Mixing Thermodynamics of Ternary Block–Random Copolymers

Article pubs.acs.org/Macromolecules

Mixing Thermodynamics of Ternary Block−Random Copolymers Containing a Polyethylene Block Bryan S. Beckingham, Adam B. Burns, and Richard A. Register* Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: The mixing interactions among polyolefins and other hydrocarbon polymers are of strong fundamental and practical interest, especially in mixtures involving the simplest member of the family, polyethylene (E). The present work examines the interaction energy densities between E and random copolymers of styrene and hydrogenated isoprene (SrhI), and between E and random copolymers of vinylcyclohexane and hydrogenated isoprene (VCHrhI), by measuring the order−disorder transition temperatures of near-symmetric E−SrhI and E−VCHrhI diblock−random copolymers. The E−SrhI case is of special interest, since the solubility parameters δ fall in the order δS > δE > δhI; if regular mixing were obeyed, zero interaction energy between E and SrhI could be obtained for a suitable SrhI composition. However, large positive deviations from regular mixing are observed in the E−SrhI system, while smaller but significant negative deviations are observed in the E−VCHrhI system. Notwithstanding these irregularities, a ternary mixing model (“copolymer equation”), using independently determined values of the three component interaction energy densities, provides a good representation (within ≈15%) of the experimental interaction energies.

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INTRODUCTION The mixing thermodynamics of hydrocarbon polymers especially saturated hydrocarbon polymers, including the archetypal polyethylenehave been extensively studied over the past two decades.1,2 In many cases, such blends show regular mixing behavior,1,3,4 meaning that a unique value of the solubility parameter δ (square root of cohesive energy density) can be assigned to each polymer and that the interaction energy density X between the two polymers is simply given by XR = (Δδ)2, with the “R” subscript emphasizing regular mixing. (X ≡ χRT/Vref, where χ is the Flory interaction parameter between the two polymers, Vref is the reference volume used in the definition of χ, T is absolute temperature, and R is the gas constant.) Since only simple dispersive interactions exist between saturated hydrocarbon polymers, one might expect regular mixing to be a good model for the experimental interaction energy density, XX. Nonetheless, even in polyolefin blends, significant deviations from regular mixingin both the positive direction (XX/XR > 1, “extra repulsion”1,4,5) and the negative direction (XX/XR < 1, “extra attraction”1,4,6)have been observed. Yet the relative simplicity of such materials, coupled with the practical importance of polyolefins,7 warrants both further study of their mixing (ir)regularity, and an expansion of the palette of hydrocarbon monomer units examined (to include aromatic and cycloaliphatic units, for example), to provide greater diversity in the physical properties of the polymers. In previous work,8 we showed that alkyllithium-initiated anionic copolymerization of styrene (S) and isoprene (I) in a © 2013 American Chemical Society

50/50 v/v cyclohexane/triethylamine mixture proceeded in a living fashion and with no down-chain compositional gradient, yielding truly random copolymers (SrI) for any monomer ratio. These polymers could then be hydrogenated with different catalysts to yield polymers in which only the isoprene units were saturated (SrhI) or in which the S units were also saturated to vinylcyclohexane, VCH (VCHrhI).8,9 SrI random copolymers could also be incorporated as blocks into welldefined block copolymers. Within each series of hydrogenated derivatives (SrhI, VCHrhI), regular mixing was obeyed, and moreover the solubility parameter of the random copolymer simply varied linearly with hI volume fraction, providing a useful rule for the design of SrhI-based or VCHrhI-based random copolymers with a desired X (or analogous block− random copolymers with a targeted order−disorder transition temperature, TODT).9 Intriguingly, an SrhI copolymer with 50 wt % S, (SrhI)50, was postulated8 to have a value of δ very similar to that of polyethylene (E), based on the similarity of the experimentally measured interaction strength, (XX)hI−(SrhI)50 in hI−(SrhI)50 diblocks, to the calculated interaction strength between E and hI, (XR)E−hI, from well-tested assignments of solubility parameters obtained from polyolefin blends. Here, we extend this work to a class of ternary systems (generically represented as monomers A, B, and C): “block− random” copolymers of the C−ArB type. Specifically, we Received: February 12, 2013 Revised: March 10, 2013 Published: March 26, 2013 2760

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Table 1. Characteristics of B−S and B−SrI Diblock Copolymers and Their Hydrogenated Derivatives polymer B-S-8

B-S-7

B-(SrI)51-86

B-(SrI)49-68

B-(SrI)50-44

B-(SrI)50-23

block

Mn (kg/mol)

B S diblock B S diblock B SrI diblock B SrI diblock B SrI diblock B SrI diblock

3.6 4.9 8.4 2.8 4.1 6.9 44.7 40.8 85.5 36.3 32.2 68.5 22.2 22.3 44.5 10.9 11.9 22.8

Mw/Mn

wt % styrene

% vinyla3,4-(1,2-)

wcb VCHrhI (SrhI or S)

