Fractionation of block copolymers for pore size control and reduced dispersity in mesoporous inorganic thin films

: Mesoporous inorganic thin films are promising materials architectures for a variety of applications, including sensing, catalysis, protective coatings, energy generation and storage. In many cases, precise control over a bicontinuous porous network on the 10-nm length scale is crucial for their operation. A particularly promising route for structure formation utilizes block copolymer (BCP) micelles in solution as sacrificial structure-directing agents for the co-assembly of inorganic precursors. This method offers pore size control via the molecular weight of the pore forming block and is compatible with broad materials library. On the other hand, the molecular weight dependence impedes continuous pore tuning and the intrinsic polymer dispersity presents challenges to the pore size homogeneity. To this end, we demonstrate how chromatographic fractionation of BCPs provides a powerful method to control the pore size and dispersity of the resulting mesoporous thin films. We apply a distinct molecular weight and narrowed dispersity allowed us to not only tune the characteristic pore size from 9.1±1.5 to 14.1±2.1 nm with the identical BCP source material, but also significantly reduce the pore size dispersity compared to the non-fractionated BCP. Our findings offer a route to obtain a library of monodisperse BCPs from a polydisperse feedstock and provide important insights on the direct relationship between macromolecular characteristics and the resulting structure-directed mesopores, in particular related to dispersity.

To this end, block copolymer (BCP) based co-assembly represents a promising bottom-up approach to create ordered mesoporous structures with tunable size and morphology. [15][16][17][18] In the so-called persistent micelle templating method, inorganic precursors (typically sol-gel derived) are embedded into the corona of BCP micelles via preferential supramolecular interactions. [19] In a subsequent step, the hybrid composite can be transformed into an ordered inverse opal-type mesoporous structure by either thermal calcination, [19] or different physical or chemical treatments including UV-ozone degradation, [20] oxygen etching [21] or photocatalytic reactions. [22] The use of BCP as structure-directing agent offers reliable control over porosity and pore size.
While porosity is commonly tuned by the mixing ratio between organic and inorganic precursor, the pore size is predominantly determined by the molecular weight of the sacrificial block forming the micelle core, [23,24] leading to final pore dimensions in the range of 5 to 50 nm.
Several recent studies have identified the close relationship between the BCP dispersity and the size distribution of the obtained co-assembled features, [25][26][27] highlighting the requirement of precise control over the macromolecular characteristics of the structure-directing agent. In general, the synthesis of BCPs with bespoke molecular weight and narrow dispersity (Ð) is an elaborate process that involves multiple steps, some of which are furthermore difficult to control. Synthesis is either conducted by sequential addition of monomers via living/controlled chaingrowth polymerization procedures [28,29] or relies on coupling reactions between different endfunctionalized chains segments. For the former, close control must be achieved over reaction dynamics and conversion efficiency in order to obtain defined molecular weights and low polydispersity. [30] Anionic and cationic polymerization [31] as well as some types of controlled radical polymerization [32] have been successfully employed in the synthesis of low polydisperse BCPs. The second strategy requires end-group functionalization for effective coupling, e.g. via Diels-Alders, thiol-ene or cycloaddition reactions. [33] In this case, coupling reaction must be rapid and selective to ensure efficient linking between the chains. [34] In all cases, synthesis is highly sensitive to impurities and precise reactions conditions. Furthermore, adequate purification processes are necessary for the employed reagents, making the synthesis procedure overall very sensitive and time consuming. [30] Size exclusion chromatographic (SEC) fractionation is routinely applied for purifying BCPs from their side reaction products, mainly unreacted precursors or unlinked homopolymers. [35][36][37][38] More recently, Park et al. have extended liquid chromatography to the separation of BCPs in terms of its molecular weights. [39] Fractions containing polystyrene-block-polyisoprene copolymers with narrower distribution in molecular weight and chemical composition were collected using a HPLC with two separation stages, showing the great potential of this approach to obtain an extensive BCP library with reduced dispersity and synthetic effort. Further experiments have established chromatography fractionation as a reliable and effective technique to provide systematic control over the macromolecular parameters (i.e. molecular weight and polydispersity) of the BCP. [40][41][42][43] In this work, we present the application of BCP chromatographic fractionation to create tailored inorganic mesoporous thin films. Crucially, we identify the role of molecular weight, composition and dispersity on the resulting pore size distribution. We first isolate different BCP fractions from a polydisperse amphiphilic poly(isobutylene)-block-poly(ethyleneoxide) (PIBb-PEO) sample and characterize their molecular weight and composition via gel permeation chromatography (GPC) and nuclear magnetic resonance (NMR). Different BCP fractions then serve for formulation with aluminosilicate sol. After deposition, the obtained thin films are characterized in both hybrid and calcined form via grazing incidence small angle x-ray scattering (GISAXS). Atomic force microscopy (AFM) and ellipsometric porosimetry (EP) to enable a full validation of this approach.

