Composition Fluctuation Inhomogeneity of Symmetric Diblock

Note Cite This: Macromolecules XXXX, XXX, XXX−XXX

Composition Fluctuation Inhomogeneity of Symmetric Diblock Copolymers: χN Effects at Order-to-Disorder Transition Taesuk Jun,† Yonghoon Lee,† Seongjun Jo,† Chang Y. Ryu,*,‡ and Du Yeol Ryu*,† †

Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea Department of Chemistry and Chemical Biology, Rensselaer Polytechnic Institute, Troy, New York 12180, United States

‡

S Supporting Information *

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INTRODUCTION Block copolymer (BCP) composed of chemically different blocks has attracted researchers over decades because the BCP generates fascinating self-assembled structures in nanoscale dimensions, and researchers have proposed many applications in nanotechnology, microelectronics, and clean energy.1−5 To correlate the physical properties of BCP with specific applications, it is imperative to attain fundamental understanding on the thermodynamic behaviors and phase transitions of BCPs in terms of their molecular parameters, as reported in many theoretical and experimental studies.6−13 In the case of symmetric A−B diblock copolymers, the BCPs undergo an order-to-disorder transition (ODT) from a lamellar structure to a disordered state upon decreasing segregation power of χN, where χ and N represent the Flory−Huggins interaction parameter between two blocks and the overall degree of polymerization, respectively.6,10 Thus, an ODT-type phase transition of BCPs similarly pertains to the upper critical solution transition (UCST) in the binary polymer blends, as the χ is inversely proportional to temperature (T).14,15 Mean-field (MF) theory of BCPs was studied by Leibler in weak segregation regime to highlight the importance of χN as a function of volumetric composition (f) in phase behavior.6 For a symmetric BCP (f = 0.5), the MF prediction of (χN)MF = 10.495 had been believed to be a thermodynamic criterion for microphase separation in the limit of infinite N. Later, Fredrickson and Helfand (FH) later extended Brazovskii’s Hartree approximation to suggest fluctuation correction model of the ODT at finite N.7 Their study was particularly insightful to explain the experimental ODT results, in which a disordered state approaching to an ODT was characterized to be a compositionally fluctuating structure, not a homogeneous phase.9,16 The FH theory suggested a first-order transition character of ODT, since the discontinuous change in temperature-dependent intensity was observed in small-angle X-ray scattering (SAXS) profiles.17−19 Similarly, the latent heat (ΔHODT) at ODTs, measured from an endothermic peak on heating, indicated the obvious evidence of the first-order transition due to the fluctuation effects on phase transition of BCPs with finite N.20,21 The FH fluctuation model also provided a quantitative equation to define the thermodynamic criterion for the ODT of symmetric BCPs with an additional parameter of invariant degree of polymerization (N̅ ) by (χN)FH = 10.495 + 41.022N̅ −1/3 in the limit of N̅ ≥ 104.7 Furthermore, Morse, Matsen, and co-workers further refined the ODT equation by (χN)ODT = 10.495 + 41.022N̅ −1/3 + 123.0N̅ −0.56 © XXXX American Chemical Society

particularly for symmetric BCPs having experimentally more relevant range of 102 ≤ N̅ ≤ 104.12,22,23 Recently, Lee and Bates investigated the fluctuation-induced ODTs for low-molecular-weight series of high-χ poly(1,4isoprene)-b-poly(DL-lactide)s (PI-b-PLAs) with a modest polydispersity (i.e., Đ ∼ 1.10).24 The results showed that the rheological ODTs match nicely with the onset temperatures from endothermic peaks in DSC on heating. They demonstrated that even out of the FH limit (N̅ ≥ 104), the disordered state in the vicinity of ODT is not a homogeneous phase but a compositionally fluctuating structure. However, as being observed for less than 2% change in the Porod invariant (Q) at ODT, it is unclear whether their PI-b-PLAs can best serve as the representative BCP system to study the structural discontinuity in local composition profile at ODT. In this paper, we have studied the composition fluctuation inhomogeneity at ODTs for symmetric BCPs with finite and modest molecular weights using the DSC and SAXS measurements. To examine the effects of (χN)ODT deviation from (χN)MF = 10.495, we selected three different styrenic BCPs of PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA with narrow dispersity (less than Đ ∼ 1.06), making the decreasing (χN)ODT sequence of χNPS‑b‑P2VP > χNPS‑b‑PMMA > χNPS-b‑PnHMA. The measured values of ΔHODT by DSC on heating and cooling were compared with the maximum and minimum of ΔHODT, which were estimated using the structural information (i.e., q* values) from the SAXS results and interfacial energy of BCPs. Finally, we proposed the universal descriptions to demonstrate the (χN) ODT effects on the composition fluctuation inhomogeneity at ODTs based on temperature dependence of Q and d-spacing from the SAXS measurements.

