Block copolymer–based porous carbon fibers

The use of block copolymers as precursors revolutionizes the synthesis of porous carbon fibers with highly uniform pores.

Section S2. Calculation of carbon fiber porosity using geometric analysis Section S3. Calculation of carbon fiber porosity using BET analysis Section S4. Calculation of the degree of mesopore interconnectivity Fig. S1. Additional SEM images, flexibility, and size distribution of PAN-b-PMMA-CFs. Fig. S2. Thermogravimetric analysis. Fig. S3. Wide-angle XRD spectra, Raman spectra, and FFT spectra. Fig. S4. Comparison of the pore size distributions from image analysis and NLDFT fitting.
where and are the diffraction angle and the full width at half maximum (FWHM) of diffraction peaks in radians, respectively. All the calculated values of these parameters for the carbon fibers are listed in table S2.

X-ray photoelectron spectroscopy (XPS):
The chemical structures and elemental analyses of the porous carbon fibers were carried out on an X-ray photoelectron spectroscope (PHI VersaProbe III) under a pressure of 10 -9 torr. The XPS spectra were acquired using monochromatic Al K α X-ray source (1486.6 eV) at 100 W over an area of 1400 × 100 µm 2 at an incident angle of 45°. The voltage step size was 1 eV for surveys and 0.1 eV for high-resolution scans. The dwell time at every step was 50 ms. All binding energies were referenced to adventitious C 1s at 284.8 eV. The chemical states of elements in the carbon fibers were assigned based on the PHI and NIST XPS databases. The atomic fraction of each element was calculated based on the area of each fitted peak.
Physisorption analysis: The surface area, absorbed volume and pore-size distribution (PSD) of carbon fibers were determined from N 2 (77.4 K) and CO 2 (273.2 K) adsorption-desorption isotherms using a Micromeritics-3Flex surface characterization analyzer. The surface area was calculated using a Brunauer-Emmett-Teller (BET) method in the linear range of P/P 0 = 0.01-0.1.
The total pore volume was measured using a single point absorption at P/P 0 of ~0.99. The PSD was determined using non-local density functional theory (NLDFT). The micropore surface area and volume were calculated using the t-plot method (Harkins and Jura thickness equation) within the thickness range of 3.5 to 5.0 Å. Since the contribution from macropores was negligible for most carbon fibers (except the carbon fibers from PAN/PMMA blends), the mesopore area and volume were obtained by subtracting the micropore portions from the BET total surface area and total volume, respectively. The volume of macropores in porous carbon fibers derived from the PAN/PMMA blends was estimated using NLDFT.

Electron Microscopy:
The as-electrospun polymer fibers, the oxidized fibers, and the pyrolyzed carbon fibers were imaged using a field-emission scanning electron microscope (SEM, LEO Zeiss 1550) at an acceleration voltage of 2 kV and a working distance of ~2-4 mm. The high-resolution transmission electron microscope (TEM, FEI Titan 300) operating at 300 kV was used to image the carbonaceous structures of carbon fibers.
Raman analysis: Raman spectra were obtained on a Raman spectrometer (WITec alpha500 in combination with a Confocal Raman Microscope) in the range of 1000-1800 cm -1 at a laser excitation wavelength of 633 nm.
Small angle X-ray scattering (SAXS): SAXS was performed on a Bruker N8 Horizon (Cu K α radiation, λ = 1.54 Å) at a generator voltage of 50 kV and a current of 1 mA. The Porod analyses were performed in the high-q range to extract the power index (x) of the Porod's Law, I ~ q x . The extracted power indices are listed in table S2.

Contact angle measurement:
The contact angles of porous carbon fiber mats were measured on a goniometer (KINO Industry Co. Ltd.) using a solution of 6 M KOH as the liquid of interest. The droplet size was set to be ~8-10 μL for consistency of the measurements.

Four-point probe measurement:
The bulk resistivity of carbon fiber mats was measured using a four-point probe system (JANDEL RM3-AR). The bulk resistivity ( , Ω·cm) is described as where S is the probe spacing (0.1 cm), V is the voltage (V) and I is the current (A).

