Insights into Melting Behavior of Propyl-Bridged Di(cyanate ester

Article pubs.acs.org/crystal

Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX

Insights into Melting Behavior of Propyl-Bridged Di(cyanate ester) Monomers through Crystal Packing, Thermal Characterization, and Computational Analysis Kamran B. Ghiassi,*,† Andrew J. Guenthner,*,† Neil D. Redeker,‡ Jerry A. Boatz,† Benjamin G. Harvey,§ Matthew C. Davis,§ Andrew P. Chafin,§ and Thomas J. Groshens§ †

Aerospace Systems Directorate and ‡ERC Incorporated, Air Force Research Laboratory, Edwards Air Force Base, California 93524, United States § Research Department, Chemistry Division, Naval Air Warfare Center Weapons Division, China Lake, California 93555, United States S Supporting Information *

ABSTRACT: Four isomeric propyl-bridged di(cyanate ester) monomers having an unexpectedly wide range of melting points were analyzed using X-ray crystallography, thermal analysis, and both empirical and semiempirical modeling, in order to examine the structure−property relationships that determine the melting characteristics. The four monomers’ crystal structures were determined, and intermolecular contacts and packing were examined. Enthalpies and entropies of melting were determined experimentally via differential scanning calorimetry and compared against two empirical models. Computational insights were provided by examining the monomers’ energetic rotational barriers. Significant effects that could not be accounted for within the framework of either the empirical or semiempirical models altered the entropy of melting over a range spanning about 40% of the average value, while the enthalpy of melting varied over a range equivalent to 50% of the average value. These large variations, even within an isomeric series exhibiting a high similarity in chemical structure, combined with an apparent correlation between the two parameters, complicate the prediction of melting phenomena for technologically important molecules, even when data for close structural analogues are available.

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INTRODUCTION In recent years, the process of liquid molding has become increasingly important for the production of composite materials for extremely demanding applications, such as heat shields on the Orion space capsule,1 scientific instrument support structures on the James Webb Space Telescope,2 and magnetic coils on the ITER thermonuclear fusion reactor.3,4 In these applications, the availability of a chemically solidified, lowviscosity liquid (such as an aryl cyanate ester)5−8 at temperatures near ambient has proven to be the key to creating structures with the unique properties needed to perform as required. Recently, a number of chemical structurebased approaches for producing low-viscosity cyanate ester monomers that exist as liquids due to inhibition of crystallinity (such as the use of enantiomorphic,9 enantiomeric,10 and polydisperse mixtures11−13) have been demonstrated. In practice, however, it is preferable that such liquids actually take the form of crystalline solids with low melting points in order to achieve the levels of purification needed to control the chemical solidification process adequately. Therefore, a reliable method for creating chemically reactive monomers with melting points over a fairly narrow range of temperatures © XXXX American Chemical Society

(270−330 K) would represent an achievement with significant technological impact. In previous work, the ability to manipulate melting points toward the desired range by controlling the entropy of melting in aryl cyanate ester monomers was shown to be effective for a limited range of monomer types in which silicon atoms were substituted for carbon atoms.14 An important unresolved question from that work is whether the same approach can be applied more generally, including to systems with other types of organic moieties present. In particular, the propylbridged aryl di(cyanate ester)s, shown in Scheme 1, are a class of recently synthesized compounds that exhibit an unexpectedly wide range of melting points,15,16 although the reasons for this surprising behavior were not previously explored in detail. These molecules may be derived from bio-based lignin feedstocks containing cresol isomers and thus contain a variety of substructures not typically encountered in monomers derived from petroleum feedstocks. Because compound 1 Received: October 26, 2017 Revised: January 2, 2018 Published: January 8, 2018 A

DOI: 10.1021/acs.cgd.7b01496 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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predictable on the basis of known structure−property relationships. We find significant differences in crystal structure, along with large variations in both the enthalpy and entropy of melting, that cannot be accounted for within the frameworks of either empirical or simple semiempirical models. While this result indicates that predictions of melting behavior for these monomers are currently too limited to provide a technologically useful level of discrimination among compounds, it also indicates that the study of additional monomers, particularly those derived from bio-based sources, along with advanced techniques, may provide many more examples of monomers having highly desirable melting behavior in combination with other useful performance characteristics.

