Abstract. Atmospheric aerosols play critical roles in air quality, public health, and visibility. In addition, they strongly influence climate by scattering solar radiation and by changing the reflectivity and lifetime of clouds. One major but still poorly understood source of atmospheric aerosols is new particle formation, which consists of the formation of thermodynamically stable clusters from trace gas molecules (homogeneous nucleation) followed by growth of these clusters to a detectable size (~3 nm). Because freshly nucleated clusters are most susceptible to loss due to high rate of coagulation with pre-existing aerosol population, the initial growth rate strongly influences the rate of new particle formation and ambient aerosol population. Whereas many field observations and modeling studies indicate that organics enhance the initial growth of the clusters and therefore new particle formation, thermodynamic considerations would suggest that the strong increase of equilibrium vapor concentration due to cluster surface curvature (Kelvin effect) may prevent ambient organics from condensing on these small clusters. Here, the contribution of organics to the initial cluster growth is described as heterogeneous nucleation of organic molecules onto these clusters. We find that the strong gradient in cluster population with respect to its size leads to positive cluster number flux. This positive flux drives the growth of clusters substantially smaller than the Kelvin diameter, conventionally considered the minimum particle size that can be grown through condensation. The conventional approach neglects the contribution from the cluster concentration gradient, and underestimates the cluster survival probabilities by a factor of up to 60 if early growth of clusters is due to both condensation of sulfuric acid and heterogeneous nucleation of organic vapors.