Computational and Experimental Study of Phenolic ... - ACS Publications

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Computational and Experimental Study of Phenolic Resins: Thermal−Mechanical Properties and the Role of Hydrogen Bonding Joshua D. Monk,† Eric W. Bucholz,∥ Tane Boghozian,‡ Shantanu Deshpande,⊥ Jay Schieber,⊥ Charles W. Bauschlicher, Jr.,§ and John W. Lawson*,∥ †

Mail Stop 234, ERC Inc. Thermal Protection Materials Branch, ‡Mail Stop 223, ERC Inc. Thermal Protection Materials Branch, Mail Stop 230, Entry Systems and Technology Division, and ∥Mail Stop 234, Thermal Protection Materials Branch, NASA Ames Research Center, Moffett Field, California 94035, United States ⊥ Center for Molecular Study of Condensed Soft Matter, Department of Chemical and Biological Engineering, Department of Physics, Illinois Institute of Technology, 3440 S. Dearborn Street, Suite 150, Chicago, Illinois 60616, United States §

S Supporting Information *

ABSTRACT: Molecular dynamics simulations and experimental measurements were used to investigate the thermal and mechanical properties of cross-linked phenolic resins as a function of the degree of cross-linking, the chain motif (ortho−ortho versus ortho−para), and the chain length. The chain motif influenced the type (interchain or intrachain) as well as the amount of hydrogen bonding. Ortho− ortho chains favored internal hydrogen bonding whereas ortho−para favored hydrogen bonding between chains. Un-cross-linked ortho− para systems formed percolating 3D networks of hydrogen bonds, behaving effectively as “hydrogen gels”. This resulted in differing thermal and mechanical properties for these systems. As crosslinking increased, the chain motif, chain length, and hydrogen bonding networks became less important. Elastic moduli, thermal conductivity, and glass transition temperatures were characterized as a function of cross-linking and temperature. Both our own experimental data and literature values were used to validate our simulation results.

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INTRODUCTION Thermosetting resins, such as phenolic, polycyanurates, epoxies, and polyimides, have numerous applications as adhesives, coatings, and constituents for composite materials. The irreversible three-dimensional cross-linked networks formed during cure distinguish them from their thermoplastic analogues. Cross-linked structures result in stiffer mechanical properties even at elevated temperatures. Phenolic resins in particular are an important component of ablative thermal protection materials due to their high strength, low thermal conductivity, and high char yield. Ablative composites are stateof-the-art heat shield materials that protect space vehicles from extreme atmospheric entry conditions; examples of this class of materials include PICA1−3 and Carbon Phenolic.4,5 Experimental characterization of phenolic resins has spanned many decades due to their versatile applications in industry,6,7 academics,8−11 and government.12−16 Numerous experimental results on isolated phenolic resins as well as in composites have been published to understand their characteristics and properties as a function of cure,17−22 processing,23−27 and composite design.10,28−33 In addition, experimental properties such as the coefficients of thermal expansion,12,20,34 thermal conductivity,18,19,32 and elastic moduli15,35,36 have been reported. Phenolic resins also have disadvantages, however, which include void formation and shrinkage that occur during processing as well as its brittle nature when highly cured. Recent experimental work has shown that thermomechanical proper© 2015 American Chemical Society

ties can be improved substantially by introducing additives and varying processing conditions.2,3 Understanding the relationship between chemical structures, properties, and processing will lead to improved, high-performance resins for this important class of materials. Advanced simulation studies are expected to play an important role in complementing and guiding experimental design for these systems. Recently, Li and Strachan reviewed computational approaches for thermosetting polymers, focusing primarily on epoxy systems.37 A range of structural and thermomechanical properties can be determined from simulations of these systems, including glass transition temperatures,38−42 elastic moduli,43−46 and thermal conductivities.40,47,48 Only a handful of such simulations, however, have been performed for phenolic resins.43,49−52 Schürmann and Vogel used molecular dynamics (MD) simulations in conjunction with infrared experiments to study un-cross-linked phenolic resins.49 They concluded that for these systems chain motif could affect the degree of intramolecular hydrogen bonding with a corresponding effect on Tg. Pawloski et al. also performed MD simulations of un-cross-linked phenolic to explain features observed in nanolithography.50 Their work showed that ortho−para chains tend toward intermolecular Received: June 1, 2015 Revised: September 18, 2015 Published: October 7, 2015 7670