Scheme 1. Chemical Structures of the Four Isomeric Di(cyanate ester) Monomers

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RESULTS AND DISCUSSION Crystal Structure Analysis. Structural Analysis of 1. This structure is found in the monoclinic setting, space group P21/c with Z = 4. The asymmetric unit contains one fully ordered monomer. Figure 1 shows the molecular components for the four isomeric dicyanate ester monomers. Crystal data are given in Table 1. The packing for this monomer is primarily composed of C−H---π interactions (2.78−2.95 Å), C−H---N interactions (2.70−2.84 Å), and OCN---OCN interactions (2.94−2.99 Å), as shown in Figure 2. The less common OCN---OCN interaction is produced by the positive polarization of the −OCN carbon atom in conjunction with the electronegative oxygen and nitrogen atoms. This polarization coupled with a neighboring −OCN group can afford an interaction between an oxygen lone pair and the carbon, forming a dimer-like arrangement (Figure 2). It is intriguing that this interaction is only present in monomer 1, and was originally thought to play a prominent role in other di(cyanate ester) systems.18 An additional OCN---π (3.15 Å) contact is also present, but to a lesser extent. It is noteworthy that this structure does not show any significant π---π stacking. Figure 3 shows the Hirschfeld surface of the monomer illustrating the neighboring close contacts. Table 2 shows relevant packing information for the four monomers.

(and to some extent, compound 3) provide highly desirable melting characteristics, whereas compounds 2 and 4 do not, the study of these isomers may provide insights into important structure−property relationships that can be used to predict melting behavior. These relationships may have gone undetected previously because the range of compounds afforded through petroleum processing did not encompass a sufficiently broad variety of chemical substructures. Such a situation was recently encountered when studying the fire resistance behavior of resveratrol-based cyanate ester monomers.17 These monomers, owing to unique structural characteristics not present in petroleum-derived analogues, provide an extraordinary level of fire resistance despite containing only the elements C, H, N, and O. In this report, we examine an isomeric series of four propylbridged aryl di(cyanate ester) monomers (Scheme 1) by determining their X-ray crystal structures, examining their thermal properties, and assessing their freedom of motion by modeling and simulation in order to attempt to map their structure−property relationships. We also examine empirical models to determine whether the unexpectedly large differences in melting behavior among these compounds is

Figure 1. Molecular components of the four isomeric dicyanate ester monomers drawn with 50% thermal contours. Colors represent carbon (black), nitrogen (blue), and oxygen (red). Hydrogen positions are omitted for clarity. B



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Table 1. Crystallographic Data for the Four Isomeric Di(cyanate ester) Monomers chemical formula formula weight radiation source, λ (Å) crystal system space group T (K) a (Å) b (Å) c (Å) α (deg) β (deg) γ (deg) V (Å3) Z dcalc (g cm−3) μ (mm−1) F(000) crystal size (mm) reflections collected data/parameters/restraints R(int) R1 [I > 2σ(I)]a wR2 (all data)a largest difference peak and hole (e− Å−3) a

R1 =

Σ ||F o| − |F c|| Σ |F o|

; wR2 =

{

Σ[w(F o2 − F c 2)2 ] Σ[w(F o2)2 ]

1

2

3

4

C19H18N2O2 306.35 0.71073 monoclinic P21/c 100(2) 7.3468(5) 12.2384(7) 17.4410(11) 90 91.9650(10) 90 1567.25(2) 4 1.289 0.085 648 0.30 × 0.18 × 0.14 27631 5322/211/0 0.0345 0.0502 0.1427 0.447 and −0.204



C19H18N2O2 306.35 1.54178 triclinic P1̅ 90(2) 8.0681(1) 8.4499(1) 12.5839(2) 101.5149(5) 104.2418(5) 102.3937(6) 782.754(2) 2 1.300 0.683 324 0.08 × 0.06 × 0.05 14262 3034/212/0 0.0156 0.0358 0.0982 0.258 and −0.228

1/2

}

.

Figure 3. Hirschfeld surface of monomer 1 illustrating close contacts as a function of color contour. The red “spots” indicate interactions with neighboring atoms that possess a distance that is less than the sum of their van der Waals radii.

Figure 2. Crystal packing diagram of 1 looking down the crystallographic b axis illustrating the C−H---N, C−H---π, and OCN---OCN close contacts shown as turquoise dashed lines. Other colors represent carbon (gray), hydrogen (white), nitrogen (blue), and oxygen (red). Additional contacts are not shown for clarity.