Tmc (°C) VCHrhI (SrhI or S)

Tgd (°C) VCHrhI (SrhI)

(8) 1.08

(103) (8)

1.09

(101) 51

(8) 44 (2)

49

(8) 45 (2)

50

(8) 46 (2)

50

(8) 45 (3)

1.08

1.07

1.06

1.09

0.29

99

22

0.27

101 (99)

23 (14)

0.31 (32)

101 (101)

21 (13)

0.27 (32)

103 (104)

20 (10)

a

Percent of the butadiene units enchained as (1,2-) and isoprene units enchained as 3,4- (1,2-), determined by 1H NMR spectroscopy. bE block degree of crystallinity measured by DSC for the hydrogenated derivatives, VCHrhI (SrhI or S); for representative data, see Supporting Information. c Peak melting temperature of the E block observed by DSC. dGlass transition temperature of the VCHrhI (SrhI) domains observed by DSC. samples taken from the reactor and upon completion (>99% of the desired units saturated, corresponding to the detectability limit) freed from catalyst and precipitated into methanol. A Ni/Al catalyst was used to selectively saturate the diene units while retaining the styrene aromaticity.13,14 The catalyst was prepared by mixing triethylaluminum (1 M in hexanes, 10 mL) with nickel 2-ethylhexanoate (0.1 M in cyclohexane, 30 mL; Al:Ni = 3.3:1 atomic ratio) in a dry round-bottom vessel previously purged with N2. The catalyst was injected directly into the reactor, followed by N2 and H2 purges, before a final charge of H2 was added. In polymers containing an SrI block, catalyst deactivation typically mandated multiple catalyst charges to achieve complete saturation of the I units. The catalyst was removed by vigorous stirring with aqueous citric acid (16 wt %) until the catalyst color disappeared. For saturation of all double bonds (olefinic and aromatic), palladium supported on calcium carbonate was used (Pd0/ CaCO3, Pd0 content 5 wt %, Alfa Aesar; approximately 2:1 Pd0/ CaCO3 to polymer by weight). The Pd0/CaCO3 catalyst was removed via filtration. Molecular weights and compositions for the hydrogenated diblocks were calculated from the unhydrogenated precursors assuming complete hydrogenation of the relevant double bonds. Molecular Characterization. Gel permeation chromatography (GPC) was conducted at 35 °C using two 30 cm Polymer Laboratories PLgel Mixed-C columns and either a Wyatt Optilab T-rEX or a Waters 410 differential refractive index detector. THF was used as the mobile phase, and the systems were calibrated with narrow-distribution polystyrene standards. The apparent “polystyrene-equivalent” molecular weights obtained by GPC were converted to the true values by correcting for the differences in hydrodynamic volume15 between polystyrene and the relevant block as described in detail elsewhere.8,15 GPC measurements were conducted on the final diblock; Mn of each block was determined from the diblock Mn and the overall composition from 1H NMR spectroscopy using the Chang combining rule.15,16 Compositions were determined using 1H NMR spectroscopy conducted at 500 MHz on a Bruker AVANCE, using the areas of the S aromatic protons and the various B and I olefinic protons corresponding to different modes of addition (1,4-/1,2-/3,4-). Thermal and Morphological Characterization. Differential scanning calorimetry (DSC) measurements were made on ≈10 mg specimens, with a PerkinElmer DSC 7 equipped with a Type II intracooler, calibrated with indium and tin. Specimens were heated into the melt (130 or 140 °C), cooled at 10 °C/min to −30 °C, and immediately reheated at 10 °C/min, during which the reported data

examine the interblock mixing energies in polymers where the C block is hydrogenated low-vinyl polybutadiene (polyethylene, E), namely E−SrhI and E−VCHrhI diblocks. We find substantial deviations from regular mixing, in the negative direction for VCH-based systems and in the positive direction for S-based systems, such that (XX)E−(SrhI)50 is unexpectedly large and positive. However, a ternary mixing model (the “copolymer equation”1,10−12), with independently determined values of XA−B, XB−C, and XA−C, gives a good representation of the measured interaction strengths.

