New Method To Predict the Thermal Degradation Behavior of

Article pubs.acs.org/Macromolecules

New Method To Predict the Thermal Degradation Behavior of Polybenzoxazines from Empirical Data Using Structure Property Relationships Ian Hamerton,*,† Scott Thompson,† Brendan J. Howlin,† and Corinne A. Stone‡ †

Department of Chemistry, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH, U.K. Dstl, Porton Down, Salisbury, SP4 0JQ, U.K.

‡

S Supporting Information *

ABSTRACT: The degradation behavior of five polybenzoxazines is studied and the effect of selected experimental parameters (particle size, heating rate, and atmosphere) on the nature of the degradation pathway is examined. The particle size within the samples (systematically varied in four discrete size ranges: 250 μm) influences the progress of the early stage in the degradation mechanism (the cleavage of the bridging groups) such that the smaller particles are less stable, but the latter stages of the degradation mechanism remain largely unaffected. In contrast, the change in heating rate (5, 10, 15, 20 K min −1 ) of the thermogravimetric analysis has little effect on the first step in the degradation mechanism, but has a strong influence on the progress of the ring breakdown mechanism. Molecular simulation is shown to reproduce the thermo-mechanical behavior of the polybenzoxazine of bisphenol A/aniline very well, with the nuances of the glass transition and degradation onset temperatures simulated very closely (e.g., within 10 °C of the degradation experiment at a mass loss of 5 wt %). Quantitative structure property relationships are shown to predict the experimental char yields for all the polybenzoxazines studied within the data set, with the calculated values for the polymers based solely on the volume and surface area of the monomer structures.

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INTRODUCTION It has been reported1 that approximately 20% of the 1153 fatalities on U.S. transport airlines between 1981 and 1990 were caused by fire, with the vast majority resulting in postcrash fire accidents; 40% of the passengers who survive the impact of an aircraft accident subsequently die in these postcrash fires.2 The development of structural materials with improved fire resistance relative to commodity plastics is key to retard the fire, increase the time available for passengers to escape the aircraft interior, and thus reduce the loss of life. The EC has restricted the use of brominated diphenyl oxide flame retardants because highly toxic and potentially carcinogenic brominated furans and dioxins may form during combustion.3 The World Health Organisation (WHO) and the US Environmental Protection Agency (EPA) also recommend exposure limit and risk assessment of dioxins and similar compounds.4,5 It is essential that new (halogen-free) flame retardant systems are developed to meet the constantly changing demand of new regulations, standards, and test methods. This is often achieved by introducing highly aromatic or heteroaromatic materials such as thermoset polymer composites that form intumescent chars during the combustion process, with the polymer swelling and becoming porous to protect the underlying structure.6 Thermoset polymers have an © XXXX American Chemical Society

established history in civil aviation, in applications involving decorative panels, secondary composite structures and adhesivesaround 90% of the interior furnishings of a typical civil airliner will contain thermoset composites.7 Polybenzoxazines (PBZs) form a comparatively new family of thermosetting resins that are being explored8 as potential higher performance replacements for phenolic or epoxy resins and they occupy a niche intermediate between high glass transition temperature (Tg), tetrafunctional epoxy resins, cyanate esters, and bis(maleimide)s.9 While they are not currently widely used in civil aviation, PBZs potentially offer the best properties from conventional phenolics (in particular the combination of high thermal stability and flame resistance), and might be able to be used in place of phenolics in a number of applications. The synthetic route employed (in which both polyphenol and amine might be varied) offers the potential to yield polymers with improved toughness over conventional phenolics. PBZs are formed through step growth ring-opening polyaddition from bis(benzoxazine) monomers (Figure 1), which are in turn the products of the Mannich reaction Received: July 10, 2013 Revised: September 5, 2013

A

dx.doi.org/10.1021/ma401444z | Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Schematic showing polymerization of bis(benzoxazine)s through ring-opening and cross-linking.

