The Effect of Particle-Size Distribution on the Electrochemical Performance of a Red Phosphorus-Carbon Composite Anode for Sodium-Ion Batteries

Effect of Distribution on the Electrochemical Performance of a Red Phosphorus-Carbon determined that the length of time of the second milling step affects the uniformity of the carbon distribution in the composite. Photoelectron spectroscopy and transmission electron microscopy confirms the successful formation of a carbon coating, thus improving the performance of the resulting material. The RP with a Dv90 of 0.79 µm mixed with graphite for 48h delivered 1,354 mA h g -1 with high coulombic efficiency (>99%) and cyclability (88% capacity retention after 100 cycles). These results are an important step in the development of cyclable, high-capacity anodes for sodium-ion batteries. a Sodium-ion batteries will have an important role as a complement to lithium-ion in a future where lithium or cobalt, two critical elements for lithium-ion batteries, become scarce or prohibitively expensive. Red phosphorus (RP) is a promising candidate as an anode for sodium-ion batteries because of its low potential and high specific capacity. Its main disadvantage is its 490% volumetric expansion during sodiation. This leads to particle pulverization and substantial reduction of the cycle life. Furthermore, RP has an extremely low electronic conductivity of 10 -14 S cm -1 . Both issues have been previously addressed by ball milling RP with a carbon matrix. This decreases the RP particle size and also forms a more electronically conductive composite. However, it is challenging to determine the RP particle size independent of the size of the composite particles. Consequently, little is known about how much the RP particle size must be reduced to improve anode performance. Here we quantify the relationship between the RP particle-size distribution and its cycle life for the first time by separating the ball milling process into two steps. An initial wet ball milling is used to control the RP particle-size distribution, which is measured via dynamic light scattering. This is followed by a dry milling step to produce RP-graphite composites. We found that wet milling breaks apart the largest RP particles in the range of 2 to 10 µm decreases the Dv90 from 1.85 to 1.26 µm and significantly increases the cycle life of the RP. Furthermore, we determined that the length of time of the second milling step affects the uniformity of the carbon distribution in the composite. Photoelectron spectroscopy and transmission electron microscopy confirms the successful formation of a carbon coating, thus improving the performance of the resulting material. The RP with a Dv90 of 0.79 µm mixed with graphite for 48h delivered 1,354 mA h g -1 with high coulombic efficiency (>99%) and cyclability (88% capacity retention after 100 cycles). These results are an important step in the development of cyclable, high-capacity anodes for sodium-ion batteries. for


Introduction
The rate of global energy use in 2015 was about 16 TW and has been estimated to grow to about 24 TW by 2035. 1 Increasingly, this energy is stored electrochemically in batteries for transportation or later use. Deeper penetration of intermittent, renewable power sources and the wider adoption of electrified powertrains will further increase the need for high-performing energy storage. Lithium-ion batteries (LIBs) with high specific energies, rate capabilities, and cycle lives, are today the most promising candidates for these and other applications. [2][3][4][5][6] However, two critical elements in LIBs, lithium and cobalt, suffer from substantial price and availability concerns. 7,8 These two elements are distributed unevenly around the globe; interruptions in their supply line can lead to prohibitive spikes in materials cost or their total, if temporary, unavailability. In the case of cobalt, analyses have even shown that the total known cobalt reserves may be inadequate for future energy storage needs. 9 For these reasons, a complementary technology with comparable performance, but built from inexpensive and widely available materials, is desirable. Sodium-ion batteries (SIBs) are one such technology. 