulation and to compare these with experimental data for the bulk state. Calculations Molecular simulation A Silicon Graphics Indigo RS4000 running the computer program 'Professional POLYGRAF v3.2.1' (Molecular Simulations, Inc.) on IRIX v5.1.1.2 was employed to generate models of the monomer from crystal data." It was also used to model the polycyclotrimerization product of bisphenol A dicyanate (the unit shown in Fig. 1). The inherent symmetry of the models is used to duplicate the dihedral angles of interest. The generic force field Dreiding-I1 which was used has been described previously.12 Modelling of the polycyanurate of bisphenol A dicyanate (BPADC) under bulk conditions.A repeat unit containing the bisphenol A moiety linked to cyanurate ring was constructed with one head and two tails in the polymer module of POLYGRAF (Fig. 1).When this repeat unit was polymerised by removal of the tail atoms which are replaced by the head atoms a three-dimensional network polymer was constructed. Owing to the 200 atom limit in the ELASTICA module in this version of POLYGRAF, only five repeat units can be added before this limit is reached. Partial atomic charges were assigned by the Gasteiger method.13 This was then converted into an amorphous network at the experimental densityi4 of 1.26 g ~rn-~ at a temperature of 300 K. The method used to generate the amorphous system was the Monte Carlo tech- nique.15 Fifteen random struFtures were built into a cubic periodic cell of length 12.95 A and extended using periodic boundary conditions (PBC).Tail correction16 was performed to join the simulated cell to the imaginary cells. Structures were chosen where the head atoms of one structure were as close to the tail of the image as possible. Six structures which fulfilled these criteria were used in the remainder of the simulation. These structures were then minimised using conju- gate gradient^'^ at constant volume until energy convergence Fig. 1 The repeat unit of the bisphenol A polycyanurate. The hydrogen tail atoms (t) are removed and the fragment joined to the head atom of the next repeat unit (h).J. Mater. Chem., 1996, 6(3), 311-314 311 t H Fig.2 The repeat unit of the four ring poly(ary1ene ether sulfone) polycyanurate. The hydrogen tail atoms (t) are removed and the fragment joined to the head atom of the next repeat unit (h). was achieved. The energy convergence was defined as an energy change in two subsequent cycles amounting to less than 0.01 kcal mol-l.7 Canonical dynamics under both con- stant pressure and temperature conditions (NPT) were per- formed. The Nos& formulation18 was used to integrate the velocities over the time period of 1OOps after equilibration at the temperature concerned for the six remaining structures. Two simulation temperatures, 300 and 400 K respectively, were used. Calculation of the mechanical properties of bisphenol A polycyanurate. After the molecular dynamics simulations (MD) the six lowest energy structures from each simulation were extracted for further use.Their periodic images were unex- tended so that only the original cell and the structure remained. Constant volume minimisation was then carried out on these structures until energy convergence was achieved. During the MD stage the structure moved away from a cubic cell into an anisotropic form. In the ELASTICA module the triclinic function was used to calculate the elastic properties, due to the structure becoming anisotropic in the MD stage. Consequently, the elastic properties have to be averaged over many different forms of the bisphenol A dicyanate model so that the anisotropic nature can be overcome. Modelling of the polycyanurate of a six-ringed poly(ary1ene ether sulfone) PAES.Mechanical properties. The repeat unit used to build the six ringed PAES polycyanurate network is shown in Fig. 2. This consisted of adding another bisphenol A and a bisphenol S moiety to the bisphenol A polycyanurate model generated earlier. This model also had one head and two tails. Owing to the 200 atom limit only two repeat units of this polymer were allowed by the current version of the software. The network is built up from this ideal two monomer unit using the