Table 2. Packing Data Obtained from the Crystal Structures of the Four Monomers 1 2 3 4

Structural Analysis of 2. This structure is found in the monoclinic setting, P21/c with Z = 4. The asymmetric unit consists of the fully ordered monomer, as shown in Figure 1. As seen with monomer 1, packing is governed by intermolecular forces, namely, C−H---π (2.78−2.96 Å), C−H---N (2.62−2.83 Å), and OCN---π (3.37 Å). In addition, there are slippedstacked π---π (3.52−3.53 Å) interactions between molecules. It

density

packing fraction

VDW surface (Å2)

VDW volume (Å3)

1.289 1.274 1.289 1.300

0.713 0.699 0.708 0.713

324.52 325.64 326.11 323.17

268.68 267.52 268.48 267.76

is interesting to note that while 2 appears to possess slippedstacked π---π contacts, monomer 1 does not. Thus, the C



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positions of the methyl groups on the phenyl rings are a critical influence on the steric effects of packing. Also noteworthy is the lack of OCN---OCN interactions. There appear to be interactions between −OCN groups and phenyl rings, forming many additional π---π interactions, as shown in Figure 4. The Hirschfeld surface is shown in Figure 5 and clearly illustrates many of the C−H---π and C−H---N interactions.

Figure 6. Crystal packing diagram of 3 looking down the crystallographic a axis illustrating the π---π, OCN---π, C−H---π, and C−H---N close contacts shown as turquoise dashed lines. Other colors represent carbon (gray), hydrogen (white), nitrogen (blue), and oxygen (red). Additional close contacts are not shown for clarity.

ring and an −OCN group. By a qualitative visual inspection of the Hirschfeld surface shown in Figure 7, it appears that there are less interactions that fall below the sum of the van der Waals radii (red “spots”). It is noteworthy that this monomer possesses an intramolecular C−H---π interactions, shown in the top left of Figure 6, that falls below the sum of the van der Waals radii. As such, out of the four monomers presented, 3 is the only one with a strong intramolecular interaction. This is most likely due to the asymmetric placement of the methyl and cyanate ester groups around the phenyl rings.

Figure 4. Crystal packing diagram of 2 looking down the crystallographic c axis illustrating the OCN---π, C−H---π, and C− H---N close contacts shown as turquoise dashed lines. Other colors represent carbon (gray), hydrogen (white), nitrogen (blue), and oxygen (red). Additional close contacts are not shown for clarity.

Figure 7. Hirschfeld surface of monomer 3 illustrating close contacts as a function of color contour. There are two prominent close interactions (red spot), one of which is not shown (hydrogen atom on the left methyl group).

Structural Analysis of 4. This structure is found in the triclinic setting, P1̅ with Z = 2. The asymmetric unit is composed of one fully ordered monomer, as shown in Figure 1. The packing diagram, shown in Figure 8, shows slipped π---π stacking (3.42 Å), C−H---π (2.76−2.93 Å), and C−H---N (2.76−2.85 Å) interactions. Figure 9 shows the Hirschfeld surface. The monomers arrange in a zigzag fashion with C−H--N contacts along the crystallographic a direction and C−H---π and slipped π---π stacking along the c axis. As shown in Scheme 1, the only difference between monomers 2 and 4 is that the latter has a quaternary bridging carbon. As a consequence, it is unsurprising that the two methyl groups on the bridge of

Figure 5. Hirschfeld surface of monomer 2 illustrating close contacts as a function of color contour. The red “spots” illustrated show prominent C−H---π and C−H---N interactions.

Structural Analysis of 3. This structure is found in the monoclinic setting, P21/c with Z = 4. The asymmetric unit is a fully ordered monomer. The intermolecular interactions presented in the packing diagram (Figure 6) include slipped π---π stacking, C−H---π (2.88−3.04 Å), OCN---π (3.38 Å), and C−H---N (2.63−2.87 Å) interactions. Like monomer 2, there are two types of π---π interactions present: the traditional slipped-stacking of phenyl rings and another between a phenyl D



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monomers in which many additional constraints on structure, reactivity, and performance requirements must also be satisfied. Calorimetry Data. The key thermodynamic characteristics of the melting transition in compounds 1−4 as determined by differential scanning calorimetry (DSC) are shown in Table 3. DSC traces are shown in Figure 10. Note that the melting

Figure 8. Crystal packing diagram of 4 looking down the crystallographic b axis illustrating the π---π, C−H---π, and C−H---N close contacts shown as turquoise dashed lines. Other colors represent carbon (gray), hydrogen (white), nitrogen (blue), and oxygen (red). Additional close contacts are not shown for clarity. Figure 10. DSC traces showing the melting endotherms for the di(cyanate ester) monomers 1−4.

characteristics at 298 K are determined from examination of the melting endotherm in combination with measurements of the difference in heat capacity between the crystalline and melt state, as detailed in a previous publication.14 The properties of the di(cyanate ester) of bisphenol A (BADCy), which is structurally equivalent to monomer 4 with the methyl groups ortho- to the −OCN groups replaced by hydrogen, are also included for comparison. A consistent melting endotherm for monomer 1 was not attainable. Experience in handling this monomer revealed that the supercooled liquid is stable for very long periods,16 with crystal growth requiring time periods that are impractically long for DSC analysis. Among the remaining isomers 2−4, there is considerable variation in both the enthalpy (range equal to about 50% of the average value) and entropy (range equal to about 40% of average) of melting when measured at the melting point. Such large variations in properties among structurally similar compounds likely derive from the large variations in crystal packing and close contact networks. In contrast, the melting points cover a range of 38 K, which is only about 11% of the average value. This result suggests that the enthalpy and entropy of melting are positively correlated on a molar basis, and because these compounds are isomers, on a per unit mass basis as well. Furthermore, because the density of these crystals varies by only about 1%, the apparent correlation exists on a per unit volume basis as well.