between a bis(phenol), formaldehyde, and a primary amine.10 Unlike many other commercial thermosetting resins, which evolve condensation products such as water or ammonia, benzoxazine monomers react relatively cleanly to form a polymer with few reaction byproducts,11 although the exact mechanism of the polymerization reaction to form a network has not been fully elucidated, a recent report has focused on the development of phenolic and phenoxy network structures as a function of the catalyst used.12 Recent work in our group has also examined the influence of additives on the nature of the polymerization mechanism, the formation of the polymer network structure and the resulting final properties.13 We are particularly interested in rationalizing the effects of thermal conditioning on the development of char structure in cured PBZs. The ability to predict the degree to which char formation occurs and the thermal degradation onset, based on monomer structure, would assist with the design of polymers with specific thermal characteristics. If this approach is more widely applicable then this could be an important tool in the design of flame retardant polymers. In the present context, the nature of the bisphenol has been varied to examine the effect of the chemical structure on the manner in which the cross-linked polymer undergoes degradation.

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Figure 2. Structures of the monomers examined in this study. same time period that the other samples were degassed. Following degassing, all samples were placed in an air circulating oven at 120 °C and the following cure schedule was applied: heating 2 K min−1 to 180 °C (isothermal 2 h) followed by heating at 2 K min−1 to 200 °C (isothermal 2 h). Characterization and Measurements. Differential scanning calorimetry (DSC) was undertaken using a TA Instruments Q1000 running TA Q Series Advantage software on samples (5.0 ± 0.5 mg) placed in hermetically sealed aluminum pans. Experiments were conducted at a heating rate of 10 K min−1 from −10 to +400 °C (heat/cool/heat) under flowing nitrogen (50 cm3 min−1). In order to gauge the reactivity of the monomer in the bulk, dynamic DSC analysis was performed on all of the systems. Thermogravimetric analysis (TGA) was performed using a TA Q500 on milled, cured resin samples (6.5 ± 0.5 mg) in a platinum crucible and heating from 20−800 °C at 10 K min−1 in static air and nitrogen (40 cm3 min−1). Prior to analysis cured PBZ samples were separated, using three sieves of specified mesh size, into four discrete size ranges 250 μm. Dynamic mechanical thermal analysis (DMTA) (in single cantilever mode at a frequency of 1 Hz) was carried out on cured neat resin samples (3 mm × 5 mm × 17 mm) using a TA Q800 in static air from −50 to +260 °C at 2 K min−1 at 0.1% strain. Molecular Simulation. The molecular modeling program Accelrys Materials Studio versions 5.5 and 6.014 were utilized within this work and all the modeling work was carried out using an in house PC. The potential energies for all models throughout this work were calculated using the condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS),15 a force field specifically designed for polymer calculations. The benzoxazine monomers were drawn atom by atom in the polymer builder module, six copies of the

EXPERIMENTAL SECTION

Materials. 2,2-Bis(3,4-dihydro-3-phenyl-2H-1,3-benzoxazine)propane (BA-a, Figure 2), bis(3,4-dihydro-3-phenyl-2H-1,3benzoxazine)methane (BF-a, mixture of isomers), bis(3,4-dihydro-3phenyl-2H-1,3-benzoxazine)-2-benzofuran-1(3H)-one (BP-a, mixture of containing ca. 30 wt % BF-a), 3,3′-bis(3,4-dihydro-3-phenyl-2H-1,3benzoxazine) sulfide (BT-a), and bis(3,4-dihydro-3-phenyl-2H-1,3benzoxazine)tricyclo[5.2.1.0]decane (BD-a, mixture of isomers) were all characterized fully using 1H NMR, Raman spectroscopy, and elemental analysis and were used as received without further purification (unless otherwise stated). In the interests of brevity the characterization data for the monomers have been deposited as Supporting Information. It is well-known that monomer purity (in particular the oligomer content) can have a significant effect on both cure mechanism and kinetics. 1H and 13C NMR spectroscopic analyses were performed in parallel on the monomers (e.g., using DEPT-135, HSQC, and HMBC pulse sequences) and the NMR spectroscopic data are deposited as Supporting Information. All monomers (Figure 2), except BP-a, were degassed at approximately 90 °C for 1 h using a vacuum oven to reduce void formation during the subsequent curing process. BP-a was found to be very difficult to control under degassing conditions (excessive void formation) and so was simply melted and held at 120 °C over the B


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Figure 3. TGA data for of PBA-a in nitrogen as a function of heating rate.