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EXPERIMENTAL SECTION

Polymerization. B−S diblocks were synthesized S block first (initiated by sec-butyllithium, s-BuLi) in neat cyclohexane, while B−SrI block−random copolymers were synthesized B block first (initiated by t-BuLi) in cyclohexane followed by addition of triethylaminean effective randomizer for styrene−isoprene polymerization as discussed elsewhere8for the random copolymer blocks. Polymers were synthesized at a final solids concentration of ≈15 wt %. Glass reactors were flamed out under vacuum and rinsed with t-BuLi and subsequently with cyclohexane prior to charging with initiator (s- or t-BuLi) in a nitrogen-filled glovebox. Solvents triethylamine and cyclohexane were stirred over diphenylhexyllithium (adduct of s-BuLi and 1,1-diphenylethylene), degassed via freeze−pump−thaw cycles, and vacuum-transferred into the reactor. Butadiene was condensed in a liquid-nitrogen-submersed trap containing n-butyllithium; the trap was immersed in an ice−water bath prior to vacuum-transferring the butadiene into the reactor. Triethylamine was added, in equal volume to the initial cyclohexane solvent charge, prior to polymerization of the random copolymer block. For random copolymerizations, styrene (S) and isoprene (I) monomers were mixed, stirred over dibutylmagnesium, degassed via freeze−pump−thaw cycles, and vacuum-transferred into the reactor. Unmixed S for S homopolymer blocks was handled similarly. Random copolymer blocks (SrI) were polymerized at 30 °C, while S and B blocks were polymerized at 60 °C. Hydrogenation. After polymerization, the polymers were catalytically hydrogenated using one of two catalyst systems. Both saturations were performed in a stirred 2 L Parr batch reactor with 4−10 g/L polymer in cyclohexane at 100 °C and 400−500 psi of H2. The extent of hydrogenation was monitored with infrared spectroscopy on 2761

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were recorded. Peak melting temperatures (Tm) of the E blocks and glass transition temperatures (Tg) of the random copolymer blocks (SrhI or VCHrhI), determined as the midpoint of the step change in heat capacity, are presented in Table 1. The enthalpy of melting for each material (ΔHm) was converted to a weight fraction crystallinity (wc) of the E block by wc = (ΔHm)/[wE(ΔHm,100)], where wE is the weight fraction of E block in the diblock and ΔHm,100 is the heat of melting17 of 100% crystalline E (277 J/g). Overlap of the E melting endotherm and the S block glass transition prevented the determination of accurate values of Tg and wc for the E−S diblocks. Small-angle X-ray scattering (SAXS) patterns were collected with an Anton-Paar compact Kratky camera fitted with a hotstage, 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 OED50 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.18 Absolute SAXS intensities (I/IeV) are plotted against the magnitude of the momentum transfer vector q = (4π/λ) sinθ, where θ is half the scattering angle; calibration was via silver behenate.19 Intensities were multiplied by q2 to approximately correct for the form factor of lamellae.20

All diblocks are nearly symmetric (similar molecular weights for the C and ArB (or A), blocks). While our previous work8 demonstrated that SrI copolymers of any composition synthesized in 50/50 v/v cyclohexane/triethylamine show no down-chain compositional gradient, here all SrI blocks contain ≈50 wt % S. The code in Table 1 indicates the block chemistry, with the numerical suffix indicating the total molecular weight in kg/mol. For the block−random polymers, the subscript indicates the wt % S in the random block in the unsaturated precursor. So, for example, B-S-8 is a diblock copolymer of butadiene and styrene with a total number-average molecular weight (Mn) of 8 kg/mol, while B-(SrI)50-23 is a block− random copolymer of B and SrI with Mn = 23 kg/mol and 50 wt % S in the random (SrI) block. Upon hydrogenation, “B” and “I” in the sample code are replaced by “E” and “hI”, respectively; if the Pd0/CaCO3 catalyst was used, “S” is replaced by “VCH”. The three rightmost columns in Table 1 contain measured values of E block fractional crystallinity wc and peak melting temperature Tm, and the glass transition temperature Tg for the VCHrhI (SrhI) random copolymer domains. Tests of Regular Mixing Thermodynamics. Values of TODT were determined using hot-stage small-angle X-ray scattering (SAXS). As an example, SAXS patterns of the four E−VCHrhI diblocks are shown at room temperature in Figure 2a, where the dominant feature is the broad hump near q = 0.5 nm−1 resulting from scattering between E crystallites. SAXS patterns for the same polymers above the Tm of the E crystallites are shown in Figure 2b, where Bragg peaks are observed at q/q* ratios of 1:2:3 (q* is the position of the firstorder peak), confirming the expected lamellar melt morphology. While the three highest molecular weight E−VCHrhI diblocks remained microphase-separated at all temperatures tested (up to 195 °C), a distinct ODT was observed for E(VCHrhI)50-23 via a sharp decrease in the primary peak intensity coupled with a sharp increase in the primary peak full width at half-maximum intensity (Figure 2c,d), indicating TODT = 125 ± 1 °C from the midpoint of the step change in peak breadth.21 TODT values were determined analogously for E(SrhI)50-23, E-S-8, and E-S-7 (see Supporting Information), as listed in Table 2. The experimental interaction energy density XX may be determined14 from the measured TODT value as XX = (χN) ODTρRT ODT/Mn, where Mn is the number-average molecular weight, N is the effective degree of polymerization of the diblock, ρ is the diblock’s mass density at TODT (see Supporting Information), and (χN)ODT is the theoretical value of χN at the ODT for a polymer with the corresponding volume fraction of E block (ϕE). For (χN)ODT, we use the selfconsistent field phase diagram of Matsen and Bates,22 corresponding to N → ∞ and χ → 0. An advantage of using X over χ in the analysis is that it avoids the selection of an arbitrary reference volume and thus facilitates comparison across systems of different chemistry (such as the series examined in this paper). For E-(VCHrhI)50-23, the measured TODT yields (XX)E−(VCHrhI)50 = 1.27 J/cm3 = 1.27 MPa at 125 °C as shown in Table 2, with values obtained analogously for the S-containing block copolymers. Figure 3 illustrates the approach taken to assess the mixing regularity in hydrogenated B−SrI block−random copolymers. This scheme builds upon our recent results9 for block−random copolymers that consisted of only the monomers S and I, which yielded the left portion of Figure 3, i.e., the upper series hI→