10,11 Their operation and manufacturing process are largely similar to LIBs, but the charge-carrying lithium is substituted with sodium, a ubiquitous element. One major obstacle to SIB deployment is the development of suitable electrode materials. While cathode materials like the cobalt-free transition metal oxides [12][13][14] have been adapted from LIBs into viable positive electrodes in SIBs, the most common LIB anode, graphite, is unusable in SIBs because of the instability of the Na-C intercalation compound. [15][16][17] Hard carbon is a candidate negative electrode for SIBs. 18 It can reversibly (de)insert sodium ions at a low potential. However, the rate capability of this material is limited, and the large surface area produces a high irreversible capacity, mostly due to the formation of the solid-electrolyte interface (SEI). 19 Furthermore, it has recently been shown by Passerini and colleagues that the specific capacity of hard carbon (about 300 mA h g -1 ) is too low for SIBs to achieve performance or cost competitiveness with LIBs 9 . Their modelling suggests that SIB viability requires a long-lasting anode with a specific capacity above 900 mA h g -1 . Therefore, the development of an inexpensive, scalable, and highperforming anode material remains an unsolved challenge. 20,21 Phosphorus is a promising candidate because of its low potential of about 0.4 V versus Na + /Na and its ability to store up to three sodium ions per phosphorus atom to form the alloy Na3P, delivering a high theoretical specific capacity of 2,596 mA h g -1 . 22,23 While phosphorus exists as several allotropes, most are either too toxic or expensive for use as battery materials. For instance, white phosphorus is notorious for its violent reactivity in air. The allotrope red phosphorus (RP), however, is both inexpensive and stable in air up to 260 °C, at which point it auto-ignites. The sodiated alloy can react with water to produce toxic gases, but it is safe under the normal, anhydrous operating conditions inside a battery. Despite these advantages, RP has a very poor electronic conductivity (10 -14 S cm -1 ) and undergoes substantial volume expansion of over 490% during the alloying reaction, which leads to pulverisation of the particles, rapid capacity fade, and low coulombic efficiency. 24 These issues have been addressed previously by ball milling RP with a carbon additive to (1) reduce the RP particle size and (2) produce a RP-carbon composite with much higher electronic conductivity. [25][26][27][28][29][30][31] However, this method precludes the determination of the RP particle size independently of the particle size of the RP-carbon composite. The statistical distribution of the particle sizes in a material can be probed via dynamic light scattering (DLS), but DLS cannot distinguish between the RP and the carbon particles.
Here we separate the milling process into two steps, which allows us to determine the RP particle-size distribution. In the first step, the RP is wet milled to reduce the particle size, after which the product's particle-size distribution is measured via DLS. This step allows us to control the particle size of the RP that will be used to form the composite. The conductive composite is formed in the second step by dry ball milling a mixture of the RP of a known particle-size distribution with graphite. This second step is operated using a smaller number of bigger balls to prevent further reduction of the RP particle size. 32 The RP and the composite are characterized physically and electrochemically via DLS, X-ray diffraction, Raman spectroscopy, both scanning and transmission electron microscopy, synchrotron-based energy-tuned photoelectron spectroscopy, and galvanostatic cycling. The data allow us to quantify the relationship between RP particle-size distribution and improved cycle life of the RP-carbon composite anode. We show that breaking the largest particles (in the range of 2 -10 µm) is necessary to prevent the characteristic capacity loss associated with pulverization of the RP particles.

Experimental Section
Particle size control and composite preparation Control of the RP particle size was investigated by ball milling 3.4 g of commercial RP (Fisher, -100 mesh, 98.9%) in a zirconium oxide jar (Fritsch Pulverisette Premium 7) with 10 mL of ethylene glycol (Sigma Aldrich, 99.8%) in argon atmosphere using a milling frequency of 500 rpm. The volume of the jar was 45 mL and 180 zirconia balls (⌀ = 5 mm) were used. The ball to weight ratio used was 70:1. Samples were collected from the mill at increasing milling times, then washed 3 times by centrifugation at 14,000 rpm using equal volumes of water and ethanol. Finally, the material was dried overnight at 60 °C under vacuum. This RP was mixed with graphite (TIMCAL, SFG 6) with a 7:3 ratio using a ball-milling procedure (Retsch PM100). A stainless-steel jar (12 mL) and 5 balls (⌀ = 10 mm) were used. The ball to weight ratio was 20:1. The milling was operated in argon atmosphere using a milling frequency of 500 rpm.