Figure 4. TGA data for PBA-a in nitrogen as a function of particle size. consistent with the density found for the polymer (1.195 g cm−3) in the literature.16 A super cell of two cells was used to link the polymer in three dimensions and this super cell was replicated 2 × 2 × 2 in space to make a cubic structure containing 3136 atoms. Oxazine rings in close proximity in this superstructure were then linked and the resulting network copied to produce a double cube.

monomers were made and monomers that were in close proximity were manually linked to form the polymer by opening the oxazine ring, energy minimization was performed at each stage. After this procedure one oxazine ring was left effectively uncured. The amorphous cell module was used to replicate the polymer in three dimensions with the target density for the cell set to 1.2 g cm−3, C


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Table 1. Mass Loss Temperatures of the Polybenzoxazines Measured in Nitrogen and (in Air) Obtained Using TGAa temperature (°C) at which mass loss (%) recorded sample PBA-a PBF-a PBT-a PBP-a PBD-a a

5% 260 254 289 285 237

(295) (269) (323) (317) (238)

10% 313 309 315 351 310

(371) (377) (390) (406) (365)

20% 348 381 369 437 378

(450) (473) (479) (469) (415)

30% 368 428 451 472 398

40%

(499) (504) (511) (498) (420)

389 480 535 516 412

(524) (531) (532) (520) (423)

50% 417 562 N/A N/A 426

(542) (554) (549) (542) (426)

60% 456 N/A N/A N/A 440

(558) (572) (566) (564) (428)

Yc (%) 27.07 45.48 52.63 52.50 22.06

(1.64) (1.42) (1.65) (1.42) (1.17)

NB, char yield (Yc) measured at 800 °C. Italicized entries were recorded in air.

Figure 5. TGA data for polybenzoxazines in nitrogen atmosphere. Molecular dynamics (MD) simulation was performed under the NPT ensemble at 300 °C (573 K) for 10 ps and the resulting model was subjected to temperature ramped MD simulations using the temperature cycle option in the amorphous cell protocols. A collection of MD simulations was run over different temperatures, with decrements of 10 K from the starting temperature. The starting temperature was set at 300 °C (573 K) and a total of 31 MD simulations were performed, ranging between 300 °C (573 K) and 0 °C (273 K). At each temperature stage a 125 ps MD simulation was created. The first 25 ps of each simulation were used to equilibrate the system and the subsequent 100 ps simulation was used to record the results. The NPT ensemble (25 °C, 298 K, 0.0001 GPa) with a time step of 1 fs was utilized with the Anderson thermostat in combination with the Parinello Barostat.17 COMPASS was used with the atomic van der Waals summation, a cutoff at 9.50 Å, a spline width of 1.00 Å, and a buffer width of 0.50 Å. The Tg is a second order phase change, which shows a change in thermal expansion coefficient when the temperature and volume of a polymer are plotted.18 The gradient change in the plot locates the Tg and a further transition locates the Td. Generation of QSPR Models. The molecular operating environment (MOE) software (Chemical Computing Group, Cambridge, U.K.) was used for QSPR modeling. MOE was used to generate models to calculate char yield (Yc) for various bis(benzoxazine) monomers. The general procedure used can be summarized as follows: the variable of interest (e.g., char yield) was fitted to a range of independent variables (descriptors) within the database to generate a

preliminary QSPR model. The process for selection of appropriate descriptors was broadly based on trial and error, with the criteria that a suitable QSPR model should incorporate as few descriptors as possible and display a correlation coefficient value (R2) greater than 0.99. The descriptors were “pruned” by removing those in which poor correlation was found (a discussion of this process follows within the paper) in order to select the optimum set. The most significant or influential descriptors or sets of descriptors were identified for the char yield.

