3.1. Thermal Analysis of the Homopolymerization Reactions
The monomers were each analyzed using DSC to determine (a) the degree of cure and (b) the glass transition temperature (
Tg) for later use in the simulation study. In each case, the temperature program applied involved ‘heat-cool-heat’ with the sample being heated from room temperature to 300 °C at 10 K/min during each heat cycle. The DSC data produced from the first step of the heat, cool, heat cycle are presented in
Table 1 (average of three measurements) with examples shown in
Figure 2.
During the first heating cycle it was apparent that two of the five monomers (BP-a) and (BD-a) underwent very visible endothermic melting transitions. All of the monomers used in this work are solid at room temperature and one might expect to see these endotherms in all of the samples. What these data demonstrate is that it takes more energy for the BP-a and BD-a samples to melt, which may be due to a higher degree of crystallinity in these monomers. These benzoxazines, containing phenolphthalein and dicyclopentadiene moieties, respectively, have much bulkier bridging groups than those of the other three monomers, this may be the cause for this greater requirement of energy.
The exotherms, showing the polymerization reaction for all six monomers, display peak maxima within a narrow range of 218–242 °C. The monomers that display melting also show broad exotherms; the remaining monomers display much more pronounced peaks whilst curing. If a single exothermic peak is observed, then it is assumed that the curing results represent a single chemical process as a first approximation, although two or more simultaneous or very close chemical reactions cannot be ruled out [
21] and previously we have used mathematical modelling to deconvolute the thermal data [
9] to reveal contributions from several processes to the reaction exotherm. In addition, it has to be assumed that all of the heat generated is a result of the curing reaction, which is irreversible ring-opening and formation of the methylene bridge in the case of benzoxazines. The most symmetrical, Gaussian curve appears to be produced by the BF-a monomer with BA-a and BT-a appearing quite symmetrical, although there does appear to be slight trailing on the curve, perhaps suggesting that there is a small change in viscosity occurring in the system which has resulted in the reaction becoming more diffusion controlled. Both BP-a batches and BD-a form especially broad peaks representing a slower reaction and perhaps a combination of more than one reaction process occurring.
The lowest energy transition occurs for the BD-a sample at 183.5 J/g (50.9 kJ/mol Bz ring) and the highest, almost double, occurs at 326.0 J/g (73.8 kJ/mol Bz ring) for BT-a, based on the sulphur containing benzoxazine. The exotherm for BA-a (
Tmax ca. 240 °C and ∆
Hp = 309.3 J/g) agrees reasonably closely with a literature value of
Tmax = 243 °C, although the enthalpy is significantly higher, ∆
Hp = 240 J/g [
22]. Pure benzoxazines typically show symmetrical exotherms between 200 and 250 °C, with ∆
Hp = 150–600 J/g, although the exotherm may be skewed and reduced to lower temperatures in the presence of phenolic and amino impurities, arising from the synthesis of the monomer. In an extreme case, there will be multiple peaks, although none of the exotherms recorded here are truly multimodal.
3.2. Determination of Glass Transition Temperature Using DSC
The second heating cycles of the DSC experiments were interpreted to yield the
Tg of the monomers in their now cured resin form (
Table 1). All the cured resins demonstrated a single
Tg, which strongly implies that the samples are homogeneous. The
Tg values given here experimentally have been interpreted using the inflexion as exemplified by
Figure 3.
The trend of the average glass transition temperature is: PBA-a < PBT-a < PBF-a < PBD-a < PBP-a, with PBP-a Batch 2 having the highest average
Tg of all. This fits well with the knowledge that PBP-a Batch 2 and PBP-a have the same polybenzoxazine backbone. It is interesting to note that increasing the butanol content and decreasing the BF-a content of the BP-a formulation to create BP-a Batch 2 has resulted in a higher glass transition temperature by 17 K, presumably reflecting the increased reactivity (and higher crosslink density) of the system through a hydroxyl-initiated ring opening. The greatest
Tg values found in this set of materials belong to the structures that contain the largest bisphenol linkages. The bulk of the dicyclopentadiene and phenolphthalein moieties no doubt restricts the molecular mobility of the chains with the ring structures limiting rotation. This will particularly be the case for the phenolphthalein group of PBP-a, which contains both a rigid aromatic ring and an oxygen atom, which may result in extra interactions with neighbouring chains (e.g., hydrogen bonding), which would also hinder chain motion and increase
Tg. When comparing the measured values to those available in the literature for the same monomer there is good agreement for PBA-a (151 °C measured, 150 °C literature [
23]) and PBD-a (187 °C measured, 183 °C literature [
24]).
