Introduction {#sec1}
============

Precise control of morphologies of microphase-separated structures requires well-defined block copolymers with monodispersity in molecular weights and in compositions.^[@ref1]^ However, polymer synthesis techniques (living polymerization) and a special chromatographic method of fractionation (two-dimensional HPLC fractionation) are required for this purpose.^[@ref2]^ These are quite heavy tasks for general researchers and create a high barrier. On the contrary, binary blends of block copolymers provide a facile strategy of precise control of compositions. In this regard, two block copolymers with antisymmetric compositions are preferred, although the composition is not monodisperse for the case of the blends. Since the blending is much easier as compared to the case of synthesizing a well-defined neat block copolymer with the targeted composition, mimicking a phase diagram of the microphase-separated structures has been studied. The binary blends of diblocks, AB/AB, have been intensively examined both experimentally and theoretically since the 1980s,^[@ref3]−[@ref39]^ not only for the purpose of the morphology control^[@ref3],[@ref7],[@ref10]−[@ref12],[@ref14],[@ref15],[@ref18],[@ref21],[@ref22],[@ref25],[@ref33]^ but also for many other aspects, such as elucidation of the cosurfactant effects (mixtures of small amounts of short diblocks in the long diblocks),^[@ref3]−[@ref5],[@ref8],[@ref9],[@ref13],[@ref16],[@ref17],[@ref26],[@ref28]−[@ref31],[@ref33],[@ref35],[@ref36],[@ref38]^ anomalous temperature behavior of the domain spacing,^[@ref11],[@ref19],[@ref24],[@ref27],[@ref29],[@ref31],[@ref35],[@ref39]^ elucidation of the effects of cast solvent on the morphology in thin films,^[@ref32],[@ref34]^ and examination of the grain boundary structure between the macroscopically phase-separated grains of thick and thin lamellae.^[@ref6]^ For these many purposes, a variety of AB/AB binary blends have been examined, such as \[long symmetric AB\]/\[short symmetric AB\] blends,^[@ref3]−[@ref6],[@ref8],[@ref9],[@ref13],[@ref16],[@ref17],[@ref26],[@ref29],[@ref36]^ \[long asymmetric AB\]/\[short symmetric AB\] blends,^[@ref14],[@ref24],[@ref28],[@ref30],[@ref31],[@ref35],[@ref38]^ \[asymmetric AB\]/\[symmetric AB\] blends (with similar molecular weights),^[@ref15],[@ref25]^ and antisymmetric AB/AB blends (with similar molecular weights).^[@ref7],[@ref10]−[@ref12],[@ref18]−[@ref23],[@ref27],[@ref32]−[@ref34],[@ref37],[@ref39]^ Furthermore, binary blends of AB/ABA^[@ref3],[@ref40]−[@ref44]^ and ABA/ABA^[@ref45]−[@ref47]^ have attracted interest from the viewpoint of mechanical properties because the ABA triblock copolymers possess good elastomeric property due to the bridge conformation of the B midblock chains between the dispersed A microdomains.^[@ref40],[@ref45]−[@ref47]^ As a matter of fact, the blends of SI/SIS are technologically applied to adhesive materials,^[@ref42]−[@ref44]^ where SI and SIS denote a polystyrene-*block*-polyisoprene diblock copolymer and a polystyrene-*block*-polyisoprene-*block*-polystyrene triblock copolymer, respectively. For such AB/ABA blends, the Monte Carlo simulation has also been performed to study the microdomain structures in thin films.^[@ref41]^ As another notable report on the miscibility of binary blends, the miscibility between SI and SB (polystyrene-*block*-polybutadiene diblock copolymer) has been reported with similar molecular weights^[@ref48]^ but immiscibility between SI and (SI)~4~ (a linear tetrablock copolymer with similar entire molecular weights to the SI diblock).^[@ref49]^ By noting good miscibility between SI and SIS (with similar molecular weights of an entire polymer chain), the above-mentioned miscibility/immiscibility results indicate a nice contrast in the fact that the dissimilarity in chemical structures of the chain segments does not matter, but the difference in the architecture of a polymer chain matters to the miscibility between two block copolymers.

As for the anomalous temperature dependence of the lamellar spacing in diblock copolymer blends, we have reported it for the first time for lamellar microdomains formed in binary blends of antisymmetric SI/SI of which compositions are 0.5 -- *x* and 0.5 + *x* (0 \< *x* \< 0.5), respectively, with similar molecular weights.^[@ref19]^ That is to say, the domain spacing (*D*) increased with temperature, which is very different from the common knowledge that *D* decreases with temperature as *D* ∼ *T*^--1/3^ (*T*: the absolute temperature in Kelvin)^[@ref50],[@ref51]^ for the UCST (upper critical solution temperature) type miscibility change with temperature; namely, the miscibility is increased when temperature increases. Such an anomality has been first theoretically predicted by Shi and Noolandi^[@ref11]^ and later reported experimentally by many different groups^[@ref24],[@ref27],[@ref29],[@ref31],[@ref35],[@ref39]^ not only for the lamellar microdomain but also for the bicontinuous microdomain.^[@ref31]^ The increase of *D* at high temperature has been ascribed to delocalization (solubilization) of short diblock chains into both of the polystyrene (PS) and polyisoprene (PI) lamellar phases, which has been evidenced by small-angle neutron scattering for the case of a \[long asymmetric SI\]/\[short symmetric SI\] blend.^[@ref24]^ As for the antisymmetric case, the delocalization mechanism would be applicable, as pointed out by Park et al.^[@ref39]^ However, this process is clearly the onset of the macroscopic phase separation. Our result previously reported^[@ref19]^ clearly indicated almost reversible temperature dependencies upon cooling from the highest temperature subsequently after heating. This fact clearly indicates that the anomalous temperature dependence cannot be ascribed to the macroscopic phase separation process. In other words, the anomality cannot be ascribed to delocalization (solubilization) for the case of the antisymmetric blends.