Figure 9. Hirschfeld surface of monomer 3 illustrating close contacts as a function of color contour. The close contacts of note (red spots) involve hydrogen atoms featuring C−H---π and C−H---N interactions.

monomer 4 do not interact to the same extent as the other three monomers. Although the four monomers possess similar density values, 4 has the highest value (Table 2). In general, despite the fact that these isomers are chemically quite similar in structure, they possess a wide variety of crystal packing conformations and a wide range of both the types and extent of close contacts present. This result is similar to other studies of the crystal packing of structurally similar compounds, which find wide differences produced by very modest differences in chemical structure.19−25 This result illustrates the difficulty in determining, a priori, a chemical structure with a targeted set of crystalline characteristics, a problem that becomes even more difficult for compounds such as reactive

Table 3. Thermodynamic Melting Characteristics as Measured by DSC Tm0 (K)a 1 2 3 4 BADCye

310.20 372.08 334.03 353.64 355.27

± ± ± ± ±

0.66 0.09 0.10 0.10 0.18

ΔHm0 (Tm) (kJ mol−1)a d

n/a 39.2 23.9 30.1 28.4

ΔHm0 (298 K) (kJ mol−1)b d

± ± ± ±

0.5 0.7 0.4 0.5

n/a 33.8 21.8 25.0 24.9 ± 0.5

ΔSm0 (Tm) (J mol−1 K−1)a d

n/a 105.3 ± 1.3 71.5 ± 2.1 85.1 ± 1.2 80.0 ± 1.4

ΔSm0 (298 K) (J mol−1 K−1)c n/ad 88.6 64.9 69.2 69.2 ± 3.0

a

Using corrected data from van’t Hoff analysis of melting peak. bUsing melting point data corrected by heat capacity difference, with an estimated (but not computed) uncertainty of 1 kJ mol−1 if not shown. cUsing melting point data corrected by heat capacity difference, with an estimated (but not computed) uncertainty of around 3 J mol−1 K−1 if not shown. dSamples did not show consistent melting behavior. eData for BADCy (except) ΔHm0 (298 K) were reported previously.14 E



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Figure 12. Maximum steric interactions occur at τ = −180 and τ = +92°, with interaction energies of approximately 8 kcal/mol relative to the fully relaxed local minimum. The calculated PEC for monomer 2 is similar to that of 1, with the fully relaxed local minimum at τ = −45° and two local maxima at τ = −150 and τ = +72°, with relative energies of 7 and 5 kcal/mol, respectively, as shown in panel 2a in Figure 12. In contrast, the curves for monomers 3 and 4 (panels 3a and 4a in Figure 12) are essentially flat, indicating minimal change in steric interactions as a function of the constraint angle τ. The composite PECs shown in the left panel in Figure 13 show that monomer 1 has the largest degree of intramolecular steric interactions as a function of phenyl group orientation. This is presumably due to the location of the methyl groups in the sterically crowded positions ortho to the bridging group between phenyl rings. In monomer 2, the methyl groups are in the position meta to the bridging group, thereby leading to less severe steric interactions relative to 1 as the phenyl rings twist past each other. For monomer 3, in which the locations of the methyl and cyanate ester groups on one of the phenyl rings have been exchanged, there is minimal variation in intramolecular interactions. This suggests, at the α position on the phenyl ring, a cyanate ester group is less sterically demanding than a methyl group. Monomer 4 likewise has an essentially flat PEC. Note that this monomer differs structurally from 2 only in the saturated substituents on the central quaternary carbon (−H and −CH2CH3 in 2 versus two −CH3 in 4). Therefore, the difference in the respective PECs is due to the change in interactions of the phenyl groups with the alkyl groups on the central carbon. Presumably, the symmetrical pair of methyl groups on the central carbon in 4 affords a more uniform steric interaction with the phenyl rings as a function of τ, resulting in an essentially featureless torsional potential energy curve. Since the PECs as a function of the single constrained torsion angle τ failed to fully differentiate the internal steric interactions in the four monomers (i.e., the PECs of monomers 3 and 4 are basically featureless), a second series of optimizations was performed in which more stringent constraints were imposed.14 In this approach, the structure of each monomer was first optimized subject to the constraint ω1(5−1−2−3) = 180°. Then, while continuing to maintain the ω1 = 180° constraint, a second constraint on dihedral angle ω2(6−5−1−2) was imposed. The dihedral angle ω2 was varied from −180° to +180° in increments of 30°, allowing the remaining 3N − 8 = 116 degrees of freedom to fully relax at each fixed value of ω2 and with ω1 = 180°. The resulting PECs of the four monomers as a function of dihedral angle ω2 are shown in panels 1b-4b of Figure 12, with a composite plot displayed in the right panel in Figure 13. The four PECs are qualitatively similar, each with local energy maxima at ω2 = −180, 0, and +180°. Of the four monomers, 1 (panel 1b in Figure 12) has the largest steric interaction energy, 25 kcal/mol, at ω2 = 0°, which is consistent with the steric demands of the methyl groups in positions ortho to the bridging group. As illustrated in panel 2b in Figure 12, monomer 2 has three local maxima, each with a relative energy of approximately 18 kcal/mol. Monomers 3 and 4 have quantitatively similar PECs, with local energy maxima of approximately 8−9 kcal/mol. Therefore, the predicted relative order of internal rotational steric hindrance is 1 > 2 > 3 ≈ 4. On the basis of these results, one might expect decreased entropy of melting in 1 and 2 compared to 3 and 4, based on the connection between freedom of motion in the molecule