3.4. Determination of Cure Kinetics Using DSC
Two different methods of kinetic analysis, proposed independently by Kissinger and Ozawa, were used in this work, which use variations of the Arrhenius equation [
25]. The Kissinger method is depicted in Equation (1):
where β = heating rate,
Tmax = temperature of DSC peak maxium,
Ea = activation energy,
A = pre-exponential (collision) factor,
R = gas constant. and employs thermal data determined using DSC. When lnβ is plotted against reciprocal temperature (
Figure 4) the determination of activation energy is derived from the gradient and the pre-exponential factor from the intercept (
Table 3). The Ozawa method is similar to the Kissinger method, where the inverse relationship between the logarithm of heating rate to exothermic peak temperature in Equation (2) (also
Figure 4) allows graphical determination of activation from the slope of the plot of lnβ/
T2max versus reciprocal temperature. The results are also presented in
Table 3.
where β = heating rate,
Tmax = temperature of DSC peak maxium,
Ea = activation energy,
A = pre-exponential (collision) factor, R = gas constant, and F(α) is a constant function.
All analyses using both of the aforementioned methods showed a good linear relationship between heating rate and exothermic peak temperature with R2 values no lower than 0.99 throughout.
The activation energies calculated by the two methods are very similar for each sample giving a degree of confidence in the results and the results for BA-a also match very closely to literature values (81 and 85 kJ mol−1 by Kissinger and Ozawa respectively. The similarity in activation energy of BA-a, BF-a and BT-a where only 1 kJ mol−1 separates both Kissinger and Ozawa values suggests that very similar cure processes occur in these materials. The values for BD-a are much greater at ~110 kJ mol−1 and greater still for BP-a at ~135 kJ mol−1, such a jump in activation energy suggests a change in the manner of cure. An obvious pattern to note is that BA-a, BF-a and BT-a all have small bisphenol linkages and have low activation energies, whereas the monomers with larger bisphenol linkages have the greater activation energies with the bulkiest linkage of BP-a having the greatest energy barrier. It is therefore easy to assume that the size of the bisphenol linkage has a significant effect on polymerization with larger groups hindering cure. This seems counterintuitive when one attempts to relate the kinetic information to degree of cure where PBD-a gives by far the greatest conversion value. It has therefore been found that polymerization with a large activation energy does not necessarily lead to a lower degree of cure when cured under standard conditions.
3.5. Determination of the Glass Transition Temperature Using Dynamic Mechanical Thermal Analysis
DMTA is the primary method for determining the glass transition temperature (
Tg) of many polymers and has been identified to be several times more sensitive than DSC [
26]. For this work a temperature range of −50 to 260 °C was used to allow identification of
Tg and where possible β-transitions whilst remaining within the calibration range of the instrument.
Figure 5 shows the DMTA plot produced for PBA-a from which a clear a clear
Tg can be ascertained as the storage and loss moduli and tan δ change dramatically in the region of 125 to 240 °C as the polybenzoxazine loses its stiff, glassy nature, first becomes more plastic and ultimately more rubbery.
Figure 6 shows the portion of the DMTA plots, which reveal the β-transitions, which occurs in the range −25 to 120 °C with the PBT-a β-transition occurring at the highest temperature and PBP-a (Batch 2) occurring at the lowest. The β-transition allows a much more limited degree of movement and is usually localised to side-chains or branches from the main polymer backbone. In
Figure 6 an even more restricted transition (γ-transition) can be seen at lower temperatures in some of the materials e.g., in PBA-a centered around 0 °C, with the other materials all showing what might be the end of this peak at −50 °C.
Table 4 presents the DMTA data for all of the polybenzoxazine materials used in this work, from which it is clear that the sulfur- and phenolphthalein-containing polybenzoxazine backbones give rise to greater values of
Tg than their counterparts. The phenolphthalein backbone in both of its formulations gives the highest
Tg, with the ‘purified’ batch 2 version proving slightly superior (+3 K). This is to be expected as the Batch 1 sample contains a quantity of BF-a, which would depress
Tg. The order of
Tg by DMTA then is: PBP-a > PBT-a > PBA-a > PBF-a > PBD-a with the PBD-a value being 20 K lower than the next lowest PBZ and PBP-a and PBT-a being 25 K higher than the next highest. It is difficult to postulate why this trend is apparent. PBA-a and PBF-a which have very similar backbones give close matching
Tg values (within 7 K) of each other, whilst PBP-a and PBT-a match even more closely (within 2 K) whilst having markedly different bridging groups. When analyzed via differential scanning calorimetry (DSC) a similar trend in glass transition temperature was seen, however via DSC PBD-a gave the second highest
Tg after PBP-a. It was suggested that this result showed a clear relationship between bisphenol linkage size and
Tg, where the large linkages would restrict molecular motion and increase
Tg. The change in PBD-a value when analyzed via DMA opposes this hypothesis as the materials with the two largest bisphenol linkages now give both the highest and lowest values for
Tg.
To gain a better understanding of these properties of the polybenzoxazines crosslink density has been calculated from the DMTA analyses using Equation (3). In theory, higher crosslink density of polymer networks can lead to increases in storage modulus and glass transition temperature (
Tg)
3.
where
Ge is the storage modulus at equilibrium,
Φ is the front factor (unity for ideal rubbers),
R is the gas constant,
v is the crosslink density (number of moles of network chains per unit volume of cured polymer) and
Te is
Tg + 50 °C [
27].