In the current study, we will first provide a summary of the phase diagram by using SI/SI blends with appropriately adjusting the overall PS average volume fraction (ϕ~PS~) in the plot of χ*Z* vs ϕ̅~PS~ where χ and *Z* are the interaction parameter between A and B segments and the average degree of polymerization as defined in refs ([@ref21]) and ([@ref22]). Actually, this is the comprehensive version of the phase diagram as previously reported^[@ref22]^ based on our experimental results using SI samples with similar molecular weights, and it is compared with a theoretical phase diagram for the antisymmetric AB/AB blend (with the same molecular weights) by Matsen and Bates^[@ref12]^ and with a theoretical phase diagram for a neat diblock.^[@ref1]^

In this study, we intend to examine the temperature dependency of *D* for the lamellar morphology. Therefore, it is important to examine in advance whether the lamellar phase prevails in the average composition range of 0.4--0.6 at χ*Z* ≈ 20, as in the case of the neat diblock copolymers. As a matter of fact, this can be clearly confirmed later ([Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}). Thus, it is possible to examine the temperature behaviors not only for the average PS fraction of 0.50 but also for the case of not exactly being identical to 0.50. Since the latter case lacks the balance of the stoichiometric numbers of the antisymmetric AB/AB diblock chains, the latter possesses the significance to highlight a feature of the lamellar structure comprising stoichiometric numbers of the antisymmetric diblock copolymer chains, as shown in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}. In this sense, [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"} plays an important role to examine in advance whether the lamellar morphology can be formed for the binary blend having the average composition not exactly being identical to 0.50.

![Schematic illustration showing the concept of the packing condition of block chains in lamellar microdomains for the case of binary blends (50/50) of diblock copolymers having antisymmetric compositions with respect to the volume fraction of 0.5. The concept of this figure is the same as Figure 3 of ref ([@ref19]) (copyright ACS).](ao-2017-01075r_0001){#fig1}

![Experimentally established morphology diagram for binary blends of SIZ-3/SIZ-4 with adjusting the average composition at the required value. The morphologies were examined by the in situ small-angle X-ray scattering measurements. The red broken curves indicate the theoretical morphology diagram by Matsen and Bates for the neat diblocks.^[@ref1]^](ao-2017-01075r_0002){#fig2}

We then examine the temperature dependence of the lamellar spacing in various binary blends of poly(methyl acrylate)-*block*-polystyrene (MS) diblock copolymers with the synchrotron small-angle X-ray scattering (SAXS) measurements. For this purpose, the antisymmetric binary blends were prepared by using MS diblock copolymers 1 and 2, with compositions of 0.5 -- *x* and 0.5 + *x* (0 \< *x* \< 0.5), respectively. In this study, more than 20 samples have been synthesized with a wide range of compositions from 0.20 to 0.87 and the range of the molecular weight of 12 000--33 800 ([Table [1](#tbl1){ref-type="other"}](#tbl1){ref-type="other"}). The significant point of using the MS specimens is that the segregation between PMA (poly(methyl acrylate); M) and PS (S) is much larger than that for the SI specimens. Using the following temperature dependencies of χ for the SI and the MS segmental interaction^[@ref19],[@ref63]^

###### Sample Characteristics

  specimen code   *M*~n~[a](#t1fn1){ref-type="table-fn"}   *M*~w~/*M*~n~[a](#t1fn1){ref-type="table-fn"}   ϕ~PS~[b](#t1fn2){ref-type="table-fn"}   specimen code   *M*~n~[a](#t1fn1){ref-type="table-fn"}   *M*~w~/*M*~n~[a](#t1fn1){ref-type="table-fn"}   ϕ~PS~[b](#t1fn2){ref-type="table-fn"}
  --------------- ---------------------------------------- ----------------------------------------------- --------------------------------------- --------------- ---------------------------------------- ----------------------------------------------- ---------------------------------------
  MS1             16500                                    1.09                                            0.20                                    MS12            19400                                    1.09                                            0.57
  MS2             12500                                    1.08                                            0.21                                    MS13            14200                                    1.06                                            0.58
  MS3             12900                                    1.08                                            0.27                                    MS14            19800                                    1.09                                            0.59
  MS4             14700                                    1.06                                            0.30                                    MS15            16900                                    1.12                                            0.61
  MS5             20900                                    1.14                                            0.31                                    MS16            33800                                    1.13                                            0.65
  MS6             14000                                    1.12                                            0.37                                    MS17            20600                                    1.11                                            0.70
  MS7             21000                                    1.13                                            0.38                                    MS18            14000                                    1.10                                            0.73
  MS8             15200                                    1.12                                            0.42                                    MS19            14500                                    1.10                                            0.81
  MS9             16500                                    1.06                                            0.44                                    MS20            13000                                    1.09                                            0.85
  MS10            12000                                    1.05                                            0.46                                    MS21            13000                                    1.11                                            0.87
  MS11            17300                                    1.10                                            0.50                                                                                                                                              

Determined by GPC (PS equivalent).

