Regular Mixing Thermodynamics of Hydrogenated Styrene–Isoprene

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Regular Mixing Thermodynamics of Hydrogenated Styrene− Isoprene Block−Random Copolymers Bryan S. Beckingham and Richard A. Register* Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: Random copolymerization of A and B monomers represents a versatile method to tune interaction strengths between polymers, as ArB random copolymers will exhibit a smaller effective Flory interaction parameter χ (or interaction energy density X) upon mixing with A or B homopolymers than upon mixing A and B homopolymers with each other, and the ArB composition can be tuned continuously. This approach can also be used to tune the segregation strength in A−ArB “block− random” copolymers. Simple models of polymer mixing thermodynamics suggest that the effective interaction energy density in such block−random copolymers should follow XA−ArB = f B2XA−B, but this prediction has not been tested quantitatively. The present work systematically assesses the validity of this rule for thermally stable hydrogenated derivatives of styrene−isoprene block copolymers, through measurements of the order−disorder transition (ODT) temperature on near-symmetric diblock and diblock−random copolymers of varying composition and suitable molecular weight (M). Both hydrogenated derivatives wherein the styrene aromaticity is retained, and derivatives wherein the styrene units are saturated to vinylcyclohexane, are examined, and both are found to closely obey the XA−ArB = f B2XA−B prediction, thereby confirming the utility of this simple relationship in designing block copolymers with targeted interaction strengths using only these two common monomers. The reduction in XA−ArB over XA−B permits the synthesis of polymers having much larger M and domain spacing d while maintaining a thermally accessible ODT; measured domain spacings are found to closely follow the expected scaling, d ∼ X1/6M2/3.

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INTRODUCTION The morphology adopted by an A−B diblock copolymer is principally dependent on three quantities:1 the Flory−Huggins interaction parameter χA−B, which depends modestly on temperature and strongly on the chemical identity of the A and B monomers; the diblock’s degree of polymerization N; and the block volume fraction, ϕA or ϕB. For any ϕA, there exists a χN value, denoted (χN)ODT, at which an equilibrium order−disorder phase transition (ODT) should occur, between a mixed disordered state (at χN < (χN)ODT) and a spatially ordered, microphase-separated state (at χN > (χN)ODT); if χ is manipulated by changing temperature, the ODT occurs at a particular temperature (T ODT). Block copolymers with thermally accessible ODTs are often sought due to their enhanced processability in the disordered state, and the dramatic changes in material properties which occur at the ODT. However, for any given A−B monomer combination, if a thermotropic ODT is desired, χ and N are connected through the product (χN)ODT. Consequently, the range of N (range of molecular weights) which will yield a diblock with a thermotropic ODT is rather limited for any given A−B monomer combination, often to values which are lower than one might desirefor solid-state toughness, for example, or for accessing a large value of the interdomain spacing2 d. Living polymerizations which proceed with random monomer addition (no gradient) permit the synthesis of “block− random” copolymers, such as diblock copolymers represented generally by the structure (AxrB1‑x)−(AyrB1‑y), where each of the two blocks is a random copolymer of monomers A and B, simply with different fractions of A (x and y). Since x and y can be varied continuously, the effective χ between the blocks can © 2013 American Chemical Society