DOI: 10.1021/acs.macromol.5b01183 Macromolecules 2015, 48, 7670−7680

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Macromolecules

ranged from 318 to 943 g/mol, which correlate well with stage A and stage B phenolic resins as described by Lee.55 The dimensions of the 50 and 256 chain systems have cubic edges of 4.12 and 4.91 nm, respectively. Additionally, larger 216 chain systems were also created with a cubic side of 6.70 nm. The properties studied at the two system sizes were in very good agreement; therefore, the 50 chained systems with (n = 7) systems were used for higher temperature simulations. Figure 1C,D shows the carbon backbone of the 9-ring ortho−ortho and ortho−para systems which differ by the position of the phenol hydroxyl relative to the carbon backbone. The hydroxyl group is an electron withdrawing group, and therefore it will weaken the adjacent C−C bonds in the aromatic rings. For this reason we anticipate that the ortho−ortho backbone will be somewhat weaker than the ortho− para backbone which avoids the hydroxyl. Realistic phenolic chains will, in general, consist of a distribution of ortho−ortho and ortho−para components.49 In our simulations, we considered both distinct ortho− ortho and ortho−para systems in order to study the effects of these different cross-link motifs independently. We focus on linear chains due to experimental observation of linear tendencies in novolac systems.54 However, it will be shown that as a function of cure, the initial structure becomes less important. In addition, in Figure 1C,D, we also see that due to the relative positions of the hydroxyls groups, ortho−ortho chains have significantly more opportunities to form hydrogen bonds within the chain. However, ortho−para chains tend to form intermolecular hydrogen bonds rather than intramolecular. We investigated the effect of chain length and chemical motif on the physical, mechanical, and thermal properties as a function of crosslinking. To model curing within these systems, methylene was used to bridge available reactive sites through a cross-linking algorithm described in detail in our previous work.52 In that work, only “ortho” and “para” sites are available as possible reactive sites.8,9,56 During the dynamic evolution of the phenolic structures, reactive sites are identified and randomly selected within a 5 Å search radius. Individual rings consisting of one, two, or three bridged sites are described as terminal, linear, or branched, respectively. The degree of cross-linking (D) is defined as

hydrogen bonding rather than the intramolecular hydrogen bonding of ortho−ortho systems. More recently, Izumi et al. performed MD simulations of cross-linked phenolic resins using the DREIDING force field.43 Cross-linked networks were generated from ortho−ortho chains using a static approach, and thermal and mechanical properties were evaluated. Computed elastic moduli from these simulations, however, were lower than experimental values as acknowledged by the authors.53 Recently, we examined various algorithms for constructing atomistic models of cross-linked phenolic systems. In that work, we considered the sensitivity of structures and properties of ortho−ortho based systems on algorithmic parameters52 and identified the optimal parameters to construct well-equilibrated models. In the present paper, we significantly expand that work by performing simulations of the mechanical and thermal properties of phenolic resins as a function of the degree of cross-linking, the chain motif (ortho−ortho versus ortho−para), and the chain length. The role of hydrogen bonding was also investigated as a function of temperature and the degree of cross-linking.

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METHODS

System of Interest. In Figure 1, we show a schematic of two linear phenolic chains bridged at the “ortho−ortho” sites located at atomic

D=

no. of branched rings × 100% no. of total rings

(1)

where D = 100% indicates all possible reactive sites are occupied. Note that due to geometric constraints it is unlikely that our algorithm would obtain D = 100%. Experimental evidence suggests phenolic cannot reach a fully cured state due to the highly constrained 3D networks formed.6 In our previous study on the sensitivity of algorithm parameters to generate low energy/stress cross-linked structures, the volume of the un-cross-linked sample was found to be influential on the final crosslinked densities and energies.52 Un-cross-linked samples that were equilibrated at temperatures in the range of 300−800 K produced the lowest energy structures due to the relationship of the bonded and nonbonded interactions. Therefore, in the present paper, we initially equilibrated the structures at 800 K38 to randomize the chain positions and then cooled the un-cross-linked samples to 550 K at a rate of 10 K/100 ps. These equilibrated bulk samples were used as input for the cross-linking algorithm. In order to generate equilibrated phenolic cross-linked structures, we used the optimized parameters defined by our previous sensitivity study. Specifically the dynamic approach was used with a stepwise minimization to reduce the local stresses followed by a temperature cycle between 300 and 800 K for 300 ps every iteration to evolve the structure and update the reactive sites. The relaxed structure was used as the template for the next cross-linking iteration. At each iteration, ten randomly selected reactive pairs are cross-linked. Once the crosslinking algorithm was completed, structures at specific degrees of cross-linking between D = 0% and D = 87% were selected for mechanical and thermal characterization. To remove any residual stresses in the selected systems, additional heating and cooling simulations were conducted for 3 ns using an NPT ensemble. Multiple structures were generated for each chain type.

