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[Sadaki Samitsu](https://orcid.org/0000-0002-4139-1656), [Sirawit Pruksawan](https://orcid.org/0000-0002-9380-1872), Hideaki Yokoyama, [Izumi Ichinose](https://orcid.org/0000-0002-2236-0942)

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in [Solvent Effects during the Flash-Freezing Fabrication of Mesoporous Polystyrenes], copyright © 2022 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://pubs.acs.org/doi/10.1021/acs.macromol.2c00535.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Solvent Effects during the Flash-Freezing Fabrication of Mesoporous Polystyrenes](https://mdr.nims.go.jp/datasets/0e050ab8-4d32-4894-987b-29bf5be73ff0)

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Microsoft Word - Samitsu_Main_R2_clear 1 Solvent effects during the flash freezing fabrication of mesoporous polystyrenes  Sadaki Samitsu1*, Sirawit Pruksawan1,3,†, Hideaki Yokoyama2, Izumi Ichinose1 1 National Institute for Materials Science (NIMS), 1-2-1, Sengen, Tsukuba, Ibaraki 305-0047, Japan 2 Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Toudaikasiwakyanpasu, Kashiwanoha, Kashiwa-shi, Chiba 277-8561, Japan 3 Program in Materials Science and Engineering, Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1, Tenodai, Tsukuba, Ibaraki 305-8571, Japan For Table of Contents use only   ABSTRACT  2 A polymer solution can be flash frozen to prepare homopolymers with mesoporous structures in a template-free manner. The flash freezing method is derived from the ice-templating or freeze-casting method. Herein, we comprehensively investigated the effects of 13 good solvents for polystyrene as well as the polystyrene concentration on the fabrication process. Solvents with high boiling-point-to-melting-point ratios yielded uniformly sized mesoporous polystyrenes at polymer concentrations ≥20 wt%. Such solvents provided a high specific surface area (328 m2/g) and large mesopore volume (1.78 g/cm3) at the optimal polystyrene concentration. Solvents with medium-boiling-point-to-melting-point ratios formed bimodal mesopores, while a low polystyrene concentration gave hierarchical structures composed of mesopores and macropores. These results provide an understanding of the mechanism associated with the formation of mesopores and enable control over the desired mesopore morphology.   INTRODUCTION Mesoporous polymers are in strong demand for energy, environmental, and biomedical applications;1–6 therefore, these methods for their fabrication have been widely developed over the past few decades,7–10 most of which rely on block copolymers.11–13 In particular, self-assembled block copolymer nanostructures have been used as templates for well-ordered mesopores,14–18 as summarized in an excellent review article.19 The block copolymer approach has also recently been extended to the fabrication of hierarchal pore structures.20–22 Despite the great successes of block copolymers, fabricating mesoporous structures of commercially available homopolymers is a desirable objective from an industrial perspective.  3 Polymer solution phase separation23 has been used to industrially fabricate porous polymers because it is simple, template-free, versatile, and has a high production rate. Fabrication methods based on liquid-liquid phase separation are well-known and have been described in polymer physics24 and membrane science textbooks.25 Nonsolvent-induced phase separation forms asymmetric macroporous membranes bearing mesopores only on their surfaces.26 The thermally induced phase separation method enables the construction of homogeneous porous structures that contain almost-spherical interconnected pores.27 Despite popular usage, preparation method are limited because pores larger than a few micrometers are obtained in the bulk,28 and specific surface areas are usually less than 30 m2/g.29 Liquid-solid phase separation driven by crystallization in solution is another principle that can be used to fabricate porous polymers. While polymer crystallization has been comprehensively investigated30 and used to form membranes,31 the method based on the crystallization of solvent molecules, otherwise known as “ice templating”32 or “freeze casting,”33,34 has, to the best of our knowledge, not been investigated in detail in the polymer science field. Pure solvent crystals grow when a polymer solution is cooled to a temperature below the melting point of the solvent, with polymer molecules selectively expelled and concentrated between crystals. Such a phase-separated structure remains porous after freeze-drying, thereby replicating the shapes of the solvent crystals. In addition, rapid crystal growth along a temperature gradient results in the formation of anisotropic hierarchical macropores.35,36 Despite its impressive porous morphology, the pores of such a structure tend to be more than several tens of micrometers in size, with relatively small specific surface areas.37 Based on the ice templating mechanism, mesopores will form if the solvent crystals can be reduced to several tens of nanometers in size. Small crystals usually form at high nucleation densities and under slow crystal-growth conditions, which is  4 satisfied by crystallization at low temperature, in accordance with common crystallization theory.38 Based on the abovementioned concept, we previously introduced a new method for fabricating mesoporous polymers inspired by the ice templating method, which is referred to as the “flash freezing method.”39 The flash freezing of a polymer solution facilitates solvent molecule crystallization at low temperature, which results in the co-continuous microphase separation of solvent nanocrystals and nanofibrous polymer networks. Since the solvent nanocrystals act as a spontaneous mesoporous template, solvent extraction at low temperature results in a mesoporous polymer with a large specific surface area (>300 m2/g) as well as a sharp pore-size distribution in the 5–20 nm range, which successfully extends mesoporous designs achievable by phase separation methods. This method is facile, robust, and applicable to a wide range of commercially available homopolymers, including engineering thermoplastics with high glass-transition temperatures (Tg) (polystyrene, polycarbonate, polyvinylchloride, polyacrylonitrile, polysulfone, polyethersulfone, and polyetherimide). In addition to molding thick sheets, such mesoporous polymers can be shaped into films by casting and into fibers and pellets by spinning. The flash freezing method is