Counit Inclusion in Hydrogenated Polynorbornene Copolymer

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Counit Inclusion in Hydrogenated Polynorbornene Copolymer Crystals Michael T. Showak,† Adam B. Burns, Andrew J. Stella,‡ and Richard A. Register* Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: Model crystallizable copolymers of norbornene and two 5-alkylnorbornenes were synthesized to investigate the extent and consequences of defect inclusion into hydrogenated polynorbornene (hPN) crystals. Living ringopening metathesis polymerization yielded narrow-distribution polymers of targeted molecular weights, with modest downchain compositional gradients controllable through the polymerization conversion; hydrogenation yielded semicrystalline copolymers. When the comonomer was 5-methylnorbornene (MeN), extensive inclusion of MeN units into the hPN crystal was observed; the copolymers showed substantial crystallinities even above 30 mol % MeN, and the dependence of the melting point Tm on crystal thickness followed that for hPN homopolymer. By contrast, when the comonomer was 5hexylnorbornene, the more usual case of strong exclusion of the counits from the crystal was observed. hPN shows a transition between two crystal polymorphs below Tm, at a temperature Tcc; comonomer incorporation reduces Tcc more rapidly than it reduces Tm, expanding the region over which the high-temperature rotationally disordered polymorph is stable and providing insight into the dependence of the free energy for the two polymorphs on crystal thickness.

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INTRODUCTION As a general rule, comonomer units are excluded from polymer crystals, causing a precipitous decrease in the degree of crystallinity and the average crystal thickness when even modest contents of comonomer are distributed randomly along the chain.1 And as with any general rule, there are exceptions: among the better-studied examples where extensive inclusion of defect units has been observed are the cases of propylene units (methyl branches) in polyethylene crystals;2−6 D-lactide units in poly(L-lactide) crystals;7,8 and poly(ethylene terephthalate-coethylene 2,6-dicarboxynaphthoate)9−11 and poly(β-hydroxybutyrate-co-β-hydroxyvalerate),12−16 both of which exhibit isodimorphism. However, each of these polymers is synthesized by step-growth polymerization or by chain-growth polymerization (synthetically or biologically) with uncontrolled chain termination and/or transfer. Living polymerizations, which would provide architectural and molecular weight control, have been applied extensively in the synthesis of block copolymers but have been less frequently applied in the synthesis of random (or nearly random) copolymers.17−22 In particular, to our knowledge, there have been no reports of narrow-distribution crystallizable random copolymers in which extensive comonomer inclusion into the crystals has been observed, nor any reports of well-defined architecturally complex polymers (e.g., block copolymers) containing such sequences. Here, we report on copolymers of hydrogenated polynorbornene (hPN) with 5-methylnorbornene (MeN), synthesized by ring-opening metathesis polymerization (ROMP), which show a high degree of MeN unit inclusion into the hPN © 2013 American Chemical Society

crystal. As shown herein, ROMP provides good incorporation of alkylnorbornene units into the PN chain, yielding narrowdistribution copolymers with only modest compositional gradients. hPN is interesting as a parent polymer for at least two reasons: (1) though hPN is essentially atactic (random stereosequence of backbone cyclopentylene units), it is highly crystalline, suggesting that hPN crystals might be more tolerant of other defects such as comonomers;23,24 (2) hPN undergoes a polymorphic transition from a three-dimensionally ordered monoclinic crystal to a rotationally disordered pseudohexagonal structure prior to melting,23,24 at a temperature Tcc. The present copolymers thus allow for an examination of how comonomer affects the relative stability of the two crystal polymorphs (rotationally ordered and disordered), through its effect on Tcc. The hP(N-co-MeN) copolymers are compared with a smaller set of copolymers wherein the counits are 5hexylnorbornene (HxN), which are expected to be strongly excluded from the hPN crystal due to their much larger volume. The chemical structures of the repeat units for the two series of copolymers are shown in Scheme 1.

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EXPERIMENTAL SECTION

Polymerization. The monomers norbornene (bicyclo[2.2.1]hept2-ene, Sigma-Aldrich, 99%), as well as 5-methylnorbornene and 5hexylnorbornene (provided by Promerus, Brecksville, OH; endo/exo Received: September 3, 2013 Revised: November 8, 2013 Published: November 22, 2013 9288