Figure 1. Linear novolac-type phenolic chains (A) ortho−ortho and (B) ortho−para diagrams. Terminal sites are hydrogen atoms. (C, D) The 9-ring chains are colored according to carbon backbone (red), hydrogen (white), oxygen (yellow), and non-backbone carbon (cyan). Intrachain hydrogen bonding is shown by diffusely shaded bonds. Sequential intrachain hydrogen bonding is observed in (C) but not in (D). positions 2 and 6 (Figure 1A) and “ortho−para” sites at positions at 2 and 4 (Figure 1B). The phenol rings are connected by methylene bridges which are prevalent in both resole and novolac phenolic resins.54 Other bridging motifs are possible including those based on oxygen; however, we only consider methylene bridges in this work. Commercially available phenolic consists of low-molecular-weight oligomers with a distribution of chemical types and molecular weights.49,53 Therefore, we studied three unique phenolic systems: 50 identical linear ortho−ortho chains of 9 rings (n = 7) each, 50 linear ortho−para chains with 9 rings (n = 7), and 256 linear ortho−ortho chains with 3 phenol rings (n = 1). We designate these as 9OO, 9OP, and 3OO. The number-averaged molecular weight of these samples 7671


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Macromolecules Simulation Details. Atomistic molecular dynamics simulations were conducted using the software package LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The standardized parameters for bond stretching and angle bending were taken from the all-atom OPLS force field, which are consistent with the all-atom AMBER force field.57−59 Soldera et al. used AMBER/OPLS force fields for a number of amorphous polymers and found good agreement with experimental results.38 Modifications to the general AMBER/ OPLS force field were developed by Jorgensen et al. for 34 organic liquids, including phenol. Therefore, modified partial charges as well as nonbonded and torsional energy terms for the aromatic carbons and hydroxyl groups were taken from Jorgensen’s parameters.60,61 The O− H bonds were constrained according to the OPLS parameters defined by Jorgensen et al.60 The conventional geometric combination rule was implemented for all pairs of atoms separated by three or more bonds. Lennard-Jones and Coulomb interactions were given a 12 Å cutoff, and a weighting factor of 0.5 was used for 1−4 interactions as defined by Jorgensen. Long-range Coulombic interactions are computed using the PPPM solver with the desired relative error in forces within 10−6 accuracy. Unless otherwise stated, a time step of 1.0 fs was used. The temperature and pressure were controlled by the Nosé−Hoover thermostat and barostat with a dampening factor of 500.62,63 To avoid surface effects, 3D periodic boundary conditions were specified. Structural Analysis. Soldera et al.38 compared experimental Tg results for various polymers with atomistic simulations. They showed that there are advantages in using atomistic simulations to calculate the Tg at cooling rates inaccessible to experiment. They also demonstrated that the calculated Tg depends on these cooling rates. However, very few experimental results are available for the glass transition temperature of phenolic and those that were obtained have a wide range as will be discussed. In addition, the degree of curing is generally not reported, which makes direct (or adjusted) comparisons difficult for these thermoset systems. To calculate the glass transition temperature using simulations, we performed linear fits to the specific volume as a function of temperature.41,43−45,64−66 Two regimes are found using this method, giving linear response above and below Tg. The intersection of these two lines identifies the Tg. In our study, the specific volume was calculated at multiple temperatures over the range of 300−600 K at D = 0% and 400−800 K at D = 80%. A preliminary study was performed to find a heating/cooling rate that would produce adequate linear responses above and below Tg. A stepwise transition from lower temperatures to higher at 25 K/100 ps, corresponding to a heating rate of 1.5 × 1013 K/min, was found to be sufficient. Each subsequent structure began from the previous equilibrated configuration. An example of the response of the specific volume as a function of temperature is shown in Supporting Information Figure 1 for D = 80% of the 9-ring ortho−para system. Li and Strachan compared the DiBenedetto and Venditti−Gillham equations to model the relationship between the glass transition temperature and the degree of cross-linking for the thermosetting epoxy DGEBA and the curing agent 33DDS.41 Little difference was found between these fitting equations; therefore, we only use the more general Venditti−Gillham model given by ln(Tg) − ln(Tg0) ln(Tg∞) − ln(Tg0)