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RESULTS AND DISCUSSION Two poly(butadiene-b-styrene) diblock copolymers (B−S), and four poly(butadiene-b-(styrene-r-isoprene)) diblock−random copolymers (B−SrI), were synthesized via lithiuminitiated anionic polymerization and sequential monomer addition. Monomodal and narrow molecular weight distributions were obtained in all cases, as typified by the GPC traces in Figure 1.

Figure 1. GPC traces from the synthesis of a representative B−SrI block−random copolymer, B-(SrI)49-68. (- - -) Sample of the B block, removed from the reactor prior to the second monomer charge, showing a small amount of coupled material generated in the aliquot; () B-(SrI)49-68 block−random copolymer product.

For the block−random copolymers the polybutadiene block was synthesized first in neat cyclohexane to achieve the high (92%) 1,4-addition desired to form a crystallizable E block upon hydrogenation. Before addition of the S + I monomer mixture for the random copolymer block, triethylamine was added to the reactor to form a 50/50 v/v cosolvent mixture with cyclohexane. Triethylamine is necessary to randomize the copolymerization of S and I and also increases the vinyl content of the I units in the random copolymer block.8 Key characteristics of the precursor (unsaturated) polymers, including the “true” (absolute) number-average block molecular weights Mn, and the I microstructures, are given in Table 1. 2762

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Figure 2. SAXS patterns of E−VCHrhI block−random copolymers at (a) room temperature and (b) in the melt; intensities offset by indicated factors for clarity. (c) SAXS patterns of E-(VCHrhI)50-23 near the order−disorder transition and (d) SAXS peak intensity (▼, left axis) and full width at half-maximum (△, right axis) plotted against temperature, indicating TODT = 125 ± 1 °C.

Table 2 polymer

TODTa (°C)

XX (MPa)

XRb (MPa)

XTc (MPa)

E-(VCHrhI)50-23 E-(SrhI)50-23 E-S-8 E-S-7

125 208 200 159

1.27 1.45 4.20 4.83

2.07 0.003 1.10 1.10

1.47 1.27

TODT measured by hot-stage SAXS, ±1 °C. bX calculated from assigned solubility parameters according to regular mixing at TODT, as XR = (Δδ)2. cX calculated from ternary mixing, eq 1, at TODT.

a

(SrhI)50 → S and the lower series hI → (VCHrhI)50 → VCH. Within each of these two series, regular mixing was obeyed; i.e., unique values of δ could be assigned to each polymer and used to quantitatively predict values of X. Moreover, for the random copolymers, δ was found to scale linearly with the volume fraction of hI in the copolymer.9 Values of δ (in MPa1/2) for these polymers at 160 °C are given in square brackets in Figure 3, with the value set for δhI (14.47 MPa1/2) serving as the reference; for simplicity (and with no loss of generality in computing values of X), δhI is further set to be temperatureindependent. For any of the other polymers in the left portion of Figure 3, values of δ at temperatures other than 160 °C are then computed from the temperature-dependent X, as discussed previously.9 To incorporate E, we use the extensive data of Graessley and co-workers1,23 to determine δE − δhI (0.88 MPa1/2 at 160 °C).24 Thus, on the premise of regular mixing, X can be calculated for any combination of the polymers in Figure 3 simply as (Δδ)2; the values so calculated are denoted XR, with the subscript emphasizing the premise of regular mixing. Values of XR can then be compared with experimental interaction energy densities (XX, Table 2) obtained from the order−disorder transition (ODT) temperature (TODT) of near-symmetric diblocks comprised of E and each of the four polymers shown at left in Figure 3 (comparisons shown as dashed lines

Figure 3. Diagram of connections employed in evaluating the mixing regularity of hydrogenated derivatives of block copolymers of B with S or SrI. Unidirectional arrows (all beginning at hI) indicate the method of assignment of the values of δ for the other polymers (S, VCH, E), while bidirectional arrows indicate assessments of regularity in the behavior of diblock copolymers. Solid lines indicate that regular mixing was confirmed previously,9,23 while dashed lines (- - -) indicate block and block−random copolymers examined herein and (···) indicates values for VCH−E diblocks from the literature.25

with bidirectional arrows). Note that of the block−random copolymers, only those with lowest molecular weight (23 kg/ mol) showed thermally accessible ODTs; note also that both hydrogenated block−random copolymers in Table 2 (E(VCHrhI)50-23 and E-(SrhI)50-23) were derived from the 2763