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RESULTS AND DISCUSSION Dependence of Thermal Stability on Experimental Parameters. All monomers (see Experimental Section) are referred to by designations indicating the components used in their preparation. Thus, BA-a is formed from bisphenol A (BA) and aniline (a); the cured polybenzoxazine is prefixed with a P (e.g., PBA-a). Initially, a series of parameters (experimental heating rate, atmosphere and particle size) were varied to optimize the analytical methodology. Thus, as expected the heating rate was observed to have an effect on the position of the peak maximum in the derivative data for PBA-a (Figure 3) and with increasing heating rate the peak maximum is raised to a higher temperature regime. D


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Figure 6. DSC data for benzoxazine monomers in nitrogen atmosphere (heating rate 10 K min−1).

the smallest particles display lower thermal stability with the first thermal event occurring at a lower temperature than the larger particles (with the largest sizes, > 250 μm, occurring between 50 and 75 °C higher). On the other hand, the influence on the thermal events occurring at higher temperatures is less marked. The char yield (measured at 800 °C) is also influenced by particle size (Figure 4), with the largest particles yielding a value some 3%−5% greater than the smallest. Thermal and Thermo-Oxidative Stability of Polybenzoxazines. The nature of the polymer backbone has a dramatic effect on the thermal stability and char yield of the polymers when analyzed under air and nitrogen. For instance, the char yields measured at 800 °C in nitrogen for both PBA-a and PBD-a are less than 30%, in contrast with PBT-a and PBP-a which show char yields of around 54%, suggesting that superficially the phenolphthalein (benzofuran-1(3H)-one) and sulfur linkages contribute more strongly to char formation than their counterparts. PBF-a shows intermediate stability with a char yield of 45% (Table 1). The TGA profiles of the polybenzoxazines in the current study (Figure 5) show significant differences in three temperature regimes (i.e., covering initial degradation, maximum mass loss, and char yield). DSC analysis of the five monomers was carried out to determine the degree of polymerization (from a comparison of the polymerization enthalpy) achieved during the curing process from the first heating cycle. The exotherms representative of ring-opening for all five monomers (Figure 6 shows the first cycle of a heat/cool/heat experiment for all monomers) fall within a similar range of 220−242 °C (Table 2).

The char yield is very slightly elevated as the heating rate increases, but it seems to have less influence on the nature of the initial degradation (between 200 and 300 °C), which is apparently invariant with increasing heating rate. Low and Ishida19,20 identified aniline as a major degradation component in the initial stages of the thermal decomposition of PBA-a, which was postulated to arise from the cleavage of the Mannich base (Figure 4) as evidenced by the presence of an infraredactive band at 1735 cm−1, consistent with a carbonyl group, that became negligible at 390 °C, arising from a secondary amide. In the same study, it was proposed that the cured polybenzoxazines contain terminal Schiff base and secondary amides as defect structures. In contrast, the maximum derivative peak in the TGA data at 388 °C has also been assigned6 to the phenolic cleavage; the latter appears much more sensitive to heating rate. Low and Ishida6 proposed a degradation mechanism wherein the nitrogen atom of the Mannich base is hydrogen bonded resulting in a stable six-membered ring.21 This degradation scheme involves two routes: one producing aniline and the other a stable conjugated Schiff base. Primarily, cleavage of the C−N bond outside of the six-membered ring is more likely to occur1 as it is less energetically stable than that inside. The C− N bond is more susceptible to cleavage than the C−C bond of the Mannich base as it has a lower dissociation energy than the latter.22 The effect of particle size on the degradation mechanism, through thermal lag, is more pronounced. In this study the PBA-a was milled to a variety of particle sizes from below 106 μm to greater than 250 μm before being analyzed at a single heating rate (10 K min−1) under nitrogen. The major effect of changing particle size is to influence the temperature stability: E


