with Palladium Nanoparticles - American Chemical Society

Jan 31, 2013 - PMMA) block copolymer (bcp), alter its order−disorder transition ... neat bcp and the nanocomposites are investigated by small-angle ...
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Order−Disorder Transition of Nanocomposites: Polystyrene-blockPoly(methyl methacrylate) with Palladium Nanoparticles Yue Zhao,†,* Kenji Saijo,‡ and Takeji Hashimoto†,§,* †

Quantum Beam Science Directorate (QuBS), Japan Atomic Energy Agency (JAEA), Tokai-mura, Ibaraki, 319-1195, Japan Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan

‡

ABSTRACT: We studied how the palladium nanoparticles, (Pd)ns, incorporated into poly(styrene)-block-poly(methyl methacylate) (PS-bPMMA) block copolymer (bcp), alter its order−disorder transition (ODT). The (Pd)ns were incorporated into the lamellar template of PS-b-PMMA by the thermal reduction of Pd(acac)2, dissolved uniformly in the bcp before the reduction, at 230 °C where both the neat PS-b-PMMA and the PS-b-PMMA incorporated with (Pd)ns (nanocomposite) are in the disordered state. The ODT behavior of the neat bcp and the nanocomposites are investigated by small-angle X-ray scattering as a function of temperature. We found that: (i) the average size and size distribution of (Pd)ns did not change at all during the heating and cooling processes across the ODT; (ii) the incorporation of a very small amount (1 wt %) of (Pd)ns significantly increased the ODT temperature (TODT) by ∼8 °C and the lamellar spacing D by ∼1%. These trends were found to be completely opposite to those previously reported on the (Pd)ns incorporated in the lamellar template of poly(styrene)-block-polyisoprene (PS-b-PI), in which (Pd)ns were neutral to both PS and PI and acted as quench disorders (Zhao, Y.; et al. Macromolecules 2009, 42, 5272−5277). These intriguing effects observed for PS-b-PMMA are attributed to effects of (Pd)ns enhancing thermal stability of the ordered lamellae, hence raising the thermal-fluctuation-induced first-order phase transition temperature, TODT. These effects of (Pd)ns are anticipated to be mediated by relatively stronger attractive interactions of (Pd)ns with PS block chains than with PMMA block chains, which increases the net effective segregation power between PS and PMMA block chains and hence stabilizes the ordered lamellae. The selective attractions were experimentally confirmed by (1) a selectively larger incorporation of (Pd)ns in PS lamellae (∼70%) than in PMMA lamellae (∼30%) and by (2) the selective incorporation of (Pd)ns in the lamellae being conserved during the cooling and heating cycles of the nanocomposite across the TODT as evidenced by the thermo-reversible change in the scattering profiles. The attractive interactions account for the conservation of the average size and size distribution also, i.e., no coarsening of (Pd)ns, with the thermal treatments.

I. INTRODUCTION

We found the following results: (i) The reduction mechanism of Pd(acac)2 and the growth mechanism of (Pd)n are independent of the reduction temperature, Tr; only the reduction rate and the growth rate depend on Tr. At the end of the reduction, both the number-averaged particle radius, Rn ∼ 2.7 nm, and the relative standard deviation of the particle size distribution, σR/Rn ∼ 0.26, reach steady values independent of Tr. Moreover, we found the following pieces of evidence (ii to v) after the completion of the reduction reaction. (ii) The scattering profiles around the first-order peak at the scattering vector qm change thermoreversibly with temperature T, upon heating and cooling across the ODT temperature, TODT, and hence the spatial distribution of (Pd)n in the lamellar template is statistically conserved with T in the heating and cooling

We have reported a simple way to create a nanocomposite composed of palladium nanoparticles, (Pd)n, and a symmetric diblock copolymer (dibcp) of poly(styrene)-block-poly(isoprene) (PS-b-PI):1 The dibcp film having uniformly dissolved metal complex, palladium acetylacetonate [Pd(acac)2], over the length scale larger than the characteristic domain (lamellar) spacing of the dibcp was first prepared by the solvent-casting method; Then Pd(acac)2 was reduced to form (Pd)n in the dibcp template by a subsequent thermal treatment at 142 or 180 °C (in the ordered lamellae or disordered state of the neat dibcp, respectively) without any significant changes in chemical structures of dibcp.2 We investigated in situ the growth of (Pd)ns during this thermal reduction process of Pd(acac)2 and the influence of (Pd)n on the order−disorder transition (ODT) of the dibcp after the completion of the reduction by small-angle X-ray scattering (SAXS).1,3 © 2013 American Chemical Society

Received: October 2, 2012 Revised: December 20, 2012 Published: January 31, 2013 957

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cycles across the TODT. (iii) However, the scattering profiles at the scattering vector q larger than qm, where the scattering from (Pd)n dominates the scattering from the lamellae, did not change at all with the temperature variations across TODT, and hence the average size and size distribution of (Pd)n are unaltered with the thermal treatments. (iv) The incorporation of a small amount of (Pd)n (only 1 wt %) significantly lowered TODT by ∼13 °C. (v) The presence of (Pd)n broadened the TODT window (the temperature span between the onset and completion of the ordering or disordering) and decreased the lamellar spacing, D. These changes were attributed to the ordered phase of the nanocomposite having the smaller thermal stability compared to that of the neat block copolymer (bcp). We explained that these phenomena were caused partially by the larger interface to volume ratio of the ordered microdomains and partially by the larger distortion of conformations of the dibcp chains in the ordered lamellae in the presence of (Pd)n. In this study, we prepared a nanocomposite composed of (Pd)n and symmetric dibcp of poly(styrene)-block-poly(methyl methacrylate) (PS-b-PMMA), designated hereafter as (Pd)n/ PS-b-PMMA, via the same method as described above. We aimed to investigate how (Pd)ns alter the ODT behavior of the lamellar template of PS-b-PMMA for the nanocomposite specimens obtained after the completion of the reduction: (i) whether or not the ODT exists in the nanocomposite; (ii) if it exists, how it differs from TODT of the neat dibcp; (iii) how the effects of (Pd)ns on the ODT depend on the bcp templates, PSb-PMMA and PS-b-PI. So far, only a few papers4−7 including one of our early studies7 have been published on the scattering analysis of the ODT of PS-b-PMMA. As per Russell et al., the Flory−Huggins interaction parameter, χ, between PS and PMMA blocks is only weakly temperature dependent.5,6 Thus, the corresponding molecular weight window where the ODT can be observed is remarkably small for PS-b-PMMA4−7 in comparison to other bcp systems, though the PS-b-PMMA working temperature window is relatively large from a lower bound of the glass transition temperature, Tg, (∼100 °C) to the upper bound of the polymer thermal degradation temperature, Td, (∼250 °C). If TODT of this newly developed nanocomposite exists in the temperature range between Tg and Td, the nanocomposite may become thermally tunable, which might offer technological opportunities in future. The nanocomposites made of the bcp templates and nanoparticles have attracted much attention, because bcps are well-known to organize into diverse multiphase structures with nanoscale periodicity,8−12 and the incorporation of the nanoparticles is of great importance for manufacturing electromagnetic, optical, and mechanical devices.16−14 The added nanoparticles have the potential to perturb the nature of the phase transitions of bcps also and influence the ordering process of bcps.3,18−23 As a consequence, TODT of the nanocomposites shifts upward or downward. Theoretically, the magnitude of the TODT shift is predicted to be dependent on the size, shape of the nanoparticles, and the nature of the surface interactions between the nanoparticles and the bcps.18,19,21 Some experimental evidence on the shift of TODT and its relationship with the nature of the nanoparticles were also reported lately, including our previous work.3 Our another previous study 23 showed that only 0.4 wt % of C 60 nanoparticles added into the PS-b-PI dibcp matrix causes a significant decrease (∼15 °C) of TODT relative to that of the neat bcp. In the C60-bcp system, C60 is expected to cluster into