Volume fraction of polystyrene determined by ^1^H NMR (200 MHz)

the values of χ at 150 and 180 °C for SI are 0.040 and 0.036, respectively, and those for MS are 0.083 and 0.080, respectively. Thus, the ratios of the χ values are 2.06 and 2.25 for 150 and 180 °C, respectively. This means that a lower molecular weight is required for the MS specimens to match the segregation power χ*Z*. As a matter of fact, the molecular weights of the MS specimens listed in [Table [1](#tbl1){ref-type="other"}](#tbl1){ref-type="other"} are less than those of the SI specimens in the literature, which reports the anomalous temperature dependence of χ.^[@ref19]^ Since the lower molecular weight specimens have much lower viscosity, the required experimental time can be reduced for the examination of the equilibrium behavior of the temperature dependence of *D*, not only in the heating process ([Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}) but also in the multiple cycles of the heating/cooling processes ([Figure [10](#fig10){ref-type="fig"}](#fig10){ref-type="fig"}).

[Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"} is a schematic illustration showing the concept of the packing condition of block chains in lamellar microdomains for the case of the antisymmetric binary blends (50/50). This kind of mutual-compensating chain packing in the lamellar microdomains has been supported experimentally by the neutron reflectivity measurements^[@ref23]^ and by theoretical consideration.^[@ref37]^ Since we found the temperature-independent *D* for a particular case of the antisymmetric blend of diblock copolymers, it would be important for manufacturing materials with properties (for instance, the optical property) independent of temperature. Actually, based on our experimental results, one can prepare lamellar microdomains for which spacing does not change with temperature by blending two diblock copolymers.

Results and Discussion {#sec2}
======================

[Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"} is the result of the morphology diagram in the weak-segregation limit for the binary blends of SI diblock copolymers SIZ-3 and SIZ-4. [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"} also compares our experimental results with the theoretical result of Matsen and Bates for the neat diblocks,^[@ref1]^ as indicated with red broken curves. It is noted here that Matsen and Bates have reported the morphology diagram for the antisymmetric AB/AB blend with 0.25/0.75 of the compositions,^[@ref12]^ which should be more appropriate for comparison with our experimental results. However, their theoretical result (Figure 3 of ref ([@ref12]) for 0.25/0.75 antisymmetric composition relevant to the SIZ-3/SIZ-4 blends) is found at a glance to be different from our experimental one. One of the major differences is that there is no double-gyroid phase existing in their theoretical phase diagram.^[@ref12]^ Therefore, we decided to make a comparison with the theoretical result for the neat AB diblocks in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}. Definitely good agreement between the experimental and theoretical morphology diagrams can be recognized, although it has been reported that the cylinder region expands while the lamellar region shrinks in the morphology diagram upon blending two diblocks.^[@ref33]^ One important disagreement found in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"} is that the experimental morphology diagram exhibits the wider region of the disordered state, such that the direct transitions to the disordered state were observed from the cylinders or from the gyroid phase upon heating without passing through the spherical (body-centered cubic) phase. However, this is a well-known phenomenon as the *fluctuation effect* reported by Khandpur et al. for the neat block copolymers.^[@ref53]^ Therefore, the disagreement in the morphology diagram in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"} is not ascribed to the blending. Thus, the mimicking of the morphological phase diagram can be stated to be almost perfect for this particular pair of the SI diblocks.

[Figure [3](#fig3){ref-type="fig"}](#fig3){ref-type="fig"} shows the SAXS profiles measured at room temperature for MS5 and MS17 specimens. The specimens were thermally annealed at 150 °C for 24 h in advance. Here, *q* denotes the magnitude of the scattering vector, defined aswith λ and θ being the X-ray wavelength and the scattering angle, respectively. For both profiles, reflection peaks with *q* positions can be assigned relatively to 1:√4:√7 (= √(*h*^2^ + *hk* + *k*^2^)), and these can be considered to be reflections of {*h k i* 0} planes of the hexagonal lattice. Since ϕ~PS~ = 0.31 and 0.70 for MS5 and MS17, respectively, observation of the hexagonal lattice of cylindrical microdomains is reasonable. Furthermore, the √3 reflection peak is completely extinguished. It was reported that the √3 peak completely disappears when the volume fraction equals to 0.326 (and 0.674 complementarily).^[@ref54]^ These compositions are also in good accord with the MS5 and MS17 specimen characteristics. It is also found that the *q* positions of the first-order peaks are identical to each other for these specimens. This result is again reasonable because of the similar molecular weights of these specimens.

![SAXS profiles measured at room temperature for MS5 and MS17 specimens. The specimens were thermally annealed at 150 °C for 24 h in advance.](ao-2017-01075r_0003){#fig3}