be varied continuously as well, allowing (χN)ODT (and thus TODT) to be tuned independently of molecular weight using only two monomers, via the difference3 between x and y. Moreover, physical properties, such as the block glass transition temperatures, can be tuned through the absolute magnitudes of x and y. This flexibility makes block−random copolymers a versatile platform for the exploration of polymer phase behavior and structure−property relationships.3−7 An important consideration for predicting phase behavior is thus how χ, or equivalently the interaction energy density8 X, varies with the composition of the random block. X is proportional to χ; XϕAϕB is the portion of the free energy of mixing of A and B homopolymers (or the A and B blocks in a diblock copolymer) which is contributed by A−B interactions (ideally, the enthalpic component). The simplest useful model of polymer mixing8 is based on regular solution theory, in which X = (Δδ)2, where δ is the solubility parameter (square root of cohesive energy density), and Δδ is the difference between the δ values of the two polymers which are being intimately mixed. Consider the case of an A−ArB diblock (x = 1). If δ varies linearly with the volume fraction of B in the random copolymer block, f B, then XA−ArB = f B2XA−B, where XA−B is the interaction energy density between A and B hompolymers. This same result is obtained from the wellknown “copolymer equation”,8−11 for the case of blending A homopolymer with ArB random copolymer. This simple resultif borne out experimentallyprovides a very attractive Received: February 3, 2013 Revised: March 13, 2013 Published: April 2, 2013 3084

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“design rule” for the generation of block−random copolymers of desired X (and thus TODT) simply by knowing XA−B and adjusting f B. Moreover, some nonenthalpic (“irregular”) contributions to X, such as that from the mismatch in thermal expansion coefficients (free volume densities)8,12 between A and B homopolymers, are also expected to scale with f B2, so the relation XA−ArB = f B2XA−B may in fact apply more broadly than simply to those cases where homopolymers A and B mix regularly. However, even for systems as seemingly simple as ethylenebutene random copolymers (hydrogenated polybutadienes) where copolymers of different butene content can be assigned unique values of δ, and where blends of these copolymers follow X = (Δδ)2 wellit is found that δ can show a strongly nonlinear dependence8,13 on f B, meaning that the X ∼ f B2 scaling is not obeyed. Here, we investigate the applicability of this simple rule to block−random copolymers made from two common monomers, styrene (S) and isoprene (I), and subsequently hydrogenated with two different catalysts to yield either S−hI polymers, where the styrene aromaticity is retained, or VCH−hI polymers, where VCH is vinylcyclohexane (saturated S).

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mandated multiple catalyst charges to achieve complete saturation. 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), a heterogeneous palladium catalyst supported on calcium carbonate was used (Pd0/CaCO3, Pd0 content 5 wt %, Alfa Aesar; approximately 2:1 Pd0/CaCO3 to polymer by weight). Supported palladium 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 a Waters 410 Refractive Index Detector. THF was used as the mobile phase, and the system was calibrated with narrow-distribution polystyrene standards. The apparent “polystyreneequivalent” molecular weights obtained by GPC were converted to the true values by correcting for the differences in hydrodynamic volume16 between polystyrene and the relevant block as described in detail elsewhere.6 For all block−random copolymers, GPC measurements were conducted on aliquots of the first block and the diblock; Mn for the second block was thus determined by difference, with all Mn values employing the appropriate correction for hydrodynamic ratio.6 For the S−I diblocks, Mn of each block was determined from the diblock Mn and the overall composition from 1H NMR spectroscopy using the Chang combining rule.16,17 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 I olefinic protons corresponding to different modes of addition (1,4-/3,4-/1,2-). Morphological Characterization. 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 CuKα radiation (λ = 0.15418 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.18 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.19 Intensities were multiplied by q2 to approximately correct for the form factor of lamellae.20