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EXPERIMENTAL SECTION

Symmetric diblock copolymers of PS-b-P2VP, PS-b-PMMA, and PS-bPnHMA were synthesized by sequential living anionic polymerization of styrene and the second monomers, 2-vinylpyridine, methyl methacrylate, and n-hexyl methacrylate, respectively. All the monomers were degassed in the presence of CaH2; then styrene and the others were vacuum-distilled over dried dibutylmagnesium and trioctylaluminum, respectively, until each characteristic color was observed in monomers. The vacuum-distilled tetrahydrofuran (THF) from CaH2 (Aldrich) was stirred over fresh sodium−benzophenone complex until it showed a deep purple color, indicating an oxygen- and moisture-free solvent. A sec-butyllithium (1.3 M, Aldrich) was used as Received: September 8, 2017 Revised: November 27, 2017

A

DOI: 10.1021/acs.macromol.7b01946 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Table 1. Sample Characteristics Used in This Study BCPs

Mn (g/mol)

Đ (Mw/Mn)

f PS

N

N̅ a

TODT (°C)

(χN)ODTb

ΔHODT (J/g)c heating (cooling)

PS-b-P2VP PS-b-PMMA PS-b-PnHMA

18100 30300 39800

1.06 1.05 1.02

0.51 0.49 0.50

173 296 299

1230 2750 4860

202.0 218.0 228.0

16.6 14.9 14.0

0.371 (0.255) 0.242 (0.139) 0.202 (0.112)

N̅ is evaluated as a mean value using eqs 2 and 3. b(χN)ODT is calculated using eq 4. cΔHODT is measured from DSC experiments upon heating and cooling runs. The values shown in parentheses indicate the ΔHODT on cooling.

a

an initiator in THF solvent at −78 °C under a purified argon environment. Especially for PS-b-PMMA and PS-b-PnHMA, a small amount of LiCl (purity ≥99.99%, Aldrich) was predissolved in THF solvent before polymerization. The living polymers were terminated with a degassed isopropyl alcohol, and they were precipitated in excess nonsolvents such as hexane for PS-b-P2VP and methanol/water (80/ 20 by wt %) for PS-b-PMMA and PS-b-PnHMA. The BCP samples were dried under vacuum for more than 48 h, and the powder samples were further annealed at 130 °C, still above the glass transition temperatures (Tg) of each block. The number-averaged molecular weight (Mn) and dispersity (Đ = Mw/Mn) of BCPs were evaluated using multiangle laser light scattering (MALLS) combined with size exclusion chromatography (SEC) (Figure S1). PS volume fraction ( f PS) in BCPs was determined by nuclear magnetic resonance (NMR) measurements (Figure S2), based on the mass densities of components (1.05, 1.14, 1.184, and 1.006 g/ cm3 for PS, P2VP, PMMA, and PnHMA, respectively). Sample characteristics are summarized in Table 1. Synchrotron SAXS experiments were performed in 4C and 9A beamlines at the Pohang Light Source (PLS), Korea. All the BCP samples were compression-molded above Tg of each block and annealed at 150 °C under vacuum. The wavelength (λ) of X-ray beam was set to 1.2 Å with an energy resolution, ΔE/E = 2 × 10−4. A 2-D Mar CCD camera (Rayonix LLC., Marccd-165) was used to collect the scattered intensities. The experimental conditions were set up with a typical beam size of 0.8 × 0.8 mm2, a sample-to-detector distance of 2 m, sample thickness of 1.5 mm, and exposure times of 10−20 s. A DSC (PerkinElmer Diamond) was used to scan the latent heats (ΔHODT) at ODTs of BCPs at heating and cooling rates of ±20 °C/ min from −40 to 250 °C. Note that a large amount (typically 20−25 mg) of BCP samples was loaded in order to enhance the signal-tonoise ratio in the DSC experiments. After prolonged thermal annealing at 150 °C for 24 h under vacuum, all the samples had been cooled to −40 °C and held in an isothermal state for 10 min prior to the first heating run. The ΔHODT for each BCP was measured more than 10 times, and the values were averaged for reporting in this paper.