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K). This equation25 is technically most appropriate for lightly cross-linked materials, so it should only be used as a comparison between similar materials. From this analysis, it is apparent that perhaps unsurprisingly, similar cross-link densities are calculated for the PBA-a and PBF-a polybenzoxazines (given the similarity in the bridging groups) with PBT-a yielding the highest value, Table 4. This might be influenced by the rotational freedom of the thio ether allowing perhaps the unreacted benzoxazine ring more latitude to move within the network to meet unreacted monomers. The value calculated for PBF-a (intermediate between PBA-a and PBF-a) is less easy to explain, but might relate to the bulk of the bridging group inhibiting the polymerization reaction and limiting the cross-link density. It is known26 that while high glass transition temperatures can achieved for this polybenzoxazine, a carefully designed progressive cure schedule is required to achieve its full potential. In a previous study, Howlin et al. reported27 the comparative flexibility of the (analogous) ether and isopropylidene groups, showing that the simulated energy barrier to rotation was 6 kcal/mol for the isopropylidene linkage and 4 kcal/mol for the ether linkage; the phenylphthalein bridge should confer the greatest rigidity/greatest barrier to rotation, given the bulkiness of the group, coupled with the polar nature of the substituted γ-butyrolactone ring. Comparison of the nitrogen and air TGA thermograms demonstrates that the type of atmosphere has a considerable effect on the degradation processes that are occurring. Not unexpectedly, under an atmosphere of air (Figure 8) all the polybenzoxazines showed near complete degradation at 800 °C, but the initial stages of the degradation also show the influence of the bridging group. Thus, the presence of oxygen yields additional reaction pathways alongside those arising solely from thermal degradation. Interestingly, the initial mass loss is more pronounced in a nitrogen atmosphere for all of the polymers studied. Hemvichian and Ishida28 used evolved gas analysis (EGA) to reveal a complex thermal degradation pathway involving polymer degradation and recombination of radical species to yield a range of primary decomposition products (substituted benzenes, anilines, phenols, and Mannich bases), secondary products (biphenyl compounds, benzofurans, isoquinolines, and phenathridines) and ultimately char. Examination of the derivative plots of the mass loss curves is very informative in visualizing these degradation processes. For example, the derivative data for PBA-a in air and nitrogen (Figure 9) atmospheres display significantly different profiles, particularly in the proportion of the data collected between 450 and 700 °C. There are at least three processes visible, but their relative proportions differ in air or nitrogen. In nitrogen, the first process (between 200 and 350 °C) is slightly pronounced when compared with the air atmosphere; the second process (between 300 and 450 °C) is also more prominent. The effect of atmosphere is most marked in the case of the third process (between 450 and 700 °C), wherein the thermal event is significantly delayed in air and also accounts for the greatest rate of mass loss in the thermogram. Low and Ishida observed similar TGA profiles in their study,20 and found the initial mass loss rates under an oxidative environment to be lower than those observed under a nitrogen environment. They attributed these differences to possible mass gains arising from oxidation processes. Results presented here suggest that similar processes might be associated with higher temperature thermal events. Work continues in this program to examine the

Table 2. DSC Data of First Heat Cycle for Benzoxazine Monomersa ΔHpd b

c

sample

Tm (°C)

Tmax (°C)

BA-a BF-a BP-a BT-a BD-a

36 − 70 − 57

242 241 230 221 234

J/g (kJ/mol) 311 298 263 323 174

(128.8) (115.0) (132.6) (130.5) (87.7)

kJ/mol, Bz 64.4 57.5 66.3 65.3 43.9

N.B., all samples heated under nitrogen from 20 to 300 °C at 10 K min−1. bTm = melting temperature (measured from minimum in endotherm). cTmax = temperature of polymerization peak maximum. d ΔHp = polymerization enthalpy (expressed as J/g or kJ/mol of monomer and kJ/mol of benzoxazine groups). a