A strong correlation between the enthalpy and entropy of melting could make it more difficult to design compounds with a low melting point by deliberately increasing the entropy of melting, as suggested by us earlier,14 because of the relative inability to predict the enthalpy of melting for a given compound, and therefore to control the correlated entropic effects. There does appear to be some correlation between the enthalpy of melting and the extent of close contacts in the three monomers for which data are available. Monomer 3, with just one prominent close contact, has an enthalpy of melting of 24 kJ/mol at the melting point, which is the lowest of all of the cyanate esters we have thus far characterized. In contrast, 2, with many prominent close contacts, has an enthalpy of melting of 39 kJ/mol at the melting point, which is the highest of all of the cyanate esters we have precisely characterized thus far. Computational Methods. In a prior study of cyanate ester monomers,14 the PM3 semiempirical molecular orbital method26,27 was used to calculate internal rotational potential energy surfaces of 2,2-bis(4-cyanatophenyl)propane di(cyanate ester), 1,1,1-tris(4-cyanatophenyl)ethane tri(cyanate ester), and their silicon-substituted analogues. A similar computational approach is utilized here to investigate the degree of internal steric hindrance, as a function of phenyl group orientation, of the four ester monomers of interest. All computations were performed using the GAMESS quantum chemistry package.28,29 An initial series of optimizations was performed in which a single torsional constraint was imposed, while allowing the remaining 3N − 7 = 117 structural degrees of freedom to fully relax at each chosen value of the constraint. The constraint was constructed as a linear combination of four dihedral angles ω(i−j−k−l) as defined in eq 1 below, with the atomic labels i,j,k,l referring to the atomic numbering scheme shown in Figure 11. As constructed, the constraint τ measures the relative “twist” angle between the two phenyl groups. τ = [ω(5 − 1 − 2 − 3) + ω(5 − 1 − 2 − 4) − ω(2 − 1 − 5 − 6) − ω(2 − 1 − 5 − 7)]/2

(1)

Figure 11. Atomic numbering scheme defining torsion angles used in constrained structural optimizations. Hydrogen atoms are omitted for clarity.

Constrained potential energy curves (PECs) were obtained by adjusting the constrained torsional angle τ in steps of approximately ±15° and optimizing the remaining degrees of freedom at each value of τ. The τ-constrained PECs of the four monomers are provided in Figure 12, with a composite energy plot shown in Figure 13. For monomer 1, the fully relaxed structure corresponds to τ = −43°, as illustrated in panel 1a in F



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Figure 12. Constrained potential energy curves of monomers 1−4 as a function of the single constraint angle τ (see eq 1 in text) in panels 1a−4a and the simultaneous constraints ω1 = 180 and ω2 (see text for definitions) in panels 1b−4b.