Structural and morphological characterization
The ball-milled RP was characterized using a Rigaku Smartlab 9 kW diffractometer with a Cu source to acquire the X-ray diffraction (XRD) patterns. The particle size of the RP was checked with a Malvern Mastersizer 2000 DLS analyzer. The sample is first dispersed in water using a probe sonicator to destroy aggregates. The dispersion is then added to the tank of the DLS analyzer where a He/Ne laser (633 nm) and a diode laser (466 nm) are both used to determine the particle size distribution. A Zeiss Merlin scanning electron microscope (SEM) was also used to analyze the particle size. A built-in Oxford Instruments X-Max 150 Energy dispersive X-ray (EDX) was used to analyze the elements distribution in the sample. For the cross-sectional analysis, samples were cut using a precision etching and coating system II (PECS) Gatan, using an argon ion beam. A JEOL 3000F Field emission gun transmission electron microscope (TEM) was used to check the composites. A Renishaw InVia Raman Microscope was used to acquire the Raman spectra, using a 785 nm diode laser.

Photoelectron spectroscopy measurements
Energy-tuned photoelectron spectroscopy measurements (PES) were made at the Surface and Interface Structural Analysis beamline (I09) at Diamond Light Source (Oxfordshire, UK). The composite electrode was mounted on a copper plate using copper tape and loaded onto the end-station at the synchrotron. Hard X-ray photoelectron spectroscopy (HAXPES) was performed using excitation energies of 2350 eV and the 3 rd order light 7050 eV, monochromatized by a Si(111) doublecrystal monochromator. Soft X-ray photoelectron spectroscopy (SOXPES) measurements were made at 1090 eV on a branch of the beam line that uses a plane grating monochromator. The beam was spread out using defocused settings to minimize radiation damage; the spot at the sample is estimated to be approximately 300 μm (H) and up to 1 mm (W). No charge neutralizer was used during the measurements. A hemispherical VG Scienta EW4000 analyser set to a pass energy of 50 eV for 1.09 keV soft X-rays, 70 eV for 2.35 keV and 200 eV for 7.05 keV was used to record spectra. Binding energies were calibrated to the C=C sp 2 peak, from the carbon black in the electrodes, at 284.2 eV in the C 1s spectra. The software package CasaXPS was used for analysis of photoelectron spectroscopy data. To fit the peaks, a Shirley background was used and the Gaussian/Lorentzian peak shape GL(30) was used throughout the fitting. The probing depth was calculated using the TPP-2M equation for both the phosphorus and the carbon.

Electrochemical measurements
Galvanostatic cycling with potential limitation (GCPL) was performed using CR2032 coin cells assembled in an argon filled glovebox (H2O < 0.5 ppm, O2 < 0.5 ppm), with sodium metal (⌀ = 12 mm) acting as both the counter and the reference electrode. A glass fibre (Whatman) disk (⌀ = 16 mm) was used as the separator. The working electrodes were prepared mixing the active material with Super P carbon (TIMCAL carbon black Super P) and polyacrylic acid (Sigma Aldrich, Mw ~450000 Da) in the weight ratio 8:1:1, respectively. This mixture was dispersed in N-Methyl-2-pyrrolidone to prepare the slurry which was cast onto a copper foil using a doctor blade. The casting was first dried in the fume hood, then dried under vacuum at 100°C overnight. Disks of 10 mm diameter were punched out, each of them having an active material loading of phosphorus of about 1 to 1.2 mg cm -2 . The electrolyte used for the electrochemical tests was a solution of 1 M sodium hexafluorophosphate (NaPF6) in EC:DEC 1:1 v/v with 10% fluoroethylene carbonate (FEC) as additive. GCPL was performed between 0.01 V and 1.0 V versus Na + /Na. Coin cells were fabricated in triplicate and tested according to identical charging protocols.