Section S2. Calculation of carbon fiber porosity using geometric analysis
If the polymer fibers are fully consolidated to non-porous carbon fibers (NPCF) after pyrolysis, the diameter of the resulting non-porous carbon fibers can be estimated based on the densities of the polymers and carbon, the volumes of the polymer and carbon fibers, and the carbon yield (30.5%, as measured with thermogravimetric analysis (TGA)). In principle, the total mass of carbon should be balanced as follows where the volume of the polymer fibers can be calculated assuming a fiber length of and the volume of the non-porous carbon fibers can be similarly calculated assuming a fiber length of where , , , and are the density, diameter, length, and volume of the block copolymer fibers, respectively; , , , and are the density, diameter, length, and volume of the non-porous carbon fibers, respectively.
According to the SEM images, the average diameter of PAN-b-PMMA fibers is 911 ± 122 nm.
The densities of the polymer and carbon are 1.18 and 2.25 g/cm 3 , respectively. Assuming the length of fibers remains the same before and after pyrolysis ( ≈ ), the diameter of non-porous carbon fibers can be estimated as follows According to the SEM images, the measured diameter of the porous carbon fibers ( ) is 519 ± 96 nm. Thus, the porosity (∅ ) of the porous carbon fibers (PCF) can be estimated by the fraction of pore volume in the measured carbon fibers, as follows where is the volume of non-porous carbon fibers.

Section S3. Calculation of carbon fiber porosity using BET analysis
In addition to the geometric analysis, Brunauer-Emmett-Teller (BET) measurements can also be where is the total pore volume of PAN-b-PMMA-CFs measured by BET (as shown in table S2), is the total carbon volume based on carbon density (2.25 g/cm 3 ). The porosity of PANb-PMMA-CFs after pyrolysis at 800 °C was calculated to be ~50.6%, in excellent agreement with that determined using the geometric analysis (50.8%).

Section S4. Calculation of the degree of mesopore interconnectivity
Since the pyrolysis of PAN contributes little to the mesopore volume, as evidenced by the poresize distributions (PSDs) of PAN-CFs (Fig. 3D), we assume that the mesopores mostly arise by the removal of PMMA. In addition, assuming that all mesopores generated by PMMA are interconnected, we can calculate the theoretical total mesopore volume using the mass fraction of PMMA ( PMMA ). PMMA can be determined using the following equation where ,PMMA and ,PAN are the number-averaged molecular weights of PMMA and PAN, respectively, as determined by SEC.
In 1 g of PAN-b-PMMA, the mass of PMMA is PMMA = BCP × PMMA = 1 g × 35.8% = 0.358 g where BCP is the total mass of PAN-b-PMMA. Note that the mass of the block copolymer is arbitrary and its value does not alter the final conclusion. We chose 1 g for simplicity.
Converting PMMA to volume, we have where the density of PMMA is PMMA = 1.18 g cm −3 . The char yield of PAN-b-PMMA is 30.5% according to TGA ( fig. S2A). Thus, the carbon from 1 g of PAN-b-PMMA is = 30.5% × 1 g = 0.305 g Because the block copolymer fibers shrink significantly after pyrolysis, the mesopores shrink accordingly. The percentage of the volumetric shrinkage (V shrink %) can be estimated by the difference in fiber diameters, assuming that the length of the fibers remains unchanged during the where V C , V BCP , d C and d BCP are carbon fiber volume, block copolymer fiber volume, carbon fiber diameter, and block copolymer fiber diameter, respectively. Therefore, the theoretical mesopore volume is The experimentally measured mesopore volume (V mesopore,exp ) is 0.310 cm 3 g -1 (  During oxidation, PAN self-stabilized and crosslinked into a ladder molecular structure, which was critical to maintain the integrity of the fibrous structures after pyrolysis. In addition, due to the microphase separation of PAN and PMMA, the PAN-b-PMMA block copolymer selfassembled into well-defined nanostructures.    S4D. Assuming that the pore openings are circles, the pore sizes (d) can be calculated from the pore areas (S) according to the following equation The Barrett-Joyner-Halenda (BJH) model is also commonly used for fitting mesoporous structures, and thus it is used to analyze the porous structures of our PAN-b-PMMA-CFs. As shown in fig. S4F, the PSD curve of PAN-b-PMMA-CFs obtained from the BJH model is similar to that from the NLDFT model in the pore size range >4 nm. The two fitted PSDs differ in the pore size range <4 nm. The shoulder peak at ~3-4 nm is absent in the PSD from the BJH model.
Because the PSD from the NLDFT model matches with that from the image analysis, we have chosen NLDFT as the final model for pore size determination. to both the carbon surface (double-layer capacitance, CPE1) and the heteroatoms (pseudocapacitance, CPE2). Thus, the Warburg impedance (W 0 , the ion diffusion resistance) and the equivalent series resistance (R s , the combination of the electrolyte resistance, the internal electrode resistance, and the interface resistance between the electrodes and the current collectors) are placed in series with the two capacitors, CPE1 and CPE2. Note that CPE1 is parallel to CPE2 because of their independent charge storage processes. For the pseudocapacitance CPE2, the redox electrochemical reaction is controlled by the kinetics of the charge transfer at the electrodeelectrolyte interface, in other words, how fast the charges are transferred from the electrolyte to the electrode surface. Therefore, a charge transfer resistance (R ct ) is connected in series with CPE2 to describe the charge storage process associated with the heteroatoms.