As shown in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}, formation of the lamellar morphology is expected for the antisymmetric binary blend of MS5 and MS17. This is confirmed by the SAXS profiles shown in [Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}a, where reflection peaks of *q* positions are assigned relatively to 1:3. Here, the disappearance of the second-order peak should be noted. It is because the average composition is 0.50 which meets the condition of the extinguishment of the second-order peak for the case of lamellar microdomains.^[@ref55]^ Note that the peak breadth did not change as a function of temperature for the neat MS11 and MS5/MS17 (50/50) blend specimens. Furthermore, it should be noted that the reflection peaks are wider for the binary blend as compared to the neat block (see the SAXS profiles shown in [Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}b). This reminds that the grains of lamellae are smaller in the blend than in the neat block. To analyze the grain size quantitatively, it is evaluated according to the method of Hosemann^[@ref56],[@ref57]^ from the breadth of the reflection peaks by using [eq [4](#eq4){ref-type="disp-formula"}](#eq4){ref-type="disp-formula"}.where Δ*q* is the integral width of the reflection peaks (Δ*q* = *S*/*I*~m~, where *S* and *I*~m~ denote, respectively, the peak area (integrated intensity) and the scattering intensity at the peak top). *D*~G~ is the average grain size; *d* is the average spacing of the reflection planes; *m* is the order of the reflection peak; and *g* is the lattice distortion factor, as defined bywhere Δ*d* is the standard deviation of the distribution of the spacing *d*. It should be noted here that the experimentally observed peak breadth contains an error due to the instrumental broadening. To correct for this effect, the following relationship should be usedwhere Δ*q*′ denotes the observed peak breadth (integral width). Note here that *B*^2^ = 1.16 × 10^--4^ (nm^--2^) was estimated from the standard sample (chicken tendon collagen) according to the procedure provided in our previous paper.^[@ref57]^ By conducting a computational peak decomposition of the 1d-SAXS profiles, the peak breadth, Δ*q*′, was evaluated for the first- and third-order reflections, respectively, as *m* = 1 and 3. After the correction according to [eq [6](#eq6){ref-type="disp-formula"}](#eq6){ref-type="disp-formula"}, the (Δ*q*)^2^ values were obtained. [Figure [5](#fig5){ref-type="fig"}](#fig5){ref-type="fig"} shows the plots of (Δ*q*)^2^ vs *m*^4^ for the neat MS5, MS11, and MS17 specimens and the MS5/MS17 (50/50) blend specimen. From the slope and the intercept of the approximated lines, values of the *g* factor and *D*~G~ were estimated, respectively, which are summarized in [Table [2](#tbl2){ref-type="other"}](#tbl2){ref-type="other"}. At a glance of the SAXS profiles shown in [Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}, the fact that the grain size in the blend was smaller as compared to that of the neat lamellar specimen (MS11) might be ascribed to blending. However, this is not appropriate because the grain sizes of the neat MS5 and MS17 specimens (before blending) are found to be as small as that of the blend. By examining the results shown in [Table [2](#tbl2){ref-type="other"}](#tbl2){ref-type="other"}, it can be concluded that both the grain size and the *g* factor were almost unchanged upon blending.

![Changes in the SAXS profiles as a function of temperature for the (a) MS5/MS17 (50/50) (the antisymmetric binary blend of MS5 and MS17) specimen and (b) MS11 (the neat block copolymer). These are the results of the in situ SAXS measurements in the course of the temperature ramp of 2.0 °C/min.](ao-2017-01075r_0004){#fig4}

![Hosemann plots ((Δ*q*)^2^ vs *m*^4^) for the neat MS5 (cylinder), MS 11 (lamella), and MS 17 (cylinder) specimens and MS5/MS17 (50/50) blend specimen (lamella).](ao-2017-01075r_0005){#fig5}

###### Results of the Hosemann Analysis

  specimen           morphology   grain size (nm)   *g* factor
  ------------------ ------------ ----------------- ------------
  MS5                cylinder     141               0.0350
  MS11               lamella      432               0.0250
  MS17               cylinder     132               0.0379
  MS5/MS17 (50/50)   lamella      175               0.0343

We now examine the temperature dependence of the lamellar spacing. To clearly examine the unusual behavior, the exponent α in the relationship of *D* ∼ *T*^α^ is evaluated with assuming the scaling behavior between *D* and *T* in the short experimental range of 150--180 °C. Actually, this assumption can be confirmed in [Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"} (the double logarithmic plots of the lamellar spacing *D* and the absolute temperature *T*) for all of the antisymmetric blends (with similar molecular weights), although our previous result showed nonlinear dependence for much wider temperature range (120--220 °C).^[@ref19]^ Note here that *D* is evaluated by *D* = 2π/*q*\* from the *q* position (*q*\*) of the first-order peak in the SAXS profile. In order to accurately determine *q*\*, the computational peak fitting was performed on the first-order peak. As seen in the plot of [Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}c (for the neat MS11 diblock copolymer), the usual behavior is observed with a slightly higher value of α than the usual one (α = −0.33). On the other hand, unusual behaviors are seen for all of the blend specimens. Especially, completely opposite temperature dependence is observed for the MS1/MS19 blend specimen. Note that this specimen has the most biased compositions of the blended diblock copolymers. It is also noted here that the temperature-independent *D* is also recognized for the MS3/MS18 blend specimen (as shown in [Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}d) as well as for the MS5/MS17 blend specimen (as shown in [Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}b) for which SAXS profiles were shown in [Figure [4](#fig4){ref-type="fig"}](#fig4){ref-type="fig"}a as a function of temperature.

![Double logarithmic plots of the lamellar spacing *D* and the absolute temperature *T* for the binary blends of MS diblock copolymers having antisymmetric compositions with respect to the volume fraction of 0.50. (a) MS1/MS19 (50/50), (b) MS5/MS17(50/50), (c) MS11 neat diblock, (d) MS3/MS18 (50/50), and (e) MS8/MS13 (50/50) specimens. Note here that the two diblock copolymers in each blend specimen have similar molecular weights.](ao-2017-01075r_0006){#fig6}

It is important to examine the effect of thermal expansion on α. For the rubbery state (*T* \> *T*~g~), the literature values of the thermal expansivity β \[= (d ln*V*/d*T*)~p~\] for PS are located in the range of 5.1--6.0 × 10^--4^ K^--1[@ref58]^ and β for PMA is 5.6 × 10^--4^ K^--1^.^[@ref59]^ Assuming the isotropic thermal expansion, the scaling exponent α can be expressed byFor the temperature range of the examination of the scaling behavior in [Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"} (150--180 °C), the scaling exponent due to the thermal expansion can be estimated using [eq [7](#eq7){ref-type="disp-formula"}](#eq7){ref-type="disp-formula"} as 0.072--0.091, which is quite a bit smaller than α = 0.42 at most experimental values found by this study.