Results and Discussion
Reduction of the red phosphorus particle size In the first step (Scheme 1, yellow arrows), commercial RP is ball milled in ethylene glycol (EG) under argon in a zirconium oxide jar to decrease the particle size. EG was added for four reasons. First, it prevents oxidation of the phosphorus. Second, its high viscosity decreases the impact energy of the balls, which can convert the material to a different allotrope called black phosphorus, with different electrochemical properties from the RP. 26,33 Third, it prevents the reaggregation of secondary particles. Fourth, its high boiling point (197.3 °C) reduces the risk of overpressure inside the jar due to the evaporation of the solvent. In Figure 1a, the evolution of the particle-size distribution of the RP during milling, as determined by DLS, is shown. To understand how the milling is affecting the particle size, we also use the Dv90 value, defined as the diameter at which 90% of the particles (by volume) has a diameter less than that value. When commercial RP is milled with EG, its Dv90 (12.49 µm) rapidly decreases to 2.75 µm (t1 = 6h), and finally achieves 0.79 µm at t1 = 60h (Figure 1b). The addition of EG significantly speeds the milling process; after 24h milling without solvent the Dv90 fell to 10.53 µm versus 1.13 µm in the presence of EG ( Figure S1). Water was also tested as the solvent, and the results show that it also accelerates the milling process ( Figure S1). However, its low viscosity, high dielectric constant and chemical reactivity with RP led to the introduction of impurities such as phosphates and zirconium oxide from the jar, as shown in the X-ray diffraction (XRD) pattern in Figure S2. The morphology of the RP particles was probed using scanning electron microscopy (SEM). Figure S3a shows the commercial RP in which particles larger than 1 µm are visible. At t1 = 60h ( Figure S3b), the material shows particles smaller then 1 µm, although they tend to aggregate into secondary particles few µm in size. The ball milled RP is mixed with a carbon additive (Scheme 1, step 2) to form a matrix with a higher electronic conductivity than the RP alone. It is paramount that in step 2 the RP particle size is not affected. To minimize further decrease in the RP particle size, we used a smaller number of larger balls. 32 To ensure that all the capacity measures in later electrochemical tests was from the RP (and not the carbon additive), graphite was chosen because it does not intercalate sodium. However, it does have high electrical conductivity, lubricating properties (which mitigate further pulverization of the phosphorus particles), and the ability to exfoliate to form graphene layers when ball milled. 34 A 7:3 mass Figure 1. a) The particle-size distributions of the ball-milled RP shift left (to smaller primary particle sizes) relative to the commercial RP with increasing milling time. After 12 h the particle-size distribution moves to smaller size, with mode of about 0.6 µm. After 18 h, the mode is almost unchanged (0.55 µm), but most particles in the range 2 -10 µm have been broken apart. After 60 h, the particle-size distribution further shifts to smaller particles size, showing a mode of about 0.30 µm. b) The Dv90, as determined by DLS, falls rapidly as a function of milling time in the EG solvent. Scheme 1. Shown here is a schematic of the division of the milling procedure for preparing the RP-carbon composite. In the first step (gold arrows), commercial RP is wet ball milled in EG for time t1 to reduce the particle size, which mitigates pulverization on sodiation. Milling the RP alone allows for the accurate measurement of its particle-size distribution before formation of the composite. In the second step (silver arrows), the RP from step one is combined with graphite in a 7:3 ratio and dry ball milled for time t2 to form an electronically conductive RP-carbon composite suitable for use as an anode. ratio of RP to graphite is used to increase substantially the electronic conductivity of the composite. 28 The composite was prepared by simple dry ball milling.