nanoparticles and to cross-link the double bonds in PI and to link the benzene rings in PS. The resultant C60-mediated polymer associations work as “quenched disorder”27−25 in the bcps and perturb the ordering process. On the contrary, Lee and Han.22 reported that the addition of Cloisite 30B (chemically modified clay) nanoparticles into the functionalized bcp, polystyrene-block-hydroxylated polyisoprene (PS-bPIOH), greatly increases the TODT by ∼40 °C. This change is attributed to the formation of hydrogen bonds between the hydroxyl groups in PIOH blocks and the polar groups in Cloisite 30B, which consequently increases the effective repulsive segmental interactions between PS and PIOH blocks. The recent reports by Gaines et al.29 and Tirumala et al.30 also indicated a tendency for the TODT to shift upward with the addition of highly selective nanopartilcles or homopolymer toward one of the blocks.31,32 In this paper, we present an experimental study of the influence of (Pd)n on the ODT of a lamella-forming PS-bPMMA. It is organized as follows. We first present the characterization of (Pd)n/PS-b-PMMA in the reduction process which forms and grows (Pd)ns in the bcp template (section III1), the characterization of (Pd)ns after the completion of the reduction with respect to their size and size distribution (section III-2), thermal stability of (Pd)ns on whether or not they change upon further heat treatments and variations of SAXS profiles involved by the ODT (section III-3), and the assessments of TODT of the nanocomposite (section III-4). Then we present discussion, which first points out an opposite effect of (Pd)ns on TODT found for PS-b-PMMA and PS-b-PI (section IV-1). In order to clarify the intriguing opposite effect, we then extend our discussion for detailed and profound comparisons of the two systems in both the ordered and disordered states with respect to temperature dependence of the scattering profiles (section IV-2), thermal stability of the ordered phase and thermal composition fluctuations in the disordered state (section IV-3.1), the characteristic length (section IV-3.2), and the selective incorporation of (Pd)ns into the PS and PMMA (or PI) lamellar templates (section IV-4). Finally, section IV-5 presents discussion on a possible interpretation of the physical origin of the conserved spatial distribution of (Pd)n in the ordered state with the heattreatments across the ODT process, which provides a profound and key insight into the opposite effects of (Pd)ns on the TODT of the PS-b-PMMA and PS-b-PI as described in section IV-6 and the conclusion section V.

II. EXPERIMENTAL SECTION II-1. Sample Preparations. PS-b-PMMA (14900−13100, number-averaged molecular weight, Mn = 2.8× 104 g/mol, polydispersity, Mw/Mn ∼ 1.05) was used directly as purchased from Polymer Source Inc. (Table 1). We then prepared two film samples, neat bcp films (film A) and bcp films containing 1.0 wt % Pd(acac)2 (film B), by first dissolving a prescribed amount of PS-b-PMMA (4.95 wt %) without/ with Pd(acac)2 (0.05 wt %) in benzene as a solvent and then slowly evaporating the solvent at room temperature in air for one week and then in a vacuum oven for another week. Here we confirmed that the added Pd(acac)2 was homogeneously dissolved in the solution without precipitates. Both films had dry thickness of about 0.45 mm. II-2. SAXS Measurements and Thermal Reduction of Pd(acac)2 To Prepare Nanoparticles (Pd)n. The SAXS profiles were measured in situ during the reduction process as well as during the ODT measurements with the apparatus described elsewhere.33 The profiles were corrected for absorption, air scattering, background scattering arising from thermal diffuse scattering, and slit-height and slit-width smearings, as detailed elsewhere.34 The sample chamber was 958

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III. RESULTS III-1. Characterization of Reduction Process for Formation and Growth of (Pd)ns in the bcp Template. Details of the thermal reduction process of Pd(acac)2 for the formation and growth of (Pd)ns in bcp templates were previously reported for PS-b-PI.1 Moreover, our experimental results suggested that the reduction process in the PS-b-PMMA templates is essentially the same as that in the PS-b-PI templates. Thus, we would not repeat to report the details of the reduction process in this work, except for the following main results: The number-averaged radius, Rn, and its relative standard deviation, σR/Rn, of (Pd)n rapidly increases and decreases, respectively, with time for the first 30 min and then both of them gradually approaches the steady values of 3.2 nm and 0.23, respectively. It indicates that, on one hand, (Pd)n is formed and grows into a larger size in the polymer matrix according to the general mechanisms such as (i) diffusion and coalescence of Pd(0) atoms into (Pd)ns in the gaseous state of Pd(0) atoms, (ii) the coarsening of small (Pd)ns via Ostwald ripening or the Lifschitz−Slyozov−Wagner process38 and the diffusion−coalescence in the liquid state of (Pd)n,39 and (iii) the growth of (Pd)ns by absorbing Pd(0) atoms. It also indicates that, on the other hand, an increased surface area brought by the particle growth increases the number of tethered bcp chains on the surface and hence hindered the coarsening mechanism of (ii) due to the entropic repulsion of the tethered chains. The repulsion controls the steady value of Rn and decreases σR/Rn to the steady value because of a starvation of Pd(acac)2 at the end of the reduction and because of the coarsening (ii) being enhanced and suppressed for the growth of small and large particles, respectively. We would like to report below another crucial physical factor concerned with a selective incorporation of the (Pd)ns into one of the ordered domains (PS or PMMA) during the reduction process. Figure 2 presents SAXS profiles for the as-cast films of

Table 1. Characterization of Block Copolymers Used in This Study Mn (×10−3) Rg (nm)a

Mw/Mn TODT (°C)b STODT (°C)c

(PS-block) (PMMA-block) (PI-block) (cooling) (heating) (cooling) (heating)

PS-b-PMMA

PS-b-PI

14.9−13.1 3.3 3.2 − 1.05 205 208 2 4

12.5−9.0 3 − 3.2 1.02 159 161 2 3

a

Unperturbed chain dimension of each block chain calculated from its molecular weight Mn.35 bTODT defined by the arithmetic average of the onset and completion temperatures of ordering in the cooling cycle and disordering in the heating cycle, respectively. cSharpness of ODT as characterized by the difference between the onset and completion temperatures of ordering in the cooling cycle or disordering in the heating cycle, respectively. filled with nitrogen gas to reduce the possible thermal degradation, and T was controlled with an accuracy of ±0.03 °C. The T protocols for a series of SAXS experiments are shown in Figure 1. The SAXS

Figure 1. Thermal protocols adopted in the SAXS measurements in order to investigate the ODT behaviors for A, the neat PS-b-PMMA film, and B, the PS-b-PMMA film with 1.0 wt % (Pd)ns after the completion of the reduction. The TODTs determined by the SAXS measurements are marked with the arrows labeled by a1 and a2 for A and the arrows labeled by b1 and b2 for B.

measurements for the A film were conducted in a cooling−heating cycle started at 230 °C for the determination of its TODT. The measurements were done at 1 degree increments across TODT. The B films were first subjected to the reduction process of Pd(acac)2 at 230 °C for 180 min in order to prepare (Pd)n in the disordered state. We note that the reduction does not cause any significant changes in the chemical structure of dibcps based on the work reported by Lee et al.2 as will be detailed later in section IV-1. The reduction was completed under the condition described above, and the (Pd)ns thus formed in the films were analyzed by using the sphere model as will be shown later in Figure 4 and as detailed in ref 1. Then the SAXS measurements of TODT of the film B were conducted in a cooling−heating cycle started at 230 °C and with 1 degree increments across its TODT. At each T, the samples, for both A and B, were first held for ∼30 min, and then the SAXS measurement was conducted with an exposure time of ∼30 min for the incident X-ray beam. The TODTs determined are marked with the arrows labeled by a1 and a2 for A and by b1 and b2 for B in Figure 1.

Figure 2. SAXS profiles for as-cast films of the neat PS-b-PMMA (circles) and those containing 1 wt % Pd(acac)2 (triangles) [PS-bPMMA/Pd(acac)2], measured at room temperature.

the neat PS-b-PMMA (blue circles) and those containing 1 wt % Pd(acac)2 (red triangles) [PS-b-PMMA/Pd(acac)2] measured at room temperature. The two profiles are identical except for those in the small q range at q < qm ∼ 0.35 nm−1, where qm is the q value at the scattering maximum for those two profiles, and q is the magnitude of the scattering vector q [q ≡ (4π/λ) sin(θ/2), λ = 0.154 nm; θ is the scattering angle]. The scattering maximum suggests existence of the ordered domain having the average domain spacing D ∼ 17.9 nm with a fairly 959