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same B−SrI precursor. This is already a surprising finding, as based on the δ values in Figure 3, much larger values of X were anticipated for the E−(VCHrhI)50 system than for the E− (SrhI)50 system, but the two are clearly comparable, and in fact (XX)E−(SrhI)50 > (XX)E−(VCHrhI)50 from the measured values of TODT. It is immediately apparent from Table 2 that these polymers all show substantial departures from regular mixing, i.e., XX ≠ XR. For the VCH-containing block−random copolymer (E− (VCHrhI)50), significant negative deviations from regular mixing are observed, with (XX/XR)E−(VCHrhI)50 = 0.6. A comparison can be made with E−VCH diblocks, using the extensive data of Cochran and Bates,25 whose eight symmetric E−VCH diblocks with thermotropic ODTs yield XE−VCH(MPa) = 832 K/T + 0.618, and therefore XX = 2.54 MPa at 160 °C; the numbers in Figure 3 yield XR = 3.61 MPa, hence (XX/ XR)E−VCH = 0.7. Thus, the E−VCH pair shows systematic negative deviations from regular mixing. By contrast, the E−S pair shows systematic positive deviations from regular mixing, with a much larger magnitude. Each of the two E−S diblocks in Table 2 shows (XX/XR)E−S ≈ 4; both XX and XR are fairly large (>1 MPa), so the large ratio does not reflect a fortuitous near-match in the δ values used to calculate XR. For E−(SrhI)50, the calculated XR is quite small due to the similarity of δE and δ(SrhI)50; however, the measured XX = 1.45 MPa is rather large. Since (XX/XR)E−VCH < 1 and (XX/XR)E−S > 1, one might suspect that the deviations lie in an erroneous assignment of the value of δE used to calculate XR (i.e., that δE at 160 °C is significantly less than the value of 15.35 MPa1/2 shown in Figure 3). However, a quick calculation shows that there is no value of δE which can simultaneously yield (XR)E−S ≈ 4.8 MPa and (XR)E−VCH ≈ 2.5 MPa, using the values of δS and δVCH given in Figure 2. If one demands consistency with only one of the two series (VCH and VCHrhI, or S and SrhI), then it is possible to assign values of δE which yield (XX/XR) ≈ 1; at 160 °C, these values are δE ≈ 15.03 MPa1/2 (δE − δhI = 0.56 MPa1/2) for the VCH series, and δE ≈ 14.27 MPa1/2 (δE − δhI = −0.20 MPa1/2) for the S series. However, the first of these values of δE − δhI is already somewhat beyond the uncertainty implied by the consistency checks made by Graessley and coworkers on their solubility parameter assignments,3 and the second is clearly implausible (wrong sign). The latter inconsistency is evident directly from the raw data: a nearsymmetric hI-S diblock9 with slightly higher molecular weight than E-S-7 shows a lower TODT (126 °C vs 159 °C), clearly indicating that (XX)E−S > (XX)hI−S, despite the expected relative values of δ shown in Figure 3. Thus, the inescapable conclusion is that significant deviations from regular mixing occur in the E−VCH and E−S systems, and these deviations are not in the same direction. However, the origin of these deviations remains obscure, as with other deviations from regular mixing in hydrocarbon systems documented previously in the literature.1,4−6 One source of positive deviations from regular mixing can arise from differences in free volume density (thermal expansion coefficient) between the two polymers,1,26 and it is true that the thermal expansion coefficient of E is significantly higher (by ≈1.3×) than that of S or VCH (see Supporting Information). However, the deviations from regularity for the E−VCH and E−S systems are of opposite sign, while the thermal expansion coefficients of S and VCH are themselves quite similar, so this cannot be the source of the deviations observed here.

Ternary Mixing Thermodynamics. An alternative to the regular mixing relation is the “copolymer equation”,1,10−12 which allows all of the component interactions (Xij) to vary independently. Specializing this to the present casea mixture of homopolymer E with random copolymer ArhI, where monomer “A” is either VCH or Syields27 XE−Ar hI = fA XE−A + fhI XE−hI − fA fhI XA−hI

(1)

where in fA and f hI are the volume fractions of A and hI in the random copolymer ( fA + f hI = 1), calculated from the copolymer composition using the specific volume relations given in the Supporting Information. No assumption of mixing regularity is incorporated into eq 1, and therefore the three necessary Xij valueswhich must all be obtained independentlyneed not be consistent with regular mixing. As an extreme case,10−12 if the interactions between the two units making up the random copolymer are strongly repulsive (e.g., in eq 1, if XA−hI were to show much larger positive deviations from regular mixing than XE−A or XE−hI), then it is possible to obtain a negative XE−ArhI even though all the individual Xij are positive. We test the ternary mixing prediction by calculating XE−ArhI at TODT via eq 1 for E-(VCHrhI)50-23 and E-(SrhI)50-23, respectively; these ternary mixing predictions are denoted XT in Table 2. The required inputs for these calculations are shown schematically in Figure 4, where three binary interaction energy