=

λD 1 − (1 − λ)D

where V0 is the volume at the reference temperature T = 300 K and V is the volume of the simulation cell at temperature T. The linear slopes were calculated with a 95% confidence level. Each unique topological structure was calculated separately, and the results from all structures were averaged to produce the error bars. Mechanical Analysis. Several classes of methods have been reported in the literature to compute moduli of polymer systems. The first class of methods fits the linear elastic region of the stress−strain curve from shear, compression, and tension deformations during finite temperature MD simulations. This method has been shown to produce reasonable results when compared to experiments for thermosetting epoxies.37 The advantage of this method is that temperature-dependent quantities can be obtained. A disadvantage is the uncertainty introduced in fitting the slope of the elastic regime. Typically, the elastic moduli are calculated by fitting the slope of the stress strain curves for strains 10 ns), we chose not to utilize this analysis method for all systems.68−70 Thermal Analysis. Equilibrium molecular dynamics (EMD)71−74 and nonequilibrium molecular dynamics (NEMD)75,76 have been used in the past to calculate transport properties in amorphous materials.40,47,48,77 Since our systems consisted of cubic simulation cells, we calculate the lattice thermal conductivity with EMD simulations using the Green−Kubo (GK) approach. This approach is based on the fluctuation−dissipation theorem and relates transport quantities such as diffusion coefficient, viscosity, and thermal conductivity to fluctuations in equilibrium properties. The GK relation gives the lattice thermal conductivity tensor κij as the time integral of the heat current autocorrelation function by

κij =

1 ⎛⎜ ∂V ⎞⎟ V0 ⎝ ∂T ⎠ P

∫0

∞

⟨Ji (0)Jj (t )⟩ dt

(4)

where kB is the Boltzmann constant, T is the system temperature, V is the system volume, and i, j = x, y, z. Twenty nanosecond NPT simulations at room temperature were repeated five times to account for statistical variations in the samples at different degrees of crosslinking. The directional heat currents were calculated and recorded every femtosecond using LAMMPS. The heat current was averaged using a 400 ps sliding window. The error was calculated with a leaveone-out cross validation for five simulations per structure at each degree of cross-linking.78 Experimental Methods. Multiple samples of cured phenolic resin with varying cross-link densities were produced for experimental measurements. We began with Durite SC-1008, which is a solution of resole-type phenolic and isopropyl alcohol (IPA). The first step was to remove most of the IPA from the SC-1008 while limiting the extent of curing. The samples were produced with different amounts of cure time and the peak curing temperature. The samples were cured with stepwise temperature increments starting at room temperature for 3 h followed by 1 h at 45, 65, 85, and 105 °C. The sample that was removed after the 85 °C step had malleable and gel-like physical characteristics which are consistent with a resin with a lower cross-link density. Samples that were cured for longer times and/or higher temperatures produced highly brittle characteristics and were assumed therefore to be highly cross-linked (an estimated 70% < D < 90%). The thermal diffusivity was measured using two different techniques. The first technique was the commonly used laser flash analysis (LFA).79 In this technique the front side of a plane-parallel

(2)

T0g and T∞ g are the glass transition temperatures for un-cross-linked and fully cross-linked phenolic resins, respectively. D is the degree of cross-linking, and λ is the fitting parameter equal to ΔCp/ΔCv, where Cp and Cv are the specific heats at constant pressure and volume, respectively. Linear fits to the specific volume are used to calculate the volumetric coefficient of thermal expansion (CTE) above and below Tg41,67 α=