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detector. The system was calibrated with narrow-distribution polystyrene standards; the “polystyrene-equivalent” number-average molecular weight Mn obtained from GPC was converted to the true Mn using the known hydrodynamic equivalence factors R = 1.96,24 1.68,25 and 1.3225 for PN, PMeN, and PHxN homopolymers, where the weight-fraction-weighted average of R was employed for each copolymer.29 An additional 2 g/mol per repeat unit was added to the value of Mn for the unsaturated precursor to yield Mn for the hydrogenated polymer. For measurement of fractional monomer conversion during the test polymerizations, a separate GPC system was used wherein the mobile phase was toluene (nominally identical columns, Waters 590 pump and 410 refractometer). Fractional conversion was determined as the ratio of polystyrene-equivalent Mn for each aliquot to the polystyrene-equivalent Mn obtained at long reaction times. For the “production runs”, fractional conversion was determined as the true value of Mn relative to the theoretical value at complete conversion (total mass of monomers charged, divided by moles of Mo initiator). Thermal and Structural Characterization. Differential scanning calorimetry (DSC) measurements were made on 5−9 mg specimens, with a PerkinElmer DSC 7 equipped with a Type II intracooler, calibrated with indium and tin. Specimens were heated into the melt (180 °C), cooled at 10 °C/min to −30 °C, held for 5 min, and immediately reheated at 10 °C/min, during which the reported data were recorded. Peak melting temperatures Tm and peak crystal−crystal transition temperatures Tcc were determined from the thermograms, along with the combined enthalpy of both transitions (ΔH = ΔHm + ΔHcc) integrated from 40 °C up to the melt, as the two endotherms could not be completely resolved (see Supporting Information for representative thermograms). The value of ΔH was converted to a weight fraction crystallinity wc(DSC) by dividing by 86 J/g.23,30 Note that this neglects the effects of finite crystal thickness on ΔH as well as any effect31,32 of comonomer inclusion; both of these are generally expected to reduce the ratio of ΔH/wc slightly. We estimate the precision on wc(DSC) as ±0.03 (±2 standard deviations) due largely to baseline determination. Small-angle X-ray scattering (SAXS) patterns in transmission were collected at room temperature with an Anton-Paar compact Kratky camera, a PANalytical PW3830 X-ray generator with a long-fine-focus Cu tube producing Cu Kα radiation (λ = 0.154 18 nm), and an MBraun OED-50 M position sensitive detector. Data were corrected for detector sensitivity and positional linearity, empty beam scattering, sample thickness, and transmittance, placed on an absolute intensity scale via a polyethylene standard, and desmeared for slit length.33 Absolute SAXS intensities (I/IeV) are plotted against the magnitude of the momentum transfer vector q = (4π/λ) sin θ, where θ is half the scattering angle; calibration was via silver behenate.34 Intensities were multiplied by q2 to approximately correct for the form factor of lamellae.35 Wide-angle X-ray scattering patterns in reflection were acquired with a Phillips-Norelco wide-range goniometer and scintillation counter, fitted with an Advanced Metals Research graphite focusing monochromator, using Cu Kα X-rays produced by the same generator. Angular calibration was via a quartz standard. Films 100− 200 μm thick were melt-pressed for SAXS and WAXS and cooled to room temperature at ∼10 °C/min to match the thermal history used in the DSC. A single film was used for WAXS measurements to reduce peak broadening, while films were stacked to ∼1.5 mm thickness for SAXS. The degree of crystallinity wc(WAXS) was also estimated from the WAXS data, using the relative areas of the crystal peaks and amorphous hump (see Supporting Information for representative WAXS patterns and details). We estimate the precision on wc(WAXS) as ±0.03 also (±2 standard deviations), due again principally to baseline determination. To confirm that the thermal history used for the SAXS/WAXS films was comparable to that employed in the DSC runs, separate DSC scans of several of the SAXS/WAXS films were run; the value of Tm measured on the first heat was within 1 °C of the Tm value obtained on the separately prepared DSC specimens, confirming the near-equivalence of the two thermal histories.

Scheme 1. Structures of the Repeat Units in (left) the hP(Nco-MeN) Copolymers and (right) the hP(N-co-HxN) Copolymersa

a

Though the alkyl substitutents are drawn in the 5-position, there is regioirregularity in their addition (4- vs 5-position) and also endo/exo isomerism in the monomer structure. In addition, the cyclopentylene units, drawn here as planar, pucker in and out of the page in an essentially atactic sequence.23,24