⎛ [M]0,A [M]0,B ⎞1/2 ⎟⎟ Vref = ⎜⎜ ρB ⎠ ⎝ ρA

(1)

where [M]0 and ρ are the monomer molecular weight (g/mol) and density (g/cm3) of A and B blocks, respectively. The Vref values are calculated to be 0.96, 0.92, and 1.29 cm3/mol for PSb-P2VP, PS-b-PMMA, and PS-b-PnHMA, respectively. Compared with the statistical segment length (b = 0.68 nm) of the first PS blocks, the b values of P2VP, PMMA, and PnHMA are characterized as 0.68, 0.74, and 0.87 nm, respectively,25−29 indicating an increase in chain stiffness of the second blocks. This chain stiffness effect is incorporated into the definition of invariant degree of polymerization (N̅ ), which is equivalent to the square form of the ratio of the pervaded volume (N1/2bAB)3 to the occupied volume (Nv0) of polymer chain. The symbol v0 = 0.118 nm3 represents a common segment volume of BCPs, as used in the literature.16,30,31 A mean value of N̅ is evaluated with N̅ = NbAB6 /v0 2

(2)

and bAB = (fA bA 2 + fB bB 2)1/2

(3)

where f is the volume fraction of A and B blocks, leading to the increasing N̅ sequence of N̅ PS‑b‑P2VP < N̅ PS‑b‑PMMA < N̅ PS‑b‑PnHMA (Table 1). Particularly in the case of PS-b-PMMA and PS-bPnHMA, it is notable that the difference in N̅ definitely is solely originated from the difference in chain stiffness (i.e., bPS‑b‑PMMA < bPS‑b‑PnHMA) because NPS‑b‑PMMA ≈ NPS‑b‑PnHMA. To calculate the values of (χN)ODT, we adopted an empirically modified equation proposed by Morse, Matsen, and co-workers:22,23

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(χN )ODT = 10.495 + 41.022N̅ −1/3 + 123.0N̅ −0.56

RESULTS AND DISCUSSION Three different symmetric BCPs of PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA were synthesized, and their molecular weights were manipulated to attain ODTs above 200 °C. These BCPs were designated to represent the contrasts in the average statistical segment length (bAB) of A−B diblocks because the chain stiffness difference between two blocks can affect the pervaded volume of BCP chains that relates to the spatial persistence of interchain interactions during composition fluctuation in the vicinity of ODTs. Therefore, both factors of N and bAB are included to define the invariant degree of polymerization (N̅ ), and these values are further considered to evaluate the extent of (χN)ODT deviation from (χN) MF prediction in the limit of infinite molecular weights (i.e., N → ∞).7,22 The overall degree of polymerization (N) for a A−B diblock copolymer is calculated by N = (VA + VB)/Vref, where VA and VB are molar volumes of A and B blocks, respectively. Here, the reference volume (Vref) is defined as

(4)