periodic boundary conditions. The density used was 1.20 g cmP3, the value being detFrmined from experiment. The periodic cell was of length 15.1 A and the structures to be used as input to the ELASTICA module were generated in the same manner as described in the previous section.Calculation of the glass transition temperature (Tg).The only limit on the size of the model to be used for determination is the amount of computer time that the simulation will take, unlike the elastic properties calculation. The compromise that we have chosen is to use six repeat units as described above (Fig. 3). Partial charges were assigned by the Gasteiger method13 and Monte Carlo simulation was used to build ten different models at a den$ty of 1.20 g cm-3 at a temperature of 3W0K, cell length 17.1 A. The starting volume was therefore 4983 A3. The model that was most amenable to tail correction was used for the rest of the simulation.PBC were imposed and extended to 26 image tails. The structure was energy minimised to convergence using constant volume minimisation. Canonical (NPT) dynamics were performed on this model starting at 800 K and dropping by 100 K every 250 ps. The final structure from each simulation was used as the starting structure for the next simulation. The temperature was decreased rather than increased in order to attempt to smooth out the effects of high energy transitions. The first 50ps of t 1 cal=4.184 J. 312 J. Muter. Chem., 1996, 6(3), 311-314 Fig. 3 Model of the six-ringed poly(ary1ene ether sulfone) polycyan- urate used in the Tg simulation each simulation was discarded as the structure was equilibrat- ing during this time period and the volume thermal expansion coefficient (VTEC) at each temperature was calculated using eqn.(1) VTEC=AV/V=(V-&)/V (1) where Vo is the original cell volume and V the average cell volume at a particular temperature. Results and Discussion Tests for equilibration and consistency The potential energy and volume were monitored over time and were seen to equilibrate after the first 50ps of the simulation under NPT conditions. Roe et a1.l’ have shown for thermoplastic polymers that the volume of the cell continues to decrease slowly over a nanosecond of simulation but that the majority of the decrease is over in about 50ps. Hence, there will be an error associated with the use of a volume after 250 ps, but this will be unlikely to have a major effect on the calculated properties.Mechanical properties of the polycyanurate of bisphenol A dicyanate This simulation was performed in order to validate the model- ling techniques used by correlating with an experimentally well determined and well known commercial polymer system. The elastic constants for the bisphenol A polycyanurate are given in Table 1 along with the experimental data. Experimental values were determined by us using standard mechanical testing procedures. The details of this will be published separ- ately.” The Young’s modulus from simulation was 4.04 GPa and that of experiment 3.39 GPa. Poisson’s ratio for the same system was 0.39 (simulated) and 0.35 (experimental).The only Table 1 Elastic constants of the bisphenol A polycyanurate obtained from the ELASTICA module in POLYGRAF ~ ~~~~~ mechanical property experimental result simulation result bulk modulus, B/GPa 3.79 &0.28 3.89 f2.04 Poisson’s ratio, u 0.35 k0.01 0.39 0.13 Young’s modulus, E/GPa 3.39 k0.16 4.04 2.14 Lame constant, A/GPa 2.95 k0.25 4.32k2.17 Shear modulus, G/GPa 1.25& 0.05 1.28& 0.75 constant to be above a 50% error margin was the Lame constant 2 (which has no physical meaning). In this and other simulation work21*22 the elastic constants are generally higher than the experimental values. Additionally, they are always at the upper limit of these values. One problem with the model was that it fails to address the formation of cage structures arising from intramolecular cyclisation (Fig.4) which have been reported by Fang et ~21.