Electrochemical performance: particle size
To understand how the particle-size distribution affects the electrochemical properties of the RP-carbon composite, three separate composites were prepared from RP samples that were wet milled for 12, 18, and 60h, which had approximately evenly spaced Dv90 values of 1.85, 1.26, and 0.79 µm, respectively. The samples were mixed with graphite for 24h and the composites were tested in coin cells with sodium metal as the counter (and reference) electrode. We would like to reiterate how measuring the RP particle size in the composite is very challenging, due to the overlap between the RP and the graphite particle size distributions. In Figure S4 we show the particle-size distribution of the three composites. Aggregates form and there is no indication of the presence of particles smaller than the initial RP particles (that is, it is unlikely that the RP particle size is further reduced in the second milling step). In Figure 2a-c, the galvanostatic profiles of the three composites tested at C/15 are shown. The plateau at about 0.2 V is due to the reduction of RP to Na3P which leads to the volume expansion of the RP particles. During desodiation, the alloy is oxidized at about 0.6 V to produce amorphous phosphorus. The evolution over many cycles of the capacity and the relative coulombic efficiencies are shown in Figure 2d,e. The sample with a Dv90 of 1.85 µm shows a capacity of about 1,224 mA h g -1 on the first desodiation and retains almost the same capacity for 20 cycles before abruptly decreasing and delivering 376 mA h g -1 after 50 cycles. This behaviour is well documented and is usually attributed to pulverization followed by electronic isolation of the particles. 26,27 On the other hand, smaller particles showed improved cycle life and no sudden capacity loss as when big particles are used. This can be explained with a reduced amount of stress in smaller particles during the alloying process, thus mitigating the pulverization of the particles. In particular, the material with Dv90 of 1.26 µm shows a superior cycle life. It is important to note that the particle-size distribution of RP used to make this electrode and the one with Dv90 of 1.85 µm both have a mode at about 0.55 µm (Figure 1a). However, further ball milling of the material for a total of 18h allowed to break apart particles in the range 2 -10 µm, leaving the mode of the particle size essentially unchanged. This resulted in a material with a longer cycle life, retaining 67% of the initial capacity after 100 cycles. The reduction of the particle-size distribution to a Dv90 of 0.79 µm substantially changed the position of the mode of the distribution to about 0.30 µm. This however, resulted only in an increase in capacity of the electrode material, but left the cycle life similar to when the RP with Dv90 of 1.26 µm is used. This shows that the breaking of particles bigger than 2 µm plays an important role in increasing the cycle life of the composite. All three samples have low first-cycle coulombic efficiencies of around 70%. This is primarily due to the build-up of the solidelectrolyte interphase (SEI). Generally, the amount of SEI increases with the surface area of the material. In this case, the coulombic efficiencies were similar despite the different sizes and surface areas of the primary particles because of the formation of agglomerated secondary particles with roughly equivalent surface ( Figure S3b). Although the increased cycle life can be attributed to the smaller particle size that reduces the effect of the pulverization of the particles this does not prevent the volume expansion of the material, as shown in Figure S5. To study the rate capability of the composites, they were cycled at different currents. The specific capacity decreases as the rate increases from C/20 to C/5 for the samples with the smallest and largest particles. The sample with intermediate particle-size distribution, however, remains nearly constant. All three samples have good capacity retention at these rates. At C/2 and 1C, the specific capacity continues to decrease for all the samples. At C/2 the sample of intermediate particle-size distribution has good capacity retention, but the capacity retention for the other two samples is very poor. At 1C the capacity retention is poor for all three samples. This capacity decay is related to the electronic conductivity of the materials.

Electrochemical performance: red phosphorus-carbon mixing
The effect of t2 (the mixing time to form the composite) on the electrochemical performance was also studied. The smallest RP sample (Dv90 = 0.79 µm) was mixed with graphite for 1, 24, and 48h. This material was chosen because it exhibited the highest capacity in the previous experiment. In Figure 3a-c the galvanostatic profiles of the three composites tested at C/15 are shown. The composite ball milled for 1h shows a poor cycle life, delivering only 20.9% of the initial charge capacity after 20 cycles. The composite ball milled for 48h, however, shows a charge capacity on the first cycle of 1,354 mA h g -1 and a high capacity retention after 100 cycles, delivering 88% of the initial capacity with a coulombic efficiency above 99%, as shown in Figure 3d,e. These samples deliver most of the initial capacity at C/5, but a slow capacity decay is observed when higher rates are used (Figure 3f). The decay is related to the electronic conductivity of the material, that limits the capacity at higher C-rates. This did not damage the material, though, as the composite was able to deliver its full capacity again when returned to cycling at C/10 after the high-rate test. The origin of the superior cycle life of the composite was investigated using several characterization techniques. The comparison between the electrodes made with the three composites ( Figure 4) demonstrates that the mixing of the components improves with time, leading to a more uniform and homogeneous composite for increased electronic conductivity.