Using this equation with each N̅ of BCPs, the (χN)ODT of PS-bP2VP, PS-b-PMMA, and PS-b-PnHMA was evaluated to be 16.6, 14.9, and 14.0, respectively (as also summarized in Table 1). These values should be distinguished from the calculated χN at ODTs as 16.9, 14.3, and 12.8 for PS-b-P2VP, PS-bPMMA, and PS-b-PnHMA, respectively, based on the temperature-dependent χ equations of χPS‑b‑P2VP = 91.6/T − 0.095, χPS‑b‑PMMA = 20.4/T + 0.0074, and χPS‑b‑PnHMA = 3.93/T + 0.0035.32−34 Such a deviation from the calculated χN of 12.8 for PS-b-PnHMA is caused by only the mean-field assumption ((χN)MF = 10.495) applied to the χ equation.34 Figure 1 shows the differential scanning calorimetry (DSC) thermograms of PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA, which were scanned at heating and cooling rates of ±20 °C/ min from −40 to 250 °C. The samples were preannealed at 150 °C for 24 h under vacuum prior to the measurements. All the latent heat (ΔHODT) per gram at ODTs listed in Table 1 represent the average values after repeating the DSC experiments for more than 10 times. The ΔHODT was positive from B

DOI: 10.1021/acs.macromol.7b01946 Macromolecules XXXX, XXX, XXX−XXX

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°C/min was so weak as to measure ΔHODT from the baseline noise. Although the fast heating and cooling rates were used for the best resolution, our DSC thermograms consistently showed that the onset temperatures of endothermic and exothermic peaks not only occur at similar temperatures but also correspond well with the ODTs from the small-angle X-ray scattering (SAXS) profile analysis (Figure 3). Interestingly, the value of ΔHODT on heating and cooling is more significant in PS-b-P2VP, having the largest value of ΔH ODT , and decreasingly followed by PS-b-PMMA and PS-b-PnHMA in sequence (will be discussed later in terms of (χN)ODT effects). Figure 2 shows the SAXS intensity profiles for BCPs as a function of the scattering vector (q), where q = (4π/λ) sin(θ/ 2), and θ and λ are scattering angle and wavelength of the incident X-ray beam, respectively. The BCP samples were preannealed at a constant temperature of 150 °C to ensure an equilibrium state prior to the measurements at various temperatures. All the profiles were measured at various temperatures at a heating rate of 1.0 °C/min, and the starting temperatures were recorded during the heating process. For all the BCPs, the intensity profiles measured at 30 °C showed the primary peaks (at q*) and third-order peaks (at 3q*) with no second-order peaks (at 2q*), indicating a volumetric symmetry in lamellar morphology.35 The primary peaks remain distinct and sharp at low temperatures (140−150 °C), while the thirdorder peaks already disappear. As temperature increases across ODTs, the primary peaks weaken and broaden significantly, corresponding to a transition from a lamellar structure to a disordered state. The broad maxima above ODTs are attributed to the correlation hole scattering of disordered BCPs in the length scale of Rg (radius of gyration). To experimentally determine the ODTs of PS-b-P2VP, PS-bPMMA, and PS-b-PnHMA, as shown in Figure 3, the

Figure 1. DSC thermograms of PS-b-P2VP, PS-b-PMMA, and PS-bPnHMA, which were scanned at heating and cooling rates of ±20 °C/ min from −40 to 250 °C. The data are shifted vertically by a factor of 0.5 for clarity. The dotted lines indicate the baselines used for calculation of ΔHODT. The arrows above each curve indicate ODTs, as the onset points of endothermic and exothermic peaks during heating and cooling runs, respectively. These ODTs by DSC correspond well with those from the SAXS profile analysis.

the endothermic peak on the first heating runs, and it was reproduced as negative heat during the subsequent cooling runs, as a thermal signature of a weakly first-order transition for symmetric BCPs. It should be pointed out that the magnitudes of ΔHODT on cooling are consistently smaller than those from heating runs of these BCPs due to the sluggish ordering dynamics of BCP chains; this cooling rate of 20 °C/min is too fast to allow well-developed grain structures of lamellar morphology. However, the DSC signal at slower rate of ±10

Figure 2. SAXS intensity profiles for (a) PS-b-P2VP, (b) PS-b-PMMA, and (c) PS-b-PnHMA. All the profiles were measured at various temperatures at a heating rate of 1.0 °C/min. The arrows indicate the relative peak positions of q/q* = 1:3, and the absence of peaks at q/q* = 2 represents a volumetric symmetry in lamellar morphology. The intensity profiles are vertically shifted by a factor of 103 to avoid overlapping. C

DOI: 10.1021/acs.macromol.7b01946 Macromolecules XXXX, XXX, XXX−XXX

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Figure 3. Temperature dependence of three parameters from SAXS profiles. (a) Inverse of the maximum intensity (1/I(q*)), (b) full width at halfmaximum (fwhm), and (c) domain spacing (d = 2π/q*) as a function of the inverse temperature (1/T). The data are vertically shifted to avoid overlapping.