~~using mass spectral data and these structures may account for the low observed crosslink density of these polymer systems. Naturally, our model assumes a ‘perfect’ polymer lacking voids, defects or structures like those mentioned above. Mechanical properties of the polycyanurate of a six-ringed poly (arylene ether sulfone) The averaged results, together with standard deviations for the mechanical properties are given in Table 2. The Young’s modu- lus and Poisson’s ratio had simulated values of 3.64 GPa and 0.35 respectively. Experimental values for these parameters were 2.50 GPa and 0.33 respectively. It is interesting to note that the simulated results are higher than the experimental results but are of the same order of magnitude.The difference in the parameters is indicative of the limited nature of the model where the Young’s modulus of elasticity is higher in the simulation. In their simulation of a thermoplastic polymer system, Fan and Hsu~~have reported errors of between 20 and 40% on Young’s, bulk and shear moduli in a simulation of UDEL poly(ether sulfone). Their results were consistently Fig. 4 Diagram depicting the proposed cage structure comprising three bisphenol A dicyanate oligomers (after ref. 23) Table 2 Elastic constants of the six-ringed poly(ary1ene ether sulfone) polycyanurate obtained from the ELASTICA module in POLYGRAF mechanical property experimental result simulation result bulk modulus, B/GPa 2.53 k0.28 3.68 & 2.43 Poisson’s ratio, u 0.33 k0.02 0.35k0.19 Young’s modulus, E/GPa 2.50 0.04 3.64 & 1.86 Lame constant, A/GPa 1.91 k0.29 3.45 5 2.54 Shear modulus, G/GPa 0.89 0.10 1.12 k0.79 higher than experimental values although the Young’s modulus was lower.They concluded that the difference in results might arise from the idealised interactions between atoms and mol- ecules. Our results, which of course relate to a much more complex network, are still remarkably well reproduced. Physical properties of the polycyanurate of a six-ringed poly (arylene ether sulfone) The initial volume of the system was 4983.6 A3 and the results are given in Table 3.A plot of volume thermal expansion coefficient versus temperature was used to calculate the Tg (Fig. 5). The intercept of the best fit lines to the data gave a calculated Tp of 490 K. A plot of total energy versus temperature was also used to determine the Tg and this gave a value of 495 K (Fig. 6). The experimental value for this system is 413 K as determined by dynamic mechanical thermal analysis. This value is very low for a crosslinked p~lycyanurate~’ and prob- ably reflects the low degree of conversion achieved as a result of the cure schedule used. From Fig. 6 the volume thermal expansion coefficients for the glassy (a,) and liquid states (al) were calculated and from these the linear thermal expansion coefficient was determined.These are compared with the literature values2’ in Table 4. The good agreement between Table 3 Average energies, volume and change in volume (AVIV)values for the six-ringed poly(ary1ene ether sulfone) polycyanurate 100 807.4 5626.9 0.114 200 899.6 5884.9 0.153 300 1030.4 5798.2 0.140 400 1035.2 6217.3 0.185 500 1338.7 6264.3 0.204 600 1343.2 6283.3 0.207 700 1630.9 6525.5 0.236 800 1790.8 7093.1 0.297 0.351 0.05 0 100 200 300 400 500 600 700 800 TIK Fig. 5 Plot of AV/Vversus temperature for the six-ringed poly(ary1ene ether sulfone) polycyanurate model for the G determination. The straight lines of the plot are least square fits to the data points. I. I lbo 260 300 400 500 600 700 800 TIK Fig.6 Plot of total energy uersus temperature for the six-ringed poly(ary1ene ether sulfone) polycyanurate model for the G determi-nation. The straight lines of the plot are least squares fits to the data points. J. Muter. Chem., 1996, 6(3), 311-314 313 Table 4 Volume thermal expansion coefficient (VTEC) and linear thermal expansion coefficient (LTEC) in the glassy (a,) and liquid (al) states of the six-nnged poly(ary1ene ether sulfone) polycyanurate simulated VTEC expenmental VTEC simulated LTEC experimental LTEC a,/K a,/K 189x10 309 x 10 226x10p4 576 x 629x10 103 x 752x10 192x lop4 calculated and experimental values is indicative of the validity of the simulation, ag agrees more closely than does al indicating that the liquid transition is not handled as well These results indicate that simulated Tgs can be obtained accurately to within 70 K of the actual expenmental value, providing