The
Tg data (
Table 5) yield three groups of values: PBD-a by far the lowest, PBA-a and PBF-a intermediate and PBP-a and PBT-a the greatest, the same grouping can be seen in the crosslink density. PBD-a gives a crosslink density of 1.4 × 10
−3 mol cm
−3, less than half the value of PBA-a and PBF-a (3.6 and 3.8 × 10
−3 mol cm
−3 respectively) which are ca. 1.7 × 10
−3 mol cm
−3 below that of PBP-a and PBT-a. This is consistent with the accepted view that crosslink density has an influence on
Tg. As crosslink density increases chain movement/molecular mobility is further reduced resulting in more energy being required to overcome this obstacle. However, the results suggest that another factor may be at work as PBT-a has a greater crosslink density than PBP-a by 20% yet their
Tg values only differed by 2 K. It has been suggested that free volume, hydrogen bonding, chain interaction and intermolecular packing can also influence these properties [
28]. It is interesting to note how in the PBP-a, the crosslink density changes with removal of the BF-a (20%) in its formulation. The crosslink density of the PBP-a Batch 1 is 5.5 × 10
−3 mol cm
−3 compared with the 18.4 × 10
−3 mol cm
−3 of PBP-a Batch 2 has an increase of more than 300%. Particularly intriguing is that the large increase in crosslink density only results in a 3 K (1.5%) increase in
Tg, thus confirming that although crosslink density does influence
Tg it is not the only influence.
3.6. Determination of the Glass Transition Temperature Using Molecular Dynamics Simulation
Molecular dynamics (MD) has been used to estimate
Tg by simulating the location and velocity vector for each atom within a molecular model over time at specified conditions of temperature and pressure. The region representing the
Tg is typically determined by performing simulation experiments at different temperatures and calculating the density of the model at each simulation temperature;
Tg is estimated as the point of intersection between the thermal expansion gradients for higher and lower temperature data. In this work, the method reported by Hall et al. [
17] was used to find the best point of gradient change (the ‘hinge point’) by finding when the fit quality of a line is at its maximum, based on finding the best fit for a gradient change as a function of temperature. An in-house program, written in Perl script, was used to analyze the raw data from the MD simulations, yielding a probability trace for
Tg, mapped against temperature. A peak position may represent the
Tg and the breadth of the peak also indicates the overall quality of the simulation data. The ‘quality of fit’ is determined by centering an ellipse, of the same eccentricity as the standard deviation error bars and of sufficient radius to make a tangent with the best fit line.
A Beckerman box refinement method was employed to fit the line and minimize the total of the semi minor axis radii, which quantify the fit quality. Having calculated these parameters for a number of simulation temperatures, they were superimposed on the original density vs. temperature data. Examples of the calculations are shown on the simulated plots as the red line (the peak occurs where the gradient changes i.e., the transition midpoint certainty, TMC). Thus, the
Tg is determined by the data rather than the experimentalist’s preconceived notion. A good example of this is shown for PBP-a (
Figure 7) where two clear transitions are apparent, one over the range 190–240 °C and another above 290 °C. For comparison, the DMTA data for this material reveal an empirical
Tg of 190–225 °C (
Table 6).
The second clear transition in the MD simulation for PBP-a is attributed to the onset of thermal degradation. Whilst a discussion of this phenomenon falls outside the scope of the present paper, this has been shown to correlate well with thermal stability data determined using thermogravimetric analysis [
27].
Generally, the MD data show good agreement with the
Tg data produced using DMTA, but some simulated transitions are more easily discerned than others (
Figure 8). For instance, in the case of PBA-a, the density starts to fall between 160 and 190 °C, which matches the empirical
Tg for the same polymer measured by DMT; the TMC trace reveals a slightly lower value (150 °C). PBP-a shows a change in density between 190 and 220 °C (compared with a value of
Tg of 200 °C determined using DMTA). The data for PBD-a are presented (
Figure 8), but it is significantly harder to discern changes in the density plot, which is more uniform in the observed changes. A small change can be identified between 150 and 160 °C, but the TMC trace shows a maximum at 170 °C. This may suggest that the model for PBD-a is not a good representation (in terms of crosslink density and bulk density) of the authentic network. It may be that our simplified model does not capture the complexity of the isomeric mix. The parent benzoxazine would originally have been prepared commercially from dicyclopentadiene and a phenolic derivative via reaction at the C=C double bonds on each ring (the resulting bisphenyl molecule would have been subsequently reacted with aniline and formaldeyde (or paraformaldehyde) to yield the benzoxazine monomer [
29]. Consequently, not only may the structural motif, which makes up the bridge of the monomer exists in both
exo and
endo forms [
30] (
Figure 9), but the initial reaction of dicyclopentadiene with the phenol derivative at either ends of the double bonds might have led to different isomers (or more likely different isomeric mixtures). These structural differences would all potentially lead to polymers for which the free volume and
Tg values would vary, but further work is required to confirm this.