ratio24 of 77/23 for both), were stirred over sodium, degassed by freeze−pump−thaw cycles, and vacuum transferred prior to polymerization. The Schrock-type initiator 2,6-diisopropylphenylimido(neophylidene) molybdenum(VI) bis(tert-butoxide) was purchased from Strem Chemicals and used as received. Trimethylphosphine (PMe3, Sigma-Aldrich, 97%) was dried over sodium, degassed, and vacuum transferred. Toluene, the polymerization solvent, was dried over diphenylhexyllithium (adduct of sec-butyllitium and 1,1-diphenylethylene), degassed, and vacuum transferred, while the ROMP terminating agent benzaldehyde (Sigma-Aldrich, 99.5+%, SureSeal) was used as received. ROMP was conducted at room temperature under a nitrogen atmosphere in an MBraun Unilab glovebox (99.9% saturation.24 The hydrogenated polymer was separated from the catalyst via hot filtration, precipitated into methanol, and vacuum-dried. Molecular Characterization. Since the crystalline hydrogenated copolymers are generally insoluble at room temperature, all characterization of polymer composition and molecular weight was conducted on the unsaturated polymers prior to hydrogenation. Previous studies of similar norbornene-type polymers hydrogenated with this catalyst have shown that backbone rearrangements do not occur.26−28 Polymer compositions (mole fraction comonomer, FB) were determined by 1H NMR spectroscopy in CDCl3, using a Bruker Biospin AVANCE-500 MHz spectrometer. Compositions were determined from the areas of the methyl resonances of the comonomer side group (at a chemical shift δ ≈ 0.8−0.9 ppm relative to tetramethylsilane) and the olefinic resonances of the polymer backbone (at δ ≈ 5.2−5.4 ppm). Molecular weights and dispersities Đ reported herein were measured by gel permeation chromatography (GPC) in tetrahydrofuran (THF), using two 30 cm Polymer Laboratories PLgel Mixed-C columns, a Waters 515 HPLC pump, and Wyatt Optilab T-rEX differential refractometer 9289

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Table 1. Molecular, Thermal, and Morphological Characteristics of hP(N-co-MeN) and hP(N-co-HxN) Copolymers counit B

FB

Mn (kg/mol)

Đ

peak Tm (°C)

ΔH (J/g)

wc (DSC)

wc (WAXS)

d110 (Å)

D (nm)

tc (nm)

peak Tcc (°C)

none MeN MeN MeN MeN MeN MeN HxN HxN HxN HxN

0 0.006 0.016 0.027 0.073 0.152 0.325 0.010 0.022 0.044 0.088

65 61 62 57 64 56 49 56 56 58 59

1.12 1.10 1.07 1.10 1.11 1.10 1.08 1.09 1.09 1.10 1.05

140 138 135 133 123 99 53 136 126 115 96

66 66 60 55 48 26 14 56 40 27 16

0.77 0.77 0.70 0.64 0.55 0.30 0.17 0.65 0.46 0.31 0.19

0.64 0.60 0.57 0.56 0.45 0.29 0.15 0.51 0.38 0.23 0.18

4.577 4.596 4.602 4.600 4.644 4.743 4.839 4.586 4.610 4.695 4.729

33.4 32.7 32.2 31.0 28.3 20.4 19.8 27.2 20.9 19.2 16.4

25 25 22 19 15 5.9 3.1 17 9.3 5.7 2.9

111 110 102 104 90

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RESULTS AND DISCUSSION Since the 5-alkyl substituent in MeN and HxN is rather distant from the locus of polymerization, it might be anticipated that the reactivity ratios ri in both the N-MeN and N-HxN systems should be approximately unity and that good incorporation of the comonomer should be achieved. However, systematic studies of statistical ROMP copolymerizations are relatively rare,36 and there do not appear to be any such published studies with this particular initiator. Consequently, it was necessary to first measure the reactivity ratios in the present cases, so that the compositional gradient formed during these batch polymerizations could be quantified and so that the polymerizations could be halted at conversions low enough that the gradient would be modest. For the N-MeN case, numerous polymerization trials were run, varying the initial monomer ratio and taking aliquots at different conversions. By assuming first-order Markov statistics and numerically integrating the copolymerization equation37 up to the measured conversion, reactivity ratios of rMeN = 1.58 ± 0.03 and rN = 0.61 ± 0.04 were obtained, where the quoted ranges correspond to ±1 standard deviation of the fit (see Supporting Information for data and details). The reactivity ratio product (rMeNrN = 0.96) corresponds closely to the value of unity expected if monomer incorporation depends only on the relative proclivity of the two monomers to coordinate with the Mo active site and not on the identity of the preceding unit in the chain. Based on these reactivity ratios, “production” polymerizations were taken to approximately 50% conversion; the average composition of the product polymer (measured by 1H NMR spectroscopy) was within 0.6 mol % of the predicted value of MeN content in all cases, and based on these ri values, the ratios of the compositions of the chain ends to the average composition of the chains differ by at most 20% from unity (e.g., the calculated compositions of the two chain ends for the N−MeN copolymer containing an average of 32.4 mol % MeN are 29.7 and 36.1 mol % MeN; see Supporting Information for a plot of calculated instantaneous composition as a function of relative chain length). To a satisfactory approximation, then, these copolymers may be considered as random. A few copolymers of N with a minor quantity of hexylnorbornene (HxN) were also synthesized to serve as a reference; it was anticipated that the much greater volume of the hexyl branch would lead to strong exclusion of HxN units from the hPN crystal. The limited number of polymerizations, all at low HxN contents, precluded an accurate determination of both reactivity ratios; under the assumption that rHxNrN = 1, rHxN = 1.33 was estimated, so the N−HxN copolymers are expected to show nearly random sequences as well.