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the corresponding as-cast film shown in Figure 2, again due to the annealing effect at 190 °C. Figure 3b presents time evolution of the peak intensity, Im(tr) and Im,corr(tr), and the q value at the peak intensity, qm(tr), of the first-order scattering peak shown in Figure 3a. Im(tr) is the observed peak intensity at the reduction time tr, the time evolution of which depends on the increase of the form factor at qm due to the increasing number of (Pd)n, defined by Im,(Pd)n(tr), as well as the change of the peak intensity, Im,corr(tr), due to the change of the lamellar structure which incorporates an increasing number of (Pd)n,

large polydispersity of D so that only the first-order scattering maximum was clearly observed. It is crucial to note the identical scattering intensity for the two SAXS profiles at q ≥ qm. This suggests such important facts that: (i) Pd(acac)2 is equally incorporated into the PS and PMMA domains; (ii) Thus, Pd(acac)2 equally well interacts with PS and PMMA block chains in the dry films. Figure 3a shows time evolutions of SAXS profiles observed in situ at 5 min (profile 1 shown with black squares) and 3 h

Im(tr) = Im,(Pd)n(tr) + Im,corr(tr)

(1)

The decrease of Im,corr(tr) up to tr ∼ 45 min is due to the decrease of the electron density difference between the PS and PMMA lamellae involved by a selectively larger incorporation of (Pd)n in the PS lamellae than in the PMMA lamellae, because the electron density increases in the order of PS, PMMA, and (Pd)n as will be elaborated later in section IV-4. The complex time evolution of Im at tr ≤ 100 min is a consequence of a continuously increasing Im,(Pd)n(tr) and a complex time-evolution behavior of Im,corr(tr) as characterized by the first decrease and then increase in this time span. It is important to note that qm tends to decrease with tr, and hence D tends to increase with tr, the significance of which will be further discussed in section IV-3.2 in conjunction with Figure 11. As will be discussed later in conjunction with Figures 5, 7, and 8, the dibcps with and without (Pd)n at 190 °C are in the ordered state, so that the reduction took place in the ordered state via the reduction of Pd(acac)2 equally dissolved in both PS and PMMA lamellae. Thus, the results shown in Figure 3 reveal that: the incorporation of (Pd)n in the ordered bcp template first lowers the first-order scattering maximum of the neat bcp as shown by the change from profile 3 to profile 1 taken at the reduction time tr = 5 min (Figure 3a) and by the decrease of Im,corr(tr) at tr < 45 min (Figure 3b); then the maximum intensity increases with tr due to the increasing amount of (Pd)n incorporated in the template domain as shown by the change from profile 1 to profile 2 (Figure 3a) and by the increase of Im,corr (tr) at tr > 45 min (Figure 3b). The (Pd)ns increase also the scattering at q > qm, where the form factor of (Pd)n dominates the scattering from the phase structure of the domain, i.e., lamellae. This intriguing intensity change of the first-order maximum Im,corr with tr is due to a selectively larger incorporation of (Pd)n in the PS lamellae than in the PMMA lamellae. This selective incorporation makes the electron density difference Δρel ≡ ρel,PMMA − ρel,PS between PMMA lamellae (ρel,PMMA) and PS lamellae (ρel,PS) smaller with tr from a positive value to zero and then negatively increase with a further elapse of tr, because the electron density decreases in the order of (Pd)n, PMMA and PS, and the scattered intensity is proportional to (Δρel)2. This point will be further elaborated in section IV-4. III-2. Characterization of (Pd)n Formed in the bcp Template. Figure 4 demonstrates a representative SAXS intensity profile I(q) for B measured in situ at 230 °C after the complete reduction at 230 °C. The experimental scattering profile (symbols) and the best-fitted theoretical curve (red solid line) based upon the form factor for spheres with a polydispersity in the radius R given below. The normalized size distribution function, P(R), used for the best-fitting is given by eq 2 below and presented in the inset

Figure 3. (a) Time evolutions of the SAXS profiles observed at 5 min (profile 1 with squares) and 3 h (profile 2 with triangles) after the onset of the reduction process at Tr = 190 °C. The SAXS profile for the neat PS-b-PMMA at 190 °C is also plotted by the solid line as a reference. (b) Time evolutions of SAXS from [PS-b-PMMA/ Pd(acac)2] as a function of the reduction times tr: the observed peak intensity, Im, the peak intensity corrected for the form factor for (Pd)n, Im,corr, and the scattering vector qm at the first-order scattering peak.

(profile 2 shown with blue triangles) after the onset of the reduction process at Tr = 190 °C, where the reduction was almost completed at 3 h, together with profile 3 for the neat dibcp at 190 °C (shown by the red line) as a reference. The reduction was done deliberately at 190 °C in order to investigate a possibility of the selective incorporation of the reduced (Pd)n into the PS or PMMA lamellae. The neat dibcp films clearly showed at least up to the third-order scattering maximum at q = qm, 2qm, and 3qm with qm ∼ 0.30 nm−1, indicating the lamellar microdomains having the similar spacing as that for the neat as-cast film (see Figure 2). Thus, the annealing at 190 °C creates more ordered lamellae than the lamellae formed in the as-cast films. The films under the reduction process of Pd(acac)2 have the first-order scattering maximum at almost the same qm as the neat dibcp films. However, the scattering maximum is much sharper than that for 960

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out in the cooling−heating cycle across TODT, during the period of which the size and size distribution of (Pd)n were utterly unaltered, as will be clarified later in Figure 6. Figure 5a shows

Figure 4. Scattering profile measured in situ at 230 °C for the sample B (symbols) after the completion of the reduction at 230 °C for 180 min and the best-fitted theoretical profile (red line) based on the independent scattering from spheres having the normalized size distribution function in radius R, P(R), given by the inset.

P(R ) = (2π )−1/2 σR −1exp[− (R − R n)2 /(2σR 2)]

(2)

where Rn is the number-averaged radius of the particle, and σR is the standard deviation of Rn. The steady-state values of Rn and σR/Rn of (Pd)n formed in PS-b-PMMA matrix were thus determined from the best fitting: Rn ∼ 3.2 nm, and σR/Rn ∼ 0.23 (Table 2). The fitting details can be found in ref1. The Table 2. Characterization of the Nanocomposites PS-bPMMA/(Pd)n and PS-b-PI/(Pd)n wPd(acac)2 (wt %)a Tr (°C) Rn (nm) σR/Rn TODT (°C)b STODT (°C)c

(cooling) (heating) (cooling) (heating)

(Pd)n/PS-b-PMMA

(Pd)n/PS-b-PI

1.0 230 3.2 0.23 213 216 5 5

1.0 180 2.7 0.26 146 148 4 4

Figure 5. SAXS profiles around the first-order peak obtained in the cooling process: Part (a) for A and part (b) for B show the profiles in over all temperature (T) range covered in this work. The profiles in part (c) for A and part (d) for B highlight only those in the T range of the disordered state.

a

Wight fraction of Pd(acac)2 incorporated in PS-b-PMMA and PS-bPI. bTODT defined by the arithmetic average of the onset and completion temperatures of ordering in the cooling cycle and disordering in the heating cycle, respectively. cSharpness of ODT as characterized by the difference between the onset and completion temperatures of ordering in the cooling cycle or disordering in the heating cycle, respectively.

the SAXS profiles around the first-order scattering peak for A at representative Ts in the cooling process across TODT, while part c highlights the profiles for A only in the disordered state. An abrupt variation in the SAXS profiles is observed at T between 210 °C (the red profile) and 204 °C (the blue profile), which enables a clear-cut determination of the TODT of A at 204 < TODT < 210 °C. The scattering data for A shows an obvious increase of the scattering intensity maximum, Im, and a decrease of the peak width, σq, upon cooling below TODT. This is the ‘normal’ scattering behavior for a neat bcp. Figure 5b shows the scattering profiles I(q) of the nanocomposite sample (B) at the representative Ts in the cooling process across TODT, while part d highlights the profiles for B only in the disordered state. We observe that (1) I(q) changes abruptly from a broad peak (shown by the red profile) to a sharp one (shown by the blue profile) when T decreased from 215 to 210 °C, whereas on the neat bcp (A), this abrupt change occurs between 210 and 204 °C. This elucidates that both the neat bcp and the nanocomposite display, commonly the ODT, as characterized by the thermal-fluctuation-induced first-order phase transition,40 but the TODT of the nanocomposite clearly is shifted upward. In addition to those effects as described above, we observe the following trends with the incorporation of (Pd)n: (2) The scattering intensity maximum

deviation of the observed scattering profile from the best-fitted profile shown by the red line at q < 0.35 nm−1 is due to the contribution of the scattering from the lamellar microdomains. It is important to note that the size distribution of (Pd)ns obtained after the completion of the reduction does not change at all upon further heat treatments as will be discussed below in section III-3. Note also that (Pd)ns are more or less uniformly distributed in the polymer template, which can be simply proved by the SAXS profiles at low q region. No significant increase in the intensity at low q region was found during the reduction and the subsequent thermal treatments employed for the investigation of ODT. The TEM verification of this result may be very useful and, thus, deserves future work. III-3. Variations of SAXS Profiles Accompanied by the Order−Disorder Transition of Nanocomposites. After the completion of the reduction, SAXS measurements were carried 961