EXPERIMENTAL SECTION

Polymerization. Polymers were synthesized at a final solids concentration of approximately 15 wt % in a 50/50 v/v mixture of cyclohexane and triethylamine. Glass reactors were flamed out under vacuum, rinsed with tert-butyllithium (t-BuLi) and subsequently with cyclohexane prior to charging with initiator (t- or s-BuLi) in a nitrogen-filled glovebox. A 50/50 v/v mixture of cyclohexane/ triethylamine was stirred over diphenylhexyllithium (adduct of sBuLi and 1,1-diphenylethylene), degassed via freeze−pump−thaw cycles, and vacuum transferred directly into the reactor. 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 and I monomers for S and I homopolymer blocks were handled similarly, though I monomer was stirred over n-BuLi. Random copolymer blocks (SrI) were polymerized at 30 °C, while S and I blocks were polymerized at 60 °C. In the 50/50 v/v cyclohexane/triethylamine mixture, both s- and t-BuLi appear to be rapid and efficient initiators for both S and I polymerizations, and the blocks (S, I, SrI) could be polymerized in any order. S-I-31 was polymerized S block first, with sBuLi as initiator, while S-I-29 and S-I-7 were polymerized I block first, with t-BuLi. The I−SrI block−random copolymers were synthesized I block first, except I-(SrI)24-97, which was synthesized SrI block first; both of the S−SrI diblocks were also synthesized SrI block first, and tBuLi was used as initiator for all the I−SrI and S−SrI polymers. For each of the block−random copolymers, an aliquot of the reaction mixture was collected immediately prior to the second monomer charge to permit separate characterization of the first block and the diblock. 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 H2. The extent of hydrogenation was monitored with 1H NMR spectroscopy on 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 homogeneous Ni/Al catalyst was used to selectively saturate the diene units while retaining the styrene aromaticity.14,15 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. Catalyst deactivation typically

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RESULTS AND DISCUSSION Figure 1 illustrates the approach taken here to assess the mixing thermodynamics of hydrogenated styrene−isoprene block− random copolymers. Hydrogenated medium-vinyl polyisoprene (hI) is common to all polymers studied herein, so we assign a solubility parameter to hI as the reference material. Solubility parameters for polystyrene (S) and polyvinylcyclohexane (VCH) are then determined by measuring TODT for S−hI and VCH−hI diblock copolymers, as illustrated at left in Figure 1. The values of δhI, δS, and δVCH are then used to reveal how the interaction energy density X between A and ArB polymers scales with the volume fraction of B (f B) in ArB, using a series of A−ArB block copolymers (hI−SrhI, S−SrhI, hI−VCHrhI, VCH−VCHrhI). Finally, as illustrated at right in Figure 1, we compare our assigned values of δS and δVCH with literature results through the intermediary of hydrogenated low-vinyl polyisoprene (EP, poly(ethylene-alt-propylene)), which is closely related to hI and which has been previously studied in VCH−EP15,21 and S−EP15,22 diblocks. Key characteristics of the precursor (unsaturated) polymers, including the “true” (absolute) block molecular weights and isoprene microstructures, are given in Table 1. All diblocks are nearly symmetric (similar molecular weights for the A and B, or ArB, blocks). Our previous work6 has demonstrated that SrI copolymers of any composition synthesized in 50/50 v/v 3085

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mol, while I-(SrI)24-97 is a block−random copolymer of I and SrI with Mn = 97 kg/mol and 24 wt % S in the random block. Upon hydrogenation, “I” in the sample code is replaced by “hI”; if the Pd0/CaCO3 catalyst was used, “S” is replaced by “VCH”. The four rightmost columns in Table 1, which are arranged in two pairs (one pair for S and one pair for VCH), contain measured values of TODT, and values of X obtained therefrom (corrected to 160 °C for ease of comparison23) for the corresponding saturated derivative (S or VCH). Styrene-Containing Hydrogenated Polymers. All values of TODT were measured by hot-stage small-angle X-ray scattering (SAXS). As an example, SAXS patterns for S-hI-7 are shown at room temperature in Figure 2a, and upon heating through the order−disorder transition in Figure 2b. At room temperature, Bragg peaks are observed at q/q* ratios of 1:2:3, where q* is the position of the first-order peak position, characteristic of its lamellar morphology. The width of the primary peak (full width at half-maximum intensity), and primary peak intensity, are plotted against temperature in Figure 2c where TODT is determined to be 126 ± 1 °C from the midpoint of the step change in peak breadth.24 The interaction energy density X may be determined15 from the measured TODT as X ≡ χ(Nρ/Mn)RT = (χN)ODTρRTODT/ Mn, where Mn is the number-average molecular weight and N is the effective degree of polymerization of the diblock, ρ is the diblock’s mass density, and R is the gas constant. Values of X can thus be calculated from the second of these equalities, using the measured TODT, the known Mn and ρ (at TODT), and the value of (χN)ODT calculated from theory (for which we use the self-consistent-field results of Matsen and Bates,25 corresponding to N → ∞ and χ → 0; (χN)ODT = 10.7 for S-hI-7 at its TODT). Correlations for the specific volume vs temperature, drawn from literature data, for all the homopolymers relevant to this work are given in the Supporting Information; for copolymers, specific volumes were computed simply from the weight-fraction-weighted values for the homopolymers. An advantage of using X over χ is that it avoids the selection of an arbitrary reference volume, and thus facilitates comparison across systems of different chemistry (such as the various series examined in this paper, and illustrated in Figure 1). For S-hI-7, the measured TODT yields XS−hI = 4.27 J/cm3 = 4.27 MPa at 126 °C.