104 80

Table 1 shows key molecular, thermal, and morphological characteristics of the hP(N-co-MeN) and hP(N-co-HxN) copolymers examined in this work. Both series show the qualitative trends expected for random copolymers: as the comonomer content increases, progressive decreases in the peak melting temperature Tm, total transition enthalpy ΔH (= ΔHcc + ΔHm), and weight fraction crystallinity wc measured by both DSC and WAXS are observed. However, the two series show very large quantitative differences: Figure 1a shows Tm vs

Figure 1. Trends in (a) peak melting temperature Tm and (b) weight fraction crystallinity wc (from DSC) vs comonomer mole fraction in the polymer FB for (□) hPN homopolymer, (●) hP(N-co-MeN) copolymers, and (▲) hP(N-co-HxN) copolymers. Lines are guides to the eye for each copolymer series.

comonomer content (mole fraction monomer B in the polymer, FB), while Figure 1b shows wc(DSC) vs FB. When comonomers are completely excluded from the lattice, Tm is expected to be essentially independent of the comonomer type; this expectation has been repeatedly confirmed in the heavily studied case of polyethylene.2,38,39 However, inclusion of comonomers into the crystal allows for a greater crystal thickness tc and consequently a higher Tm at a given FB; again, in the case of polyethylene, Tm for ethylene−propylene 9290

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copolymers lies systematically above that for other ethylene copolymers.2 Thus, the 2-fold difference in slope observed in Figure 1a already suggests extensive inclusion of MeN units within the hPN crystal. This effect is seen more dramatically in Figure 1b, where the crystallinity falls off far more slowly with comonomer content when the comonomer is MeN vs HxN. This may be compared with the case of polyethylene, where a comonomer mole fraction FB of only 0.2 is sufficient to render the copolymer wholly amorphous when the counits are excluded from the crystal (butene,38 hexene,38 octene,38,39 styrene4,39); when the counits are propylene,4,40 which are extensively included into the crystal, the crystallinity is higher but is still small or nonexistent when FB ≥ 0.3. Inspection of Figure 1b shows that to achieve the same reduction in wc, approximately 4 times as much MeN as HxN is required on a molar basis (∼4 times higher FB for MeN vs HxN copolymers); in other words, it is as if 3/4 of the MeN comonomer units are “invisible”, at least as regards their impact on reducing wc. At first glance, then, we might estimate that the hP(N-co-MeN) system shows inclusion of MeN units at the level of ∼3/4 of the overall MeN content. Note that in Figure 1b, and throughout the rest of this article, the values of wc from DSC were used; however, the values of wc from WAXS could just as easily have been employed, yielding the same conclusion (see Supporting Information for analogous figure). As is clear from Table 1, the wc values from WAXS are slightly and systematically lower than the values from wc from DSC, an effect which is commonly observed and attributed to how material at the crystalline−amorphous interface is perceived by the two techniques.41 When comonomer is preferentially or completely excluded from the crystal, then a portion of the reduction in Tm with FB, as observed in Figure 1a, should be due to the difference in chemical potential between molten homopolymer and molten copolymer, as noted originally by Flory.42 However, for random copolymers crystallized simply via dynamic cooling from the melt, a comparable or larger effect is expected to result from the reduction in crystal thickness tc as FB increases.43 The roomtemperature SAXS patterns for all of the copolymers are shown in Figure 2 and are typical for semicrystalline copolymers: at high crystallinities (wc > 0.50), a relatively narrow primary peak is observed, along with a broad second order peak, while at lower crystallinities, only a broader primary peak can be resolved. The average intercrystal spacing D (long spacing) for each copolymer was determined from the primary peak position q* as D = 2π/q*; these values are listed in Table 1. To estimate the average crystal thickness tc, we simply assume that the material consists of space-filling lamellar stacks, an assumption revisited below. In this case, the linear crystallinity of the lamellar stack and the overall crystallinity are identical, and tc = ϕcD, where ϕc is the volume fraction of crystals (using the 23 °C densities of 0.947 and 1.012 g/cm3 for amorphous hPN and crystalline hPN in the rotationally ordered polymorph, respectively44). These values of tc are also listed in Table 1; they vary by nearly an order of magnitude across the series, as both D and wc decrease progressively with comonomer content. As noted in the Introduction, hPN has two known crystal polymorphs: a rotationally ordered (RO) monoclinic structure at room temperature, which transforms at Tcc (prior to melting) to a rotationally disordered (RD) pseudohexagonal structure, wherein the stems exhibit a hexagonal packing transverse to their axes.23 As indicated in Table 1, Tcc = 111 °C for the hPN