Figure 4. Diagram of connections employed in applying the ternary mixing equation (eq 1) to the hydrogenated derivatives of B−SrI block−random copolymers. Each C−ArB system (E−SrhI, E− VCHrhI) is represented by a triangle, with the connections between the vertices representing the Xij; since the Xij are obtained independently, there is no directionality to the connections between vertices (all are bidirectional), unlike Figure 3. The two triangles share an edge, corresponding to XE−hI.

densities (XA−C, XB−C, XA−B = XE−A, XE−hI, XA−hI) are required for each system. For the VCH-containing case (TODT = 125 °C), XhI−VCH = 1.09 MPa from our previous work,9 while XE−VCH = 2.71 MPa from the data of Cochran and Bates.25 For E−hI, we estimate XE−hI = 0.90 MPa from the solubility parameter data of Graessley and co-workers,1,24 assuming regular mixing (an assumption bolstered by internal consistency tests of these δ values3,4 and by the agreement of this XE−hI value with that derived from the limited available data on related block copolymers28−30). This yields (XT)E−(VCHrhI)50 = 1.47 MPa, in good agreement with the experimental value of (XX)E−(VCHrhI)50 = 1.27 MPa. Analogously, for the S-containing 2764

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Figure 5. (a) Lamellar domain spacings d obtained from SAXS data in the melt, below TODT and above Tm and Tg of all of the constituent blocks. (b) Domain spacings corrected to a common segregation strength by (Xref/X)1/6, where Xref is XhI−(SrhI)50 at 180 °C. Solid line () in both (a) and (b) represents d (nm)= 2.29Mn2/3 fit to the series of hI−(SrhI)50 block−random copolymers,8 where Mn is in kg/mol. Dashed line (- - -) in (a) represents d (nm) = 2.88Mn2/3 fit to the observed d values for E−(VCHrhI)50 and E−(SrhI)50. Dotted line (···) in (b) represents d(Xref/X)1/6 = 2.62Mn2/3 fit to the E−(VCHrhI)50, E−(SrhI)50, and E−S block copolymers.

case (TODT = 208 °C), XS−hI = 3.63 MPa from our previous work,9 while XE−S = 4.19 MPa from the E−S diblocks presented in Table 2, and we estimate XE−hI = 0.62 MPa by the method described above (here at 208 °C, requiring an extrapolation of the solubility parameter data1,23 beyond their 167 °C limit). This yields (XT)E−(SrhI)50 = 1.27 MPa, again in good agreement with the experimental value, (XX)E−(SrhI)50 = 1.45 MPa. This analysis shows that the copolymer equation (with independently determined Xij) can give a good prediction (within ≈15%) for XC−ArB in these all-hydrocarbon C−ArB systems, even though the deviations from regular mixing (in the individual Xij) are quite large. However, this particular experimental system does present one disappointment: given the similarity of the δ values presented in Figure 3 for E and SrhI, one might have expected the two to form miscible blends and block copolymers to very high molecular weights (minuscule XR = 0.003 MPa at 208 °C, see Table 2). However, with the experimentally determined values of Xij used in the preceding analysis, the minimum value of XE−SrhI is calculated to occur when f S = 0, i.e., in an E−hI diblock. This result arises from the fact that it is the first term in eq 1 (involving XE−S) that shows a large positive deviation from regular mixing and not the last term (involving XS−hI, the two units which make up the random copolymer). In the E−VCHrhI case, it is also true that the minimum (XT)E−VCHrhI occurs at f VCH = 0 but that result is expected even from regular mixing (with a simple linear dependence of δ on f VCH for the random block9)the SrhI case is potentially more interesting (if ultimately disappointing), since δS > δE > δhI (Figure 3). Domain Spacing. While only the lowest molecular weight block−random copolymer in Table 1 (B-(SrI)50-23) produced hydrogenated derivatives with thermally accessible ODTs, the higher molecular weight materials provide an opportunity to examine how the interdomain spacing d varies not only as a function of Mn but also with block−random copolymer chemistry. The lamellar repeat distance, d = 2π/q*, for all block copolymers examined here is plotted in Figure 5a against Mn, supplemented with values for hI−(SrhI)50 diblocks studied previously.8 Within each series (E−S, E−VCHrhI, E−SrhI, and hI−(SrhI)50), good consistency with the expected31 strongsegregation scaling, d ∼ Mn2/3, is observed, though the different series vary by ≈50% in d. A significant portion of this difference is due to X, since d ∼ X1/6 in the strong-segregation limit;31 to remove this effect, we scale the observed domain spacings to a common reference, Xref, set equal to XhI−(SrhI)50 at 180 °C, as

