Mesoporous hollow carbon spheres for lithium–sulfur batteries: distribution of sulfur and electrochemical performance

Hollow carbon spheres (HCS) with a nanoporous shell are promising for the use in lithium–sulfur batteries because of the large internal void offering space for sulfur and polysulfide storage and confinement. However, there is an ongoing discussion whether the cavity is accessible for sulfur. Yet no valid proof of cavity filling has been presented, mostly due to application of unsuitable high-vacuum methods for the analysis of sulfur distribution. Here we describe the distribution of sulfur in hollow carbon spheres by powder X-ray diffraction and Raman spectroscopy along with results from scanning electron microscopy and nitrogen physisorption. The results of these methods lead to the conclusion that the cavity is not accessible for sulfur infiltration. Nevertheless, HCS/sulfur composite cathodes with areal sulfur loadings of 2.0 mg·cm−2 were investigated electrochemically, showing stable cycling performance with specific capacities of about 500 mAh·g−1 based on the mass of sulfur over 500 cycles.

: SEM image of monodisperse silica spheres with a solid core and a mesoporous shell. The diameter of the solid core was determined to be 380 nm by dynamic light scattering, while the diameter of the coreshell particles was about 515 nm. From SEM images a diameter of about 490 nm was determined for the coreshell spheres. Figure S2: a) Powder X-ray diffraction (XRD) pattern of silica spheres with a solid core and a mesoporous shell, b) nitrogen physisorption isotherm (measured at 77.4 K) and c) pore size distribution calculated by non-local density functional theory (NLDFT). The powder XRD pattern shows two diffraction peaks at 2 = 2.34° and 2 = 4.67°. These can be assigned to the (100) and (200) diffraction peaks of a wormlike pore structure. In literature this pattern is assigned to a hexagonal pore structure in which the (110) reflection is scarcely pronounced because of the curved shell [1,2]. From the nitrogen physisorption isotherm a surface of 404 m²/g can be determined by the Brunauer-Emmett-Teller method. The pore size distribution is narrow and centered at 3.78 nm. pore size distribution and c) cumulative pore volume. Pore size distribution and cumulative pore volume were obtained from the isotherm by NLDFT analysis. From the pore size distribution and plot of cumulative pore volume it can be seen that HCS contain a considerable amount of pores smaller than 1.5 nm. The cumulative pore volume of these small pores is as high as 0.26 cm 3 /g.

Calculation of the total possible sulfur loading in HCS
Equations derived from the formula for the volume of a sphere: Expressing the mass of sulfur by its volume V sulfur and density ρ sulfur (Equation 5) leads to Equation 6. sulfur sulfur sulfur The volume of sulfur in the case of complete pore filling can be described by the sum of the volume of all cavities V cavities in 1 g of HCS and the pore volume of the shells V pores in 1 g of HCS.
pores cavities sulfur In Equation 7 V pores is known from the calculation of the pore volume in the shell (see regular article) while V cavities can be determined by multiplication of the volume of a single cavity V i with the number of spheres N spheres in 1 g of HCS.
i spheres cavities From here on the geometry of a sphere can be taken into account. The equations that will be used are summarized in Figure S4. The volume of the inner sphere V i of a single hollow sphere is given by Equation 3. The number of spheres can be derived by dividing the volume of all shells V shells by the volume of a single shell V shell (Equation 3 in Figure S4).
shell shells spheres The volume of all shells is amounted to by the volume of the pure carbon V carbon and the volume of the pores in the shell V pores .
The volume of the carbon can be calculated from the mass of HCS m HCS and the density of carbon ρ carbon .