Figure 2. SAXS patterns for (a) hP(N-co-MeN) copolymers and (b) hP(N-co-HxN) copolymers of the indicated comonomer mole fraction (FMeN or FHxN). The SAXS pattern for the hPN copolymer is presented at the top of each panel for comparison. To avoid overlap, intensities are shifted vertically by the factors indicated in parentheses.

homopolymer, and Tcc falls off in both series as comonomer content increases. For the two highest comonomer contents in both series (FMeN > 0.1, FHxN > 0.03), the endotherm corresponding to the crystal−crystal transition is no longer visible, meaning that the copolymer exists in the RD state at room temperature. This was confirmed by WAXS, where the patterns for these four copolymers show only one narrow peak over the range 15° < 2θ < 25° (Cu Kα radiation), along with the broad amorphous hump (see representative DSC and WAXS data in Supporting Information). WAXS was used to determine the Bragg spacing of the principal reflection for each of the 11 polymers; in the monoclinic RO structure, this peak is the (110) reflection, while at elevated temperatures, the monoclinic (110) and (020) peaks merge to form the (10) reflection of the pseudohexagonal RD lattice. The Bragg spacing of this peak will be denoted d110 for simplicity; a modest discontinuity in d110 is expected on transforming between polymorphs.24 Table 1 shows that d110 increases for both series as comonomer content is increased. However, there are potentially two factors contributing to this increase. If counits are included in the crystal, then the unit cell (and, by inference, d110) would be expected to expand, given the larger repeat unit volume of the counits.6 However, the progressive reduction in tc with FB will also affect d110, since the crystal lattice is expanded by the stresses exerted by the fold surfaces; as tc is reduced, the same surface stress will have a greater effect on the average unit cell dimensions.45,46 Thus, Figure 3 plots d110 against tc−1 for the two copolymer series separately. Both series show a jump in d110 (dashed line) where the room-temperature crystal structure transitions from rotationally ordered to disordered. But in both the RO and RD phases, the MeN copolymers show significantly more unit cell expansion (larger d110) than the HxN copolymers. One might expect the surface stresses to be similar in the two copolymer series, suggesting 9291

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Figure 4. Peak crystal−crystal transition temperature Tcc, plotted against reciprocal crystal thickness tc−1, for (□) hPN homopolymer, (●) hP(N-co-MeN) copolymers, and (▲) hP(N-co-HxN) copolymers. Solid lines are least-squares fits to each copolymer series (including the homopolymer).

Figure 3. Room-temperature Bragg spacing of most intense WAXS peak, d110, plotted against reciprocal crystal thickness tc−1, for (□) hPN homopolymer, (●) hP(N-co-MeN) copolymers, and (▲) hP(N-coHxN) copolymers. Solid lines are guides to the eye for each copolymer series; dashed lines indicate the discontinuity which accompanies the polymorphic transition from the RO crystal (smaller values of tc−1) to the RD crystal (larger values of tc−1).

140 °C·nm for the MeN series, −480 ± 40 °C·nm for the HxN series), implying that σRO > σRD. The small enthalpy of the crystal−crystal transition, coupled with its breadth in the DSC thermogram, makes an accurate determination of ΔHcc difficult, but it is approximately 4% of the total endotherm, which has been determined as 86 J/g for 100% crystalline hPN.23 The slopes thus suggest that σRO is approximately 5−8% greater than σRD, which has previously been estimated30 as 0.045 J/m2. This modest reduction in σ on passing from the RO to the RD phase seems consistent with the small density decrease in the crystal, leading to a looser packing at the crystal−amorphous fold interface. Third, the two series do differ, with the points for the MeN series lying systematically below those for the HxN series (and with a correspondingly steeper slope in Figure 4). The reason for this is unclear, but since the crystals in the MeN case contain significant contents of comonomer, it may reflect a differential contribution of these inclusions to the free energy of the RO vs RD crystals, since comonomer content and tc−1 are strongly correlated (see Table 1). In this case, the steeper slope in Figure 4 for MeN vs HxN would imply that inclusion favors the RD polymorph over RO, which seems entirely plausible. However, the different slopes for the two series in Figure 4 could also reflect differences in σRO and σRD between the two series of copolymers or variation in σRO and σRD with FB within a series. This possibility will be discussed further below. Returning to the Tm data in Table 1, further quantitative analysis demands more precise values of T0m and σRD than the previous rough estimates. A proper determination requires measurement of tc and extrapolation according to the Gibbs− Thomson equation, written here for lamellae of large lateral extent:47