Figure 1. Diagram of connections employed in evaluating the mixing regularity of hydrogenated derivatives of block and block−random copolymers of styrene and isoprene. Unidirectional arrows (all beginning at hI) indicate the method of assignment of the values of δ for the other polymers (S, VCH, EP). Bidirectional arrows indicate assessments of regularity in the behavior of diblock copolymers: dashed lines (- - -) indicate block−random copolymers with varying composition, while dotted lines (···) indicate comparison with literature values of XA−B determined on A−B diblock copolymers similar to those studied herein, but where the precursor isoprene block has a higher 1,4-content (leading to EP, vs the medium-1,4 polyisoprene which becomes hI after hydrogenation).

cyclohexane/triethylamine show no down-chain compositional gradient, and that the reaction mixture can fully solubilize all of the blocks (S, I, SrI). 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 precursor. So, for example, S-I-31 is a diblock copolymer of styrene and isoprene with a total number-average molecular weight (Mn) of 31 kg/

Table 1. Molecular Characteristics of Diblock and Diblock−Random Copolymers polymer

Mn(I) (kg/mol)

Mn(SrI) (kg/mol)

PDI

I-(SrI)52-114 I-(SrI)51-65 I-(SrI)69-16 I-(SrI)24-97

53.7 30.9 8.1 49.7

59.8 33.7 8.3 47.6

1.08 1.08 1.09 1.06

polymer

Mn(S)

Mn(I)

PDI

S-I-31 S-I-29 S-I-7

16.0 16.3 4.4

15.1 13.3 3.1

1.07 1.08 1.10

polymer

Mn(S)

Mn(SrI)

PDI

S-(SrI)37-75 S-(SrI)50-30

39.9 14.9

37.5 15.0

1.06 1.09

S wt % in SrI

I blocka 3,4(1,2-)

52 51 69 24 I blocka 3,4(1,2-) 46 (3) 42 (3) 43 (3) S wt % in SrI 37 50

44 43 45 44

SrI blocka 3,4(1,2-)

(2) (3) (3) (3) TODT S

43 46 47 45 (°C)

(3) (2) (2) (3)

TODT (°C) S

X (MPa) Sb

>250 81 119 X (MPa) Sb

126 SrI blocka 3,4(1,2-)

TODT (°C) S

X (MPa) Sb

45 (3) 46 (1)

