Revisiting the density profile of the fuzzy sphere model for microgel colloids

Common neutral polymer microgels exhibit an inhomogeneous density profile with a gradual decay that is commonly described using the fuzzy sphere model. The model is based on the idea of convolving the collapsed solid sphere profile with a Gaussian to describe inhomogeneous swelling of the microgel in a good solvent. Here we show that the corresponding density profile in real space used in several recent works - such as in super-resolution microscopy - is different from the fuzzy sphere model, and we explain how to correctly transition between reciprocal space modelling to real space. Our work aims to clarify the application of the model so that errors can be avoided in the future. Our discussion is also crucial when comparing alternative real-space models for the density profile with the established fuzzy sphere model. Microgel density profiles evaluated with the complementary error function and the popular fuzzy sphere model are not compatible with each other.