Results and discussion
Several molecular weight (M w ) BCP were isolated following the methodology sketched in  A16 and A20 at the respective tails of the elution peak did generally not provide sufficient material to perform the macromolecular characterization, hence only fractions A17, A18 and A19 were considered for further experiments. In order to determine the composition and molecular weight of the isolated fractions 1 H NMR and GPC experiments were carried out. Figure 2B shows the GPC traces of the as-synthesized PIB-b-PEO BCP (black), and the three fractions studied during this work A17 (blue), A18 (green) and A19 (red).     Corresponding pore diameter histograms obtained by image analysis using the software Pebbles [39].
Image analysis of the topographic AFM images was carried out using the software Pebbles [45] to provide quantitative information about the in-plane pore dimension (Di-p) on the sample surface.

Counts
Pore diameter (nm) To this end, ellipsometric porosimetry (EP) has emerged as a reliable characterization technique to probe porosity, pore size and pore morphology of thin films. [46] Figure 4 (left column) shows the EP adsorption isotherms obtained for the respective samples. Please note that the films exhibited a porosity in the range of 47% to 54%. Analysis of the adsorption isotherms allowed to determine the pore radius distribution of the mesoporous thin films via a modified Kelvin equation. [47] The Isotropic Inorganic Pore Contraction model [47] was applied to calculate the inplane (D i-p ) and out-of-plane (D o-p ) pore diameter distribution (PDD) data based on the EP measurements. Figure 4 (right column) shows the PDD for the mesoporous aluminosilicate samples created using different M w BCP. the M w of the BCP used as structure-directing agent. In order to study the dependence between both parameters, the results were fitted to the following scaling law: is the pore radius, C is a constant, and N represents the degree of polymerization of each block. [48] Since, N PEO was found approximately constant for the three different fractions, the relation can be simplified as R p = C'[N PIB β ]. Indeed, a linear variation with a β = 0.8 was previously observed for excluded-volume BCP micelles, [49,50] confirming the above-mentioned scaling law (see Figure 5A). An analogous dependence of the resulting pore size with the molecular weight of one of the BCP blocks was recently observed in TiO 2 mesoporous films made from a library of poly(N,N-dimethylacrylamide)-b-polystyrene BCP synthesized via reversible addition-fragmentation chain transfer polymerization. [51] However, while previous approaches required extensive synthetic efforts to obtain a BCP library, the herein presented chromatographic fractionation enables systematic studies on structure-function relationships with from a single polydisperse feedstock with little preparative work (see Supporting Information, Figure S4).
Moreover, analysis of EP desorption isotherms provided information about the size of the narrow restrictions connecting pores within the network. [47,52,53] As shown in the Supporting Information (Figure S5), the mesoporous films prepared using the lowest M w BCP as structure-directing agent (A19) exhibited neck pores of ≈ 4.5 nm, which expanded to ≈5.8 nm and ≈ 7.3 nm for the medium (A18) and larger (A17) sized structure-directing agent, respectively. To summarize, all structural parameters obtained by the different techniques are listed in Table 3. Table 3. Structural parameters (pore center-to-center distance (d c-c ), in-plane pore diameter (D ip ), out-of-plane pore diameter (D o-p ), porosity and pore neck radius (PNR)) determined by the different techniques used during this study, i.e. AFM, GISAXS and EP.
Notably, when comparing the fractionated results to the non-fractionated BCP, a clear narrowing of the pore size distribution is apparent. In the case of the AFM results, the dispersity Đ of the surface-accessible mesopores, defined as (coefficient of variance) 2 + 1, [54] was found to be 1.08 for the non-fractionated case, which reduced as a consequence of fractionation to  Figure 5B).  While reporting of Đ is common practice in the community, it requires the population to follow a prescribed distribution. This may not be the case for mesopores, where poly-or heterodisperse pore sizes are often found [55,56] . Indeed, the pore sizes obtained by EP herein could not be precisely described by normal distributions (see Supporting Information, Figure S6).
We have recently introduced the concept of information entropy to report on nanoparticle dispersity [57] . Crucially, this approach is assumption-free and allows a reliable comparison of dispersity between different populations via a user-friendly macro. While this approach was first presented on colloidal populations, it can be equally applied to pore size or molecular weight distributions. To this end, the absolute entropy (E) results obtained herein are shown in Table S1. In the case of the BCP molecular weight, the absolute entropy value reduced from 8150 (non-fractionated BCP) to 6090 (A17), 3760 (A18) and 5490 (A19) after the fractionation.  respectively. Linear regression of both variables (Figure 5C) confirms the direct relation between the dispersity of the BCP structure-directing agent M w and the dispersity in pore size of the final inorganic porous structure. This relation was found more pronounced in the case of the EP measurements (p value = 0.049) than in the case of the AFM data (p-value = 0.205).
While the different techniques are consistent in their findings, some deviation may be related to the fact that AFM refers to the topology of a limited number of pores on the sample surface, while EP determines pore size by capillary condensation occurring in the bulk of the film. The surface topology may not necessarily be representative of the whole film. Moreover AFM lateral resolution can be affected by tip convolution effects, and therefore some discrepancies between the data obtained by the different techniques may expected. [46] . Nevertheless, a narrower M w distribution of the BCP induced in all cases a lower pore size dispersity in the final mesoporous film. This provides further evidence that the herein presented approach of BCP chromatographic fractionation not only offers a straightforward method to obtain an extensive BCP library with little synthetic effort but also reduced dispersity in inorganic mesoporous films.
We note that out approach is fundamentally different to the more common route of pore expansion by supramolecular co-assembly with swelling agents that selectively interact with the pore-forming block, e.g. benzene derivatives, [58,59] homopolymers, [52,60] carboxylic acids, [61,62] or solvents such as toluene or xylene. [63,64] In contrast to the herein presented strategy, swelling agents present multiple challenges, i.e. macroscopic phase separation, increase in the pore size dispersity, multimodal pore size distribution and a decrease in the long-range order of the structure, [65] which limits their applicability in particular when both mean pore diameter and dispersity are important.