efficient, scalable, and suitable for industrial applications. Previously,39,40 we fabricated mesoporous polymers by flash freezing and demonstrated their potential applications, although the effect of the process parameters on the mesoporous morphology was not fully revealed. Hence, herein we report our investigations into the effects of solvent and polymer concentration on the flash freezing method (Figure 1). In particular, the effect of the solvent on the ice templating method has, to the best of our knowledge, not previously been investigated in a systematic manner. Interestingly, we found that the mesoporous morphology of a porous polystyrene is crucially affected by the ability of the solvent to  5 crystallize, which is directly related to its boiling-point-to-melting point ratio (Tb/Tm). In this study, we investigated the effects of Tb/Tm and polymer concentration on the morphology of mesoporous polystyrene. Furthermore, to understand the mechanism associated with phase separation driven by solvent nanocrystallization, we examine the crystallization kinetics of polymer solutions, especially during flash freezing at low temperature.    Figure 1. Parameters considered for the flash freezing method and the four types of pore morphology produced, including uniform mesopores, bimodal mesopores consisting of large and small mesopores, hierarchal pores containing macropores and mesopores, and macropores. While isolated mesopores are shown, they are interconnected in the three-dimensional bulk form.  EXPERIMENTAL Flash freezing method Reagent-grade organic solvents and commercial-grade polystyrene were purchased from Wako Chemicals, Japan, and were used as received. We selected polystyrene (Mw ≈ 200,000) as a model polymer because it is highly soluble in a variety of organic solvents. Polystyrene solutions  6 were flash frozen using 13 good solvents for polystyrene with Tm values in the −70 to 15 °C range. The low-temperature limit was constrained to be the lowest temperature of the cryogenic refrigerator (VT-78HC, Nihon Freezer, Japan) used in this study. The Tm and Tb of each solvent were obtained from the literature41,42 and are summarized in Table 1. The procedure used to fabricate porous polystyrene is shown in Scheme 1. Specifically, solid polystyrene was dissolved in the desired organic solvent with magnetic stirring at 25 ± 3 °C for 2–3 h or at 100 °C if not fully dissolved at room temperature. The polystyrene solution (10 g) was then added to a glass vial (diameter: 40 mm; height: 120 mm; glass-wall thickness: 1.3 mm) and quickly frozen onto the wall of the vial by horizontally rotating the vial in a liquid nitrogen bath (Scheme 1(b)). The thin (approximately 0.5–1.0-mm-thick) solution layer was frozen within 1 min, but was further cooled for an additional 5 min to ensure complete freezing. Excess pre-cooled methanol (−80 °C, 90 mL) was then added to the vial, which was maintained at −80 °C in a cryogenic refrigerator for 2–3 d. After warming to room temperature, the sample was further washed with methanol (twice, 50 mL) and solvent-exchanged with tert-butanol (twice, 50 mL). Mesoporous polystyrenes were subsequently obtained by freeze-drying the tert-butanol (usually for 1–2 days). Small pieces of solid porous polymers were usually collected because unintentional cracks appear in vitrified solutions during freezing process due to large thermal shrinkage. Hereafter, each porous polystyrene sample is referred to by the abbreviated solvent name and the polystyrene concentration; for example, “NB-40” refers to mesoporous polystyrene obtained from a 40 wt% nitrobenzene solution of polystyrene.    7  Scheme 1. (a) Outlining the flash freezing method. (b) Photographic image taken during flash freezing showing sample rolling in a liquid nitrogen (LN2) bath.   Table 1. Tm and Tb values of organic solvents used in this study41 Solvent Abbreviation Tm (°C) Tb (°C) Tb/Tm† 1,4-Dioxane‡ Diox −0.1‡, 12.0 101.5 1.37 p-Xylene pXy 13.4 138.5 1.44 1,2-Dichloroethane DCE −35.5 83.6 1.50 Carbon tetrachloride‡ CCl −47.3‡, −22.7 76.8 1.55 o-Xylene oXy −25.0 144.6 1.69 Nitrobenzene NB 5.9 211.0 1.74 N,N-Dimethylacetamide DMAc −20.0 166.3 1.74 o-Dichlorobenzene DCB −16.9 180.6 1.77 Chlorobenzene CB −45.4 131.8 1.78 m-Xylene mXy −47.7 139.3 1.83 Cyclohexanone‡ cHxone −52.2‡, −31.9 155.8 1.94 N,N-Dimethylformamide DMF −60.3 153.2 2.00 1,1,2,2,-Tetrachloroethane‡ TCE −65.7‡, −43.6 145.3 2.02 ‡Some of the solvents exhibit two Tm values due to the existence of polymorphs. The lower Tm corresponds to the transition from one crystal form to the other. Lower Tm values were obtained  8 from a database.42 †Tb/Tm was calculated using units of absolute temperature (K). The lower Tm value was used for solvents with two Tm values.  Freezing and melting behavior of polystyrene solutions The freezing and melting behavior of polystyrene solutions was monitored by differential scanning calorimetry (DSC; Q2000, TA instruments, USA), with the temperature controlled with a liquid nitrogen cooler. Characteristic behavioral temperatures, including crystallization temperature (Tf), cold-crystallization temperature (Tc), Tm, and Tg, were determined from the DSC curves. Enthalpy changes during phase transition, including crystallization enthalpy (ΔHf), cold-crystallization enthalpy (ΔHc), and melting enthalpy (ΔHm), were determined by integrating DSC peaks. Procedural details are reported in our previous paper.39  Characterizing mesoporous polystyrenes Porous polystyrenes were characterized by cross-sectional scanning electron microscopy (SEM; FE-SEM S-4800, Hitachi, Japan). The specific surface areas (SBET) and meso, macro, and total pore volumes (Vmeso, Vmacro, and Vtotal) were evaluated through N2 gas adsorption at −196 °C using a gas-adsorption analyzer (Belsorp-max, MicrotracBel, Japan). Procedural details are reported in our previous paper.10,39 Small-angle X-ray scattering (SAXS) experiments were performed on the BL-6A beamline at the Photon Factory of the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan. Further details regarding beamline setup are described elsewhere.43 SAXS profiles were recorded at a scattering vector (q) in the 0.04–2.3 nm−1 range using an X-ray wavelength of 1.5 Å and a sample-detector distance of 2420 mm (calibrated using silver behenate). Each mesoporous polystyrene (approximately 0.5–1.0-mm-thick) was mounted onto a sample holder  9 and exposed to the X-ray beam for 1–10 s at room temperature. SAXS patterns were recorded using a photon-counting detector (PILATUS3 1M, DECTRIS, Switzerland). Each two-dimensional scattering image exhibited an isotropic pattern around the center of the beam and was converted into a one-dimensional scattering intensity profile by circular averaging. Data were processed using SAngler as described in the literature.44 Peaks in the linear SAXS profiles were Gaussian curve fitted to provide characteristic wavenumbers (qSAXS) that were converted into characteristic sizes (dSAXS) using the equation: dSAXS = 2π/qSAXS.   