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Im in the ordered state and that in the disordered state become much lower. (3) The peak width σq in the ordered state becomes much larger. (4) The scattering peak position (qm) slightly shifts toward small q values upon cooling B in the disordered state until ∼TODT, then abruptly shifts toward large q values at TODT, and finally slightly shifts toward small q values upon further cooling, whereas qm of A shifts to small q values; no serious abrupt change of qm was seen upon cooling across TODT. Here it is striking to note that in the template of PS-b-PI, the TODT of the nanocomposite clearly shifts downward, in an opposite way found for the template of PS-b-PMMA. We will discuss these results further in section IV. It should be important to note in Figure 5b that the scattering profiles for B around the first-order peak at q < 0.34 nm−1 reflects the ODT behavior of the PS-b-PMMA template incorporated with (Pd)n, whereas the scattering profiles at q > 0.34 nm−1 shown in Figure 6a reflects (Pd)n themselves,

Figure 7. Im−1 and σq2 plotted as a function of T −1 for the neat PS-bPMMA film (A) in both cooling and heating cycles. Onset and completion temperatures for the ordering process observed at 206 and 204 °C in the cooling cycle, respectively, and those for the disordering process observed at 206 and 210 °C in the heating process, respectively, are marked with the arrows.

Figure 6. (a) SAXS profiles for B at various temperatures at the large q region where the form factor from (Pd)ns is dominant, (b) scattering profiles, which include those at the small q region too, for B at 213 °C in the cooling cycle and at 216 °C in the heating cycle. See the state of the sample at 213 and 216 °C shown by the vertical arrows in Figure 8.

Figure 8. Im−1 vs T −1 for A and B. Data in the cooling cycle (solid line with symbols) are shown together with the ones in the heating cycle (dotted line with symbols). The arrows with temperatures in °C have the same meaning as those in Figure 7, except for the vertical arrows which designate the TODT defined as an arithmetic average of the onset and completion temperatures of the ordering or disordering process and T = 190 °C where the scattering profiles to be shown in Figure 12b later were taken.

because it is (Pd)n rather than the bcp lamellae that dominates the scattering profiles in the large q range. This must be evident also from the results shown in Figures 3a and 4. The scattering profiles at q > 0.34 nm−1 for B do not change at all in the T range as shown in Figure 6a, revealing that the reduction of Pd(acac)2 in the bcp template is complete. It should be noted that after reduction, the average size and size distribution of (Pd)n do not change any more with T during cooling−heating cycles through ODT over the length scale relevant to the q range shown in Figure 6a, although the microdomain of bcp template varies from the disordered (or ordered) state to the ordered (or disordered) state upon cooling (or heating). This fact is crucial for our analysis of ODT and simplifies our analysis. If one assigns TODT as the arithmetic average between the two temperatures where the onset and the completion of ODT occur (as will be defined later in conjunction with Figures 7 and 8), TODT for B in the cooling and heating cycles are 213 and 216 °C, respectively (Table 2). It should be noted that the two scattering profiles at the TODTs in the cooling and heating cycles, respectively, are found to be identical as shown in Figure 6(b), the result of which is also observed in the sample (Pd)n/ PS-b-PI previously studied,3 elucidating a thermoreversible change of the microdomain structures of the nanocomposites, including the spatial distribution of the (Pd)n in the

microdomain. Note that Figure 6(b) covers the small q range relevant for the template of the bcp (the microdomain structure) itself. The ODT of the nanocomposite should involve both the transition of the bcp template and the relevant spatial organizations of (Pd)n.1,3 The bcp chains and (Pd)n cooperatively rearrange in space to exhibit the ODT between the ordered and disordered states, when T is changed across TODT. If there is a selective incorporation of the (Pd)n in the PS and PMMA lamellae, this selectivity also is expected to be conserved during the heating and cooling process. This conclusion will be further confirmed later in conjunction with Figure 8. III-4. Assessment of the TODT of the Nanocomposites. Evidently, the (Pd)n significantly alters the nature of the ODT. Thus, we next examine precisely this change. The abrupt change observed in the SAXS profiles with a variation of T across TODT reveals the ODT being the thermal-fluctuationinduced first-order phase transition for both systems A and B 962

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and enables us to unequivocally determine the TODT values. The first-order SAXS scattering peak is normally analyzed in terms of Im and the thermal correlation length ξ ≡ 1/σq of bcps for the spatial compositional fluctuations where σq is the halfwidth at the half-maximum of the scattering peak. The plot of Im−1 or σq2 vs T −1 shows a discontinuous change at TODT,41−46 a signature of the thermal-fluctuation-induced first-order phase transition.40 Figure 7 shows Im−1 and σq2 plotted as a function of T −1 for A (neat PS-b-PMMA) in both cooling and heating cycles. Both Im−1 and σq2 have similar T dependence, as predicted by the theory,40 which validates accuracy of the experiments. A sharp jump in Im−1 and σq2 occurs in a narrow T window between 206 and 204 °C in the cooling process and between 210 and 206 °C in the heating process for both Im−1 vs T −1 and σq2 vs T −1. Thus, the TODTs in the cooling and heating cycles for A are assigned to be 205 and 208 °C (Table 1), respectively, according to the definition given in section III-3. The ordered state coexists with the disordered state in the narrow T range around TODT (as characterized by STODT in Tables 1 and 2), presumably due to a small polydispersity effect and thermal fluctuation effects.47 Only a small hysteresis spanning over ∼3 °C is discerned between the order-to-disorder phase transition process (heating cycle) and the disorder-to-order phase transition process (cooling cycle) under the given thermal protocol shown in Figure 1, indicating that the cooling and heating rates are slow enough and that the thermal degradation of the bcp could hardly occur. Since the two plots on Im−1 vs T−1 and σq2 vs T −1 showed similar behaviors, we restrict our discussion to Im−1 vs T −1 in Figure 8, where the data on the cooling and heating cycles are visually guided by the solid lines and the dotted lines, respectively. Although Im−1 vs T −1 for A shown in Figure 8 is identical to the corresponding one shown in Figure 7, we deliberately added this plot in Figure 8 also as a reference for Im−1 vs T −1 for B. There is a clear upward shift of the TODT by ∼8 °C for B relative to A. The ODT temperature window STODT is broader in B (∼5 °C for both heating and cooling cycles) than A [∼4 °C and ∼2 °C for the respective cycles (see Tables 1 and 2)], indicating a kinetic slowing down of the transition in B due to the presence of (Pd)n. However, it does not affect the determination of TODT as evidenced by a similar small hysteresis to the neat bcp. The values Im−1 in the ordered state for B are found to be larger than that for A. This trend is also clearly shown in Figure 5 as well as in Figure 12 to be shown later. This is primarily due to the effects of the incorporation of (Pd)n in the lamellae as will be discussed later in section IV-4. It is also important to note that Im for B reversibly changes with T, revealing the thermo-reversible change in the spatial distribution of (Pd)n during the heating and cooling cycles.