V kBT 2

(3) 7672


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Macromolecules sample is heated by a short laser pulse. The temperature at the rear surface was measured as a function of time using an infrared detector. The second approach was to use a holographic grating technique called forced Rayleigh scattering (FRS). Details are given elsewhere,80,81,90,91,92 but the technique uses crossed coherent light to write a sinusoidally modulated temperature profile in the sample, which is detected by a lower-power reading laser. The samples here absorbed sufficient light at the wavelength of our writing beams (514 nm) such that no dye was needed to write the temperature profile. The temperature modulation gives rise to a refractive index modulation such that the sample scatters a second low-power reading laser (in our case an 8 mW HeNe beam at 633 nm). When the writing beam is switched off, the temperature modulation decays according to the thermal diffusivity, which can be detected by the time-dependent intensity of the first-order Bragg diffracted reading beam. By varying the period of the temperature grating, we can check that Fourier’s law is obeyed. Careful control of sample size, grating period, and writing time guarantees that the temperature varies by less than 10 mK and that the grating can be treated as one-dimensional. We investigated the glass transition temperature using differential scanning calorimetry (DSC) for the highly cured structure. To test in the DSC, the cured phenolic resin was ground to a powder and placed in aluminum crucibles. Special attention was taken to completely cover the bottom of the crucible. The temperature was ramped from room temperature to 823 K at a rate of 10 K/min and then cooled at the same rate. The maximum temperature was chosen due to the limitations of the aluminum crucibles. We also investigated the decomposition temperature of a fully cured sample. This analysis was completed using the common method of thermal gravimetric analysis (TGA). A section of the fully cured phenolic resin was placed in the crucible and the temperature was ramped from room temperature to 1823 K at 10 K/min.

Figure 2. Radial distribution function between hydroxyl center of mass at 300 K for ortho−ortho and ortho−para. The first peak indicates candidate hydrogen bonds.

systems with varying magnitudes and is related to hydrogen bonds. These magnitudes are not precisely related to the number of hydrogen bonds because this analysis only accounts for neighbor distances. Yet qualitative trends can be determined and are analyzed further below. Figure 2 shows larger peaks for the 9OO systems than the 9OP systems at both degrees of cross-linking, which suggest more hydrogen bonding in the 9OO system as observed by Schürmann and Vogel.49 In addition, it can be observed that the peak heights reduce as a function of cross-linking for both chain types. The small secondary peak observed for the 9OO system at D = 0% was found to be related to the hydroxyl groups along the same chain. This peak is less pronounced in the 9OP system due to the larger separation of the hydroxyl groups along the chain as seen in Figure 1D. Along with the RDF values we also conducted a more quantitative analysis of the hydrogen bonds as a function of chain motif, degree of cross-linking, and temperature. To quantify the amount of hydrogen bonding within these systems, the atomic positions of the hydroxyl groups were analyzed over 1 ns simulations at various temperatures and degrees of crosslinking. The geometric criteria used to identify a hydrogen bond was taken from Haughney et al.,82 where r(O−O) ≤ 3.5 Å and r(O−H) ≤ 2.6 Å and the angle between the O-acceptor/ H-donor/O-donor ≤30°. The total number of hydrogen bonds was divided by the number of hydroxyl groups (450) to calculate the percent of hydrogen bonding in the system. Figure 3 shows the percentage of interchain and intrachain hydrogen bonding over a range of temperatures from 300 K (T < Tg) to 750 K (T > Tg) for the un-cross-linked and highly cross-linked samples. Figure 3A presents the hydrogen bonding for 9-ring ortho−ortho structures at D = 0% and D = 85%. Figure 3A shows that the intrachain bonding dominates the uncross-linked and highly cross-linked systems for the entire range of temperatures, which is consistent with Schürmann and Vogel’s results for un-cross-linked systems. A significant decrease in the intrachain H-bonds was observed as the degrees of cross-linking increased. The decrease in intrachain H-bonds is a result of highly constrained covalent networks that reduce the possibility for sequential intrachain hydrogen bonding as seen in Figure 1C. The percentage of interchain bonding within the 9OO system only contributed 10% to the hydrogen bonding at room temperature and even less at high temperatures. Figure 3B shows the percentage of hydrogen bonding for 9ring ortho−para structures at D = 0% and D = 85%. Because of