that the additional expansion in the MeN case is due to inclusion of MeN units within the hPN crystal. As noted above, comonomer incorporation progressively depresses Tcc in both series, to the point where polymers with high comonomer content show no Tcc, but instead exist in the RD phase at room temperature. (Note that this does not necessarily mean that Tcc lies below room temperature; the chain motions required for a polymorphic transformation might be slow in the vicinity of room temperature, since the quasistatic glass transition temperature of hPN homopolymer, and of the copolymers studied here, is approximately 4 °C.25) Since Tcc should reflect the temperature at which the free energies of the two crystal polymorphs are identical, it too should depend on tc, due to the additional enthalpy imparted by the crystal− amorphous interface, whose value could differ depending on the crystal polymorph. Denoting the crystal fold surface energies in the two cases as σRO and σRD, and the mass densities of the two phases as ρRO and ρRD, we can write expressions for the free energies of melting of both the RO and RD phases as functions of T and tc (see Supporting Information). Setting these two equal at Tcc yields the following Gibbs−Thomson-like expression: Tcc = Tcc0[1 − (2/ΔH0,cctc)(σRO/ρRO − σRD/ρRD )]

(1)

where T0cc is related to point T0m of the RO and

the difference in equilibrium melting RD phases and to the enthalpy of the crystal−crystal transition for fully crystalline polymer, ΔH0,cc (see Supporting Information). Note that eq 1 has precisely the Gibbs−Thomson form when ρRO and ρRD are equal; however, for hPN, there is a small volume expansion upon heating through Tcc, such that ρRD is 0.9% less than ρRO.44,47 Figure 4 plots the data for both series in the format suggested by eq 1. Since four of the copolymers in Table 1 are in the RD phase already at room temperature, the data are rather limited, but some conclusions can nevertheless be drawn. First, the limiting value of T0cc is distinctly less than the equilibrium melting point T0m, previously estimated23 to be 156 °C; from the data for the MeN series, T0cc = 139 ± 9 °C (±1 std dev of fit) and 131 ± 3 °C from the data for the HxN series. Thus, while the finite crystal thickness contributes greatly to reducing the value of Tcc, even in the limit of infinitely thick crystals, hPN is expected to transition from the RO to the RD phase prior to melting. Second, the slopes in Figure 4 are distinctly negative (−730 ±

Tm = Tm0(1 − 2σRD/ΔH0,RDρRD tc)

(2)

Recently, our group has studied the rapid crystal thickening kinetics of an hPN homopolymer, similar to that in Table 1, at Tcc < T < Tm, by in situ hot stage SAXS.24 Specimens of that same hPN homopolymer were subjected to analogous thermal treatments in the DSC and Tm measured following a quench to −30 °C and immediate reheat at 10 °C/min; the results are plotted in Figure 5, in the form of eq 2. The best-fit line yields an intercept of T0m = 153.2 ± 0.6 °C (±1 std dev) and a slope of −334 ± 23 °C·nm. ΔH0,RD in eq 2 corresponds to the melting enthalpy of pure RD crystal, since it is the RD crystal which melts at Tm; the total enthalpy ΔH0,RO (including that of the crystal−crystal transition at Tcc) has been previously estimated 9292

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Perplexingly, however, the hP(N-co-HxN) Tm values lie well above the Tm values for the hP(N-co-MeN) series at the same tc, which as already noted, generally conform to the Tm values calculated for uniform inclusion. This is entirely unanticipated; if HxN units are excluded from the crystal, the additional chemical potential contribution should reduce Tm relative to the uniform inclusion case of eq 2. The usual framework8 for predicting Tm in the complete exclusion case combines Flory’s treatment42 of the chemical potential with the Gibbs− Thomson expression for finite crystal thickness to yield 1/Tm − 1/Tm0 = −(R /ΔH0,RDm0) ln(1 − FB) Figure 5. Peak melting temperature Tm plotted against the reciprocal crystal thickness t c −1 (Gibbs−Thomson plot) for the hPN homopolymer of ref 24 subjected to elevated-temperature annealing at 125, 130, or 135 °C for various times. Solid line is the least-squares fit, corresponding to eq 2.