Trasatti's Method
We analyzed the CV curves and the corresponding gravimetric capacitances (C) of PAN-b-PMMA-CFs at scan rates ranging from 2 to 100 mV s -1 . The reciprocal of gravimetric capacitances (C -1 ) should scale linearly with the square root of scan rates ( 0.5 ), assuming ion diffusion follows a semi-infinite diffusion pattern ( fig. S6A) [J. Am. Chem. Soc. 134, 14846-14857 (2012)]. Specifically, the correlation can be described by the following equation where C T is total capacitance. Data points at higher scan rates deviate from the relationship due to the intrinsic resistance of the electrode and the deviation from semi-infinite ion diffusion [ACS Nano 7, 1200-1214 (2013)

Dunn's Method
Dunn's method enables one to differentiate quantitatively the capacitance contributions from the surface capacitive effects (i.e., EDL capacitive effects) and the diffusion-controlled processes (i.e., pseudocapacitive reactions) [J. Phys. Chem. C 111, 14925-14931 (2007)]. At a fixed potential, the current density (i) from the CVs can be expressed as a combination of two terms, i.e.
= k 1 + k 2 0.5 where the first term k 1 accounts for the current density contributed from the EDL capacitive effects while the second term k 2 0.5 is the current density associated with the pseudocapacitive reactions. Dividing 0.5 on both sides of the equation yields −0.5 = k 1 0.5 + k 2 Therefore, by reading i from the CVs at a series of scan rates and then plotting −0.5 vs. 0.5 , one expects to obtain a linear fitting line with a slope of k 1 and a y-intercept of k 2 . Fig. S6D displays an example of an −0.5 vs. 0.5 plot collected for PAN-b-PMMA-CFs using the anodic current at a potential of -0.1 V. Using the k 1 and k 2 values in Eq. (23) allows one to differentiate the capacitance contribution from C EDL and pseudocapacitance at the specific potential V and a selected scan rate, .    *The mesopore surface area and volume were determined by subtracting the micropore surface area and volume from the total pore surface area and volume, respectively. The porous carbon fibers derived from PAN and PAN-b-PMMA had negligible macropores, while those from PAN/PMMA blends contained a substantial amount of macropores, as evident in both the SEM images and the pore-size distribution profiles. Therefore, the mesopore volume of 0.311 cm 3 /g of PAN/PMMA-CFs included the contributions from both mesopores (55.4%) and macropores (44.6%). The percentages were estimated using NLDFT.