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RESULTS Structure/Network Characteristics. Thermoset polymers are three-dimensional covalently bonded networks produced by the curing process. To generate atomistic models of these systems, we covalently bonded the phenolic chains by introducing methylene bridges at available reactive sites during dynamic evolution of the system. Supporting Information Figure 2 shows the percentage of terminal, linear, and branched rings that were produced as a function of cross-linking for two chain types: the 3OO and 9OP. 9OO results are not shown due to its similarity to 9OP. At D = 0%, the 9OP system has a ratio of 7:2 linear to terminal rings, whereas the 3OO is 1:2. Because of the random selection of reactive sites, the 9OP structure exhibits little bias between terminal or linear sites. However, the shorter chains are observed to increase in length; i.e., they produce longer linear chains prior to creating branched networks. This tendency for linear chains is a characteristic observed experimentally in novolac phenolic.54 Therefore, the 3OO systems required more cross-links to obtain the same degree of cross-linking as the 9OP and 9OO systems, since the degree of cross-linking is quantified by the number of branched rings. Hydrogen Bonding Characteristics. The major difference between the ortho−ortho and ortho−para chains is the position of the hydroxyl group with respect to the carbon backbone. This has a significant effect on the opportunities for hydrogen bonding within the chain (intrachain) versus between chains (interchain). Because of this difference, the number of hydrogen bonds differs significantly between these systems. Figure 2 shows the radial distribution function (RDF) between the center of mass of the hydroxyls. Specifically, we compared the 9OO and 9OP systems at two degrees of cross-linking: D = 0% and D = 85%. A peak is observed at 0.26 nm for all four 7673


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Figure 3. Hydrogen bonds as a function of temperature for 9-ring ortho−ortho and 9-ring ortho−para.

the different relative position of the hydroxyls, the ortho−para systems exhibited little intrachain bonding ( 60%, the room temperature densities and higher temperature densities nearly converged. Our simulated densities are slightly lower than our experimentally measured values which range from 1.12 to 1.3 g/cm3 at room temperature. However, our simulated densities do fall within 7675


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Figure 7. CTE values for three chain types as a function of cross-linking: (filled) T > Tg; (open) T < Tg. Experimental values are reported from refs 13, 20, and 34.

for the difference in cooling rates, we followed the approach by Li and Strachan to fit the linear relationship between the glass transition temperature of the experiments and the simulated data as a function of cooling rate.41 The slope of this curve provides an estimate for the adjustment made to the experimental data per order of magnitude difference. The linear fit of Tg for our four simulated cooling rates plus the experimental DSC value provided an approximate adjustment of 4.89 K per order of magnitude. This would adjust the DSC value to 596 K at a cooling rate of 1.5 × 1013 °C/min. Figure 7 gives the coefficients of thermal expansion as a function of cross-linking. For samples that are not single clusters, it was observed that shorter chains had the highest CTE values, while 9OO and 9OP had equivalent values. As the degree of cross-linking increased, the CTEs decreased for each chain type; this can be explained by the reduced mobility due to increasing covalent bond networks. For degrees of cross-linking above D = 60%, the CTE values converged for the three systems studied. A direct comparison of experimental and simulation data could not be performed, since the degree of cross-linking is not reported in the literature. However, our computed CTE values for highly cross-linked phenolic are in the range of 90−186 ppm/°C (70% < D < 90%), which is in good agreement with the experimental range of 104−310 ppm/ °C.12,20,34 Mechanical Characteristics. We analyzed the mechanical response at room temperature for the three systems of interest (9OO, 9OP, and 3OO) as a function of cross-linking. In Figure 8, the stress−strain curves for three degrees of cross-linking are shown for the 9OO and 9OP systems. In general, higher crosslinking results in higher stress response. At D = 0%, 9OP has a higher stress response than 9OO due to the resistance to deformation generated by the hydrogen-bonded network. As the degree of cross-linking increases, however, the difference between the two systems decreases. Increases in covalent bonding due to cross-linking will reduce the effect of the hydrogen network. To identify the source of the higher stress response in highly cross-linked systems, the stress contributions were calculated for the various interatomic interactions for a strain rate 4.0 m/s. The major stress contribution was found to be the bonded interactions, which accounted for 60% of the change in total stress as a function of strain ( Tg). Solid lines fit the moduli using an equation similar to eq 2 for glass/rubber-like structures. The dashed line fits the linear trend of systems above Tg. Experimental values are reported in refs 34, 88, and 89.