RESULTS AND DISCUSSION Crystallization behavior of nitrobenzene solutions and morphologies of the resulting porous polystyrenes According to our previous study,39 solvent molecule crystallization plays an important role during flash freezing. To confirm this, NB solutions with different weight percentages of polystyrene (CPS) were subjected to DSC. The 20 wt% solution exhibited a large exothermic peak due to the crystallization of molecular NB, even upon flash freezing; this behavior is similar to that observed for the pure solvent (NB) (Figure 2(a)). Based on this peak, Tf was determined to be −26 °C, while ΔHf is 51.0 J/g. The NB crystals melted at Tm = 4 °C during heating, as evidenced by an endothermic peak with ΔHm = 60.1 J/g. In contrast, the 40 wt% solution only exhibited a baseline shift at Tg = −66 °C, consistent with a lack of crystallization; instead, the solution vitrified during flash freezing (Figure 2(b)). Subsequent heating revealed a broad exothermic peak at −44 °C that extended to 0.3 °C. In addition, peak integration yielded ΔHc = 27.2 J/g, in agreement with the ΔHm value of 28.0 J/g observed at Tm. The agreement between  10 ΔHc and ΔHm reveals that this exotherm is the result of the cold crystallization of molecular NB; importantly, this occurred at a (low) temperature close to Tg, which is 18 °C lower than Tf determined for the 20 wt% solution. The 40 wt% solution behaved in a similar manner to the 20 wt% DMF solution reported in our previous study.39 Overall, the DSC traces show considerable differences in the crystallization behavior of NB solutions at CPS = 20 and 40 wt%. Porous polystyrenes were fabricated by flash freezing using 20 and 40 wt% solutions. As shown in Figure 2(c), the NB-20 porous polystyrene displays a framework with 100–200-nm-thick walls that formed anisotropic macropores, which are 0.5–1.0 μm wide and more than several micrometers long. The structure is dimensionally similar to those obtained by conventional ice templating32 and corresponds to the macropores shown in Figure 1. In contrast, the low-magnification image of NB-40 shows no macropores, while a large number of mesopores are clearly evident in the high-magnification image (Figure 2(d)). In this case, the reticular structure of the 10–20-nm-thick nanofibers formed mesopores 10–15 nm in diameter that correspond to the uniform mesopores schematically depicted in Figure 1. These mesopores are ~100-times smaller than the macropores observed in the image of NB-20. Significantly, NB pore morphology and crystallization behavior are correlated, as confirmed by DSC.   11  Figure 2. DSC curves of the NB solutions: (a) 20 wt% and (b) 40 wt% solutions. The solutions were flash frozen to −150 °C (upper panels) and subsequently heated to 40 °C at 10 °C/min (lower panels). Cross-sectional SEM images of the obtained porous polystyrenes: (c) NB-20, (d) NB-40.  The DSC data enabled the crystallization behavior of the NB solutions to be represented on a phase diagram (Figure 3(a)). As indicated, the Tm of the NB solution decreases slightly with increasing CPS, a result of melting point depression in the polymer solution.45 NB crystallized exothermically at low CPS values (10–25 wt%), which enabled Tf to be determined. Since Tf exhibits a steeper CPS dependence than Tm, the degree of supercooling (ΔT = Tm − Tf ) increases with CPS to a value of 40 °C at CPS = 25 wt%. Flash freezing resulted in polystyrene solution vitrification at CPS ≥30 wt%. CPS and Tg are related by the Gordon–Taylor expression (Eq. (1)):46 𝑇 ,        (1)  12 where Tgp and Tgs are the Tg values of the polymer and the solvent, respectively, xps is the polymer volume ratio: xps = (CPS/ρp)/{CPS/ρp+(100 − CPS)/ρs}, ρp and ρs are the densities of the polymer and solvent, and kGT is a specific parameter that expresses deviation from the simple additivity rule. The Tg values of the NB solutions were observed to decrease rapidly with decreasing CPS owing to the low Tg of NB (i.e., −112 °C).47 Eq. (1) was found to reasonably describe Tg behavior, which suggests that flash freezing provides a common glassy state for each polystyrene solution. Cold crystallization was observed close to the Tg curve when no considerable crystallization occurred during flash freezing; cold crystallization was then no longer observed at high CPS values (> 60 wt%) because the Tm line is too close to the Tg curve, which prevents sufficient supercooling for cold crystallization. Although the melting enthalpy measured for pure NB (ΔHm0 = 86.7 J/g) agrees with the database value,42 the ΔHf, ΔHc, and ΔHm values of the NB solutions depended significantly on CPS (Figure 3(b)). Since ΔHm was observed to decrease linearly with increasing CPS, its relationship can be described by Eq. (2): Δ𝐻 Δ𝐻 1 𝛼 𝐶 100⁄        (2) , where Eq. (2) is defined at the CPS range that gives ΔHm ≥ 0. Figure 3(b) shows that ΔHm lies between 0 and ΔHm0, while α, the slope of the linear plot, was calculated to be 1.62. The expected value of ΔHm can be expressed as: ΔHm0 × (1 − CPS/100) when all NB molecules in solution crystallize. Hence, each value of ΔHm determined by DSC was evidently smaller than the expected value because some NB molecules do not crystallize, as determined by α. The weight ratios of the total solvent, the uncrystallized solvent, and the crystallized solvent can be described by: (1 – CPS/100), (α – 1) × CPS/100, and (1 – αCPS/100), respectively.45 Consequently, a CPS of 61.7 wt% leads to (1– αCPS/100) = 0 when α is 1.62,  13 revealing the presence of 38.3 wt% uncrystallized NB. In addition, polystyrene chains strongly bind to NB molecules and prevent their crystallization by slowing their molecular motions in the vicinity of the polymer chains when CPS is >61.7 wt%. As a result, only the glassy solution state was observed at CPS >61.7 wt%. In contrast, excess NB molecules that were not bound to polystyrene chains were able to crystallize during DSC at CPS < 61.7 wt%. Nevertheless, polystyrene chains still affect the crystallization behavior of