Interestingly the two monomers that underwent a melting process both have particularly broad exotherms, whereas the other monomers display much more pronounced curves while curing. A single exothermic peak is observed for each monomer and demonstrates that the curing results from a single chemical process as a first approximation, but an overall process formed by two or more simultaneous or very close chemical reactions cannot be ruled out.23 The lowest energy was recorded for the BD-a sample at 87.7 kJ/mol monomer (Table 2), while the values for BA-a, BP-a, and BT-a are essentially the same within the limits of the technique; the BF-a monomer yields a value that lies between the other monomers studied. As each of the monomers are difunctional this confirms that four of those tested have undergone polymerization to a similar degree; the BD-a producing a lower degree of cure (presumably because of the bulkiness/rigidity of the bridging group). Consequently, it is possible to make a comparison of the polybenzoxazines of the four similar monomers on the basis of cross-link density. Thermomechanical Behavior of the Polybenzoxazines. BD-a displayed the poorest thermal stability of the series studied and was eliminated from the more detailed study. In order to determine whether the data reflect the nature of the monomer backbone, it is important to eliminate the effect of the cross-link density. Thus, dynamic mechanical thermal analysis (DMTA) experiments were used to generate thermomechanical data from which the cross-link density could be calculated. Typical DMTA plots are shown in Figure 7 for (a) PBA-a and (b) PBP-a and the data for the series are presented in Table 3. Although it is customary to report the Tg as the peak maximum in the loss modulus, the storage modulus and tan δ data are also given for comparison (the latter consistently presents a somewhat inflated value as is commonly seen in other polymer systems in the literature). The breadth of the tan δ peaks also indicate differences in the damping behavior of the polybenzoxazines and the peak widths represent the temperature ranges over which the glass transition temperatures occur. Thus, the broadest tan δ peak (PBA-a) can be attributed to more heterogeneous networks containing both highly- and less densely cross-linked regions.24 This, in turn, results in a broad distribution of molecular mobilities or relaxation times. The cross-link density (ν) for each polybenzoxazine was calculated from the DMTA data using eq 1:

ν = Ge /φRTe

(1)

Here φ is taken as unity, Ge is the storage modulus strictly from a sample at equilibrium, but is taken at Te, where Te = (Tg + 50 F


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Figure 7. DMTA plots for (a) PBA-a and (b) PBP-a.

would possibly contribute to the large final stage observed in air. Prediction of Thermal Degradation Using Simulation and Mathematical Techniques. It has already been demonstrated29 for thermosetting polymers that the thermal degradation can be well modeled by monitoring closely changes in the simulated cell volume (or bulk density). The simulated structure of the PBA-a network (using Materials Studio and comprising 6272 atoms) is depicted in Figure 10.

products of these degradation pathways involving pyrolysis−gas chromatography−mass spectrometry and the technique of TGA hyphenated to residual gas analysis. Low and Ishida20 attributed the second loss in mass in a thermo-oxidative environment (amounting to around 20% at 400 °C) to the loss of carbon dioxide; the final stage was attributed to the breakdown of the carbonaceous char. Carbon dioxide has been found via hyphenated analysis using TGA-FTIR20 to be the major degradation product of PBA-a above 500 °C, which G


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using DMTA) and the simulation Tg values fall well within this range. PBA-a starts to degrade from around 200 to 250 °C (TGA data), corresponding to the degradation of the bridging groups and loss of aniline, and this is also observed in the simulation with a small decrease in density prior to a catastrophic drop from 250 °C onward. This demonstrates that MD techniques yield realistic predictions of the range over which the onset of thermal degradation occurs for the cured polybenzoxazines, but the technique does not allow the higher temperature processes (notably char yield formation) to be examined, since the force field used does not allow covalent bonds to break. In some applications (e.g., the production of a flame retardant polymer), the ability to predict the formation of char would be of great interest and benefit, but in order to do so it was necessary to use another approach. In a previous study,30 we reported the use of quantitative structure property relationships (QSPR) to predict various physical data in polymers, including the onset of polymerization and glass transition temperature. Using a similar approach, an equation to predict char yield was derived from the thermal data of the five monomers presented here (Table 6). The QSPR model data were fitted to the TGA data obtained experimentally in this work and the QSPR model presented in eq 2 was applied to reproduce char yields precisely for each of the polybenzoxazines (measured at 800 °C in nitrogen) and the data are presented in Table 6.