moduli. Interestingly, the 9OP structures have slightly higher moduli which are attributed to the hydrogen bonding network shown in Figure 4. At 650 K, however, every system is above the glass transition temperature, and most of the hydrogen networks have been disrupted. This results in essentially negligible moduli for both systems at D = 0%. As the crosslinked structures become single clusters (D > 47%), the moduli continue to increase at both temperatures. For the highly cured samples, we compare to experimental results at room temperature. The simulated moduli are slightly higher than the experimental results, but it can be reasoned that our models should be higher since they are free of defects. The difference in the room temperature moduli can also be compare to the 0 K data in Figure 9. The moduli at 0 K shows a decrease of ∼18% from D = 85% to 47% due to the lower number of bonds within the D = 47% network. However, the moduli decrease at room temperature is ∼66% from D = 85% to 47%. The drop in moduli from D = 85% to 47% at room temperature can be partially explained by the lower number of bonds, as in the 0 K

approaches for calculating the Young’s modulus as a function of cross-linking for the 9OO systems. Only the structures with single cluster networks are shown. As we can see, good agreement for all three techniques was obtained. The Hill− Walpole bounds were chosen in Figure 9. Elastic Moduli: Temperature. Now that we have confidence in our stress−strain method, we proceeded to compute temperature-dependent moduli. In particular, we compare the mechanical properties above and below the glass transition temperature; we performed continuous deformation simulations and calculated the directional moduli by fitting the slope of the stress−strain curves. Figure 10 shows the Young’s modulus as a function of cross-linking for two temperatures 300 K (below Tg) and 650 K (above Tg) for the 9OO, 3OO, and 9OP systems. Each modulus in Figure 10 is an average of four systems with five uniaxial tension simulations in each direction for a total of 60 simulations. The moduli can be seen to increase as a function of cross-linking for both temperatures. In the room-temperature glassy state, every system had nonzero 7677


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results with experimental results using various techniques. We measured a thermal diffusivity of 1.90 × 10−3 cm2 for a fully cured sample (∼D = 85%) using the LFA method. The FRS method produced thermal diffusivities of 8.09 × 10−4 and 1.47 × 10−3 cm2/s for the gel-like and brittle samples, respectively. The thermal conductivity shown in Figure 12 was found using k = αρCp with densities ranging from 1.13 to 1.3 g/cm3 and a specific heat of 1471 J/(kg K). Other literature values were found to be on the same order as these results. Patton et al. used the guarded hot plate thermal conductivity test for cured phenolic and found 0.28 ± 0.07 W/(m K) and Mottram et al. used LFA to calculate a TC of 0.25 W/(m K).18,32 The degree of cross-linking was not reported in these experimental results; however, it is reasonable to assume for highly cured samples that D = 80 ± 10%. The experimental values are consistent with our simulated TC range for highly cross-linked structures (0.25−0.34 W/(m K)) and are slightly lower for the low cured sample. However, it is important to note that difference between TC for high and low cross-linking was found to be similar for the MD simulations (ΔTC = 0.09 W/(m K)) and the experimental FRS measurements (ΔTC = 0.10 W/(m K)). The simulated thermal conductivity values in Figure 12 were calculated using the Green−Kubo approach for the three systems of interest. At D = 0%, the ortho−para system has slightly higher TC values compared to 3OO and 9OO. In general, TC increases as a function of cross-linking for all three systems. The contribution of specific interatomic interactions to the thermal conductivity for amorphous polymers was considered by Kikugawa et al.47 They found that the preferred heat transfer mode was through bonded interactions. For phenolic resin, the number of thermal pathways available through the 3D covalently bonded networks increases substantially as a function of cross-linking, resulting in higher thermal conductivity for higher D.

results, but increased thermal motion associated with increased temperature also contributes. To better understand the moduli’s dependence on temperature, we plot the moduli of high (D = 85%) and low (D = 0%) cross-linked structures as a function of ΔT = (T − Tg) in Figure 11. The Tg used to plot ΔT was determined by the Venditti−

Figure 11. Young’s modulus as a function of temperature. Two degrees of cross-linking are compared for the 9-ring ortho−para and ortho−ortho systems. Tg was determined by the Venditti−Gillham fit from Figure 6.

Gillham model with parameters as described in the Structural Analysis section. For D = 0%, we see a drop in the moduli as the temperature approaches ΔT ≈ 0 from below; this is consistent with a transition from glassy to more liquid-like behavior. The relative smoothness of the transition at ΔT = 0 may result from variations in the structures generated and the overall averaging implemented. In their study of epoxy, Li et al. suggested that the strain rate may also contribute to how abruptly the moduli decreases near Tg.41 On the other hand, at higher degrees of cross-linking (D = 85%), there is a general decreasing trend of the moduli and the transition near Tg is even less pronounced than for lower cross-linked samples. As observed in Figures 8 and 10, the moduli of the 9OP system is higher than the 9OO for D = 0%, but these values converge at higher temperatures and degrees of cross-linking. Thermal Conductivity Characteristics. Figure 12 provides a comparison of our simulated thermal conductivity