Conclusions
Herein, we establish a route to pore size control in mesoporous inorganic thin film architectures based on fractionation by size exclusion chromatography of a polydisperse BCP. The various M w BCP fractions served for fabrication of aluminosilicate mesoporous architectures via coassembly. The combination of characterization by AFM, GISAXS and EP allowed the establishment of a close relationship between the molecular properties of the structure-directing BCP and the resulting mesoporous network, with significant variations in the center-to-center distance and pore sizes. Importantly, a close relationship between the entropic dispersity calculations of the BCP and the formed mesopores informs the relevance of polymer dispersity in the initial feedstock and highlights the relevance of the herein presented approach.

Preparation of mesoporous aluminosilicate films
Inorganic sol material and mesoporous inorganic aluminosilicate films were prepared as described elsewhere. [7,22] BCP samples were first dissolved in a toluene/1-butanol azeotrope solution before mixing with the inorganic sol in an organic/inorganic ratio of 2:8. All samples were spin-coated at 2000 rpm for 20 seconds and immediately annealed on a programmable hot plate using a ramp rate of 1°C per min to a final temperature of 130 °C for 30 minutes. To remove the organic structure-directing agent, samples were calcined in a muffle furnace at 450 °C for 1 hour.

Characterization of mesoporous aluminosilicate films
A Semilab SE2000 spectroscopic ellipsometer was used to perform spectroscopic ellipsometry (SE) and ellipsometric porosimetry (EP) measurements. All SE and EP data analysis was carried out on the Semilabs SEA software (v1.6.2). Prior to EP measurements, samples were placed on a hotplate at 120 •C for 10 minutes. This was to ensure that no residual atmospheric water molecules remained in the pores prior to measurement. EP porosity isotherms were derived from the evolution of the refractive index value as a function of relative humidity in the sample chamber. [47] Application of the Lorentz-Lorentz effective medium approximation allowed accurate determination of the overall porosity of each sample based on the change in refractive index as a consequence of capillary condensation inside the mesopores. [67] The incremental onset of capillary condensation was related to the pore diameter of the material via the Kelvin Equation [47,68] . All pore size and pore volume measurements were derived from the adsorption branches of the EP porosity isotherm and adjusted based on the assumption of an ellipsoidal pore shape which evolves with film contraction during template removal. [47] GISAXS data were acquired on a SAXSLab Ganesha wit at an incidence angle of 0.2. GISAXS data analysis was performed using FitGISAXS. Atomic Force Microscopy (AFM) images were obtained from a Bruker Dimension Icon atomic force microscope with a Bruker ScanAsyst Air probe (nominal tip radius 2 nm) in ScanAsyst mode.

Supporting Information
Additional structural analysis results using, AFM, GISAXS and EP