address the questions above, a careful comparison between these two systems is necessary. One might suspect that the observed rise of the TODT for (Pd)n/PS-b-PMMA might be due to chemical modifications of the bcp chains, because the reduction of Pd(acac)2 involves oxidation of the host polymer matrix. However, we believe we can exclude this suspicion based on the report by Lee et al.2 They measured the MALDI-TOF Mass spectra and FTIR spectra of the polymer before and after the loading of (Pd)n: MALDI-TOF Mass spectra showed no major changes in the molecular weight distribution, indicating that the (Pd)n loading process did not cause any degradation or cross-linking of the polymers. FTIR spectra showed no new peaks or shifts in the peaks, indicating that the (Pd)n can be introduced into the polymer without causing any significant changes in chemical structures of the polymers. In our case, we observed a thermally reversible change of both (Pd)n/PS-b-PMMA and (Pd)n/PS-bPI systems during the heating−cooling processes, which also means the formation and incorporation of (Pd)n in the polymer matrix does not affect the chemical structures of the polymers significantly so that the systems maintain the thermoreversibility. These results clearly indicate that the observed shift of TODT is due to the incorporation of (Pd)n but not due to the chemical modifications of the polymers. IV-2. Comparisons of the Two Systems: Trends Common to the Two Systems. In order to compare the two systems, we present here the temperature dependence of the scattering profiles I(q) for the neat PS-b-PI sample in Figure 9, parts a and c and the nanocomposite made of PS-b-PI and (Pd)ns (formed in the disordered state at Tr = 180 °C) in Figure 9, parts b and d, respectively. Hereafter, the neat PS-b-PI films and their nanocomposite films are denoted as C and D for brevity. These results should be compared with those shown in Figure 5, parts a and c for the neat PS-b-PMMA (A) and those shown in Figure 5, parts b and d for the nanocomposite (B), respectively. The abrupt change of Im occurs between 160 and 158 °C for C but between 154 and 145 °C for D. The same trends (2 to 4) as described earlier for PS-b-PMMA in the second paragraph of Section III-3 are also observed in Figure 9. Thus, the incorporation of (Pd)n tends to give some distortions for the ordered lamellae commonly for the two systems as revealed by the decrease of Im and increase of the line breadth σq2. It also tends to suppress the Im in the disoredred state and hence the amplitude of the composition fluctuations in the disordered state commonly for the two systems. Nevertheless, the incorporation of (Pd)n raises on one hand the TODT for PSb-PMMA but lowers the TODT for PS-b-PI on the other hand. Thus, we further elaborated to find some experimental signatures to account for the intriguing difference. IV-3. Comparisons of the Two Systems: Trends Different between the Two Systems. For this purpose, we compare log Im−1 vs T −1 and log σq2 vs T −1 for the PS-bPMMA and PS-b-PI with and without (Pd)n. Figure 10a represents log Im−1 vs T −1 for the PS-b-PMMA systems and for the PS-b-PI systems plotted in a common semilogarithmic scale where A and B or C and D correspond to the respective systems without or with (Pd)n, respectively. Figure 10b represents the similar plots on log σq2 vs T −1 for the four systems A to D. IV-3.1. Thermal Stability of the Ordered Phase. Let us first compare the thermal stability of the ordered phase in between the two systems. Generally, the relative change in Im−1 or σq2 with T −1, as indicated by ∂[log Im−1]/∂T−1 or ∂[log σq2]/∂T−1,

IV. DISCUSSION IV-1. Opposite Effects of (Pd)n on the Shift of TODT for PS-b-PMMA and PS-b-PI. The incorporation of only a small amount of (Pd)n, up to ∼1 wt %, into the PS-b-PMMA template results in an upward shift of TODT by ∼8 °C, while the incorporation of the same amount of (Pd)n into the PS-b-PI template resulted in the downward shift TODT by ∼13 °C.3 Why the incorporation of (Pd)n works in the opposite way in these two bcps forming the lamellar templates, and what is the key physical factor to determine the shift of TODT? In order to 963

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in the ordered lamellae elucidates the thermal stability of the lamellae: the smaller the value [∂Im−1/∂T−1]/Im−1 or [∂σq2/ ∂T−1]/σq2, the more thermally stable is the lamellae. Here we calculated the value of ∂(log Im−1)/∂(T−1) and ∂(log σq2)/ ∂(T−1) for each sample at T < TODT and presented them in the parentheses besides the sample codes together with the red lines in Figure 10 drawn in the T range where the linearity of log Im−1 vs T −1 or log σq2 vs T −1 is applicable. We can find the following trends: (i) TODT of the sample decreases in the order of B > A > C > D; (ii) The absolute value of ∂(log Im−1)/ ∂(T−1) or ∂(log σq2)/∂(T−1) increases in the order of B < A < C < D. The trends (i and ii) are consistent with each other and reveal themselves that the thermal stability of the ordered lamellae decreases in the order B > A > C > D; hence, the TODT is expected to decrease accordingly. Thus, (Pd)ns stabilize the ordered lamellae of PS-b-PMMA, while they destabilize the ordered lamellae of PS-b-PI, despite of the fact that the ordered lamellae incorporating (Pd)n are more distorted than the ordered lamellae for the neat bcps, commonly for the both systems, as evidenced by the increase of Im−1 and σq2 in the ordered state with the incorporation of (Pd)n. We shall discuss a possible physical interpretation later in section IV-6. IV-3.2. Characteristic Length. The characteristic lengths D (D = 2π/qm) are shown as a function of T −1 for each sample in the cooling cycles in Figure 11 where the vertical arrow

Figure 9. SAXS profiles around the first-order peak in the cooling process for C (neat PS-b-PI) in part a and D [PS-b-PI with 1.0 wt % (Pd)n] in part b. Parts a and b show the profiles in over all temperature (T) range covered in this work, while the profiles in part c for C and part d for D highlight only those in the T range of the disordered state.

Figure 11. Temperature dependence of D for samples A to D. The trend for the characteristic length D is visually assisted with the dashed red lines, and TODT for each sample is marked with the vertical arrow.

designates the TODT determined for each sample. Only a tiny change in D with T −1 is observed across TODT for the neat bcps A and C, which is consistent with the earlier reports.41−46 On the other hand, a discontinuous decrease in D at TODT is clearly observed with increasing T −1 across TODT for B and D, where the trend for D vs T −1 is visually assisted with the dashed red lines. Note that in the ordered phase, D is interpreted as the “lamellar spacing”, while in the disordered phase D measures the wavelength of the dominant Fourier modes of the thermal composition fluctuations. We observe a progressive decrease of Di in the ordered lamellae (i denotes sample A, B, C, and D) in the order of DB > DA > DC > DD in the whole T range covered, which elucidates that the order of the thermal stability of the lamellae decreases in the same order. First of all, the difference of the two sets of data between (DA, DB) and (DC, DD) are largely due to the difference of the molecular weights between PS-b-PMMA (Mn ∼ 28 000) and PS-b-PI (Mn ∼ 21 500) (see Table 1). At a given T in the ordered lamellar phase, DB is always larger than DA by 0.2 nm, while DD is always smaller

Figure 10. (a) log Im−1 vs T −1 and (b) log σq2 vs T −1 for all samples A to D. The solid red lines, which indicate the linearity between log Im−1 and T −1 or log σq2 and T −1, yielded the values of ∂(log Im−1)/∂(T−1) or ∂(log σq2)/∂(T−1) for A to D shown in the parentheses besides the sample names A to D. The arrows indicate the T −1 values for A to D which correspond to the given value of Δ (Δ = 1 × 10−5 K−1), the quench depth with respect to TODT, as will be described in Figures 12a and 13a.

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Figure 12. Scattering profiles around the first−order maximum in the ordered state for A and B. (a) Profiles at a given quench depth with respect to TODT, Δ = T −1−TODT −1 = 1 × 10−5 K−1. (b) Profiles at T = 190 °C far below TODT.

than DC by 0.4 nm. The larger DB but smaller DD compared to DA and DC for the respective neat bcps is due to the incorporation of (Pd)n into the bcp systems. Thus, it is striking to note that the incorporation of (Pd)ns expands the characteristic length for PS-b-PMMA but contracts it for PSb-PI, which is consistent with the upward and downward shifts of the TODT with the incorporation of (Pd)n, respectively. The expansion and contraction for D in PS-b-PMMA and PS-b-PI systems, respectively, were discerned in situ as a function of tr during the reduction process (see for example, Figure 3b for PS-b-PMMA system). It is also striking to note that the characteristic length tends to discontinuously expand upon disordering commonly for both systems B and D with the incorporation of (Pd)n. These trends have been clearly described also in terms of qm in Figures 5 and 9. IV-4. Selective or Nonselective Incorporation of (Pd)n in the Lamellar Templates. According to Timmerman’s rule,48 the addition of additive with a high selectivity toward one of the components in a mixture tends to destabilize its single-phase state (i.e., to raise the critical temperature Tc for the mixture having an upper critical solution temperature), while the addition of a highly unselective additive (equally incompatible or compatible) “stabilizes” the single-phase mixture or lowers Tc. Thus, the selectivity of (Pd)ns, as an additive to the bcp template, is considered to be a generally important physical factor which influences TODT. Thus, we shall evaluate below the selective or nonselective incorporation of the (Pd)n into the PS and PMMA lamellae and into the PS and PI lamellae. However, when we applied this simple rule of thumb to our systems, we should keep in mind that some differences of the two systems such as mixtures vs bcps and the size of the additive relative to the relevant domain size35,49 might play an important role on the prediction.50 Case of PS-b-PMMA. Now, let us first consider the PS-bPMMA template. Horiuchi et al51 reported that the sublimed Pd(acac)2 could be homogeneously deposited into PS-bPMMA dibcp films matrix and then was diffused and reduced to produce (Pd)n selectively in PS phase, because PS phase has a stronger reduction power of Pd(acac)2 against PMMA phase. As a result, (Pd)n are preferentially incorporated in the PS microdomains. Their observations lead us to the question about how the (Pd)ns spatially distribute in the microdomains in our study, in which (Pd)ns were prepared by the thermal reduction of Pd(acac)2 dissolved in the bcp films via the solvent-casting. Now we will analyze the selectivity of the incorporation of (Pd)n into the ordered lamellar template. We estimate below the weight fraction of (Pd)n incorporated in the PS domain, W(Pd)n/PS, by analyzing the first-order scattering maximum of