confi- dence in the prediction of the Tp of other network polymers It should be borne in mind that the simulated values represent the Tg of a ‘perfect’ polymer and the model does not take into account any defects, areas of crystallinity or voids which might yield a Tg at variance with the simulation Nevertheless, accurate results can be achieved with relatively simple models such as this It would also be possible with this model to perform further simulations around the simulated Tp value in order to determine more accurately the position of the large increase in volume thermal expansion coefficient and hence the position of Tg more precisely It should be noted that the simulated Tp was actually obtained first and corroborated by the experimental result, making it a true prediction and allowing no bias of the simulation to occur Conclusions The results of this work indicate the potential of molecular simulation in the determination of physical and mechanical properties of crosslinked polymers The relatively unsophisti- cated models give mechanical and physical properties that agreed well with literature values This level of accuracy found here for a thermoset system is comparable with that found in the literature simulations of linear polymers The major limi- tations on our models were the 200 atom limit imposed by the software With improvements in software and computing power more representative models are now possible The update to POLYGRAF, Cerius’ has a 20000 atom limit but at the time of writing does not have the facility to handle monomers with multiple heads and tails We wish to thank the Engineering and Physical Science Research Council for generously funding a research studentship for one of us (C R H ) At the University of Surrey we thank Mr R Whattingham (Materials and Science Department) for assistance in obtaining physical and mechanical measure-ments and Dr A S Deazle for his help with the use of the computational techniques References 1 E Grigat and R Putter, Chem Ber ,1964,97,3012 2 A W Snow, The synthesis characterisation and manufacture of cyanate ester monomers, in Chemistry and Technology of Cyanate Ester Resins, ed I Hamerton, Blackie Academic and Professional, Glasgow, 1994 3 E Grigat and R Putter, Angew Chem ,Int Ed Engl , 1967,6,206 4 D Martin, M Bauer and V A Pankratov, Russ Chem Rev, 1978, 47,975 5 I Hamerton, B J Howlin and V Larwood, J Mol Graphics, 1995, 13,14 6 I Hamerton, C R Heald and B J Howlin, Makromol Chem Theory Szmul, 1995, in the press 7 I Hamerton, C R Heald and B J Howlin, Molecular modelling of poly(ary1ene ether su1fone)s under bulk conditions, Modelling and Simulation in Materials Science and Engineering 1995, in the press 8 N Anscombe, I Hamerton, B J Howlin and I D H Towle, Polym Bull, submitted for publication 9 I P Aspin, J M Barton, G J Buist, A S Deazle, I Hamerton, B J Howlin and J R Jones, J Muter Chem, 1994,4385 10 J M Barton, G J Buist, A S Deazle, I Hamerton, B J Howlin and J R Jones, Polymer, 1994,35,4326 11 J M R Davies, I Hamerton, J R Jones, D C Povey and J M Barton, J Crystallogr Spectrosc Res ,1990,20,287 12 S L Mayo, B B Olafson and W A Goddard 111, J Phys Chem, 1990,94,8897 13 J Gasteiger and M Marsili, Tetrahedron, 1980,36, 3219 14 D A Shimp and W M Craig, 34th Int SAMPE Symp ,May 8-11 1989,34,1336 15 N Metropolis, A W Rosenbluth, M N Rosenbluth, A H Teller and B Teller, J Chem Phys , 1953,21, 1087 16 T A Weber and E Helfand, J Chem Phys ,1979,71,4760 17 R Fletcher and C M Reeves, J Comput, 1964,7, 149 18 S Nose and M L Klein, Mol Phys ,1983,50,1055 19 J R Roe, D Rigby, H Furayuia and H Takeuch, Comput Polym Sci ,1992,2,32 20 C R Heald, PhD Thesis, University of Surrey, 1995 21 C F Fan,T Cagin,Z M Chenand K A Smith, Macromolecules, 1994,27,2383 22 M Hutnik, A S Argon and U W Suter, Macromolecules, 1993, 26,1097 23 T Fang and D A Shimp, Prog Polym Sci ,1995,20,61 24 C F Fan and S L Hsu, Macromolecules, 1992,25,266 25 I Hamerton, Properties of unreinforced cyanate ester resins, in Chemistry and Technology of Cyanate Ester Resins, ed I Hamerton, Blackie Academic and Professional, Glasgow, 1994, p 209 Paper 5/04835D, Received 21st July 1995 314 J Muter Chem, 1996,6(3), 311-314