unbound NB molecules and alter their behavior even in this CPS range, depending on the value of CPS. Indeed, the plot shows two CPS ranges in which ΔHc is and is not observed; they are referred to as regions [1] and [3], respectively (Figure 3(b)). Region [1] corresponds to CPS values in the 30–60 wt% range, which satisfies ΔHc ≈ ΔHm with a negligible value of ΔHf. The majority of NB molecules do not crystallize during flash freezing in this region, but cold-crystallize instead during subsequent heating. Flash freezing fabrication yield pore properties that depend on the abovementioned regions (i.e., regions [1] and [3]), as shown in Figure 3(c). More specifically, large SBET values (≥165 m2/g) and large Vmeso values (≥0.40 g/cm3) were observed for region [1], whereas low SBET values (≤61 m2/g) and negligible Vmeso values were observed for region [3]. The large values of SBET and Vmeso observed in region [1] highlight the importance of ΔHc ≈ ΔHm, conditions under which a considerable number of NB molecules crystallize at (low) temperatures close to Tg. The relationship between CPS and ΔHf and ΔHc reveals that a high CPS is desirable when fabricating a mesoporous polymer; the mechanism associated with this observation is further discussed below (vide infra). We note that porous polystyrene fabrication has an upper CPS limit of 40 wt% because solvent exchange does not proceed efficiently at CPS >40 wt%. Although a CPS >40 wt%  14 enables solvent molecules to crystallize, the solvent crystals are likely to be isolated rather than interconnected, which hinders solvent exchange and an inability to fabricate a porous polymer.  Figure 3. (a) Phase diagram of NB solutions from DSC data obtained during flash freezing and heating at 10 °C/min. The Tm and Tf depressions are linearly fitted: Tm = 6.4 − 0.14 × CPS (orange line) and Tf = −14.7 − 0.69 × CPS (blue line). The Tg curve shown in red is calculated using equation (1) with Tgp = 100 °C, Tgs = −112 °C, and k = 3.19. (b) Enthalpies of NB solutions at melting ΔHm (circles), crystallization ΔHf (squares), and cold crystallization ΔHc (triangles) as functions of CPS. ΔHm values decrease linearly with increasing CPS: ΔHm = 86.7 × (1 − 0.0162 × CPS). The two regions in which ΔHc values are and are not observed are referred to as [1] and [3].  15 (c) SBET and Vmeso values of porous polystyrene as a functions of CPS. These values discretely increase as CPS transitions from region [3] to region [1].  The effect of solvent type As discussed above, the ability of the solvent to crystallize, which significantly influences the resulting porous structure, is a key parameter of the flash freezing method. Research into the glassy states of organic molecules revealed that the kinetic crystallizability (i.e., the opposite of the glass-forming ability) of a molecule is directly related to its Tb/Tm ratio, with a large Tb/Tm ratio resulting in low kinetic crystallizability.48 Based on this correlation, we tested 13 good solvents for polystyrene with various Tb/Tm ratios by fabricating porous polystyrenes from 30 wt% solutions using the flash freezing method. The SBET and Vmeso values of the porous polystyrenes are plotted as functions of Tb/Tm in Figure 4(a), which reveals that the 10 solvents with Tb/Tm ≥1.50 gave high SBET values (120–298 m2/g) and Vmeso values of 0.46–1.32 cm3/g. In addition, large numbers of mesopores were visually confirmed by SEM (Figures 4(b) and S1). These results show that various organic solvents can be used to prepare mesoporous polystyrenes, which validates the robustness of the developed method. The two solvents (Diox and pXy) with low Tb/Tm ratios (≤ 1.44) were confirmed to form only macropores without any mesopores, resulting in low SBET and Vmeso values (Figure S2(a)). Macropore formation correlates with the crystallization behavior of the solution in region [3] (Figure S2(b,c)), which is in agreement with observations made for the NB solutions. Figure 4 shows that the Tb/Tm ratio clearly divides the SBET and Vmeso trends, thereby providing a simple but informative parameter that distinguishes our method from those previously reported.49,50 In cryogel freeze-drying, a solvent with a high Tm and a low Tb value (i.e., a low Tb/Tm ratio) that ensures a practical  16 sublimination rate is preferred. Water, with a low Tb/Tm of 1.37, is the most commonly used solvent for this method, with Diox and pXy used as alternative solvents for water-insoluble polymers.51,52 Solvents with low Tb/Tm ratios are highly crystallizable and usually form only macropores while preventing the formation of mesopores. In contrast, our developed method uses solvents with large Tb/Tm ratios that facilitate the fabrication of mesoporous polymers through crystallization at low temperatures.  Figure 4. (a) SBET and Vmeso of porous polystyrene as functions of the Tb/Tm ratio of the solvent. The porous polystyrenes were fabricated from 30 wt% solutions by the flash freezing method using 13 different solvents. (b) Cross-sectional SEM image of the TCE-30 sample.  Effect of concentration on the mesoporous structure  17 DMF is a suitable solvent for fabricating mesopores because of its relatively high Tb/Tm ratio, as presented in Table 1. The phase diagram for DMF solutions (Figure 5(a)) shows that solutions with CPS values in the 5–10 wt% range crystallize during heating and cooling; this region in the diagram is referred to as region [2]. In contrast, those with CPS values in the 15–40 wt% range only undergo cold crystallization during heating, which corresponds to region [1]. Mesopores with large SBET values (183–282 m2/g) and Vtotal values of 0.94–2.39 cm3/g are formed in both regions [1] and [2]. The 5–40 wt% CPS range (Figure 5(b)) is significantly wider than that of region [1] observed for the NB solutions (30–40 wt% in Figure 3(c)). As discussed later (vide infra: Figure 11) a CPS of 5–10 wt% (region [2]) provides macropores as well as mesopores that correspond to the hierarchal pores shown in Figure 1. CPS significantly influences mesoporous polymer pore size in an ordered manner in region [1] (CPS of 15–40 wt%), as shown in Figure 5(c). These data are consistent with SEM observations. More specifically, a significantly larger pore volume was obtained at a pore diameter (d) of 60–200 nm for DMF-15, and the pore-diameter distribution peaked at dpeak = 98 nm. The distribution gradually moved to smaller values of d and Vtotal with increasing CPS. In contrast, DMF-40 presented a sharp single peak at dpeak = 15 nm, with a large Vmeso of 0.93 cm3/g. This lower Vtotal is the result of a lower solvent fraction because the volume of crystallizable solvent roughly determines the upper Vtotal limit. In addition, dpeak was observed to monotonically decrease with increasing CPS (Figure 5(d)). In a similar manner, Gutiérrez et al. investigated fabricating porous poly(vinyl alcohol)s using the ice templating method, in which aqueous solutions are frozen in liquid nitrogen, and found that average pore size decreased with increasing polymer concentration in the 2.5–10 wt% range.37 They also reported that the average pore size decreased as the freezing rate and the average molecular weight of the poly(vinyl alcohol) increased.  