PS-b-PMMA with and without (Pd)n in the ordered state close to TODT (corresponding to Δ ≡ T −1 − TODT −1 = 1 × 10−5 K−1, which corresponds to T = 211 and 203 °C with and without (Pd)n, respectively) and in the ordered state far below TODT (T = 190 °C) In Figure 12a, the scattering profiles around the first-order maximum for A and B are compared in the ordered state close to the TODT as characterized by a given value of Δ = 1 × 10−5 K−1. Δ is proportional to the difference of χ at T and TODT, and hence to the effective segregation power of the bcp. The value Δ corresponds to the T −1 values indicated by the red arrows in Figure 10, parts a and b, revealing that the temperatures are the highest limits for the systems being fully ordered state. Figure 12b shows the comparison of the first-order scattering maximum for A and B at 190 °C, far below TODT. We can estimate the selectivity of (Pd) n with respect to its incorporation into the PS and PMMA lamellae from ΔρA/ ΔρB where ΔρA and ΔρB are the electron density difference between PS and PMMA lamellae for sample A and B, respectively. The ratio ΔρA/ΔρB in turn can be estimated either from the peak intensity ratio of the scattering profiles for A and B shown in Figure 12,52 because I(qm)qm 2 ∼ (Δρ)2

(3)

Hence ⎛ Δρ ⎞2 ⎜⎜ A ⎟⎟ = [I(qm)qm 2]A /[I(qm)qm 2]B , ⎝ ΔρB ⎠

method 1 (4)

[I(qm)qm2]K

where defines the peak intensity for K (K = A or B). ΔρA/ΔρB can be also estimated from ⎛ Δρ ⎞2 ⎜⎜ A ⎟⎟ = [ ⎝ ΔρB ⎠

∫q

qmax

∫q

I(q)q2 dq]A /[

min

qmax

I(q)q2 dq]B ,

min

(5)

method 2

because

∫q

qmax

I(q)q2 dq ∼ Δρ2

min

(6)

2 Here in eq 5, [∫ qmax qmin I(q)q dq]K designated the integral for the sample K (K = A or B) under the first-order scattering maximum between the two limited values of q, qmin, and qmax below and above, respectively, which I(q)q2 goes down to zero. The electron density, ρ, is given by

ρ = dNe/M 965

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Table 3. Weight Fraction of (Pd)n Incorporated in PS Microdomain, W(Pd)n/PS, As Estimated from the First-Order Scattering Maximum in the Ordered State shown in Figures 12 and 13a methods at equal quench Δ

at 190 °C

at 142 °C

W(Pd)n/PS for sample

method 1

method 2

method 1

method 2

method 1

method 2

PS-b-PMMA PS-b-PI

0.77 0.53

0.71 0.55

0.71 −

0.66 −

− 0.53

− 0.55

Methods 1 and 2 used the peak intensity and the integrated intensity of the first-order scattering maximum of I(q)q2 vs q shown in Figures 12 and 13, respectively. The quench depth from the TODT was set equal to Δ = 1 × 10−5 K−1 for A and B and for C and D (at equal quench Δ) or it was set relatively large at 190 °C for A and B and at 142 °C for C and D. a

Figure 13. Scattering profiles around the first−order maximum in the ordered state for C and D. (a) Profiles at a given quench depth with respect to TODT, Δ = T −1−TODT −1 = 1 × 10−5 K−1. (b) Profiles at T = 142 °C far below TODT.

where d is the mass density, M is the molar mass of repeating unit, and Ne is the number of electrons per one mole of repeating unit. We estimate the ρ values for styrene, methyl methacrylate, and (Pd)n to be 0.545, 0.643, and 5.188 mol electrons/cm3, respectively. Note that the total mass fraction of (Pd)n in the polymer is 1 wt % and that of the polymer template is 99 wt %. We assume a mass fraction of W(Pd)n/PS out of the total amount of (Pd)n is incorporated into PS lamellae (i.e., the absolute amount of (Pd)n incorporated in PS domains is W(Pd)n/PS × 0.01). The mass fractions of PS and PMMA in the polymer template are 0.53 and 0.47, respectively, then we estimate ΔρA and ΔρB as follows: ΔρA = 0.643 − 0.545 = 0.098 mol electrons/cm 3

3. Thus, we can conclude roughly about 70% of (Pd)n are incorporated into PS lamellae. Consequently, our result is consistent with the work by Horiuchi et al.51 The selectively larger incorporation of (Pd)n in the PS-lamellae than in the PMMA lamellae was found also during the reduction process of Pd(acac)2 as evidenced by the time evolution of Im,corr(tr) shown in Figure 3b. Case of PS-b-PI. Now, let us consider the PS-b-PI lamellar template. In Figure 13, the scattering profiles of C and D are compared in the ordered state specified at the same quench depth, Δ = 1 × 10−5 K−1, which corresponds to T = 145 and 157 °C with and without (Pd)n, respectively (part a) and at 142 °C far below the TODT (part b). The T −1 values corresponding to the value Δ are also indicated by the red arrows in Figure 10, parts a and b. The peak intensity of C is found to be about 2.12 times larger than that of D from Figure 13a. Hence ΔρC for the neat PS-b-PI (sample C) is 1.46 times larger than ΔρD for PS-bPI with (Pd)ns (sample D) on the basis of method 1.

(8)

⎛ 0.643 × 0.47 × 0.99 + 5.188 × (1 − W(Pd) /PS) × 0.01 ⎞ n ⎟⎟ ΔρB = ⎜⎜ 0.47 × 0.99 + (1 − W(Pd)n /PS) × 0.01 ⎝ ⎠ ⎛ 0.545 × 0.53 × 0.99 + 5.188 × W(Pd) /PS × 0.01 ⎞ n ⎟⎟ − ⎜⎜ 0.53 × 0.99 + W(Pd)n /PS × 0.01 ⎝ ⎠ mol electrons/cm

3

ΔρC = 1.46ΔρD

We estimate the ρ values for isoprene to be 0.517 mol electrons/cm3. Assuming that a mass fraction of W(Pd)n/PS of (Pd)n is incorporated into PS lamellae and that the mass fractions of PS and PI are 0.58 and 0.42, respectively, we estimate ΔρC and ΔρD as follows:

(9)

Now the intensity ratio in the right-hand side (rhs) of eq 4 is estimated to be 3.3 from Figure 12a. Thus, according to this method, defined by method (1), ΔρA = 1.82ΔρB

(11)

(10)

ΔρC = 0.545 − 0.517 = 0.028 mol electrons/cm 3

From eqs 8−10, one can estimate W(Pd)n/PS ∼ 0.77. The ratio of the integral intensity in rhs of eq 5 was estimated to be 2.3 also from Figure 12a. Thus, according to this method, defined as method 2, ΔρA = 1.52ΔρB which gives rise to W(Pd)n/PS ∼ 0.71. Similarly, if one uses the scattering profiles for the ordered lamellae at 190 °C far below TODT as shown in Figure 12(b), method 1 yielded W(Pd)n/PS ∼ 0.71, while method 2 yielded W(Pd)n/PS ∼ 0.66. The results are summarized in Table

(12)

⎛ 0.545 × 0.58 × 0.99 + 5.188 × W(Pd) /PS × 0.01 ⎞ n ⎟⎟ ΔρD = ⎜⎜ 0.58 × 0.99 + W(Pd)n /PS × 0.01 ⎝ ⎠ ⎛ 0.517 × 0.42 × 0.99 + 5.188 × (1 − W(Pd) /PS) × 0.01 ⎞ n ⎟⎟ − ⎜⎜ 0.42 × 0.99 + (1 − W(Pd)n /PS) × 0.01 ⎝ ⎠ mol electrons/cm 3 966