Such unusual temperature dependence of *D* (*D* increases with temperature) has been reported already in our previous publication^[@ref19]^ for the case when the two blended diblock copolymers have biased compositions. The dependence of α on the degree of deviation in composition, Δϕ, is shown in [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}a. Here, Δϕ is defined aswhere *x*~1~ and *x*~2~ are the volume fraction of the diblock copolymers 1 and 2, respectively, in the binary blend (*x*~1~ + *x*~2~ = 1). ϕ~PS,1~ and ϕ~PS,2~ denote the volume fraction of PS in the diblock copolymers 1 and 2, respectively. It is clear that α increases with Δϕ and that its dependency is accelerated as a function of Δϕ. Although it was possible to fit the data with a mathematic equation, it is more convenient to obtain a linear dependence. For this purpose, we introduce the degree of asymmetry (τ) of the compositions for the blended diblock copolymers, as defined bywhere ϕ~PS,1~ \< 0.5 and ϕ~PS,2~ \> 0.5. For the neat diblock copolymer with the composition of 0.50, τ is so defined to be zero. As for the blend of homopolymers 1 and 2, τ becomes infinity. For the MS1/MS19 specimen exhibiting the unusual behavior as shown in [Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}a, τ is quite large (τ = 3.13). Thus, it is considered that the unusual behavior is more intensively observed (namely, the exponent α becomes positive and larger) for the larger value of τ. We now examine the relationship between α and τ quantitatively in [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}b for the blends with the average PS fraction of 0.50 (not only for the antisymmetric cases but also for the nonantisymmetric cases). In [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}b, good linearity can be confirmed. This clearly indicates that τ is a good measure of the unusual behavior of *D*. As shown in [Figure [2](#fig2){ref-type="fig"}](#fig2){ref-type="fig"}, the blends of two diblock copolymers can form the lamellar morphology in the average composition range of 0.4--0.6 at χ*Z* ≈ 20. Therefore, it was also possible to check the relationship between α and τ as shown in [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}c for the cases of the average PS fraction of 0.40 and 0.60 (not exactly identical to 0.50). On the contrary to [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}b, the linearity is poor in [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}c. Here, the broken line is shown as a guide for the eye, of which the slope is the same as the approximated line in [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}b but the broken line is shifted to set the origin of this broken line at (α, τ) ≈ (−0.25, 0.5). Interestingly, the good linearity is only found for the average PS fraction of 0.50 ([Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}b), while the linearity is poor for the case of the average PS fraction being not exactly identical to 0.50 ([Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}c). This fact clearly indicates that the temperature behavior of the lamellar microdomain spacing can be controlled almost perfectly by means of τ for the case of the lamellar structure comprising the antisymmetric AB/AB diblock copolymer chains, as shown ideally in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}.

![(a) Dependence of the exponent α on the degree of deviation in composition, Δϕ, for the average PS fraction of 0.50 (antisymmetric MS/MS blends). Note here that the exponent α denotes the scaling relation between *D* and *T* as *D* ∼ *T*^α^. The definition of Δϕ is given by [eq [8](#eq8){ref-type="disp-formula"}](#eq8){ref-type="disp-formula"} in the text. (b) Dependence of α on the degree of asymmetry (τ) of the composition for the blends with the average PS fraction of 0.50 (not only for the antisymmetric cases but also for the nonantisymmetric cases). The definition of τ is given by [eq [9](#eq9){ref-type="disp-formula"}](#eq9){ref-type="disp-formula"} in the text. (c) The same plot as (b) but for the average PS fraction of 0.40 and 0.60.](ao-2017-01075r_0007){#fig7}

Moreover, a slight breaking of the balance of the antisymmetric compositions in the two kinds of the AB diblocks (namely, those compositions do not meet ϕ~PS,1~ = 1 -- ϕ~PS,2~) can be allowed for the precise controlling of α by means of τ as long as the average composition is maintained at 0.50. On the contrary, the precise controlling of α by means of τ is difficult when the average composition is not identical to 0.50 (namely, the lamellar structure is not like that shown in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}). Thus, the illustration in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"} is considered to give a good physical insight into recognizing the anomalous temperature behavior (namely, the lamellar spacing increases with temperature).

[Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"} explains the reason for the unusual behavior of *D* for the case of the antisymmetric binary blend of diblock copolymers forming the lamellar morphology, as compared with the case of the neat diblock copolymers. Here, the UCST-type behavior is assumed. As shown in [Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}a, the repulsive interaction between A and B block chains deforms the polymer coils in the direction perpendicular to the lamellar interface. Therefore, the degree of the deformation of the polymer coil is decreased when the repulsive interaction is decreased at higher temperature. This explains qualitatively the decrease in *D* with the increase in *T* for the neat diblock copolymers (enhancement of miscibility results in *D*~2~ \< *D*~1~). As for the case of the antisymmetric binary blend of diblock copolymers forming the lamellar morphology ([Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}b and [8](#fig8){ref-type="fig"}c), the strong segregation between the longer A and the longer B chains is screened by the shorter A and the shorter B chains. Due to the screen effect, the longer chains of A and B cannot feel their existence, and therefore the longer chains are not necessarily stretched in the direction perpendicular to the lamellar interface (the longitudinal direction). On the contrary at higher temperature, the miscibility between the shorter A and the shorter B chains is increased because the value of χ*Z* (segregation power) is lower for the lower molecular-weight components. Therefore, the shorter A and B chains can be more or less partially mixed, resulting in interdigitation of the interface, as shown in [Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}b and [8](#fig8){ref-type="fig"}c. The mixed shorter A/B chain interphase can be formed, if the molecular weights of the shorter chains are small enough to meet the condition of the miscibility (i.e., the χ*Z* value is lower than the critical value of the complete miscible state). In such condition, the lateral distance between the two neighboring longer chains is decreased so that the chance of chain overlapping is increased. To avoid the chain overlaps, the longer chains tend to be stretched. Due to this effect the longer chains are more or less stretched in the longitudinal direction even at higher temperature (as schematically illustrated in [Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}c), resulting in *D*~2~ \> *D*~1~, although the stretching of the longer chains can be reduced at higher temperature because of the lower χ value. The domain spacing does not change with temperature as shown schematically in [Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}b, resulting in *D*~2~ ≈ *D*~1~, when the two effects (avoiding the chain overlaps and the decreasing χ value by increasing temperature) are balanced.