18 Although the observed concentration dependence is consistent with that observed in the current study, the reported pores are micrometer in size; i.e., nearly two orders of magnitude larger than those obtained in this study, which is attributable to the fact that the previous study used water (with a low Tb/Tm of 1.37), which crystallizes rapidly, while our method uses a solvent with a Tb/Tm ≥1.55 and a high polymer concentration, which prevents the formation of solvent macrocrystals and results in mesoporosity.   Figure 5. (a) (Upper) Phase diagram for DMF solutions determined from DSC curves recorded upon flash freezing and heating at 10 °C/min. The Tm and Tf depressions are linearly fitted: Tm = −60–6 − 0.016 × CPS (orange line) and Tf = −100–0 − 0.309 × CPS (blue line). The red Tg curve was calculated from equation (1) using Tgp = 100 °C, Tgs = −144 °C,47 and k = 2.98. (Lower) Enthalpy changes of the DMF solutions as functions of CPS. The ΔHm values were observed to decrease linearly with increasing CPS, with: ΔHm = ΔHm0 –1 − 0.0250 × CPS). Regions [2] and [1] can be identified on the basis of the observed dependences of ΔHf and ΔHc, respectively. (b) SBET and Vtotal values of the porous polystyrenes obtained from the DMF solutions as functions of CPS.  19 (c) Cumulative pore volumes of mesoporous polystyrenes obtained from DMF solutions. (d) Pore size (squares) and dpeak (circles, determined from the pore-size distribution acquired by gas-adsorption measurements) as functions of CPS. Pore sizes were calculated numerically according to a simple geometrical model (Figures S3 and S4, Supporting Information). Crystallization kinetics at low temperature With the aim of investigating crystallization behavior at low temperature, crystallization kinetics were examined by isothermal DSC using DMF solutions. No crystallization was observed when a 15 wt% solution was flash frozen, after which isothermal crystallization was observed at −96, −98, and −118 °C in the exotherms (Figure 6(a)). Crystallization was delayed for 19 min during isothermal crystallization at −96 °C, which is ascribable to low crystal-nucleation frequency; a sharp exothermic peak was observed beyond this timepoint due to rapid crystal growth. In contrast, crystallization was initiated within 2 min at −98 °C; hence, lower temperatures significantly accelerate the nucleation process. In fact, since crystallization starts immediately below 99°C, DSC could not monitor the induction time of less than 1 minute. A much broader exothermic peak was observed at −118 °C, consistent with slower DMF crystal growth at this temperature. Since nucleation and growth rate depend oppositely on temperature, the crystallization rate, which is the product of the nucleation and growth rates, is fastest at −104 °C for the 15 wt% solution, and decreases with decreasing or increasing temperature (Figure 7(a)).  Upon crystallization at −104 °C, an exotherm appeared immediately, and a significantly broad exotherm was observed when CPS increased from 15 to 25 wt%. The behavior is consistent with rapidly nucleating DMF crystals that grow extremely slowly (Figure 6(b)). This indicates that the nucleation rate is independent of CPS; however, growth rate depends significantly on CPS. The high viscosities of the polymer solutions result in slow crystal growth at low crystallization  20 temperatures and/or high CPS, which suppress the diffusive motions of solvent molecules. In addition, a high nucleation rate favorable for mesoporous polymer fabrication is achieved by crystallization at low temperature, which is almost unaffected by a high CPS value.   Figure 6. Isothermal crystallization behavior of the DMF solutions: (a) PS concentration of 15 wt%, and (b) crystallization temperature of −104 °C. The solutions were rapidly cooled from room temperature to the desired crystallization temperature, with heat flow recorded for the desired time.  The temperature- and CPS-dependences of the crystallization kinetics are summarized in the form of a time–temperature–transformation (TTT) diagram, based on the isothermal crystallization data presented above (Figure 7(a)). The crystal region is drawn as a C-shaped curve in the diagram because higher temperatures delay crystal nucleation, while lower temperatures slow down crystal growth, with the highest crystallization rate corresponding to the “nose” of the  21 curve.38,53 Although the induction time for crystallization is less than a few minutes at the “nose,” and independent of CPS, increasing the CPS value significantly delays the crystallization-rate maximum. This delay is therefore ascribable to slower crystal growth due to the high viscosity of the solution. This delay also explains the dependence of CPS on Tf and ΔT, consistent with the kinetics mechanism; hence, flash freezing results in preferential vitrification at high CPS. This diagram also reveals that crystallization rarely occurs at crystallization temperatures above −91 °C owing to the negligible crystal-nucleation frequency. Interestingly, in contrast to the lack of crystallization observed under isothermal conditions (Figure 7(a)), cold crystallization occurred between −91 and −74 °C under temperature-scanning conditions (Figure 5(a)), probably because the temperature reduced to −140 °C, which promotes crystal nucleation. Crystal growth proceeds even at temperatures higher than the upper bound of the TTT diagram when crystal nuclei are present in solution. Our fabrication process freezes a polymer solution in liquid nitrogen, which possibly promotes the formation of crystal nuclei and assists in the formation of solvent nanocrystals. As shown in Figure 7(b), the crystallization behavior of the solvent molecules is governed by the competition between their freezing and crystallization rates. The temperature