Figure 13. Composite plots of constrained potential energy curves of monomers 1 (blue circles), 2 (green squares), 3 (gray diamonds), and 4 (red triangles) as a function of torsion angle τ (left) and ω2 (right).

and entropy, as explained in an earlier publication14 and based on the empirical framework underlying the model of Lian and Yalkowsky23 discussed below. In fact, the observed experimental trend is the opposite, with 2 > 4 > 3 at the melting point, and 2 > 3 ≈ 4 at 298 K. Taking into consideration the likely freedom of motion at the bridge, the n-propylidene bridge would be expected to allow for more freedom of motion than

the isopropylidene bridge, if the bridge were unconstrained by phenyl ring substituents. This would provide for a much higher entropy of 2 compared to the other monomers, which is at least consistent with the available observations at 298 K. While these calculations provide insight into the energetic cost of the monomers’ freedom of motion, they unfortunately do not G



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Table 4. Predicted Thermodynamic Characteristics from Empirical Models

1 2 3 4 BADCy

ΔSm0 (Tm) (J mol−1 K−1)/Lian and Yalkowskya

ΔSm0 (Tm) (J mol−1 K−1) by DSCb

ΔSm0 (298 K) (J mol−1 K−1)/ Chickos and Acreea

ΔSm0 (298 K) (J mol−1 K−1)/ Naef and Acreea

ΔSm0 (298 K) (J mol−1 K−1)/by DSCc

91.1 91.1 91.1 83.7 83.7

n/ad 105.3 ± 1.3 71.5 ± 2.1 85.1 ± 1.2 80.0 ± 1.4

79.3 79.3 79.3 71.4 70.2

71.9 71.9 71.9 77.6 71.0

n/ad 88.6 64.9 69.2 69.2 ± 3.0

Reported with precision that matches the reported experimental values. bUsing corrected Tm and ΔHm from Van’t Hoff analysis of melting peak Using melting point data corrected by heat capacity difference, with an estimated (but not computed) uncertainty of around 3 J mol−1 K−1 if not shown dSamples did not show consistent melting behavior. a c

Table 5. Predicted Effects of Structural Changes on Entropy of Melting effect on ΔSm0 (Tm) (kJ mol−1 K−1)/Lian and Yalkowsky adding a methyl group−ortho to -OCN substituting an isopropylidene bridge for an n-propylidene bridge

effect on ΔSm0 (Tm) (kJ mol−1 K−1) by DSC

0

2.6 ± 1.3

−7.4

−20.0 ± 1.3

effect on ΔSm0 (298 K) (kJ mol−1 K−1)/Chickos and Acree

effect on ΔSm0 (298 K) (kJ mol−1 K−1)/Naef and Acree

effect on ΔSm0 (298 K) (kJ mol−1 K−1)/by DSC

0.6

3.3

0 ± 4.3

−7.9

+5.7

−19.4 ± 4.3

of a larger data set for the group additivity model (or more terms for the degrees-of-freedom based model) may yield little improvement in predictive power. Unfortunately, any model that takes into account “higher order” structures, such as second-nearest-neighbor atoms, would require at least several thousand groups for group additivity, in which case data might be required for over 105 compounds, in order to function effectively. Such a number may well be beyond reach until reliable virtual measurements become available. An improved empirical “degrees of freedom” model might be more useful, but with the cost of computation falling rapidly it may be simpler just to compute such a parameter on a case-by-case basis. Within the set 1−4 and BADCy, there are two systematic structural differences for which the models can predict expected effects. These predicted effects are compared with the observed effects in Table 5. Because only one example of each effect is tested, the general applicability of the conclusions is limited, but some insights into the predictive power of the models can be gained. The first effect is derived from comparisons of compound 4 and BADCy. 4 may be pictured as BADCy with two methyl groups substituted for hydrogens on the aromatic ring. The Lian and Yalkowsky model predicts no effect because methylation of an aromatic ring does not add significantly to molecular flexibility, while the group additivity models predict a small but positive effect. Experimentally, there is a near-zero effect at 298 K and a small positive effect at the melting temperature. The model predictions are essentially correct. The second effect involves the difference between compounds 2 and 4, which comes down to n-propylidene vs isopropylidene connectivity at the bridging group. In a group contribution sense, if coefficients for primary, secondary, tertiary, and quaternary aliphatic hydrocarbons are denoted as CCH3, CCH2, CCH1, and CCH0, or generally CCHn, respectively, then the net effect (Siso‑n) of this substitution (value for isopropylidene compound after subtracting the value for the analogous n-propylidene compound), is

