## 2 Materials and Methods  
The main objectives of this campaign were (i) to investigate the possibility to use constant (fixed) dilution for SPN instruments sampling directly from the tailpipe of heavy-duty engines and (ii) to monitor the fraction of sub-23 nm particles of modern heavy-duty engines. For this reason, a \"Golden\" system that was sampling directly from the tailpipe was circulated to all participating laboratories. Additional instruments that counted below 23 nm were also provided. The OEMs (original equipment manufacturers) provided the engine, the proportional partial flow dilution systems (PD) and the PMP SPN systems. The typical experimental setup is depicted in Figure 1.  
The PDs were the SPC 478 from AVL (Graz, Austria), Microtrol 6 from Nova (Roskow, Germany), PSS-20 from Control Sistem (Pianezza, Italy) and DMD from AVL. All PMP systems were the AVL particle counter (APC 489) which includes a hot dilution at 150 \({}^{\circ}\)C and an evaporation tube at 350 \({}^{\circ}\)C [21]. This configuration will be abbreviated as \"PD(ET)\". All systems were maintained and calibrated within one year from the day of the testing as required by the regulation. In addition to the internal 23 nm CPCs (model 3790) from TSI (Shoreview, MN, USA) [22; 23] included in the PMP systems, a \"Golden\" 10 nm CPC (model 3792 from TSI) was provided and connected in parallel to monitor the sub-23 nm particles [24]. The \"Golden\" tailpipe system was an APC 489 (AVL) with a catalytic stripper (CS) [25] instead of evaporation tube (ET) and a 10 nm CPC (model 3792 from TSI) internally in the device. For this reason,  
Figure 1: Experimental setup. “Golden” instruments in orange colour. CPC = Condensation particle counter; CS = catalytic stripper; ET = evaporation tube; PD = proportional partial flow dilution system; PND = particle number diluter. a 23 nm CPC (model 3790 from TSI) was also connected externally in parallel with the 10 nm CPC for this measurement campaign. This configuration will be abbreviated as \"TP(CS)\" from now on. At some OEMs a second SPN system (SPCS) was used (provided by Horiba, Kyoto, Japan) [26]. This system is a PMP system with evaporation tube at 350 \({}^{\circ}\)C and a hot dilution at 190 \({}^{\circ}\)C connected to a pre-diluter which used filtered air at approximately ambient temperature. This concept will be abbreviated as TP(cET') from now on and measured only above 23 nm. The hot dilution at 190 \({}^{\circ}\)C compared to the 150 \({}^{\circ}\)C of the \"Golden\" system should not have any effect at the results because both systems heat the sample at 350 \({}^{\circ}\)C at the next stage, so species of similar volatility will be evaporated. The catalytic stripper of the \"Golden\" system is also expected to oxidise any evaporated hydrocarbons [25]. The cold pre-diluter concept resembles more the PD(ET) as they both cool down the exhaust before thermally treating it in the PMP system. Their main difference is that the dilution is constant in the TP(cET) case, while at the PD the dilution is inversely proportional to the exhaust flow. On the contrary, the direct \"hot\" dilution of the TP(CS) avoids any nucleation and condensation to take place [12; 19]. Thus, it is possible that smaller or less particles are counted with the TP(CS) system. The measurements took place at six OEMs (one measured twice) in nine engine dynamometers from October 2018 until July 2019. The OEMs in alphabetical order were: CNH (Italy), DAF (Netherlands), Daimler (Germany), MAN (Germany), Scania (Sweden), Volvo (France). In total seven diesel and two CNG (compressed natural gas) fuelled engines were tested. All engines were Euro VI, step C or D. The diesel engines were equipped with diesel oxidation catalyst (DOC), diesel particulate filter (DPF) and selective catalytic reduction (SCR) of NO\({}_{\rm X}\). Diesel fuel with 7% content of biofuel was used. One engine was additionally tested with 100% FAME (fatty acid methyl esters).