Understanding the conformation of proteins in the nanoparticle corona has important implications in how organisms respond to nanoparticle-based drugs. These proteins coat the nanoparticle surface, and their properties will influence the nanoparticle's interaction with cell targets and the immune system. While some coronas are thought to be disordered, two key unanswered questions are the degree of disorder and solvent accessibility. Here, a model is developed for protein corona disorder in polystyrene nanoparticles of varying size. For two different proteins, it is found that binding affinity decreases as nanoparticle size increases. The stoichiometry of binding, along with changes in the hydrodynamic size, supports a highly solvated, disordered protein corona anchored at a small number of attachment sites. The scaling of the stoichiometry versus nanoparticle size is consistent with disordered polymer dimensions. Moreover, it is found that proteins are destabilized less in the presence of larger nanoparticles, and hydrophobic exposure decreases at lower curvatures. The observations hold for proteins on flat polystyrene surfaces, which have the lowest hydrophobic exposure. The model provides an explanation for previous observations of increased amyloid fibrillation rates in the presence of larger nanoparticles, and it may rationalize how cell receptors can recognize protein disorder in therapeutic nanoparticles.