account for the intermolecular interactions made or lost during rotation. Empirical Models. Similar to the approach previously employed by us,30 two types of empirical models were examined for potential insight into the melting point behavior of monomers 1−4, based on the entropy of melting. The first approach, as published by Lian and Yalkowsky,31 involves an accounting of the motional degrees of freedom that are likely to be present in the liquid state, combined with the concept that each degree of freedom should contribute approximately the universal gas constant, R, to the molar entropy. The entropy of melting (at the melting point) is then assumed to be equivalent to the entropy in the liquid state. The other approach utilizes a group contribution method to estimate the entropy of melting at 298 K. Our previous work used the contribution provided by Chickos and Acree;32 however, more recently a newer and more systematic and comprehensive group contribution method has been published by Naef and Acree.33 Both the previous as well as the newer methods were used for computation. The computed entropy values from these models are compared with experimental data in Table 4. All of the models share a common assumption, namely, that thermodynamic properties such as the entropy of melting are determined additively at the level of basic chemical units within the molecule, with account taken only of the units themselves, and in some cases connectivity with nearest neighbors. In addition, a few “special cases”, such as long-chain aliphatic hydrocarbons or ring structures, are added as corrections. From this standpoint, 1−3 are identical in that they constitute isomers built from the same basic chemical units. The differences in connectivity of these units relate to either “second nearest neighbors” in an atomic sense, or specific polyfunctional aromatic substitution patterns from the standpoint of molecular fragments. Thus, the model predictions for 1−3 are identical. Experimentally, however, the entropy of melting for 1−3 varies significantly, as mentioned earlier. The experimental data thus indicate that there is a fundamental limit to the accuracy of the empirical models, which allows for systematic errors larger than the 10−20 J mol−1 K−1 standard error of the regressions used to generate the model coefficients. Consequently, the use

Siso ‐ n = CCH0 + 2CCH3 − (CCH1 + CCH2 + CCH3) = (CCH0 − CCH1) − (CCH2 − CCH3) H

(2)



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The final form of eq 2 represents a “difference of differences” with regard to the extent of hydrocarbon substitution. This “difference of differences” is −7.9 J mol−1 K−1 per Chickos and Acree32 but +5.69 J mol−1 K−1 per Naef and Acree.33 In the Liam and Yalkowsky formulation,31 the isopropylidene bridge contains one less “flexible” aliphatic group than the npropylidene bridge, leading to a lower “flexibility number” and an equivalent to Siso‑n of −7.4 J mol−1 K−1. As mentioned earlier, a more intuitive examination of likely molecular motion at the bridge would suggest a negative value for Siso‑n, perhaps as large as a few multiples of R. Experimentally, the value of an equivalent to Siso‑n in this case is around −20 J mol−1 K−1, which is largely (but not significantly given the typical prediction error) different than all model predictions. For the group additivity models, it can be argued that predictive power emerges by averaging out the relatively large errors associated with the individual coefficients, which is equivalent to stating that “second-nearest-neighbor” effects are relatively large, making the usefulness of coefficientderived parameters such as Siso‑n very limited for “molecular design” purposes. Thus, the large differences relative to experimental values in an individual case should not be surprising. In the context of the more fundamental approach of Lian and Yalkowsky, the result suggests that the greater flexibility of the bridge goes beyond that imparted by the introduction of a single “flexible” atom (the sp3 ethylene C in this case). It may involve greater motional freedom for the entire bridge, based on the qualitative analysis of how torsional constraints interact with the bridge as a whole, as mentioned earlier. The unexpectedly large experimental effect also may be a manifestation of the strong apparent correlation between the enthalpy and entropy of melting noted earlier. From the standpoint of technological usefulness, it is 1 that exhibits the most desirable melting characteristics, and in this case, the lowest melting point, of the four isomers examined. The difficulty of growing good quality crystals of 1 precludes experimental determination of how the enthalpy and entropy of melting contribute to this desirable result. The semiempirical models suggest that 1 has the most constrained rotation of phenyl groups of any of the four compounds studied. One might therefore expect a low entropy of melting. The group contribution models predict an entropy of melting identical to 2 and 3. There is, however, no basis for an unusually high entropy of melting that would lower the melting point. On the basis of the number and type of close contacts, one might speculate that the enthalpy of melting lies somewhere near the middle of the reported range, although the distinctiveness of the packing in 1 could result in a low enthalpy of melting as the main contributor to the low melting point. In any case, the tools that we have examined thus far do not provide useful guidance for how to replicate the useful characteristics of 1 in other monomers. These results suggest that the previously reported work on using silicon atom substitution to lower the melting point in di(cyanate) monomers by increasing intramolecular flexibility leading to higher melt entropy may represent a fairly special case, in which the enthalpy of melting was not greatly affected.14 These results also represent another case of biobased molecules with uncommon structural features that exhibit properties that are difficult to explain using tools that have been developed mainly with the aid of petroleum-based compounds. In this case, however, the difficulty is compounded by the sensitivity of crystal structure to large-scale molecular structure,

even more so when the most desirable compounds, being difficult to crystallize, are the least amenable to experimental analysis.