shown in Figure 5b. This scaling collapses the E-containing polymers (E−S, E−VCHrhI, E−SrhI) satisfactorily, but the scaled d values for the E-based diblocks remain ≈14% larger than for the hI−SrhI diblocks. This difference is readily understood as resulting from differences in unperturbed chain dimensions (statistical segment lengths), since Rg2/M is larger for E than for hI,32 where Rg is the unperturbed radius of gyration; since the E and hI blocks account for ≈50 wt % of the diblock in the two dissimilar groups in Figure 5b, this effect overshadows any analogous (but much smaller) effect within each group resulting from differences in statistical segment length between VCH and S (which are minor components in all the diblocks in Figure 5), once the differences in segregation strength are accounted for.

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CONCLUSIONS Previous work9 has shown that regular mixing is closely obeyed in the hI−SrhI and hI−VCHrhI systems, with the ArhI component showing a linear dependence of δ on volume fraction hI. This regularity allowed the assignment of purecomponent solubility parameters δS and δVCH (relative to the reference δhI) as well as for the two random copolymers considered herein, δ(SrhI)50 and δ(VCHrhI)50, while a value of δE was obtained from δhI using solubility parameter differences obtained on homopolymer blends showing regular mixing.1,23 But when compared with values of the interaction energy densities XR calculated from these values of δ, the E−S system shows large positive deviations from regular mixing (XX/XR = 4 for E−S, with the ratio even higher for E−(SrhI)50), while the E−VCH system shows substantial negative deviations from regular mixing (XX/XR = 0.7 for E−VCH and 0.6 for E− (VCHrhI)50). By contrast, a ternary mixing model with independently determined values of the three interaction energy densities (XE−A, XE−hI, and XA−hI, where monomer “A” is either S or VCH) gives a good representation of the experimental XX (16% high for E−(VCHrhI)50, 13% low for E− (SrhI)50), providing a suitable quantitative guide for the prediction of X in these systems as a function of random− block composition. The relatively large value of (XX)E−S, coupled with the large value of the unperturbed Rg2/M for E (which has essentially all of its mass in the polymer backbone, unlike hI, S, or VCH), yields a lamellar spacing d for E−S diblocks which is ≈50% larger than for analogous hI−SrhI diblocks at the same diblock Mn. 2765

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addition) of the unsaturated precursor, but they do not contain a hydrogenated I corresponding to the hI employed herein (54% 1,4-). Thus, the solubility parameter value for E (δE), relative to the δhI reference employed here (δE − δhI), was estimated from the values of δE − δEP and δE − δ50SPI in ref 23, by linear interpolation in 1,4-content in the I precursor. EP is poly(ethylene-alt-propylene), a hydrogenated I having 93% 1,4-addition in the precursor, while 50SPI is a hydrogenated I with 50% 3,4-addition (37% 1,4-addition) in the precursor. (25) Cochran, E. W.; Bates, F. S. Macromolecules 2002, 35, 7368− 7374. (26) Milner, S. T.; Lacasse, M.-D.; Graessley, W. W. Macromolecules 2009, 42, 876−886. (27) Note that two of the four “monomer units” considered herein (E and hI) are themselves heteropolymers, as the precursor B and I units have mixed microstructures (92% 1,4- and 8% 1,2-addition for B; 54% 1,4-, 43% 3,4-, and 3% 1,2-addition for I, within 2%). Thus, a literal interpretation of the copolymer approach would ask for the determination of the interaction strengths between six different comonomer units in each of the SrhI and VCHrhI systems (i.e., 6!/(4! 2!) = 15 independent values of Xij for each system). However, the “lumped” approach pursued here (eq 1) is nonetheless entirely valid because we are concerned only with particular ratios of these different units (corresponding to the microstructures indicated above); all the polymers presented herein contain these units in only those specific ratios, and the experimental values of XA−B, XA−C, and XB−C were determined for polymers containing those units in the specific ratios desired. Therefore, the fact that “C” and “B” are themselves heteropolymers does not impact the validity of eq 1. (28) Prior work on hydrogenated butadiene−isoprene diblocks has typically focused on polymers derived from low-vinyl polyisoprene (∼93% 1,4-addition), which leads to poly(ethylene-alt-propylene), EP, upon hydrogenation. For E−EP, the χ correlation reported by Koo29 yields XE−EP(MPa) = 436 K/T − 0.773, or XE−EP = 0.22 MPa at 167 °C. Quiram30 measured TODT = 167 °C for one asymmetric diblock, E/MB 44, prepared from low-vinyl polybutadiene and high-vinyl polyisoprene (36% 1,4-, 54% 3,4-, and 10% 1,2-addition; hydrogenated product is denoted poly(3-methyl-1-butene), MB, for the dominant structure, hydrogenated 3,4-addition); using the same procedure discussed in the text yields XE−MB = 1.05 MPa at 167 °C. Linear interpolation in X1/2 (equivalent to linear interpolation in δ) between these two values yields XE−hI = 0.72 MPa at 167 °C. This value is in excellent agreement with the value of XE−hI = 0.75 MPa at 167 °C calculated from the blend data of Krishnamoorti23 by the method described in the text (yielding XE−hI = 0.90 MPa at 125 °C and XE−hI = 0.62 MPa at 208 °C). (29) Koo, C. M.; Wu, L. F.; Lim, L. S.; Mahanthappa, M. K.; Hillmyer, M. A.; Bates, F. S. Macromolecules 2005, 38, 6090−6098. (30) Quiram, D. J.; Register, R. A.; Marchand, G. R. Macromolecules 1997, 30, 4551−4558. (31) Semenov, A. N. Zh. Exsp. Teor. Fiz. 1985, 88, 1242−1256. (32) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A.; Zirkel, A. Macromolecules 1994, 27, 4639−4647.