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DISCUSSION Extensive molecular dynamics simulations were performed to determine the thermomechanical properties of phenolic resin as a function of cross-linking, chemical motif (ortho−ortho vs ortho−para), and chain length. The chain length was found to influence the number of terminal, linear, and branched rings as a function of cross-linking; however, the chemical motif had little effect on the ring type distribution. Hydrogen bonding was shown to be qualitatively different between ortho−ortho and ortho−para systems. These differences have the greatest effect at low cross-linking. In particular, ortho−ortho chains favored hydrogen bonding within the chains whereas ortho−para phenolic prefers hydrogen bonding between chains. This preference for interchain bonding at low cross-linking for ortho−para resulted in 3D hydrogenbonded networks that percolate the system. Thus, the system behaves essentially like a “hydrogen gel”. The total number of hydrogen bonds is also dependent on the chemical motif (9OO > 9OP), degree of cross-linking (D = 0% > D = 85%), and the temperature (300 K > 750 K). The glass transition temperature is dominated by the degree of cross-linking, but there is some evidence of a slight dependence on the chain type at D = 0%, which is likely due to the amount of total hydrogen bonding in the system. Calculated Tg values were higher than experimental results. This is most likely due to the significantly greater heating/ cooling rates used in our simulations. Note that large variations in the experimentally reported values (Tg ∼ 325−533 K) make

Figure 12. Thermal conductivity as a function of cross-linking. Degrees of cross-linking are not reported in experiments; therefore, an estimate of 80% was made with an error bar of ±10%. 7678


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Macromolecules Notes

it difficult for direct or adjusted comparisons. CTE values were found to depend on chain length and chain type at low degrees of cross-linking but converge for D > 47%. The CTE results between 70% < D < 90% are consistent with the experimental literature range. Mechanical properties were calculated for various chain types, degrees of cross-linking, and temperatures. The Young’s modulus was found to be dependent on the chain type for D < 60%, but the elastic response was dominated by the 3D covalently bonded network formation at higher degrees of cross-linking. Above D > 60% there was negligible dependence on chain length and chain type. For low cross-linking, there are observable differences in the moduli between ortho−ortho and ortho−para. These differences were attributed to hydrogen bonding effects. The moduli’s dependence on temperature was more apparent at low degrees of cross-linking. This was illustrated by difference in the Young’s modulus at 300 and 650 K for the 9OP system, ΔE = 3.3 GPa (D = 0%) and ΔE = 1.7 GPa (D = 80%). We also investigated the influence of temperature on either side of the glass transition. When comparing D = 0% and D = 85% for the ortho−para systems, it was apparent that the moduli reduced at a faster rate near Tg for the D = 0% system. However, for both degrees of cross-linking, the moduli did not have an abrupt reduction at Tg, but rather was continuously reduced as the temperature increased. Thermal conductivity was found to be dependent on the degree of cross-linking with an increasing trend as D increased. Little dependence on chain type or chain length was found. The simulated values were compared with various experimental methods, and our results agreed well within the experimental and computational uncertainties. The simulated results provided an upper bound for the experimental data for the assumed degree of cross-linking between 70% < D < 90%. In summary, molecular dynamics simulations of highly crosslinked phenolic structures produced thermomechanical properties that compare well with experimental results. At low degrees of cross-linking, chain type, chain length, hydrogen bonding, and temperature all had significant effects on the properties. Various quantities and types of hydrogen bonding resulted in the differences in properties at low degrees of cross-linking. However, once the structures became single clusters, the dominate factor was the covalently bonded network. This behavior could be seen in a range of properties including converged densities, moduli, Tg, CTE, and thermal conductivities for various chain lengths and chain types above D > 60%.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge Justin Haskins for a critical reading of the manuscript and for productive discussions. This work was funded by the ESM project of the NASA Space Technology Mission Directorate (NASA Ames) and received financial assistance from NSF DMR-706582 and NSF CBET-1336442 (IIT).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01183. Specific volume as a function of temperature, the progression of the ring characteristics during crosslinking, and the percentage of hydrogen bonds for the 3OO system at various temperatures (Figures 1−3); more detailed description of the methods used to obtain the mechanical properties (PDF)

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