Table 3. Determination of Glass Transition Temperature (Tg) for Four of the Polybenzoxazines Using Different Parameters from DMTA Dataa Tg (°C) measured by DMTA sample

from storage modulus (midpoint)

from loss modulus (peak maximum)

from tan δ (peak maximum)

PBA-a PBF-a PBP-a PBT-a

172 165 202 197

173 166 204 199

190 184 227 213

N.B., all samples (3 mm × 5 mm × 17 mm) were analyzed in single cantilever mode at a frequency of 1 Hz in static air from −50 to +260 °C at 2 K min−1 at 0.1% strain.

a

Table 4. Cross-Link Densities for Four of the Cured Polybenzoxazines Determined from DMTA Dataa sample

Teb (K)

Tec (°C)

Ged (MPa)

10‑3νe (mol cm‑3)

PBA-a PBF-a PBP-a PBT-a

496 489 527 522

223 216 254 249

21.3 14.7 19.1 67.5

5.2 3.6 4.3 15.6

a N.B., all samples (3 mm ×5 mm ×17 mm) were originally analyzed in single cantilever mode at a frequency of 1 Hz in static air from −50 to +260 °C at 2 K min−1 at 0.1% strain. bTe = equilibrium temperature (Tg + 50 K). cTe = equilibrium temperature (Tg + 50 K). dGe = storage modulus at equilibrium temperature, Te. eν = cross link density.

341.65 − 0.07(vsurfHB2) + 16.75(aheavy) + 3.41(vol)

From the plot of temperature vs density (Figure 11) the Td and Tg of the polymers can be determined from the raw data by noting the change in the cell density (the black bars are the standard deviations of the values at each point). The shaded region in the plot shows the range of Tg determined experimentally (from the fall in the storage modulus data

− 5.05(VSA)

(2)

Key: VSA = van der Waals surface area, vsurf_HB2 = H bond capacity at −0.5, a_heavy = number of heavy atoms, vol = van der Waals volume.

Figure 8. TGA data for polybenzoxazines in air atmosphere. H


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Figure 9. TGA data of PBA-a in air and nitrogen with derivative data.

Figure 10. Model of cured, pure PBA-a equilibrated at 300 °C (N.B., carbon atoms = gray, nitrogen atoms = blue, and oxygen atoms = red).

I


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Figure 11. Plot of simulated density versus temperature for PBA-a (N.B. the shaded area shows the empirically determined range for Tg for comparison; the black bars show the standard deviation in the simulation experiments).

different van der Waals surface areas. Therefore, from a molecular design point of view, in order to generate a new monomer that would give a good char yield when tested, it is necessary to develop a monomer that has a large volume and a small van der Waals surface area. In other words keeping the exposed surface small contributes to increasing the char yield. This makes excellent physical sense as producing a good char yield requires that combustion is less efficient. These data only apply to the five monomers studied so far and work continues to verify whether this conclusion holds true for a larger data set of literature data.

Table 6. Char Yields Predicted from a QSPR Model for the Five Selected Polybenzoxazinesa polymer

van der Waals Surface Area (Å2)

volume (Å3)

predicted char yield (%)

observed char yield (%)

PBA-a PBF-a PBP-a PBT-a PBD-a

463 497 464 554 582

438 473 442 533 564

27.07 45.48 52.50 52.63 22.06

27.07 45.48 52.50 52.63 22.06

N.B. Char yield measured at 800°C in nitrogen. The error in the observed char yields (based on replicate measurements) is ±0.01%. a

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CONCLUSIONS The degradation data presented here indicate that the same processes are occurring both in air and nitrogen atmospheres but that the relative proportion of each process changes with atmosphere. Thus, the second stage is dominant in nitrogen and the third is dominant in air. The observed char yield differs with respect to atmosphere (e.g., 20−30 wt % for PBA-a in nitrogen versus

New Method To Predict the Thermal Degradation Behavior of

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