160

1.16

TODT (°C) VCH

X (MPa) VCHb

122 250 °C while the VCH-containing material synthesized from the same precursor, hI-(VCHrhI)51-65, has TODT < 23 °C (SAXS pattern in Supporting Information, Figure S-4a). Symmetric diblocks VCH-hI-31 and VCH-hI-29 showed TODT values of 176 and 166 ± 1 °C, respectively (see SAXS data in Supporting Information, Figure S-3), yielding X values, at TODT, of 1.01 and 1.05 MPa, respectively. A symmetric hI(VCHrhI)52-114 showed TODT = 122 ± 1 °C (SAXS pattern in Supporting Information, Figure S-4). An “inverse” block− random copolymer, VCH-(VCHrhI)37-75, showed a strong but relatively broad SAXS peak at and below the glass transition temperature of VCH (Tg ≈ 140 °C30,31), which weakened (by approximately 2×) and broadened (by approximately 1.5×) substantially upon heating from 140 to 180 °C (see Supporting Information, Figure S-5). Such behavior is characteristic32 of polymers which have TODT in the vicinity of Tg; we thus assign

Figure 4. Solubility parameters δ for SrhI random copolymers at 160 °C, calculated via X = (δSrhI − δhI)2, or (δS − δSrhI)2 for S−(SrhI)50, plotted against the S volume fraction in the random copolymer block, f S. Red dashed line represents δSrhI = δhI + f S(δS − δhI), with the values of δhI and δS already determined from XS−hI. Estimated uncertainties in X, resulting from Mn (±5%), and in f B (±1% in absolute overall S mole fraction by 1H NMR), are indicated by vertical and horizontal bars, which are smaller than the data points in most cases.

Figure 5. Interaction energy density X plottedon (a) linear and (b) logarithmic scalesagainst the volume fraction of B, f B, in the random copolymer block for VCH-containing A−ArB diblocks. Dashed line represents the expected scaling, X = f B2XVCH−hI. Estimated uncertainties in X, resulting from Mn (±5%), and in f B (±1% in absolute overall S mole fraction by 1H NMR), are indicated by vertical and horizontal bars, which are smaller than the data points in most cases. As noted in the text, the uncertainty in X (due to additional uncertainty in TODT) for VCH−(VCHrhI)37 may be somewhat larger. 3088

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an approximate TODT ≈ 140 °C to this polymer, with a correspondingly larger (and unknown) uncertainty. As shown in Figure 5, both this VCH−(VCHrhI)37 diblock, and the hI− (VCHrhI)52 diblock with TODT = 122 °C, follow the expected X = f B2XVCH−hI line very closely. Recall that in Figure 3, modest deviations from this scaling were observed in the S−hI block− random copolymers at low f B; this range of f B was not probed in the VCH−hI system, as the much smaller value of XVCH−hI vs (XS−hI) would mandate the synthesis of polymers of much higher molecular weight to obtain a thermotropic ODT (e.g., approximately 400 kg/mol for a VCH analogue of hI-(SrhI)2497, which has TODT = 119 °C). The value of XVCH−hI = 1.04 MPa at 160 °C yields Δδ = 1.02 MPa1/2; from prior investigations of VCH−polyolefin diblocks,21 it is expected that δVCH < δhI, so δVCH = 13.45 MPa1/2. The X data in Figure 5 were thus recast in terms of δ in Figure 6, showing the linear behavior of δVCHrhI with f VCH mandated by the X = f B2XVCH−hI behavior in Figure 5.