ODTs, even though an abrupt increase in d at ODTs is not reasonably understood as of now. The values of ΔHODT were estimated using the structural values of q* at lower and higher temperatures from the SAXS results and interfacial energy of BCPs. The maximum possible change of enthalpy at ODT can be estimated using the classical mean-field theory by Helfand and Tagami with the following equation:37

temperature dependence of SAXS profiles was analyzed in terms of three parameters: (a) the inverse of the maximum intensity (1/I(q*)), (b) full width at half-maximum (fwhm), and (c) d-spacing (d = 2π/q*) as a function of inverse temperature (1/T). From the discontinuity in both 1/I(q*) and fwhm, the ODTs of these BCPs were clearly measured at 202.0, 218.0, and 228.0 °C for PS-b-P2VP, PS-b-PMMA, and PS-bPnHMA, respectively. The temperature dependence of 1/I(q*) with respect to 1/T becomes nonlinear (or curved) in a disordered state above ODT, indicating the presence of composition fluctuations.7,36 However, this effect becomes indiscernible in PS-b-PnHMA due to weak temperature dependence of χ.34 Even in a fluctuating disordered state above ODT, the values of d are estimated to be approximately 20% greater than dMF = 11.8, 16.1, and 17.7 nm for PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA, respectively, using dMF = (2π/ 1.95)Rg, where Rg = bAB(N/6)1/2.6,11 Thus, the BCP chains in a disordered state are more stretched than the mean-field Gaussian chains, indicating that the phase mixing of BCPs is not a homogeneous phase in local composition. Αs temperature increases, the overall decreases in d of these BCPs are expected due to temperature dependence of χ, as similarly observed in PS-b-P2VP. Most intriguingly, we identified the notable discontinuous increases in d (or discontinuous decrease in q*) at ODTs with increasing temperature, as indicated by the arrows in Figure 3c. Α discontinuous increase in d at ODTs might be attributed to the stronger domination of interchain interactions in a fluctuating disordered state, which was described by a renormalized oneloop (ROL) theory by Morse and co-workers.12 The extent of discontinuity in d at ODTs (Δd/dODT) is weak or negligible in PS-b-P2VP, but the effect becomes more pronounced as the (χN)ODT of BCPs decreases, leading to a large shift (1.0%) in Δd/dODT of PS-b-PnHMA. Our result indicated the (χN)ODT dependence associated with local composition profiles at

ΔHmax =

RTfA fB (χN )ODT Mn

−

Σ LAMγAB ρ

(5)

where R is the ideal gas constant, ΣLAM = 2/d = q*/π is the interfacial area per unit volume of a lamellar morphology, and γAB ≈ (kBT /b2) χ /6 is the interfacial tension between two blocks (here, kB is Boltzmann’s constant). With (χN)ODT and q* information from Table 1, the values of ΔHmax for PS-bP2VP, PS-b-PMMA, and PS-b-PnHMA are calculated to be 0.678, 0.385, and 0.270 J/g, respectively, along with the decreasing (χN)ODT sequence of BCPs. Recently, Lee and Bates proposed an another approach to estimate the enthalpy change at ODT by speculating only the changes in interfacial area between lamellar and disordered states.24 Assuming no change in local composition of BCP in the vicinity of ODT, their estimation can provide the lower limit of ΔHODT (ΔHmin) by only considering the change in interfacial topology from lamellar structure to fluctuating disordered state, giving ΔHmin =

γAB ρ

(Σ DIS−Σ LAM)

(6)

where ΣDIS ≈ 0.5q* is the interfacial area per unit volume of fluctuating disordered state.9,38 The values of ΔHmin for PS-bP2VP, PS-b-PMMA, and PS-b-PnHMA are estimated to be 0.130, 0.064, and 0.051 J/g, respectively. D

