## 2 Materials and Methods  
The studied NDs were carboxylated NDs (uDiamond(r) Vox P) from Carbedoon Oy, Vantaa, Finland. According to the manufacturer, the diameter of the NDs varied between 2 and 6 nm. The other materials used in the compound and formulation are presented in Table 1.  
Elastomers and other ingredients were mixed in a Brabender 350E mixer (Brabender GmbH, Duisburg, Germany) for six minutes. The mixing sequence is presented in Table 1. The starting temperature was 50 \({}^{\circ}\)C and the rotor speed was 60 rpm. The reference compound (ND0) contained only CB as filler in a concentration of 25 phr. In other compounds, 0.5, 1, 2.5 or 5 phr of CB was replaced by the same weight amount of NDs. The name of the compounds is related to the ND loading. Curing characteristics were measured with an Advanced Polymer Analyzer, APA 2000 from Alpha Technologies (Hudson, OH, USA). The measurements were carried out at 150 \({}^{\circ}\)C for 25 min. The compounds were then vulcanized to their t'90 value, which means the time required to reach 90% of the maximum rheometric torque. The apparent crosslink densities were studied by a swelling test. Approximately 0.4 g vulcanized rubber pieces were soaked in toluene for 72 h. The apparent crosslink density was determined from the swelling coefficient by \(1/Q\):  
\[\frac{1}{Q}=\left(\frac{w_{0}}{w_{t}-w_{0}}\right)\frac{\rho_{1}}{\rho_{2}}, \tag{1}\]where \(w_{0}\) is the initial weight of the sample and \(w_{t}\) is the weight at time \(t\), \(\rho_{1}\) and \(\rho_{2}\) are densities of the solvent and unswollen vulcanizate, respectively [32]. Three measurements per compound were done and the averages and standard deviations were calculated. Bound rubber (\(BDR\)) measurements were performed by dissolving 0.2 g of uncured rubber in toluene for 96 h. Toluene was exchanged every 24 h. After immersion, the samples were dried and weighed. The \(BDR\) content was calculated by the formula:  
\[BDR\ (\%)=\frac{m_{0}-(m_{1}-m_{2})}{m_{0}}\times 100 \tag{2}\]  
\[m_{0}=m_{s}\times\frac{100}{cpd} \tag{3}\]  
where \(m_{0}\) is the rubber content in the sample, \(m_{1}\) is the combined weight of the bag and the sample, \(m_{2}\) is the weight of the dried bag and the sample, \(m_{s}\) is the weight of the dry sample, and \(cpd\) is the total amount of rubber and filler in the compound in phr [33]. Three measurements per compound were done and the averages and standard deviations were calculated. The Payne effect was studied with a dynamic mechanical analyzer (DMA, DMA/SDTA86 le from Mettler Toledo, Columbus, OH, USA). The measurements were conducted for a circular sample with a diameter of 6 mm in strain sweep from 0.5 to 1200 um with a frequency of 1 Hz at room temperature. The state of dispersion of the CB and ND particles in the compounds was investigated by scanning electron microscopy (Zeiss ULTRaplus, Oberkochen, Germany). The fracture surfaces of the tensile test specimens were coated with a thin carbon layer to ensure the conductivity of the samples. Tensile tests of the samples were carried out by testing 5 specimens/rubber compound with Instron 5967 universal tester (Instron, Darmstadt, Germany) according to ISO 37 sample type 3 [34]. Tear resistance was tested with the same equipment according to ISO 34 with trouser type specimens (3 specimen/rubber compound) [35]. The crosshead speeds for the tensile and tear tests were 200 mm/min and 100 mm/min, respectively. Wear resistance was determined with CETR UMT-2 pin-on disk (Bruker Co, Billerica, MA, USA). Rubber samples with a diameter of 10 mm were rotated on a smooth AISI304 steel plate for 60 min with a force of 40 N. The rotation speed was 60 rpm. The change in mass was measured. The mass loss was converted to volume loss using the density of the