The growth, composition, and evolution of secondary organic aerosol (SOA) are governed by properties of individual compounds and ensemble mixtures that affect partitioning between the vapor and condensed phase. There has been considerable recent interest in the idea that SOA can form highly viscous particles where the diffusion of either water or semivolatile organics within the particle is sufficiently hindered to affect evaporation and growth. Despite numerous indirect inferences of viscous behavior from SOA evaporation or "bounce" within aerosol instruments, there have been no bulk measurements of the viscosity of well-constrained model aerosol systems of atmospheric significance. Here the viscous behavior of a well-defined model system of 9 dicarboxylic acids is investigated directly with complementary measurements and model predictions used to infer phase state. Results not only allow us to discuss the atmospheric implications for SOA formation through this representative mixture, but also the potential impact of current methodologies used for probing this affect in both the laboratory and from a modeling perspective. We show, quantitatively, that the physical state transformation from liquid-like to amorphous semisolid can substantially increase the importance of mass transfer limitations within particles by 7 orders of magnitude for 100 nm diameter particles. Recommendations for future research directions are given.