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New particle formation driven by acid-base chemistry was initiated in the CLOUD chamber at CERN by introducing atmospherically relevant levels of gas phase sulfuric acid and dimethylamine (DMA). Ammonia was also present in the chamber as a gas-phase contaminant from earlier experiments. The composition of particles with volume median diameters (VMDs) as small as 10 nm was measured by the Thermal Desorption Chemical Ionization Mass Spectrometer (TDCIMS). Particulate ammonium-to-dimethylaminium ratios were higher than the gas phase ammonia-to-DMA ratios, suggesting preferential uptake of ammonia over DMA for the collected 10-30 nm VMD particles. This behavior is not consistent with present nanoparticle physico-chemical models, which predict a higher dimethylaminium fraction when NH3 and DMA are present at similar gas phase concentrations. Despite the presence in the gas phase of at least 100 times higher base concentrations than sulfuric acid, the recently formed particles always had measured base:acid ratios lower than 1:1. The lowest base fractions were found in particles below 15 nm VMD, with a strong size-dependent composition gradient that suggests a change to a mixed-phase state as the particles grew beyond this size. The reasons for the very acidic composition remain uncertain, but a possible explanation is that the particles did not reach thermodynamic equilibrium with respect to the bases due to rapid heterogeneous conversion of SO2 to sulfate. These results indicate that sulfuric acid does not require stabilization by ammonium or dimethylaminium as acid-base pairs in particles as small as 10 nm.