XRD shows that after 48h of milling, graphite peaks are still clearly visible in the composite and weak peaks from black phosphorus, produced from the conversion from RP due to the energy produced during the dry milling, are visible ( Figure S6). Transmission electron microscopy (TEM) and energy-tuned photoelectron spectroscopy (PES) were used to study the morphology of the composite. In Figure 5a, a TEM image of the composite with longer cycle life (t2 = 48h) is shown. The image shows crystal layers separated by 0.34 nm on the surface of the particles. This separation is consistent with the spacing between graphite's (002) crystal planes, confirming that the particles' surfaces are covered by graphene layers. Figure S7 shows the elemental distribution in the composite particles, however it is unable to explain if the graphene layers have produced a carbon coating on the phosphorus particles. Raman spectroscopy of the composite clearly shows the D and G bands of graphite, but no bands from the phosphorus, thus suggesting the presence of a few layers of graphene coating the phosphorous particles ( Figure S8). PES at three different photon energies (1.09, 2.35 and 7.05 keV) was performed on the same composite to gather information about the chemical bonding at increasing probe depths. In Figure 5b, the ratio between the integrated area of the peaks fitted in the P 2p region (Figure 5c) is shown. The P-O and P-C bonds at 133 eV and 130.1 eV, respectively, 35,36 constitute a substantial fraction of the surface spectrum intensity. The P-O bonds arise from oxidation on the surface of the phosphorus particles due to exposure to air during the electrode casting, while the P-C bonds are observed between the phosphorus particles and the carbon coating. The presence of P-C bonds is also confirmed in the C 1s region ( Figure S9). A small amount of PH3 bonding, arising from the partial reduction of P by water, 37 is seen on the surface. As the probe depth is increased, producing a signal more representative of the bulk, the P-P bond character increases, while the P-O and P-C bonds decrease. This further confirms the presence of a carbon coating on the surface of the phosphorus particles.

Conclusions
In this work, we investigated how the particle-size distribution of RP affects the performance of composite anodes for SIBs. We separated the ball milling procedure for the composite preparation into two steps. First, we used a wet milling to reduce, control, and measure the RP particle-size distribution. The composites were prepared by dry milling these RP particles of known size distribution with graphite. We found that the material with a Dv90 of 1.86 µm has a short cycle life (significant capacity fade after 20 cycles) due to the pulverization of the particles during the alloying. Further ball milling of the RP for a total of 18 h breaks apart particles in the range 2 -10 µm, thus reducing the Dv90 to 1.26 µm, while leaving the mode of the distribution almost unchanged (about 0.55 µm). This material resulted in an anode with substantially improved cycle life, retaining 67% of the initial specific capacity after 100 cycles. Longer milling time beyond 18h further reduces the particle size of RP, but this only results in an increase in specific capacity without significant improvement to the cycle life. This suggests that breaking the particles in the range 2 -10 µm is critical to mitigating the pulverization and subsequent capacity loss that usually accompany the huge volume expansion during sodiation. These findings are  which graphene planes can be seen on the surface of the phosphorus particle. b) Plotting the ratio between the integrated areas of the peaks fitted on the photoelectron spectra collected from the composite versus the probing depth shows that surficial P-C chemical bonds gradually decrease while P-P bonds increase as we move deeper toward the particle bulk. The areas are calculated from the fit shown in (c-e), the photoelectron spectra of the P 2p region acquired using increasing incident radiation energy.