cooling profile intersects with the upper part of the crystallization region at a low freezing rate, or low CPS, or when the solvent is highly crystallizable, which determines the value of Tf (Figure 7(b), left). This process corresponds to the typical ice-templating or freeze-casting situation, which is referred to as “route A,” as indicated in the phase diagram in Figure 8(a). Crystallization occurs at high Tf in this case, where low nucleation density and high growth rate form large solvent crystals that result in the generation of macropores upon solvent removal. In contrast, flash freezing vitrifies the solution and cold crystallization proceeds at low temperature when gently  22 heated in the opposite case, namely at a high freezing rate, high CPS, and when solvent kinetic crystallizability is low (Figure 7(b), right). This process corresponds to our flash freezing method, which is referred to as “route B” in the phase diagram shown in Figure 8(a). This process satisfies the conditions of high nucleation density and low growth rate, and generates a large number of solvent nanocrystals that result in mesopore formation. In addition to freezing-rate control, the flash freezing method can be used to control the crystallization behavior of solvent molecules by optimizing the effects of polymer concentration and solvent kinetic crystallizability. It should be noted that the crystallization temperature used in the flash freezing fabrication method in this study was fixed at −80 °C due to the limitations of the experimental setup.   23  Figure 7. (a) Time–temperature–transformation (TTT) diagram for DMF solutions constructed from isothermal DSC data: CPS = 15 wt% (squares), 20 wt% (circles), and 25 wt% (triangles). The crystallization time depicts the offset time of the exothermic peak, which represents almost  24 complete crystallization at that specific temperature. (b) Schematic illustration of the TTT diagram in terms of the effect of freezing rate (upper), CPS (middle), and the kinetic crystallizability of the solvent (bottom). Tf appears at the intersection of the temperature cooling profile and the upper boundary of the C-shaped crystallization region in the left-hand panel.  Proposed mechanism for mesopore formation and pore-size control We propose a mechanism that determines mesopore size based on the polymer solution phase diagram. The phase diagram in Figure 8(a) shows two crystallization pathways, as discussed in the previous section, namely route A, which takes place at low CPS and/or with slow freezing and/or with a highly crystallizable solvent (i.e., the conventional method), and route B, which takes place at high CPS and/or with flash freezing and/or with a poorly crystallizable solvent (i.e., the flash freezing method). In route A, solvent crystallization occurs unintentionally at Tf, which results in rapid crystal growth and the formation of macrocrystals. Explaining macropore size in a quantitative manner is difficult due to inhomogeneous nucleation, the directional growth of solvent crystals, and the undetermined crystallization temperature. In contrast, crystallization begins at a low temperature close to Tg in route B (point B1). A large number of solvent nuclei are generated at this temperature, and each nucleus grows particularly slowly, consistent with the assumption of homogeneous nucleation. Solvent crystals facilitate the participation of only solvent molecules in the crystal arrangement, excluding polymer molecules and preventing solvent crystal contamination. Owing to limited polymer diffusion at low temperature, spontaneous polymer discharge causes CPS to increase locally around the crystal (Figure 8(b), left); this local CPS increases with crystal grow (indicated by the arrow connecting B1 to B2 in the phase diagram), as shown by the horizontal arrow, which results in the formation of a  25 concentrated polymer phase around the crystal. The concentrated polymer phase vitrifies to form a glassy shell that surrounds the solvent crystal and restricts further crystal growth when the arrow meets the Tg line (point B2) (Figure 8(b), right). According to the proposed mechanism, the uniform polymer solution results in co-continuous phase separation of the solvent crystals and the glassy polymer shell between the crystals; we assume local mass balance between the solvent crystals (CPS = 0) and the glassy polymer shell (CPS on the Tg curve) when this phase separation occurs locally, as indicated by the hatched regions in Figure 8(b). As a result, the difference in the CPS of the initial solution and the CPS on the Tg line at the crystallization temperature determines the crystal size. A high initial CPS results in a small increase in the local CPS, which causes the concentrated polymer phase to readily vitrify, thereby reducing solvent crystal size and generates small mesopores upon solvent removal. Based on the proposed mechanism, we considered a simple geometric model for the crystallization-driven phase separation process and quantitatively calculated pore size (see details in the Supporting Information, Figures S3 and S4). The dpeak values determined for the mesoporous polystyrenes obtained using DMF roughly agree with the pore sizes calculated by the model (Figure 5(d)).   26  Figure 8. (a) Proposed crystallization pathways (route A and route B) schematically illustrated on the temperature–concentration phase diagram (Figure 7(b)). Route A represents the ice-templating method that typically relies on slow freezing at low CPS (see Figure 2(a)), while route B represents our flash freezing method that relies on flash freezing at high CPS (see Figure 2(b)). (b) Schematically illustrating the nanocrystallization process highlighted by the horizontal arrow (B1 to B2) in panel (a). A large number of crystal nuclei are simultaneously generated at low temperature (i.e., at point B1) and grow slowly as the polymer concentrates around each crystal. The polymer concentration between crystals increases to that on the glass transition line (i.e., at point B2) and crystal growth is prohibited by the formation of a glassy shell of the highly concentrated polymer solution. Due to the mass balance of the polymer, two hatched regions in the lower panel have the same area. We fabricated 62 porous polystyrenes using 13 good solvents and a 5–40 wt% CPS range to comprehensively demonstrate the influence of both CPS and solvent on mesoporosity. The porous  27 structures were characterized by SEM and N2-adsorption studies, the results of which are