![(a) Schematic illustration for explaining the reason for the decrease in the domain spacing (*D*) upon heating for the case of the neat diblock copolymers forming the lamellar morphology. (b) Schematic illustration for explaining the reason for the unusual behavior of *D* (temperature-independent *D*) for the case of the antisymmetric binary blends of diblock copolymers (with smaller τ). (c) Schematic illustration for explaining the reason for the unusual behavior of *D* (increasing *D*) for the case of the antisymmetric binary blends of diblock copolymers (with larger τ). Here, the UCST-type behavior is assumed. The concept of this figure is the same as Figure 5 of ref ([@ref19]) (copyright ACS).](ao-2017-01075r_0008){#fig8}

Based on the result shown in [Figure [7](#fig7){ref-type="fig"}](#fig7){ref-type="fig"}b, one can prepare lamellar microdomains for which spacing does not change with temperature by blending two diblock copolymers with τ = 1.33 (corresponding to ϕ~PS,1~ = 0.3 and ϕ~PS,2~ = 0.7) having the same molecular weights. The relevant situation to the temperature-independent *D* for the smaller degree of asymmetry is schematically illustrated in [Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}b, which is in between the situations illustrated in [Figures [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}a and [8](#fig8){ref-type="fig"}c. Shi and Noolandi^[@ref11]^ have reported the theoretical result on this subject, and it may be recognized from their result (Figure 10 of ref ([@ref11])) that the domain spacing is unchanged upon the change of the interaction parameter (χ) in the range of 0.05--0.20 for the compositions of 0.18 and 0.82 for the diblock copolymers 1 and 2, respectively. As compared to our experimental result, these compositions are more biased. As for the more biased compositions our experimental result of the anomality in the temperature dependence of the domain spacing (*D* increases with *T*) is theoretically supported.

It is important to recognize that the spacing *D* can be scaled by the total lengths of the longer block chains A and B, according to the molecular model as illustrated in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}. To examine this insight, the values of the spacing *D* at 150 °C were plotted in [Figure [9](#fig9){ref-type="fig"}](#fig9){ref-type="fig"}a against the summation of *M*~n~ of the PMA block in the MS diblock 1 having ϕ~PS,1~ (\<0.5) and *M*~n~ of the PS block in the MS diblock 2 having ϕ~PS,2~ (\>0.5). Note here that the labels a--e indicate the data points for the blend specimens shown in [Figures [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}a--[6](#fig6){ref-type="fig"}e, respectively. It is very clear that the linearity of the data points in [Figure [9](#fig9){ref-type="fig"}](#fig9){ref-type="fig"}a is much better as compared to the plot shown in [Figure [9](#fig9){ref-type="fig"}](#fig9){ref-type="fig"}b as a function of the average *M*~n~ of the two diblocks blended, although the values of the spacing for the points at a and b and those at c and d are not appropriately in a good order as a function of *M*~n~ (PMA,1) + *M*~n~ (PS,2). However, the plots in [Figure [9](#fig9){ref-type="fig"}](#fig9){ref-type="fig"}a still show satisfactorily the good linearity as it is.

![(a) Plot of the values of the spacing *D* at 150 °C as a function of the summation of *M*~n~ of the PMA block in the MS diblock 1 having ϕ~PS,1~ (\<0.5) and *M*~n~ of the PS block in the MS diblock 2 having ϕ~PS,2~ (\>0.5). (b) The same plot as a function of the average *M*~n~ of the two diblocks blended. Here, the labels a--e indicate the data points for the blend specimens shown in [Figures [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}a--[6](#fig6){ref-type="fig"}e, respectively.](ao-2017-01075r_0009){#fig9}