(13)

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Equations 11−13 then yielded that W(Pd)n/PS ∼ 0.53. On the basis of method 2 and Figure 13a, we estimated ΔρC/ΔρD = 1.28, which yielded W(Pd)n/PS ∼ 0.55 together with eqs 12 and 13. Similarly, the scattering profiles C and D at T = 142 °C shown in Figure 13b yielded W(Pd)n/PS ∼ 0.53 for method 1 and ∼0.55 for method 2. These results also are summarized in Table 3. Thus, we can conclude that (Pd)ns are almost equally dispersed in both PS and PI lamellae and hence are neutral to the two kinds of lamellae. IV-5. Possible Interpretation on the Conservation of the Spatial Distribution of (Pd)n in the Ordered State in the Heating−Cooling Cycles through TODT. The conservation of the spatial distribution of (Pd)n in the cooling and heating processes through the ODT was already clarified in the sections III-3 and III-4 in conjunction with Figures 6b and 8, respectively. This conservation was further confirmed in the second cooling process also where Im−1 vs T −1 and σq2 vs T −1 change similarly to those in the first cooling and heating processes as highlighted in Figure 14a. The weight fraction of (Pd)n incorporated in the PS lamellae, W(Pd)n/PS, was estimated in the second cooling process also from the first-order scattering peak as shown in Figures 12 and 13 at the same quench depth Δ = 1 × 10−5 K−1, corresponding to T = 211 °C, with respect to the TODT (∼214 °C) found in the second cooling process. The method 1 yielded W(Pd)n/PS ∼ 0.76, and the method 2 yielded W(Pd)n/PS ∼ 0.69. These values are essentially identical to those shown in Table 3. Let us now envision the structural changes of the nanocomposite in the heating−cooling cycles. The black and white patterns shown in Figure 14c−e are TEM images taken for the neat bcp specimen which were frozen at a sufficiently rapid rate from the disordered state close to the TODT (part c and a left half of part d) and from the ordered state close to the TODT (a right half of part d and part e). The circles with orange color are artificially added to the image in order to illustrate schematically (Pd)ns incorporated into the disordered and ordered template. The bright and dark parts represent respectively PMMA-rich regions and PS-rich regions in the disordered state or PMMA-rich lamellae and PS-rich lamellae in the ordered state. The TEM images were proven to well represent snap shots of the dynamical thermal composition fluctuations of the bcps in the disordered state near the TODT and those of thermally fluctuating lamellae in the ordered state near the TODT.53−56 The thermoreversible changes of the scattering parameters Im as shown in Figure 14a and σq2 as well as of the scattering profiles as a whole as shown in Figure 6b and those at 215 °C in the first heating and at 213 °C in the second heating (though not included in the manuscript) must reveal that the nanocomposite (Pd)n/PS-b-PMMA undergoes statistically the same pattern changes in the repeated cooling−heating cycles through TODT. In the first cooling process, the nanocomposite after the completion of the reduction and at the temperature in the disordered state close to the onset temperature of the ODT must have the thermal-fluctuation-induced disordered structure (DF),53,55,56 as illustrated in Figure 14c, where the concentration fluctuations of PS and PMMA segments and (Pd)n are expected to have almost the same characteristic length as revealed by the single scattering maximum as shown in Figure 5b, which is slightly larger than the characteristic length of the neat bcp by ∼0.5 nm as clearly shown in Figure 11. Upon

Figure 14. (a) Im−1 vs T −1 for sample B which includes the second cooling process whose thermal protocol is identical to the one shown in the first cooling process in Figure 1. Parts c−e schematically illustrate the structures expected to be observed in the disordered state, the order−disorder coexisting state, and the completely ordered state, respectively, in the first cooling process (1st C), the first heating process (1st H), and the second cooling process (2nd C) shown in part b. The black and white patterns in parts c and e are the TEM images obtained by rapidly quenching the samples in the disordered state and ordered state below Tg, respectively. The circles with orange color are added artificially to the TEM images in parts c to e in order to illustrate the incorporation of (Pd)ns in the bcp templates.

lowering temperature the nanocomposite must exhibit the order−disorder coexisting patterns, as shown in Figure 14d and as reported by our earlier works for the neat bcp,53,55−57 over the narrow temperature span as shown in Table 2 (STODT). The nanocomposite eventually orders completely into lamellae as shown in Figure 14e, in which more than 70% of (Pd)ns are preferentially incorporated in the PS lamellae. In the first heating process after the first cooling process, the fully ordered pattern gradually looses thermal stability, as discussed earlier in conjunction with Figure 10, and is first transformed into the order−disorder-coexistence pattern, as shown in Figure 14d, and finally into the fully disordered pattern (Figure 14c). The patterns formed during the 967

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disordering process involved in the first heating process is statistically identical not only to those formed during the ordering process involved in the first cooling process but also to those formed during the ordering process involved by the second cooling process. The fact that the memory of the ordered patterns formed in the first cooling process is statistically conserved even after the second cooling process is intriguing and striking, because the memory would be lost in the disordered state, if there were no interactions between (Pd)n and bcp. Thus, we can propose that there are attractive interactions between (Pd)n and the bcp segments which are responsible for the conservation of the memory.58 Moreover, the attractive interactions of (Pd)n with PS segments are much stronger than those with PMMA segments, which accounts for the preferential incorporation of (Pd)ns into the PS lamellae. The interactions are also crucial to account for the no coarsening of (Pd)ns during the heat treatments. Figure 15a presents

may effectively suppress the Brownian motions of bcp chains in the direction normal to the interfaces mediated by the longrange interactions; They may effectively suppress also the Brownian motions parallel to the interface, through a suppressed translational diffusion of junction points of PS-bPMMA chains along the interfaces, driven by heavily suppressed Brownian motions of the anchors.60 Thus, the effect (a) described above thermally stabilizes the ordered lamellae, which is analogous to increase net segregation power between the PS and PMMA lamellae. (b) They may perturb conformations of the bcp chains and distort the interface, which are expected to destabilize the lamellae.3 If the effect (a) outweighs the effect (b), TODT is raised: This may be the case observed for the nanocomposites (Pd)n/PS-b-PMMA with a preferential incorporation of (Pd)ns in the PS lamellae. If the effect (b) outweighs the effect (a), TODT is lowered: This may be the case observed for the nanocomposites (Pd)n/PS-b-PI with nearly equal incorporation of (Pd)ns in the PS and PI lamellae due to nearly equal attractions of (Pd)n with PS and PI blocks.61 In the case of (Pd)n/PS-b-PI, (Pd)ns tethered by both PS and PI block chains may exist. These (Pd)ns may be preferentially localized at the lamellar interface, which also may effectively lower TODT and the lamellar spacing D.

V. CONCLUSION We have created the nanocomposites composed of a symmetric PS-b-PMMA and palladium nanoparticles, (Pd)n, by means of the thermal reduction of Pd(acac)2, homogeneously dissolved in the PS-b-PMMA bcp template, in the disordered state at 230 °C. After completing the reduction reaction, we have studied effects of the (Pd)n on the order−disorder transition (ODT) of (Pd)n/PS-b-PMMA. Our results indicate the incorporation of 1 wt % of (Pd)n in the lamellar template of PS-b-PMMA is sufficient to increase TODT and the lamellar spacing D. These findings should be attributed to the effects of (Pd)n increasing an apparent effective segregation power between PS and PMMA block chains, hence raising the thermal-fluctuationinduced first-order transition temperature TODT and expanding D. These trends are found to be completely opposite to those previously reported on the (Pd)n incorporated in the lamellar template of PS-b-PI, in which (Pd)ns are neutral to both blocks and act as quench disorders.3 The apparent enhancement of the segregation power due to (Pd)n in the case of PS-b-PMMA is proposed to arise from a selectively high incorporation of (Pd)n into PS lamellae (more than ∼70 wt %) compared with PMMA lamellae (less than ∼30 wt %). This selective incorporation of (Pd)n in turn elucidates existence of stronger attractive interactions of (Pd)n with PS block chains than with PMMA block chains. The attractive interactions essentially conserve not only the selective incorporation of (Pd)n in PS lamellae but also the average size and size distribution of (Pd)n formed, hence bringing about no coarsening of (Pd)n, with thermal histories involved by temperature variation across TODT. The attractive interactions bind some of the bcp chains to the surface of (Pd)ns and form the impurities of (Pd)n−(PS-bPMMA)m inside the lamellar template which may strongly affect the long-range interactions of the bcp chains in the template. The impurities may serve as anchors, which suppress Brownian motions of the bcp chains in the template over a large distance both parallel and normal to the interfaces. Hence they thermally stabilize the lamellae and raise the TODT. Above all, the addition of (Pd)ns to either bcp template is evidently able to lead to significant changes in the ODT, which offers