DOI: 10.1021/acs.macromol.7b01946 Macromolecules XXXX, XXX, XXX−XXX

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of thermodynamic segregation power in a fluctuating disordered state. To directly monitor the change in local composition profile at ODTs, we examined the temperature dependence of total integrated scattering intensity, also known as the Porod invariant (Q).39 For this process (Figure S3), all the SAXS intensity profiles were subtracted by the background scattering, and the corrected intensity profiles were calibrated into the absolute scale with a standard material (a glassy carbon film).40 Experimental Q was obtained by integrating the absolute intensity (Iabs(q)) over the range of 0.1 < q < 3.0 nm that ensures the entire scattering intensity:

Figure 4 shows the calculated ranges of ΔHmax and ΔHmin for PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA as a function of

Q=

1 2π 2

∫0

∞

q2Iabs(q) dq

(7)

Figure 5a shows the Porod invariant (Q) of PS-b-P2VP, PS-bPMMA, and PS-b-PnHMA as a function of temperature. The variation in Q of BCPs can be explained by the combined contributions from a continuous decrease in χ (with increasing temperature) and a discontinuous change of chain conformation accompanied by the distinct change of interfacial topology constraints from flat lamellar geometry to hyperbolic disordered state at ODTs. Accordingly, an abrupt reduction in Q at ODTs for these BCPs provides a direct evidence for discontinuous changes in local composition profile across ODT because the Q can be correlated with Qideal = (Δρ)2fA f B for an ideal two-phase A−B copolymer, where Δρ is the difference in electron density between two blocks.39 Moreover, our result on discontinuities could be a solid evidence to support a first-order transition character of ODT. Figure 5b displays (χN)ODT dependence on the invariant discontinuity (|ΔQ/Q|ODT) at ODTs in comparison with dspacing discontinuity (|Δd/d|ODT). As the (χN)ODT of BCPs decreases (i.e., the (χN)ODT deviation from (χN)MF = 10.495 decreases), the extent of discontinuity in Q at ODTs (|ΔQ/ Q|ODT) increases, resulting in 4.4, 14.0, and 19.4% for PS-bP2VP, PS-b-PMMA, and PS-b-PnHMA, respectively, in which the trend is in parallel with the extent of discontinuity in d-

Figure 4. Latent heats (ΔHODT) at ODTs of PS-b-P2VP, PS-bPMMA, and PS-b-PnHMA as a function of (χN)ODT. The measured values of ΔHODT (solid symbols) on heating and cooling runs by the DSC analysis are compared with the calculated ΔHmax and ΔHmin (open symbols), which are estimated using eqs 5 and 6, respectively.

(χN)ODT, in which the values are compared with the measured latent heat (ΔHODT) at ODTs by the DSC analysis. When the (χN)ODT of BCPs decreases closer to (χN)MF = 10.495, the values of two extreme estimates (the ΔHmax calculated by the mean-field approach and ΔHmin that assumes only the change in interfacial topology at ODTs) become closer to each other. Despite that our measured values of ΔHODT at ODTs are based on the fast thermal analysis during heating and cooling runs, the values located between ΔHmax and ΔHmin still support the idea of discontinuity in thermally driven composition fluctuations at ODTs. The measured ΔHODT on heating and cooling decreases as the (χN)ODT of BCPs decreases, indicating the dependence

Figure 5. (a) Porod invariant (Q) profiles of PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA as a function of temperature. All the values of Qexp were evaluated from the SAXS results using eq 7. The profiles are vertically shifted by a factor of 0.5 to avoid overlapping. The arrows in invariant profiles indicate the discontinuities at ODTs. (b) (χN)ODT dependence on the invariant discontinuity (|ΔQ/Q|ODT) and d-spacing discontinuity (Δd/dODT) at ODTs. E

DOI: 10.1021/acs.macromol.7b01946 Macromolecules XXXX, XXX, XXX−XXX

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10.495. On the contrary, we speculated that the less or little pronounced changes in the structural discontinuity at ODT can be found in strongly segregating BCPs with higher (χN)ODT, supporting that the (χN)ODT as a function of N̅ plays a key role to control the structural changes at the fluctuation-induced ODTs of BCPs.