Finally, the changes in *D* as a function of temperature are examined in the cycled heating-and-cooling processes for the blend specimens showing the temperature-independent *D* in the first heating process. [Figure [10](#fig10){ref-type="fig"}](#fig10){ref-type="fig"} shows the results in the double logarithmic plots of *D* and *T* for the MS5/MS17 (50/50) blend specimen. The temperature ramp-up rate was 2.0 °C/min, and the cooling rate was also 2.0 °C/min. The hysteresis of the changes in *D* is clearly observed, and then it can be stated that the temperature-independent *D* in the first heating process was not permanent. It is interestingly found that *D* is almost constant not only in the first heating but also in the second heating, although the level of *D* increased. Furthermore, the usual behavior with the exponent α being equal to −0.33 (which is also usual) was found in the second cooling process. The illustration presented in [Figure [8](#fig8){ref-type="fig"}](#fig8){ref-type="fig"}b is considered irreversible, and it may be speculated that the arrangement of the shorter chains giving rise to the screening effect for the longer chains cannot be retrieved completely in the cooling process. Therefore, the longer chains feeling the repulsive interaction are more stretched in the direction perpendicular to the lamellar interface in the cooling process, resulting in the increase in *D* with a decrease in *T*. The miscibility enhancement takes place only between the shorter A and the shorter B chains when heated again because the shorter chains can easily rearrange positions as compared to the longer chains. Thus, the invariance in *D* in the heating process appeared again in the second heating process. However, the invariant behavior is no longer the case in the third heating process. Therefore, it is considered that the rearrangement of the shorter chains is no longer available after the second heating process, and then the usual behavior appeared in the third heating process, as well as in the second cooling process. Since the rearrangement of the shorter chains promotes also the macroscopic phase separation, the blend specimen is considered to be no longer forming the lamellar morphology (or forming only irregular lamellae). Thus, it should be concluded that such anomalous behavior (including the temperature-invariant *D* behavior) is only transient (not permanent), taking place along the course of the macroscopic phase separation between the diblock copolymers 1 and 2, as it may be theoretically predicted by Shi and Noolandi.^[@ref11]^ As for the application for the utilization of the temperature-invariant properties (for instance, the optical properties due to the form birefringence of microdomains^[@ref60],[@ref61]^), cross-linking of constituent block chains may work for the robustness of temperature-invariant properties in many repeated cycles of heating and cooling.

![Double logarithmic plots of *D* and *T* for the MS5/MS17(50/50) blend specimen showing the hysteresis of the changes in *D* in the cycled heating and cooling process. The temperature ramp-up rate was 2.0 °C/min, and the cooling rate was also 2.0 °C/min.](ao-2017-01075r_0010){#fig10}

Conclusions {#sec3}
===========

The morphologies of the microphase-separated structures in the binary blends of diblock copolymers (SI/SI) have been studied intensively for the case of diblock copolymers bearing antisymmetric compositions with similar molecular weights. Here, the two diblock copolymers 1 and 2, of which compositions are 0.5 -- *x* and 0.5 + *x* (0 \< *x* \< 0.5), respectively, were blended, and the morphology diagram was constructed in the plot of χ*Z* vs ϕ~PS~. The temperature dependencies of the morphologies were analyzed by synchrotron SAXS measurements. It was found that the morphology diagram agrees in principle with the theoretical one by Matsen and Bates,^[@ref1]^ although the disordered phase was a bit expanded in the experimentally determined morphology diagram.

The antisymmetric binary blends of MS diblock copolymers having oppositely biased compositions were prepared to study anomalous temperature dependence of the lamellar spacing. For this purpose, more than 20 specimens have been synthesized with a wide range of compositions from 0.20 to 0.87 and the range of the molecular weight of 12000--33800. Note that the molecular weights of the blended diblock copolymers were chosen almost the same as each other and that the compositions of the blended diblock copolymers 1 and 2 are ϕ~PS,1~ = 0.5 -- *x* and ϕ~PS,2~ = 0.5 + *x* (0 \< *x* \< 0.5), respectively. By closely adjusting the average PS volume fraction in the blend specimen at 0.50, it was possible to form the lamellar morphology without macroscopic phase separation, as speculated something like the illustration shown in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}. As a result of the SAXS analyses, the following things were found. The scaling exponent α in *D* ∼ *T*^α^ was still negative but slightly larger than the usual value (i.e., α = −0.33) for the smaller degree of asymmetry in the composition (i.e., *x* is small), while α became positive for the higher degree of asymmetry. The latter result is very anomalous because the temperature dependence is opposite (i.e., the lamellar spacing increases with an increase of temperature). The value of α was found to be linearly rationalized with the degree of compositional asymmetry τ (which is especially introduced in the current paper for this purpose), including nonantisymmetric binary blend cases (however, with the average PS composition being set rigorously at 0.50). Based on this result, one can prepare lamellar microdomains of which spacing does not change with temperature by blending two diblock copolymers with τ = 1.33 (corresponding to ϕ~PS,1~ = 0.3 and ϕ~PS,2~ = 0.7) having similar molecular weights. This would be important for manufacturing materials with properties (for instance, the optical property) independent of temperature. Nevertheless, it was found that such anomalous behavior (including the temperature-invariant *D* behavior) is only transient (not permanent), taking place along the course of the macroscopic phase separation between the diblock copolymers 1 and 2. Cross-linking of constituent block chains may work for the robustness of temperature-invariant properties in many repeated cycles of heating and cooling. From the current study, the binary blends of the antisymmetric diblock copolymers were concluded to be versatile such that the precise controls of the morphologies and the temperature dependencies of the lamellar microdomains were possible.

Experimental Section {#sec4}
====================

Specimens {#sec4.1}
---------

Two SI diblock copolymers, SIZ-3 and SIZ-4, were synthesized by living anionic polymerization. The molecular characteristics are ϕ~PS~ = 0.65 and *M*~n~ = 26.1 × 10^3^ for SIZ-3 and ϕ~PS~ = 0.26 and *M*~n~ = 24.5 × 10^3^ for SIZ-4. These are the same specimens used in our previous studies.^[@ref19],[@ref21],[@ref22]^