Figure 15. Schematic illustration of (a) a single (Pd)n tethered by PS block chains of the PS-b-PMMA with an association number m, (Pd)n(PS-b-PMMA)m, and (b) a single bcp chain PS-b-PMMA and their respective coarse-grained models (a′ and b′) for their chain conformations and spatial segment distributions in the field of the lamellar template (c). The minority component (a′) with the small concentration of 0.7 wt % plays a significant role on the thermal stability of the template made by the major component (b′) as proposed in the text.

schematically a single (Pd)n tethered selectively by PS block chains, defined hereafter as (Pd)n−(PS-b-PMMA)m with m being the association number of PS blocks with (Pd)n via the attractive interactions described above. IV-6. Possible Interpretation on (Pd)ns Raising TODT. Let us next consider why the preferential attractions of (Pd)ns with PS block chains raise TODT and a net (or apparent) segregation power between PS and PMMA. We consider that the system is composed of a small fraction of impurities defined as (Pd)n-(PS-b-PMMA)m and a majority of PS-b-PMMA, as shown in Figure 15, parts a and b, respectively. When the two components (a and b) are incorporated into the lamellae, they change their conformations to a′ and b′, respectively, as schematically shown in Figure 15c. It is well-known57,59 that the long-range order of the patterns in ordered bcps is a consequence of an interplay of the short-range interactions between the two kinds of segments (PS and PMMA) and the long-range interactions due to the connectivity of the two block chains and the incompressibility of the bcp melts. It is conceivable that the impurities (Pd)n-(PS-b-PMMA)m strongly affect the long-range interactions in two ways. (a) The impurities may serve as “anchors” which suppress Brownian motions of the bcp chains in the lamellae over a large distance: The suppressed Brownian motions of (Pd)n-(PS-b-PMMA)m 968

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(30) Tirumala, V. R.; Romang, A.; Agarwal, S.; Lin, E. K.; Watkins, J. J. Adv. Mater. 2008, 20, 1603−1608. (31) Tanaka and Hashimoto32 reported that the effects of homopolystyrene (HPS), as an selectively good additive to PS blocks, on TODT of PS-b-PI generally depends on volume fraction and molecular weight (Mw) of HPS (see Figure 8 of ref 32). When the amount of the additive (ΦHS) is smaller than 0.2, the TODT always decreases with ΦHS, regardless of Mw covered by the experiments. (32) Tanaka, H.; Hashimoto, T. Macromolecules 1991, 24, 5398− 5407. (33) Hashimoto, T.; Suehiro, S.; Shibayama, M.; Saijo, K.; Kawai, H. Polym. J. 1981, 13, 501−516. (34) Sakamoto, N.; Harada, M.; Hashimoto, T. Macromolecules 2006, 39, 1116−1124. (35) Rg,x, the radius of gyration of x block in a bcp chain, is assumed to be given by Rg,x = [Nxax2/6]1/2 with Nx being the degree of polymerization of x (x = I, S or MMA) and ax being the averaged segment length of x (ax ∼ 0.68 nm according to references 36 and 37. (36) Ballard, D. G. H.; Wignall, G. D.; Schelten, J. Eur. Polym. J. 1973, 9, 965−969. (37) Petychakis, L.; Floudas, G.; Fleischer, G. Europhys. Lett. 1997, 40, 685−690. (38) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35− 50. (39) (a) Binder, K.; Stauffer, D. Phys. Rev. Lett. 1974, 33, 1006−1009. (b) Binder, K. Phys. Rev. B 1977, 15, 4425−4447. (40) Fredrickson, G. H.; Helfand, E. J. Chem. Phys. 1987, 87, 697− 705. (41) Bates, F. S.; Rosedale, J. H.; Fredrickson, G. H. J. Chem. Phys. 1990, 92, 6255−6270. (42) Stühn, B.; Mutter, R.; Albrecht, T. Europhys. Lett. 1992, 18, 427−432. (43) Wolff, T.; Burger, C.; Ruland, W. Macromolecules 1993, 26, 1707−1711. (44) Hashimoto, T.; Ogawa, T.; Han, C. D. J. Phys. Soc. Jpn. 1994, 63, 2206−2214. (45) Floudas, G.; Pakula, T.; Fischer, E. W.; Hadjichristidis, N.; Pispas, S. Acta Polym. 1994, 45, 176−181. (46) Sakamoto, N.; Hashimoto, T. Macromolecules 1995, 28, 6825− 6834. (47) Koga, T.; Koga, T.; Hashimoto, T. Phys. Rev. E 1999, 60, R1154−1157. (48) Dudowicz, J.; Freed, K. F.; Douglas, J. F. Macromolecules 1995, 28, 2276−2286. (49) It is interesting to compare the radii of gyration of PS and PMMA blocks in PS-b-PMMA (Rg,PS = 3.3 nm and Rg,PMMA = 3.2 nm for the unperturbed chains, respectively) with Rn = 3.2 nm in the (Pd)n/PS-b-PMMA system and the radii of gyration of PS and PI blocks in PS-b-PI (Rg,PS = 3.0 nm and Rg,PI = 3.2 nm, respectively) with Rn = 2.7 nm in the (Pd)n/PS-b-PI system (see Tables 1 and 2).35 This results elucidate that the incorporation of (Pd)n having the radii comparable with those of the unperturbed chain dimensions of the block chains decreases and increases the amplitude of the thermal composition fluctuations and the thermal correlation length in the disordered state, respectively, as evidenced by Figure 10. (50) We may note that this rule of thumb was not strictly applicable to our system reported in ref 23 where the additive C60 selectively good to PI block chains lowered the TODT of PS-b-PI bcp. (51) Horiuchi, S.; Fujita, T.; Hayakawa, T.; Nakao, Y. Langmuir 2003, 19, 2963−2973. (52) See for example , Roe, R. J. Methods of X-ray and Neutron scattering in polymer science: Oxford University Press: New York, 2000. (53) Hashimoto, T.; Sakamoto, N. Macromolecules 1995, 28, 4779− 4781. (54) Sakamoto, N.; Hashimoto, T. Macromolecules 1998, 31, 3815− 3823. (55) Hashimoto, T.; Koga, T.; Koga, T.; Sakamoto, N. In The Physics of Complex Liquids; Yonezawa, F.; Kazuhiko, T.; Kaji, K.; Doi, M.; Fujiwara, T., Eds.; World Scientific: Singapore, 1998; pp 291−308.

new opportunities for the development of these nanocomposites.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (Y.Z.) [email protected]; (T.H.) [email protected]. ne.jp. Notes

The authors declare no competing financial interest. § Professor Emeritus, Kyoto University, Kyoto 606-8501, Japan, and Honorary Chair Professor, National TsingHua University, Hsinchu 30013, Taiwan

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REFERENCES

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(56) Hashimoto, T. Macromol. Symp. 2001, 174, 69−83. (57) Hashimoto, T. Bull. Chem. Soc. Jpn. 2005, 78, 1−39. (58) Note that we conclude here that PS blocks bind to the surface of (Pd)ns. However, it does not mean at all that the system is partially cross-linked. It means only a small amount of bcp chains bind to the surface of the particles, but most of bcp chains are free from the particles, because (Pd)n is only 1 wt%. (59) Ohta, T.; Kawasaki, K. Macromolecules 1986, 19, 2621−2632. (60) The anchoring effects play important roles on the thermal concentration fluctuations in the disordered state also, as pointed out earlier in ref 49: The anchoring effects suppress the amplitude of the thermal composition fluctuations but increase their thermal correlation length in the disordered state. Hence, they tend to promote ordering or raising TODT, unless their effects on the conformational penalty and the interface distortion in the ordered lamellae,3 i.e., the effect (b), is not too excessive. (61) In the case of (Pd)ns/PS-b-PI, two kinds of impurities (Pd)n(PS-b-PI) and (Pd)n-(PI-b-PS) have statistically about an equal populations and their effects may interfere each other to cause the effect (b) to outweigh the effect (a).

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dx.doi.org/10.1021/ma302070r | Macromolecules 2013, 46, 957−970