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CONCLUSIONS An examination of the crystal structure and thermodynamic characteristics of melting for four bio-based cyanate ester monomers having an unexpectedly large variation in melting point revealed significant differences in both enthalpy (range equal to 50% of average value) and entropy (range equal to 40% of average value) of the isomers, despite their high level of chemical similarity. The crystal structures and packing for each of the four isomers were substantially different from each of the others, demonstrating that, as seen in other studies, small variations in structure can lead to diverse solid state arrangements. Because these variations tended not to affect the nearest-neighbor connectivity of the constituent atoms, the empirical models were able to provide guidance on only a limited number of comparisons. All models did correctly predict that methylation of the phenyl rings would not affect the entropy of melting substantially, but the models generally underpredicted the effect of substituting an isopropylidene bridge for an n-propylidene bridge. Semiempirical models did indicate that the presence of bulky group in positions ortho to the bridge connection on the phenyl rings would inhibit molecular motion; however, the expected correlation between restricted motion and the entropy of melting was not observed. In general, as with other bio-based systems, the ability to examine compounds with uncommon chemical structural features has allowed for a useful technological discovery, that is, a cyanate ester (1) with highly desirable melting characteristics. However, these same properties characteristics prove difficult to replicate because of both a general lack of understanding of the structure−property relationships in biobased materials as well as the sensitivity of crystalline structure to small variations in chemical structure. While polymers and composites based on di(cyanate ester)s continue to expand into diverse applications, the knowledge of their structure−property relationships still lag behind. The work presented here aims to elucidate some of the intricate workings of propyl-bridged di(cyanate ester) systems, specifically focusing on their monomeric properties. By using X-ray diffraction and thermal characterization in addition to computational and empirical approaches, we have explored some critical facets of di(cyanate ester) systems.

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EXPERIMENTAL SECTION

Materials. The four dicyanate ester monomers were prepared and purified according to literature methods.16,34 Solvents were obtained commercially and used as received. Crystal Growth. Crystals of the monomers suitable for X-ray diffraction were grown from saturated solutions of ether (1 and 2), 2propanol (3), and dichloromethane (4) via slow evaporation. It should be noted that these solvents are not exclusive to each monomer, and in most cases, crystals can be grown from common organic solvents. However, monomer purity is paramount. It is recommended that the monomers be purified using flash chromatography (dichloromethane as mobile phase; silica gel as stationary phase) prior to crystallization. Single Crystal X-ray Diffraction. Crystals were removed from their mother liquor solutions, coated with fluorinated oil, and examined under a conventional light microscope. Once a suitable crystal was selected, it was mounted in the nitrogen cold stream provided by an Oxford Cryostream low-temperature apparatus on the goniometer head of a Bruker ApexII CCD instrument equipped with I



Article

either a copper (λ = 1.54178 Å) or molybdenum (λ = 0.70173 Å) finefocus sealed tube. Data sets were reduced using SAINT, and empirical absorption corrections applied using SADABS.35 Structure solutions and refinements were conducted using SHELXT-2015 36 and SHELXL-2017,37 respectively. All non-hydrogen atoms were refined anisotropically. Additional details can be found within the respective CIFs. Differential Scanning Calorimetry. Analysis of the melting points, enthalpies of fusion, and heat capacity were carried out using a TA Instruments Q200 differential scanning calorimeter (DSC) under 50 mL/min flowing N2 and a heating rate of 1 K min−1. Sample sizes of roughly 20 mg were used in order to improve measurement precision. van’t Hoff analysis was carried out using the TA Instruments Universal Analysis software package. For high-precision heat capacity measurements, a custom DSC measurement method was used. The detailed procedure is given in a previous publication.14 Additional data from DSC measurements are available in Supporting Information.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b01496. DSC melting point and heat capacity data, details of the Lian and Yalkowsky calculations, details of the Chickos and Acree calculations, details of the Naef and Acree calculations, and atomic numbering scheme for the monomers (PDF) Accession Codes

CCDC 1582124−1582127 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Authors

*(K.B.G.) E-mail: [email protected]. *(A.J.G.) E-mail: [email protected]. ORCID

Kamran B. Ghiassi: 0000-0002-3557-2813 Andrew J. Guenthner: 0000-0002-6640-0176 Jerry A. Boatz: 0000-0002-7457-1610 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the following funding agencies for financial support: Air Force Office of Scientific Research (LRIR 17RQCOR457); Air Force Research Laboratory, Aerospace Systems Directorate; Office of Naval Research; Strategic Environment Research and Development Program (SERDP WP-2214). We thank Dr. Marilyn M. Olmstead for her insight on one of the crystal structure refinements.

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REFERENCES

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Insights into Melting Behavior of Propyl-Bridged Di(cyanate ester

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