Secondary organic aerosols (SOA) are a large source of uncertainty in our current understanding of climate change and air pollution. The phase state of SOA is important for quantifying their effects on climate and air quality, but its global distribution is poorly characterized. We developed a method to estimate glass transition temperatures based on the molar mass and molecular O:C ratio of SOA components, and we used the global chemistry climate model EMAC with the organic aerosol module ORACLE to predict the phase state of atmospheric SOA. For the planetary boundary layer, global simulations indicate that SOA are mostly liquid in tropical and polar air with high relative humidity, semi-solid in the mid-latitudes and solid over dry lands. We find that in the middle and upper troposphere SOA should be mostly in a glassy solid phase state. Thus, slow diffusion of water, oxidants and organic molecules could kinetically limit gas-particle interactions of SOA in the free and upper troposphere, promote ice nucleation and facilitate long-range transport of reactive and toxic organic pollutants embedded in SOA.