Quantifying the Effect of Polymer Blending through Molecular Modelling of Cyanurate Polymers

Modification of polymer properties by blending is a common practice in the polymer industry. We report here a study of blends of cyanurate polymers by molecular modelling that shows that the final experimentally determined properties can be predicted from first principles modelling to a good degree of accuracy. There is always a compromise between simulation length, accuracy and speed of prediction. A comparison of simulation times shows that 125ps of molecular dynamics simulation at each temperature provides the optimum compromise for models of this size with current technology. This study opens up the possibility of computer aided design of polymer blends with desired physical and mechanical properties.


Introduction
Cyanate esters constitute a family of addition cured high performance, thermosetting polymers, which occupy a niche intermediate between high glass transition temperature (T g ), tetrafunctional epoxy resins and bismaleimides (BMIs) [1]. The combination of favourable thermal and mechanical performance (dry T g values of 270-300uC are common with a strain at break of over 5-8%) coupled with low dielectric loss properties (a low dielectric constant of ca. 2.7 with a loss tangent of 0.003 is typical [1]) make cured cyanates attractive and able to offer a unique property profile. Although requiring toughening for some engineering applications, cyanates can be combined with inherently tough engineering thermoplastics (HexPly 954-2A, G IC = 250 J/ m 2 ) [2] or elastomers (HexPly 953-3, G IC = 450 J/m 2 ) [3] to yield impressive enhancements. In this form they typically find application as matrices in advanced composites (either in combination with epoxy resins in aerospace applications [4]) or with BMIs as dielectric polymers in the microelectronics industry [5]. The rationale for the preparation of the binary blends presented here is to examine the potential for deriving improved properties (physical and mechanical) through the co-reaction of chemically compatible monomers. To date, aside from isolated studies [6], it appears that little systematic work has been carried out to examine the potential benefits of blending and co-curing polycyanate monomers. In the current study, we have examined three common cyanate species and the binary blends thereof by simulating selected properties using atomistic modelling in our drive to improve our predictive capability.
It is fundamental to our approach that the simulations that are performed are always supported by empirical data, either single crystal data in the formation of structures or from physical or mechanical measurements when determining properties for the final polymer. In this paper we report a systematic study of the blending of the three cyanates by molecular simulation using the software suite Materials Studio [26]. This method is generally applicable to all crosslinked resin systems. There is always a compromise between how long the simulation takes and the accuracy of the predicted results. If it takes much longer to simulate the system than it takes to synthesize and measure the properties predicted then the method will be of limited usefulness in property prediction. This is a particular problem with synthetic polymers as there is an on-going debate on whether it is possible to equilibrate a long polymer chain by molecular mechanics, see for example [27].

Materials
The dicyanate ester monomers: 2,2-bis(4-cyanatophenyl)propane (1), hereafter termed BADCy 1,1-bis(4-dicyanatophenyl)ethane (2) (LECy), and the oligomeric phenolic cyanate (average value of n = 1) (3) (PT30) were the three monomers simulated in this work. (Figure 1). Experimental values of the materials were also obtained by the methods described in Crawford et. al, 2012 [28]. The blends simulated are presented in Table 1. The monomers polymerise by cyclotrimerisation, where three cyanate groups combine to form a six membered cyanurate ring, so the resulting polymer is a cross linked network composed of cyanurate rings joined by the bridging groups attached to the cyanate moieties ( Figure 2). N.B. cured blends are denoted by the use of square brackets to differentiate them from the corresponding monomer blend i.e. monomer blend (1 90 -2 10 ) becomes polycyanurate [1 90 -2 10 ] following cure.