summarized in Table S1. In addition to uniform mesopores and macropores, we found additional unique morphologies, including hierarchal porous structures consisting of mesopores and macropores, and one with a bimodal mesopore distribution. The four types of porous structure are presented in terms of their SBET-dependent Vmeso and Vtotal values (Figure 9(a)). Despite slight data-point variations, Vmeso was observed to generally increase with increasing SBET. The largest Vmeso value of 1.78 cm3/g was found for oXy-30, and corresponds to an apparent porosity of 65%. In addition, the largest SBET value of 328 m2/g was recorded for mXy-20. The cross-sectional SEM images of oXy-30 and mXy-20 confirm the presence of numerous mesopores (Figure 9(b)). Furthermore, 14 macroporous polystyrenes are located in regions that correspond to small SBET and Vmeso values, and are clearly separated by other mesoporous polystyrenes. Because the three types of mesoporous polystyrene overlap in the SBET – Vmeso plot, they were classified using additional morphological information based on SEM and pore-size data obtained from N2-adsorption studies. Uniform mesopores are characterized by SAXS and mechanisms for the formation of the structures containing hierarchical pores and bimodal mesopores are discussed in the following sections.  28  Figure 9. (a) Relationship between the SBET and Vmeso values of 62 porous polystyrenes prepared using 13 different solvents and CPS = 5–40 wt%. The solid line represents the fitted curve: Vmeso = 1.24 × 10−5 (SBET)2 + 8.26 × 10−4 (SBET). The four porous structures are represented by different symbols: squares = uniform mesopores, crosses = macropores, triangles = hierarchal pores, and circles = bimodal mesopores. (b) Cross-sectional SEM images of oXy-30 and mXy-20.  Confirming uniform mesopores by SAXS Mesoporous polystyrenes with uniform pore-size distributions were prepared by selecting appropriate solvents and CPS values. Their mesopore size distributions were analyzed by N2-adsorption (Figure 10(a)), and the relationship between Vmeso and dpeak is shown in Figure 10(b). The formation of uniform mesopores was confirmed by SEM (Figure S5), and the SAXS profile of each mesoporous polystyrene revealed a single peak that originates from its structural  29 periodicity (Figure 10(c)). The characteristic mesopore size of each polymer (dSAXS) shows a close correlation with dpeak determined by gas adsorption (Figure 10(d)), which indicates that structural periodicity is related to mesopore size and confirms that uniformly sized pores are distributed throughout the bulk specimen.  Figure 10. (a) Cumulative pore volumes of mesoporous polystyrenes with uniform mesopores. (b) Vmeso as a function of dpeak for the mesoporous polystyrenes presented in (a). (c) SAXS profiles as functions of q. (d) Relationship between dSAXS and dpeak. The solid line highlights the close correlation between dSAXS and dpeak; i.e., dSAXS = 14.1 + 0.47 × dpeak. Hierarchical pores The porous polystyrene formed when the flash freezing method was applied to a low CPS solution occasionally presented a hierarchical structure composed of both macropores and mesopores. The macropores are clearly observable by SEM, while the mesopores were detected  30 by N2-adsorption studies (Figures 11(a) and 11(b)). For example, the SEM image of oXy-10 shows a lamellar-like morphology of thin sheets that formed slit-like macropores between sheets. cHxone-10 exhibited a sponge-like morphology with mesopores on the skeletons of the sponge; similar morphologies were also observed for oDCB-10 and CCl-10 (Figure S6). Solvents with moderate Tb/Tm ratios, such as DCE and DMAc, occasionally led to hierarchical pores at moderate CPS values (Figure S7). The process that forms hierarchal pores is shown schematically in Figure 11(c). Some solvent molecules crystallize as macrocrystals during flash freezing to low temperature; this partial crystallization was detected by DSC as a small exothermic peak upon flash freezing (Figure S8). Such crystal growth results in the retention of the remaining solvent molecules as a concentrated solution between the formed macrocrystals. Subsequent holding at a temperature near to but above Tg results in additional crystal nucleation of solvent in the concentrated solution and the formation of solvent nanocrystals between the macrocrystals. After extracting the solvent macro- and nanocrystals with cold methanol, the macropores were formed on mesoporous framework, resulting in the formation of hierarchal pores.  31  Figure 11. (a) Cross-sectional SEM images and (b) pore-size distributions of porous polystyrenes with hierarchical porous structures composed of mesopores and macropores. oXy-10: SBET = 179 m2/g, Vmeso = 0.39 cm3/g. cHxone-10: SBET = 191 m2/g, Vmeso = 0.40 cm3/g. (c) Schematic of the mechanism involved in hierarchal pore formation. The picture is consistent with the enthalpy changes of solvent crystals.  Figure 12 shows that DMAc-10 has an anisotropic macroporous morphology in which the macropores on the air side are significantly larger than those on the glass side. The skeleton has a fishbone-like morphology in the thickness direction that originates from the directional crystal growth of solvent macrocrystals, similar to that observed in previous studies.35,36 Solvent crystals therefore nucleate at the sample layer of the glass side and, due to the temperature gradient, grow toward the air side. Mesopores were observed on the walls of the framework and the hierarchal  32 pores have a large SBET of 97 m2/g and a Vmeso of 0.18 cm3/g (Figure S6), which is different to previously reported systems.   Figure 12. Cross-sectional SEM images of the DMAc-10 porous polystyrene.  