ASSOCIATED CONTENT

S Supporting Information *

Representative DSC trace for E-(VCHrhI)49-68; expressions for the specific volumes of relevant homopolymers as functions of temperature; SAXS patterns for all other diblock and diblock− random copolymers at room temperature and near TODT, from which values of TODT were determined. 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]. 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). REFERENCES

(1) Graessley, W. W. Polymeric Liquids & Networks: Structure and Properties; Garland Science: New York, 2004. (2) Lohse, D. J. J. Macromol. Sci., Part C: Polym. Rev. 2005, 45, 289− 308. (3) Krishnamoorti, R.; Graessley, W. W.; Balsara, N. P.; Lohse, D. J. Macromolecules 1994, 27, 3073−3081. (4) Graessley, W. W.; Krishnamoorti, R.; Reichart, G. C.; Balsara, N. P.; Fetters, L. J.; Lohse, D. J. Macromolecules 1995, 28, 1260−1270. (5) Krishnamoorti, R.; Graessley, W. W.; Fetters, L. J.; Garner, R. T.; Lohse, D. J. Macromolecules 1995, 28, 1252−1259. (6) Reichart, G. C.; Graessley, W. W.; Register, R. A.; Krishnamoorti, R.; Lohse, D. J. Macromolecules 1997, 30, 3036−3041. (7) Peacock, A. J. Handbook of Polyethylene: Structures, Properties, and Applications; Marcel Dekker: New York, 2000. (8) Beckingham, B. S.; Register, R. A. Macromolecules 2011, 44, 4313−4319. (9) Beckingham, B. S.; Register, R. A. Macromolecules 2013, DOI: http://dx.doi.org/10.1021/ma4002512. (10) Kambour, R. P.; Bendler, J. T.; Bopp, R. C. Macromolecules 1983, 16, 753−757. (11) ten Brinke, G.; Karasz, F. E.; MacKnight, W. J. Macromolecules 1983, 16, 1827−1832. (12) Paul, D. R.; Barlow, J. W. Polymer 1984, 25, 487−494. (13) Hahn, S. F. J. Polym. Sci., Part A: Polym. Chem. 1992, 30, 397− 408. (14) Adams, J. L.; Quiram, D. J.; Graessley, W. W.; Register, R. A.; Marchand, G. R. Macromolecules 1998, 31, 201−204. (15) Sebastian, J. M.; Register, R. A. J. Appl. Polym. Sci. 2001, 82, 2056−2069. (16) Chang, F. S. C. J. Chromatogr. 1971, 55, 67−71. (17) Wunderlich, B.; Dole, M. J. Polym. Sci. 1957, 24, 201−213. (18) Register, R. A.; Bell, T. R. J. Polym. Sci., Part B: Polym. Phys. 1992, 30, 569−575. (19) Huang, T. C.; Toraya, H.; Blanton, T. N.; Wu, Y. J. Appl. Crystallogr. 1993, 26, 180−184. (20) Russell, T. P. In Handbook on Synchrotron Radiation; Brown, G. S., Moncton, D. E., Eds.; North-Holland: New York, 1991; Vol. 3, pp 379−469. (21) Winey, K. I.; Gobran, D. A.; Xu, Z.; Fetters, L. J.; Thomas, E. L. Macromolecules 1994, 27, 2392−2397. (22) Matsen, M. W.; Bates, F. S. Macromolecules 1996, 29, 1091− 1098. (23) Krishnamoorti, R.; Graessley, W. W.; Dee, G. T.; Walsh, D. J.; Fetters, L. J.; Lohse, D. J. Macromolecules 1996, 29, 367−376. (24) The data in ref 23 show a distinct dependence of δ for hydrogenated polyisoprenes on the microstructure (1,4-/3,4-/1,22766

dx.doi.org/10.1021/ma400311p | Macromolecules 2013, 46, 2760−2766