Simulation
The Materials Studio molecular modelling suite (Accelrys Inc.) was utilised in this work [26] using in house PCs (e.g. a Dell PowerEdge 1950, 26Quad Core Intel Xeon E5140 2.33 GHz, 8 GB RAM, 500 GB HDD). The Discover module was used for general simulation requirements, such as geometry optimisation and molecular dynamics as well as molecular mechanical analysis to predict values for tensile, bulk modulus, shear modulus, Poisson's ratio and the Lamé constants. The Amorphous Cell module was used to build amorphous, homogenous 3D cells composed of molecules that were drawn in silico. It also has a number of protocols designed to make greater use of the Discover module, of specific interest is the temperature cycling protocol, which can be used for T g prediction. All simulations were performed in the bulk state, i.e. without the addition of solvent as there is no added solvent in epoxy resin cure. Potential energies were calculated using the Polymer Consistent Force Field (PCFF) [29]. An attempt was made to use the COMPASS [30] forcefield but this implementation does not cope with the cyanate group. The Legacy module within Materials Studio was used to construct an amorphous cell. The amorphous cell contained an average of 4480 atoms. The simulations were also run with cell sizes double, thrice and four times this number. A unit cell of the appropriate volume was packed randomly with the correct number of monomers, either as single monomers as in the neat resin work or in the correct mole fraction in the case of the blends. The cyanate groups were inspected and those within 4.5 Å of each other were bonded manually to form 1,3,5-triazine rings and a minimization of 5000 iterations was carried out to relieve the strain using the Discover minimization module to a convergence of 1000 kcal mol 21 Å 21 . A Conjugate Gradient algorithm [31] was carried out to a convergence of 100 kcal mol 2 Å 21 . As all monomers were assumed to be equally coreactive the nature of the final structure depended ultimately on the initial random arrangement of the monomers. Hence it was possible to generate homogenous networks or blocked semi-interpenetrating networks depending on the starting conditions. Bonds were reacted through the faces of the unit cell to neighbouring periodic boxes to simulate an infinite three-dimensional highly cross-linked network. After the final cyclotrimerization the system was submitted to a final minimization of 10,000 iterations. The NPT ensemble with a time step of 1 fs was utilized with the Andersen thermostat [32] at a Pressure of 0.1 MPa under the Parrinello Barostat [33]. PCFF was used with the atomic Van der Waals summation, a cut-off of 10.00 Å , a spline width of 3.00 Å and a buffer width of 1.00 Å . 51 MD simulations were run between 773 K (500uC) and 273 K (0uC) in decrements of 10 K; at each temperature stage a 125 ps MD simulation was carried out. In accord with the problem of equilibrating long polymer chains, the simulations were also run Table 1. Designation of monomers and blends examined in this work. The data represent the percentage of each monomer in the blend.  for 1 ns at each temperature stage. A plot of calculated cell density was plotted against simulation temperature to determine both the T g and the degradation onset temperature.

Effect of Model Size
Increasing the model size had the effect of improving the statistics of the runs but made the T g value more difficult to determine. In essence we are providing more degrees of freedom for the system with the larger models and thereby increasing the error (by comparison with experiment). The equilibration problem increases with larger model sizes. A survey of the data produced by varying cell size is given in Table S1.

Effect of Simulation Length
The simulations that were run for 1 ns showed that, the statistics (in terms of the scatter of points) were much improved. However, the determination of the Tg value was more problematic, with a shift in the predicted value compared to the experiment. Additionally, the longer timescale served to remove the high temperature transition, which we have assigned to the thermal degradation of the material.

Hysteresis of the Model
It has been noticed in previous work by ourselves and others that in order to get results that correlate with experiment, it is necessary to run the simulation by cooling down from the high temperature regime to the lower. If the simulation is run by heating up the system, the T g value determined can vary by 30 degrees. This hysteresis is a function of the equilibration problem mentioned above and the cooling down is thought to serve to freeze out high energy motions thereby providing a better correlation with experiment.

Neat Polymers
The plot of simulated density versus temperature from the MD simulation for the neat polycyanurate [BADCy] is shown in Figure 3. The black crosses are the equilibrated volume at that simulated temperature and the red solid line is the derivative of the plot using the method outlined in Hall et al. [34]. There are several features apparent in the plot which correlate well with empirical data. At lower temperatures (80uC), a small drop in the density is apparent, which we have termed the c transition. This transition corresponds to the melt endotherm in Differential Scanning Calorimetry data of the uncured monomer. We have observed this experimentally at 82uC [27]. A second drop is also observed at 175uC corresponding to the b transition observed in the DMTA data for this polymer [28]. The glass transition (a transition) is marked by the larger fall at 260uC. The large drop in density at 350uC and 420uC may correspond to the thermal degradation of the polymer. The group bridging the two aromatic rings in this polymer has two pendant methyl groups.