should accentuate the difference between the S and VCH derivatives; if the polymers mix regularly, XS−hI/XVCH−hI > XS−EP/XVCH−EP is expected. To account for this microstructure effect, we assign a solubility parameter to EP which is 0.31 MPa1/2 higher than our assignment for hI, simply by assuming a linear dependence of δ on 1,4 content. As a caution, it is known that in hydrogenated polybutadienes,8,13 the dependence of δ on 1,4 content is substantially nonlinear; however, literature data on the thermodynamics of hydrogenated polyisoprenes of varying microstructure are quite limited, and the implied difference in δ between hI and EP is modest. On the basis of this value of δEP (14.78 MPa1/2), we calculate values of XS−EP(160 °C) = 2.82 MPa, and XVCH−EP(160 °C) = 1.77 MPa. The latter can be compared with the extensive data of Cochran and Bates,21 whose eight symmetric VCH−EP diblocks with thermotropic ODTs yield XVCH−EP(MPa) = 379 K/T + 0.774, and therefore a value of 1.65 MPa at 160 °C, in good agreement with our value of 1.77 MPa. Literature data for S−EP block copolymers are sparser. Two highly asymmetric (S block volume fraction ϕS ≈ 0.10) S−EP diblocks studied by Lai,22 with TODT values differing by >120 °C, yield XS−EP (MPa) = 1639K/T + 0.565 by the same method employed here (but with much larger values of (χN)ODT, corresponding25 to ϕS ≈ 0.10), or XS−EP = 4.35 MPa at 160 °C. In addition, two near-symmetric S−EP diblocks studied previously in our laboratory (S−EP 4.4−4.3 and 4.9−4.5, where the precursors were synthesized and characterized in different laboratories, and with the numbers indicating the S and EP block Mn values in kg/mol) showed TODT = 175 and 165 ± 5 °C, respectively. From these TODT values, values of XS−EP(160 °C) = 4.00 and 3.52 MPa are calculated. The scatter between these numbers is relatively large, but all exceed (by 25−50%) the value of XS−EP(160 °C) calculated from our values of δS and δEP. It is unclear whether this discrepancy simply reflects the paucity of experimental data, coupled with differences in the experimental approach (near-symmetric vs asymmetric diblocks), or whether it indicates some underlying mixing irregularity. It cannot, however, be attributed exclusively to nonlinearity in the dependence of δ on microstructure (precursor 1,4 content) in hydrogenated polyisoprenesi.e., in obtaining δEP from δhI (dot-dashed line in Figure 1)as there is no value of δEP which can yield XS−EP ≈ 4 MPa and XVCH−EP ≈ 1.6 MPa with the values of δVCH (13.45 MPa1/2) and δS (16.46 MPa1/2) obtained here. Domain Spacing. By employing the A−ArB block− random architecture, the interdomain spacing d can be increased considerably while maintaining a thermally accessible TODT, because d increases strongly with N, ideally as N2/3 in the strong-segregation limit.1 This possibility is realized here, where d (obtained from the SAXS patterns as 2π/q*, corresponding to the lamellar repeat distance) is plotted in Figure 7a against Mn for all the diblocks studied herein, supplemented by the previously studied hI-(SrhI)50 diblocks.6 Compared with S−hI7 (d = 11.8 nm), a more-than-3-fold increase in d, to 41.8 nm, is obtained for hI-(SrhI)24-97while retaining the simple diblock architecture and using only the same two monomers. Though the smaller value of X in the block−random case permits the synthesis of polymers with larger N (and thus larger d) while retaining a thermotropic ODT, the smaller X also reduces d at a fixed N, ideally as d ∼ X1/6 in the strongsegregation limit.35 We thus scale all the observed domain spacings to a common segregation strength, XhI−(SrhI)50(160

Figure 6. Solubility parameters δ for VCHrhI random copolymers at 160 °C, calculated via X = (δhI − δVCHrhI)2, or (δVCHrhI − δVCH)2 for VCH-(VCHrhI)37, plotted against the VCH volume fraction in the random copolymer block, f VCH. Dashed line represents δVCHrhI = δhI + f VCH(δVCH − δhI), with the values of δhI and δVCH already determined from XVCH−hI. Estimated uncertainties in X, resulting from Mn (±5%), and in f B (±1% in absolute overall S mole fraction in the precursor by 1 H NMR), are indicated by vertical and horizontal bars, which are smaller than the data points in most cases. As noted in the text, the uncertainty in δ (due to additional uncertainty in TODT) for VCH− (VCHrhI)37 may be somewhat larger.

