## 2 Materials and Methods
### Solid-State \({}^{13}\)C NMR Spectroscopy  
The standard CPMAS spectra of the pure cellulose and its biochar were obtained with a Bruker (Rheinstetten, Germany) Advance III HD 400 MHz wide bore spectrometer, using a triple resonance broadband probe and zirconium rotors of 4 mm OD with KEL-F-caps and applying a magic-angle spinning (MAS) speed of the rotor at 14 kHz. For all CPMAS spectra, a ramped \({}^{1}\)H-pulse amplitude was applied during the contact time, \(t_{\text{c}}=100\) us to circumvent spin modulation during Hartmann-Hahn condition. For the cellulose and biochar, 200 and 13,000 scans were accumulated, respectively, and the line broadening was between 0 and 50 Hz. The needed recycle delay was adjusted after determination of the \({}^{1}\)H spin-lattice relaxation time, T\({}_{\text{1H}}\), with an inversion recovery experiment. Proton decoupling during acquisition was obtained by using SPINAL-64 [26]. The \({}^{13}\)C chemical shift scale was calibrated relative to tetramethylsilane (0 ppm) with glycine (COOH at 176.08 ppm). The \({}^{13}\)C intensity distribution was determined by integrating the following chemical shift regions: alkyl C (0-45 ppm); methoxyl C (45-60 ppm); O-alkyl C (60-95 ppm); anomeric C in the pure cellulose (95-110 ppm); aryl C (95-140 ppm); O-aryl C (140-160 ppm); carboxyl C (160-185 ppm); aldehyde/ketone C (185-225 ppm).  
The solid-state 2D \({}^{1}\)H-\({}^{13}\)C HETCOR experiments with frequency-switched Lee-Goldburg (FSLG) irradiation during the evolution time were performed to correlate \({}^{13}\)C and \({}^{1}\)H chemical shifts [18]. In order to identify \({}^{13}\)C with strong dipolar interaction with \({}^{1}\)H, a short \(t_{\text{c}}=50\) us was applied. In addition, spectra with \(t_{\text{c}}=200\) and \(1000\) us were obtained for the detection of long-distance heterodipolar interactions. For the 2D spectra of the pure cellulose and the pyrochar, 128 single spectra with 16 and 700 scans, respectively, and an increment of the mixing time by 22.9 us were acquired for the data points in the \({}^{1}\)H indirect dimension and 1536 data points were used in the \({}^{13}\)C dimension. Recycle delays were adjusted according to pre-determined T\({}_{\text{1H}}\). Quadrature detection in \(\omega_{1}\) was achieved using StatesTPPI. Exponential line broadening between 0 and 50 Hz was applied to the \({}^{13}\)C dimension prior to Fourier transformation. The samples were spun at the magic angle with 13 and 15 kHz.  
T\({}_{\rm 1H}\) was approached with the inversion recovery pulse sequence using an array of up to 13 delay times between an initial 180 \({}^{\circ}\)C pulse and a final 90 \({}^{\circ}\)C pulse. Each spectrum of the set was phased and subjected to a manual baseline correction before their intensity was determined by integration of the respective chemical shift. Spinning side bands were not considered. The obtained intensities were used as raw data for interpolation using the software \"simFIT\" provided with the NMR software topspin 3.6.2.  
For evaluating if a t\({}_{\rm c}\) = 1000 \(\upmu\)s is sufficient for a complete cross polarization of all aromatic C in the pyrochar, a variable contact time experiment was performed. Here, 23 single spectra were acquired with increasing the t\({}_{\rm c}\) from 10 \(\upmu\)s to 4000 \(\upmu\)s. Afterwards, the intensity course of each chemical shift region was plotted as function of the contact time and fitted with a two component model using the program NMR-Relax version 1.010.002 (CMK, Munich, Germany) and based on equations provided by [27,28] (Table S1).