Effects of Parameterisation
In previous work we reparameterised the Dreiding force field [35] specifically for cyanurate rings [36]. A study of the available x-ray crystal structure data for cyanurate rings showed that the bond lengths are not equal and that the ring was slightly puckered. The new parameterization improved the simulation results significantly. The second generation force field used in this work is generally better all round than the first generation one used earlier but there is still the option to use alternating single and double bonds in the cyanurate rings or to use delocalized aromatic rings. By default Materials Studio chooses atom types as alternating single and double bonds but we tested the aromatic rings by running the simulations with wholly aromatic rings ( Figure 6). An example is shown below for the 70:30 blend of monomer 1 and 2 (Figures 7 and 8). There is more scatter on the data for the aromatic parameterization and the thermal events are different, i.e. a transition (Tg) = 250uC, b transition = 350uC, c transition = 110uC, degradation (Td) = i) 400uC ii) 430uC for the alternating single and double bonds to a transition (Tg) = 295uC, b transition = 210uC, c transition = 90uC, degradation (Td) = i) 420uC ii) 480uC for the aromatic parameterization. The experimentally determined values of the a transition (Tg) = 292uC and the degradation (Td) = i) 416uC. Hence the aromatic parameterization gives the better comparison with experiment, so was the one used.

Binary Blends
The corresponding data for the binary blend (50% of the first two polycyanurates) comprises elements of both networks: displaying a flatter response at lower temperatures (where the behaviour of monomer 1 predominates evidenced by the lower c transition at 80uC similar to the first monomer, but appears more similar to monomer 2 at higher temperature with a transition (T g ) at 295uC and the b transition at 220uC. Interestingly the blending has pushed the degradation onset to 390uC with the second stage at 440uC, which is more similar to the third monomer.
A systematic study of the blends of the three monomers was carried out from 50:50 of each of the monomers to 90:10 and the      Table 2. It can be seen that there is a general trend towards the thermal data peaking for the 80:20 and 90:10 blends, although this is not clear cut in all cases. The predicted alpha transitions and degradation onset temperatures were compared with actual experimental values for all cases (Table 3). A visual comparison of the experimental TGA and DMTA data plotted against the simulated data is given in supporting information, Table S2. As noticed for the binary blend discussed earlier there is a general trend to favour the behaviour of the less thermally stable monomer at lower temperatures and the more thermally stable monomer at higher temperatures. There is good agreement in almost all cases except for the blend of 70:30 of monomer 3 and 1, where there are 2 inflexions in the simulated data at 280 and 370 K and the experimental data gives a value of 380 K. The three dimensional structure of this blend is shown in Figure 9. This blend also shows an anomaly at the 50:50 blend, again of monomer 3 and 1 ( Figure 10). Here there are also 2   inflexions but also 2 inflexions in the experimental data, which are close to the experimental values. This blend seems to be behaving as 2 independent networks both in the simulation and also in the experiment. Molecular simulation of cyanurate polymers is shown to reproduce with a good degree of accuracy the thermal events occurring experimentally for three different cyanate containing monomers. Furthermore it is also possible to simulate the thermal events of binary blends of the three monomers, again with good agreement to experiment. These thermal events, particularly the a transition, more commonly known as the Tg, are important in selecting materials for end use applications. The Tg determines the thermal softening point of the polymer and is crucially important in e.g. aerospace applications where it is not desirable for the polymer to exceed its Tg in use. Therefore molecular simulation can be used as a tool to screen and design polymers and blends thereof for end use applications.

Supporting Information
Table S1 A survey of the data produced by varying cell size. (DOCX)