The MS diblock copolymers were synthesized by atom transfer radical polymerization (ATRP) under reduced pressure, according to the previous method.^[@ref52],[@ref62],[@ref63]^ Inhibitors of radical polymerization (or antioxidants) in styrene (Extra Pure Reagent, Nacalai Tesque Co., Ltd.), methyl acrylate (Extra Pure Reagent, Nacalai Tesque), anisole (Extra Pure Reagent, Nacalai Tesque), and toluene (Extra Pure Reagent, Nacalai Tesque) were removed by adsorption on granular activated alumina. *N*,*N*,*N*′,*N*′,*N*″-Pentamethyldiethylenetriamine (PMDETA, 99%, Aldrich Chemical Co., Ltd.), methyl 2-bromopropionate (MBrP, 98%, Aldrich), and CuBr (98%, Aldrich) were used as received. As a first component, PMA was synthesized. The initiator (MBrP), CuBr(I), and the ligand (PMDETA) with their molar ratio 2:1:1 were added to a given amount of the methyl acrylate monomer. Finally, the solvent anisole was poured into the system with the concentration of 25 wt % with respect to the monomer amount. The solution was added in a round-bottomed flask. After degassing by freeze-and-thaw cycles three times, the flask was sealed in vacuum. The sealed flask was immersed into an oil-bath at 368 K to conduct polymerization. After the polymerization, the solution was diluted with toluene. Activated alumina powders were used to remove the catalysts. Subsequently, synthesized PMA was precipitated into a large amount of methanol from the toluene solution. The PMA was dried under vacuum at 323 K for 24 h and subjected to the gel permeation chromatography (GPC) measurements to determine *M*~n~ and its distribution (*M*~w~/*M*~n~). The radical can be reproduced at the PMA chain ends and was used as a macroinitiator in the successive stage of the chain extension reaction of PS chains. This polymer was chain-extended with PS via the ATRP at 383 K using the CuBr(I) (or CuCl(I)) and PMDETA. The PMA macroinitiator, CuBr(I) (or CuCl(I)), and the ligand with 1:1:1 molar ratio were added to a given amount of the styrene monomer. Finally, the solvent anisole was poured into the system with the concentration of 25 wt % with respect to the monomer amount and then polymerized at 383 K. The catalysts were removed by the same procedure mentioned above. After the chain extension reaction, the reaction mixture was purified by the precipitation from toluene solution into excess methanol. Then, the total *M*~n~ and *M*~w~/*M*~n~ were determined by the GPC measurement. To evaluate the composition, nuclear magnetic resonance (NMR) measurements were performed on AVANCE (Bruker) operated at 200 MHz at room temperature. The deuterated chloroform (CDCl~3~) was used as a solvent. Using the densities of 1.11 and 1.04 \[g/cm^3^\] for PMA and PS, respectively, ϕ~PS~ was eventually evaluated. The characteristics of MS samples thus synthesized are summarized in [Table [1](#tbl1){ref-type="other"}](#tbl1){ref-type="other"}.

Preparation of the Blend Specimens {#sec4.2}
----------------------------------

It is very important to prepare the blend specimens without undergoing the macroscopic phase separation. As a matter of fact, there would be a large chance of the macroscopic phase separation if the general solution casting would be conducted for the binary blend of diblock copolymers 1 and 2 for which compositions are very much different. Therefore, the special solution casting protocol was employed in the current study according to the method, which was already reported in our previous publication.^[@ref19]^ In principle, this method utilizes blow drying of the casting solution developed on the water surface to quickly evaporate the cast solvent. First, the MS diblock copolymers were independently weighed to make a blend with a given ratio, and then they were altogether dissolved in toluene. The casting solution was prepared with 8 wt % of the total polymer concentration by stirring for more than 12 h. A small amount of an antioxidant (*tert*-butyl catechol) was added to set the final concentration at 0.2 wt % of the antioxidant in the polymer specimen. Then, the casting solution was developed on the surface of distilled water by using a syringe. Then, it was dried drop by drop by using a hair dryer, and the dried specimen was gathered. This treatment was repeated many times to obtain a large enough amount of the specimen. Finally, the specimens were thermally annealed at 150 °C for 24 h in an oven purged with the dried nitrogen gas in order to fabricate a regular lamellar morphology without the macroscopic phase separation, as schematically shown in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}.

Note here that the molecular weights of the blended diblock copolymers were chosen almost the same as each other. Actually the molecular weights of the blended specimens, which are used for the examination of the temperature dependence of *D* as shown in [Figure [6](#fig6){ref-type="fig"}](#fig6){ref-type="fig"}, are similar to each other, as MS1/MS19 (16500/14500; the ratio is 1.14), MS5/MS17(20900/20600; the ratio is 1.01), MS3/MS18 (12900/14000; the ratio is 1.09), and MS8/MS13 (15200/14200; the ratio is 1.07).

Synchrotron SAXS Measurements {#sec4.3}
-----------------------------

The SAXS measurements were carried out at the BL-10C beamline of the Photon Factory, High Energy Accelerator Research Organization, Tsukuba, Japan,^[@ref21],[@ref22]^ using X-ray with a wavelength of 0.1488 nm. This beamline provides a quasi point-focused beam by using a toroidal mirror, and the beam size was measured at the detector position, which was 850 μm in the vertical direction and 1000 μm in the horizontal direction. A standard slit system with widths of 0.7 × 0.7 mm was used for the SAXS collimation. The sample-to-detector distance was set at 1.9 m. A position-sensitive-proportional counter was used as a one-dimensional detector to measure the scattering-angle-dependent X-ray intensity (one-dimensional SAXS profile) at once. The scattering intensity of an empty cell was subtracted from that of a specimen by taking into account of absorption due to the specimen. For the measurements of the temperature-dependent SAXS profiles, the time-resolved measurements were performed with the heating of the specimen at 2 °C/min in a narrow temperature range of 150--180 °C.

The authors declare no competing financial interest.

The SAXS experiments were performed under the approval of the Photon Factory (High Energy Research Organization, Tsukuba, Japan) Program Advisory Committee (Proposal No. 2005G187).