Comparisons with EP-Containing Block Copolymers. Hydrogenated derivatives (both S and VCH) of styrene− isoprene block copolymers have been studied previously, providing a basis for comparison with the present results, especially for the values of XS−hI and XVCH−hI (or δS and δVCH) determined herein. However, most of this previous work employed polymers synthesized in hydrocarbon solvents, where the polyisoprene microstructure is approximately 93% 1,4addition; the hydrogenated product is typically referred to as poly(ethylene-alt-propylene), or EP. Our polymers, by contrast, have a higher vinyl content (only 54% 1,4), as an unavoidable consequence of the triethylamine used to randomize the monomer sequence within the SrI block. On the basis of the work of Graessley et al.,8,33 it is known that the precursor microstructure impacts the δ value for the hydrogenated product, with δ decreasing as the vinyl content increases, by 0.45 MPa1/2 on going from 93% to 37% 1,4-addition in the precursor.33,34 The increased vinyl content in our polymers 3089

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Figure 7. (a) Lamellar domain spacings d obtained by SAXS in the melt, below TODT and above Tg of any of the constituent blocks, plotted against diblock molecular weight. (b) Domain spacings corrected to a common segregation strength by (Xref/X)1/6, where Xref is XhI−(SrhI)50 at 160 °C. Solid line () represents d(nm) = 2.29Mn2/3 fit to the series of hI−(SrhI)50 block−random copolymers, where Mn is in kg/mol. Dotted line (- - -) represents d(Xref/X)1/6 = 2.03Mn2/3 fit to the VCH-hI-31, VCH-hI-29 and hI-(VCHrhI)50-114 block copolymers.

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°C), as shown in Figure 7b. This scaling removes most of the scatter evident in Figure 7a, and shows that the S-containing and VCH-containing block copolymers each closely follow d ∼ Mn2/3, but with slightly different proportionality constants. The lower values of d(Xref/X)1/6 at fixed Mn for the VCH-containing derivatives are readily understood as resulting from differences in unperturbed chain dimensions (statistical segment lengths), since Rg2/M is smaller for VCH than for S,36 where Rg is the radius of gyration in bulk. Moreover, this same rationale accounts for the one S-containing polymerS-(SrhI)50-30 (open circle), containing 80 wt % Swhich deviates notably from the line describing the other S-containing polymers containing only 10−22 wt % Ssince Rg2/M is smaller for S than for hI.36

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ASSOCIATED CONTENT

S Supporting Information *

Expressions for the specific volumes of relevant homopolymers as functions of temperature and 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

*(R.A.R.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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CONCLUSIONS

ACKNOWLEDGMENTS This work was generously supported by the National Science Foundation, Polymers Program (DMR-1003942).

Hydrogenated block−random copolymers of S and I were confirmed to closely obey XA−ArB = f B2XA−B, the relation expected from regular mixing coupled with a linear dependence of δArB on f B, as well as from the copolymer equation. This agreement was found for both S-containing and VCHcontaining hydrogenated derivatives, and for hI-rich and hIpoor polymers, all using values of XA−B measured independently on A−B diblock copolymers (S−hI and VCH−hI). The reduction in XA−ArB vs XA−B permits one to retain a thermally accessible TODT while greatly increasing Mn and d; for example, hI-(SrhI)24-97 has Mn larger by 13×, and d larger by 3.5×, than S-hI-7, but essentially the same TODT. The two series of hydrogenated derivatives were each found to closely follow the expected d ∼ X1/6Mn2/3 scaling, but with slightly different prefactors reflecting the different statistical segment lengths of S and VCH; S-rich and S-poor diblocks also showed a slightly different prefactor, as the statistical segment lengths of S and hI also differ. For a series of A−ArB block−random copolymers of constant block ratio (ϕA) but varying composition of the random block ( f B), these scalings indicate that TODT can be held constant by adjusting Mn and f B such that Mn ∼ f B−2. Furthermore, these scalings indicate that dA−ArB = dA−B/f B for polymers of constant TODT, for the ideal case where the statistical segment lengths of A and B are identical.

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REFERENCES

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