Bimodal mesopores The use of a solvent with a moderate Tb/Tm ratio occasionally resulted in bimodally distributed mesopores, as evidenced by N2-adsorption studies and referred to as “bimodal mesopores.” For example, DCB (Tb/Tm = 1.77) produced DCB-30, which exhibits a bimodal pore-size distribution with peaks at 25 and 11 nm (Figure 13(a)); these bimodal mesopores were also imaged by SEM (Figure 13(b)). Similarly, NB (Tb/Tm = 1.74) gave NB-35, which exhibits bimodal mesopores with dpeak values of 33 and 11 nm, and NB-30 with bimodal mesopores at dpeak values of 37 and 12 nm (Figure 13(c)); these results are consistent with the SEM image in Figure 13(d). The bimodal mesopores are evidently different from the uniform mesopore distribution observed for  33 NB-40 as well as the macropores of NB-20. The mechanism for the formation of bimodal mesopores suggests that nanocrystallization is initiated twice with a delayed interval, as schematically illustrated in Figure 13(e). Initially, a small number of crystal nuclei appear sparsely due to the moderate Tb/Tm ratio; they then grow slowly in the highly viscous solution. Further crystal nuclei are generated in the concentrated solution phase in a delayed manner prior to complete growth of the initial crystal nuclei, which rapidly terminates their crystal growth due to the high CPS value. Large and small solvent nanocrystals are obtained from the initial and second sets of nuclei, respectively, at the end of the crystal-growth process. The presence of two sets of solvent nanocrystals with different sizes finally leads to a bimodal mesopore distribution.   Figure 13. Bimodal mesopores of DCB-30: (a) cumulative pore volume and (b) cross-sectional SEM image. (c) Pore-size distributions of NB-25, -30, -35, -40, and (d) cross-sectional SEM image of NB-30. (e) Schematic illustration of the two-step crystal-nucleation of solvent molecules at low temperature. The second nucleation occurs in the concentrated polymer solution phase between the initially nucleated crystals. Larger nanocrystals form from earlier nucleation, while smaller nanocrystals form from later nucleation.  34 A porous polystyrene morphology diagram is shown in Figure 14(a) based on the CPS values and the Tb/Tm ratios of the solvents, the discussion presented above, and the results summarized in Table S1.  Notably, the data for the CCl system deviates from the overall trend of the other solvents due to the significantly higher CCl density. The four types of porous morphology are mainly located in the isolated regions of the diagram. More specifically, the macroporous morphology appeared at low Tb/Tm, hierarchal pores were formed at low CPS using solvents with high Tb/Tm ratios, uniform mesopores were obtained at both high CPS and high Tb/Tm, and bimodal mesopores occasionally appeared at moderate CPS values and Tb/Tm ratios. Consequently, our flash freezing method produces a variety of pore morphologies through judicious choice of the CPS value and Tb/Tm ratio, as schematically illustrated in Figure 14(b).   35  Figure 14. (a) Morphology diagram for porous polystyrenes with respect to the CPS value and the Tb/Tm ratio of the solvent. The four types of porous structure are represented by different symbols: crosses = macropores, triangles = hierarchal pores, circles = bimodal pores, and squares = uniform mesopores. (b) Schematic representation of the morphology diagram.  CONCLUSION  36 We demonstrated that the flash freezing method can be used to fabricate mesoporous polystyrenes in a template-free manner. The solvent effect was comprehensively investigated using 13 good solvents for polystyrene, and the effect of CPS was also evaluated. The crystallization behavior of each solution was explained on the basis of the obtained phase diagram and crystallization kinetics. Three key factors were found to be responsible for generating mesoporous polystyrenes with narrow pore-size distributions: (1) flash freezing, (2) a high CPS, and (3) a solvent with low kinetic crystallizability, which correlate well with a high solvent Tb/Tm ratio, as previously suggested by research into glassy materials. These factors prevent unintentional crystallization during flash freezing to a low crystallization temperature and enable the solvent to crystallize at a low temperature, ultimately leading to the formation of mesopores. In contrast, solvents with low Tb/Tm values only generate macropores, with morphologies similar to those produced by the previously reported ice templating and solvent casting methods. A low CPS frequently led to hierarchical structures composed of mesopores and macropores, while moderate CPS and Tb/Tm values occasionally formed bimodal mesopores. The abovementioned three factors distinguish this method from conventional ice templating and freeze casting methods. Therefore, the selection of a good solvent in addition to an optimal polymer concentration can lead to desirable porous structures with sophisticated designs, aided by a morphology diagram based on the solvent Tb/Tm ratio and the CPS value. The obtained results enable the processing parameters required to produce hierarchal pores to be extended using a solvent mixture with either low or high Tb/Tm value. Hierarchal pores can also be fabricated using the flash freezing method by implementing other well-established methods for macropore design. We expect that the flash freezing method developed in this study will also be applicable to polymer solutions retained in porous media, such as nonwoven sheets and  37 macroporous sponges, which will ultimately lead to the production of mechanically-strong mesoporous composites. The developed method is expected to provide nanoparticle-functionalized mesoporous polymers using polymer solutions of metal, carbon, or inorganic nanoparticles; such polymers are promising materials for energy, environmental, and biomedical applications. We are currently exploring novel applications of the flash freezing method and will report the results in due course.  ASSOCIATED CONTENT Supporting Information: SEM images and pore-size distributions of mesoporous polystyrenes, data for Diox and pXy solutions, numerical calculation of mesopore size, DSC profiles of 10- wt% polystyrene solutions following flash freezing, tabulated pore properties of porous polystyrenes prepared in this study.  AUTHOR INFORMATION Corresponding Author *To whom correspondence should be addressed: SAMITSU.Sadaki@nims.go.jp Present Addresses †Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, 138634 Singapore  Author Contributions  38 S.S. and I.I conceived the concept of flash freezing. S.S. conducted the experiments, analyzed the data. S.P. and H.Y supported the SAXS. S.S. and I.I. wrote the manuscript. All authors have given approval to the final version of the manuscript.  ACKNOWLEDGMENT The authors are grateful to Prof. Masanobu Naito of NIMS for instrumental support. SAXS was performed with the approval of the Photon Factory Program Advisory Committee (Proposal No. 2018G019). S.S. acknowledges financial support provided by JSPS KAKENHI Grants JP26410230, JP17K06007, and 21H02006. S.P. acknowledges a NIMS Junior Researcher Research Fellowship (2017–2018).   REFERENCES  (1)  Notario, B.; Pinto, J.; Rodriguez-Perez, M. A. 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