+ 2σRD/(TmΔH0,RDρRD tc)

(3)

where R is the gas constant, m0 is the molecular weight of the crystallizable repeat unit, and the sequence propagation probability p in Flory’s treatment is set equal to 1 − FB for a strictly random copolymer. In systematic investigations of poly(ethylene-co-octene)49 and syndiotactic poly(propylene-cooctene)50 copolymers, Strobl and co-workers have concluded that σ is unaffected by copolymerization but that the actual dependence of Tm on FB is stronger than that presented by Flory (first term on the right-hand-side of eq 3); these deviations were explained by the fact that while the Flory treatment should be true at equilibrium (for final melting, of an infinitesimal fraction of crystals of infinite thickness),51 it may not capture the actual contribution of the chemical potential difference between the phases in real polymer crystals, which are not at equilibrium. Note, however, that the deviations observed in Figure 6 are in the opposite direction; indeed, the chemical potential term would have to be of opposite sign to bring eq 3 into conformance with the data, which appears entirely implausible. Thus, the second term in eq 3 bears closer examination. One possible source of error is the simple method employed here to determine tc, which assumes space-filling lamellar stacks. It is known that the linear (stack) crystallinity can exceed the overall crystallinity, especially for stiff-chain polymers such as poly(ether ether ketone), due to the formation of interstack amorphous “gaps”.52 This effect may contribute to the discrepancy observed here but cannot be the entire cause. Using eq 3 and the observed Tm, the values of tc (and hence ϕc) required to bring the two into agreement may be calculated; nearly all of the reduction in macroscopic crystallinity would have to be due to the formation of such gaps, such that the linear volume fraction crystallinity for the FHxN = 0.088 specimen would have to be ϕc = 0.49, nearly triple the overall value. Furthermore, we have calculated tc via the correlation function approach31,53 (see Supporting Information) for the two polymers in each series with highest comonomer content (lowest crystallinity); while tc determined by that method is indeed somewhat larger for the polymer in each series with the very smallest tc, the difference is only 1.6× on average, not the 3× required for this effect to explain the discrepancy. An alternative possibility is that σRD is not constant as the comonomer content is increased. If σRD is adjusted to bring eq 3 into agreement with the measured Tm, then the apparent values of σRD presented in Figure 7 result. The apparent value of σRD decreases by nearly 3× as comonomer content is increased, a very large change. However, a qualitatively similar effect has been observed in hPN−hPEN diblock copolymers, w h e r e h P E N is a m o r p h o u s h y d r o g e n at ed p o l y (ethylidenenorbornene).30 Lengthening the hPEN block

as 86 J/g crystal,23 so if 4% of this is due to ΔH0,cc, then ΔH0,RD = 83 J/g. Combined with ρRD = 0.956 g/cm3 at 145 °C,44 the measured slope of −334 °C·nm yields a value of σRD = 0.031 J/ m2. This value is some 30% smaller than the previous rough estimate,30 which was made simply by connecting the value of T0m estimated by Hoffman−Weeks extrapolation (156 °C vs 153 °C in the present case) with the value of Tm measured on a single hPN specimen of known tc. Armed with these quantities, we may compare the measured Tm values for these copolymers with two relevant limiting cases. In the case of uniform inclusion of the comonomerthat is, when the concentration of comonomer units is identical in the crystalline and amorphous phases in the semicrystalline solid there is no additional term arising from a change in chemical potential due to mixing upon melting, and the melting point should simply be given by eq 2. Figure 6 shows the Tm data for

Figure 6. Peak melting temperature Tm plotted against the reciprocal crystal thickness t c −1 (Gibbs−Thomson plot) for (□ ) hPN homopolymer, (●) hP(N-co-MeN) copolymers, and (▲) hP(N-coHxN) copolymers. The solid line is the least-squares fit to the hPN homopolymer data in Figure 5 (Gibbs−Thomson line), about which the hP(N-co-MeN) copolymer data scatter; the dashed line is a guide to the eye for the hP(N-co-HxN) copolymer series.

both copolymer series; the MeN series is in generally good agreement with eq 2, with the parameters obtained in Figure 5 for hPN homopolymer (solid line), as expected given the extensive inclusion of MeN units in the crystal already revealed by Figure 1b, though the data of Figure 6 do not preclude a modest differential in MeN counit concentrations between crystal and amorphous phases (i.e., a small but nonzero energy of defect inclusion). 9293