spacing at ODTs (|Δd/d|ODT). It is worthwhile to point out why the PS-b-PnHMA exhibits a sharper drop in Q and dspacing at ODT compared to moderate and weak decreases for PS-b-PMMA and PS-b-P2VP, respectively. As the χ decreases (or T increases) from the lamellar structure across ODT, the BCPs become a compositionally fluctuating disordered state. However, our observation of the discontinuity in Q definitely supports an existence of gap in composition fluctuation inhomogeneity at ODTs. Since the weaker segregation power at ODTs (or smaller (χN)ODT) attenuates the amplitude in local composition profile of a fluctuating disordered state, this gap becomes more pronounced as the (χN)ODT of BCPs decreases. In other words, the larger discontinuity in Q at ODT is the smaller amplitude in local composition profile of a disordered state, as observed in PS-b-PnHMA. In contrast, the smaller discontinuity in Q of PS-b-P2VP is responsible for the larger amplitude in local composition profile of a disordered state which has the similar structural heterogeneity with a weakly ordered lamellar structure. This gap effect of composition fluctuation inhomogeneity is well reflected in |Δd/d|ODT that increases with decreasing (χN)ODT of BCPs. Therefore, little discontinuity in Q and d-spacing at ODT, observed in PI-b-PLA with (χN)ODT = 24.5,24,41 can be explained by higher (χN)ODT effect of BCPs, in which the amplitude in local composition profile of a disordered state is the same scale with that of lamellar structure. For further consideration, our results on the discontinuity in Q and d-spacing at ODTs can be discussed with (1) the conformational asymmetry (ε = (bA/bB)2) due to the chain stiffness difference between two blocks and (2) the chain length or overall degree of polymerization (N), even though these effects are incorporated into the definition of N̅ . The ε values of PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA are evaluated to be 1.0, 1.18, and 1.64, respectively. The increases in ε and N in this sequence are largely associated with an increase in entropic penalty for chain stretching, which are in accordance with the extent of discontinuity in Q and d-spacing at ODTs. Accordingly, higher N̅ and lower (χN)ODT in PS-b-PnHMA lead to larger gap of composition fluctuation inhomogeneity at ODTs as well as d-spacing. In addition, recent studies on PLAcontaining BCPs have invoked the impact of Frank−Kasper sigma phase, where higher conformational asymmetry is a key factor to stabilize the complex phases.42,43

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01946. Figures S1−S3 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (C.Y.R). *E-mail: [email protected] (D.Y.R.). ORCID

Du Yeol Ryu: 0000-0002-0929-7934 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.Y.R. acknowledges funding by NSF DMR Polymers Program (NSF-1308617). D.Y.R. acknowledges the NRF grants (2017R1A2A2A05001048 and 2017R1A4A1014569) funded by the Ministry of Science, ICT & Future Planning (MSIP), and funding (20163030013960) from the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE), Korea.

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REFERENCES

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CONCLUSIONS Thermodynamic property of BCPs at ODTs has been studied using the DSC and SAXS measurements in terms of the (χN)ODT effects on the composition fluctuation inhomogeneity. A series of symmetric A−B diblock copolymers of PS-b-P2VP, PS-b-PMMA, and PS-b-PnHMA with modest molecular weights were set as a systematic model to represent the decreasing (χN)ODT sequence of χNPS‑b‑P2VP > χNPS‑b‑PMMA > χNPS‑b‑PnHMA. We measured ΔHODT at ODTs by DSC on heating and cooling, which decreases as the segregation power of (χN)ODT decreases for a series of BCPs in between ΔHmax calculated by the mean-field approach and ΔHmin that assumes only the change in interfacial topology at ODTs. Our postulates of (χN)ODT effects on the discontinuity in Q and d-spacing from the SAXS results supported that the fluctuation-induced ODTs of BCPs are accompanied by discontinuous changes in local composition profiles. This gap in composition fluctuation inhomogeneity at ODTs increases as the fluctuation-induced (χN)ODT of BCPs decreases and becomes closer to (χN)MF = F

DOI: 10.1021/acs.macromol.7b01946 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.7b01946 Macromolecules XXXX, XXX, XXX−XXX