important to the production of RP anodes with superior cycle life Further characterization showed the presence of a carbon coating layer on the surface of the phosphorus particles caused by the exfoliation of graphite particles to graphene layers that help mitigate the low electronic conductivity of bulk red phosphorous and retain 88% of the initial specific capacity after 100 cycles. These results give important insight into the maximum particle size for developing high-performance phosphorus anodes for sodium-ion batteries.  Figure S1. DLS data were collected from the commercial phosphorus, phosphorus ball milled without the solvent, and ball milled with water and EG (t1 = 24 h) to explore wet versus dry milling and the effect of the solvent. a) The particle-size distribution shows that there is a small difference between the commercial phosphorus and the phosphorus ball milled for 24 h without solvent. The addition of water to the milling jar increased the number of small particles produced after 24 h, but some larger particles remained. The use of EG drastically reduces the particle size after 24 h. b) The Dv90 of the materials milled without solvent, with water and EG is plotted. The dry milling slightly reduces the Dv90 from 12.49 μm of the commercial phosphorus to 10.53 μm. Water as the solvent greatly reduces the Dv90 to 3.88 μm after 24 h. Milling with EG produces a material with a smaller Dv90 after just 6 h. Figure S2. XRD was performed to identify impurities introduced to the phosphorus sample during ball milling. The phosphorus ball milled without solvent shows peaks indicating the presence of the black-phosphorus allotrope. 1 The high energies involved during the milling process can provoke the conversion between allotropes. The phosphorus ball milled with water shows peaks assigned to both cubic and monoclinic phases of zirconium oxide, 2,3 the material from which the jar is made, as well as zirconium hydrogen phosphate, 4 which implies that some of the sample is oxidized in the water solvent.

Conflicts of interest
The phosphorus milled with EG shows a diffractogram that is very similar to the commercial phosphorus and shows no sign of impurities. Figure S3. SEM images of the commercial RP (a) and the RP ball milled for 60h (b). In the commercial RP, particles larger than 1 µm are clearly visible. After ball milling for 60h, the majority of the particles are smaller than 1 µm. Figure S4. DLS particle size distribution of commercial RP ball milled for 12, 18 and 60h (top), SFG 6 carbon (middle) and of the three composites prepared ball milling RP having different particle size distribution and graphite for 24h (bottom). The particle size distribution of the composites show that aggregates of various sizes are formed and it is difficult to distinguish between the RP's and the carbon's particles. Figure S5. Cross section of the electrode of the composite with the smallest particle size distribution of RP ball milled with graphite for 24 h (a) before cycling and (b) after cycling. The thickness of the casting increases from 15 µm in the pristine electrode to about 50 µm after cycling. The volume expansion is most probably related to the volume expansion of the phosphorus. The cracks visible in the electrode after cycling may be related to volume expansion and contraction on cycling, but it is also possibly damage incurred during the decrimping procedure. The strings visible on top of the electrode after cycling are glass fibre from the separator. Figure S6. XRD pattern of the composite made using the RP with the smallest Dv90 and ball milled with SFG6 for 48h. At the bottom (black) the calculated pattern of black phosphorus is shown. 1 The XRD pattern of the pristine graphite (red) and the commercial RP (blue) are shown as reference. As shown in Figure S2, no impurities are introduced after the first milling step (t1 = 60 h, pink). The XRD pattern of the composite produced during the second milling step (t2 = 48 h, green) shows peaks related to graphite and weak peaks related to black phosphorus.  Figure S8. Raman spectroscopy was performed on the commercial phosphorus, phosphorus ball-milled with EG, graphite SFG 6, and the composite having Dv90 of 0.79 μm ball milled with graphite for 48 h. The ball-milled phosphorus spectrum is very similar to commercial phosphorus, confirming that the chemical and crystalline structure of the phosphorus is preserved after milling. The composite only shows the D and G bands that are related to graphite, while the peaks from phosphorus are not visible. Moreover, the G peaks shifts from 1578 cm -1 in SFG 6 to 1597 cm -1 in the composite, suggesting a decrease in the number of stacked graphene layers that are present on the material. 5