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polymorph. At comparable tc, hP(N-co-MeN) copolymers show a lower Tcc than hP(N-co-HxN) copolymers. The hP(N-coMeN) copolymers show Tm vs tc−1 behavior (Gibbs−Thomson plot) which generally superimposes on the behavior of the hPN homopolymer, while the hP(N-co-HxN) copolymers show significant positive deviations in Tm, matching those previously reported in hPN−hPEN diblock copolymers and suggesting a progressive reduction in crystal surface energy with comonomer content. Comonomer incorporation also widens the “window” between Tm and Tcc, where the crystals exist in the RD polymorph; in the RD state, the crystals show only a very small plastic resistance, and highly oriented specimens can be obtained via solid-state processing.24 Future work will exploit the ability to tune Tm through MeN incorporation, without a large penalty in wc, to adjust the melting/freezing point of the crystallizable block in ROMP-derived crystalline−amorphous58 and crystalline−crystalline47,59 diblock copolymers.

Figure 7. Apparent crystal surface energy σRD for the (□) hPN homopolymer and (▲) hP(N-co-HxN) copolymers as a function of comonomer mole fraction FB in the polymer, determined from eq 3 with σRD as the adjusted parameter.

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induces additional folding of the hPN block and reduces tc; Tm decreases continuously with tc−1, but with a slope much less steep than the −334 °C·nm revealed in Figure 5. Moreover, at long hPEN block lengths (small values of tc, large values of tc−1), the thin hPN crystals in the diblock melt at Tm values well above the prediction of the Gibbs−Thomson equation shown in Figure 6, by as much as 40 °Ceven though those hPN− hPEN diblocks form disordered (homogeneous) melts, so there should be an additional reduction in Tm over the Gibbs− Thomson result due to the lowered chemical potential of the (mixed) melt relative to pure molten hPN. Thus, there is precedent for the unexpected behavior of the hP(N-co-HxN) copolymers exhibited in Figures 6 and 7, even if the mechanism is not obvious. Note that the value of σ is expected to decrease as the fraction of regular folding increases,54−56 which may provide an explanation at least for the hPN−hPEN block copolymer data; however, for ethylene−butene random copolymers, a small increase in σ with comonomer content has been reported,57 opposite to the present hP(N-co-HxN) case. Also, it is intriguing to note that there is no such variation in the apparent σ with FB for the hP(N-co-MeN) copolymers; apparently, the majority of MeN units behave as if “invisible” not only as regards their inclusion into the crystal, but also as regards their effect on the fold surface.

ASSOCIATED CONTENT

S Supporting Information *

Methods and data used in determination of reactivity ratios; representative DSC thermograms; WAXS patterns and amorphous fits; analogue to Figure 1b using wc(WAXS); derivation of eq 1; one-dimensional SAXS correlation functions for the polymers of highest FB and values of D and tc extracted therefrom. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.A.R.). Present Addresses †

M.T.S.: Project Development Section, ExxonMobil Chemical Company, 4999 Scenic Highway, Baton Rouge, LA 70805. ‡ A.J.S.: Corporate Strategic Research Laboratories, ExxonMobil Research and Engineering Company, Route 22 East, Annandale, NJ 08801. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was generously supported by the National Science Foundation, Polymers Program (DMR-1003942), and by the Lidow and MacCracken Senior Thesis Funds at Princeton University. The authors gratefully acknowledge Dr. Andrew Bell (Promerus) for the donation of the MeN and HxN monomers and for stimulating discussions regarding ROMP copolymerization.

CONCLUSIONS Model crystallizable copolymers, of targeted molecular weight and narrow molecular weight distribution, were successfully synthesized by ROMP of norbornene with an alkylnorbornene comonomer, followed by catalytic hydrogenation. When the counit defect is small (alkyl = Me), extensive counit inclusion into the hPN crystals is observed; significant crystallinities are retained in the copolymer even when FMeN > 0.3. Larger counits (alkyl = Hx) are excluded from the crystal; comparable crystallinities are found for the two copolymer series when the MeN content is 4× the HxN content. Incorporation of alkylnorbornene counits into the polymer progressively reduces the average crystal thickness tc in specimens crystallized during dynamic cooling from the melt, but at a much steeper rate for the excluded HxN units than for the included MeN units. The crystal−crystal transition temperature Tcc between the lowtemperature, rotationally ordered hPN polymorph and the high-temperature, rotationally disordered polymorph also decreases as tc decreases, indicating that thin crystals stabilize the RD polymorph; this stabilization reflects a reduction in the crystal surface energy on transitioning to the less-dense RD

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