A generic grid-based algorithm for computing the free volume in model macromolecules of complex architecture: Star polymers of different chemistry

In this work, we introduce a grid-based algorithm for analyzing free volume in star-shaped polymer melts , which is applicable to any macromolecular nanostructured system of arbitrary architecture and chemistry. Then, using this algorithm, we uncover variations in free volume dependent on both architecture and chemistry between melts of polystyrene (PS) and poly(ethylene oxide) (PEO) star-shaped polymers. Architecture-based differences are elucidated by comparing melts of linear chains and stars with varying numbers of arms ( f = 4 , 8 , 16 , 32 ) and arm length ( N = 40 , 80 monomers). By extending the free volume analysis to a local examination of the density of unoccupied grid points relative to the branch point of the stars, we highlight underlying differences in the intra- and inter-molecular packing of PS and PEO stars. The f -dependent region of low free volume in the vicinity of the branch point of PS stars underscores the tighter packing of PS stars compared to PEO, particularly for higher arm numbers. This detailed examination offers deeper insights into systematic studies of the linear-to-colloidal transition of these unique architectures, reaching nano-regions that are inaccessible via experimental or coarser-scale simulations. These findings complement our previous structural studies, which showed that PS arms pack more densely, being more extended and less spherical, than PEO, while PS forms a more compact and less penetrable molecule. In this way, we further advance our understanding of the factors that contribute to the soft character of star polymers and their potential for the development of new all-polymer nanostructure materials. • Optimized grid-based algorithm estimates fractional free volume in nanomaterials. • Linear and star-shaped PS melts have less free volume and lower density than PEO. • Free volume depends on arm number, length, and packing, with stronger PS effect. • Free volume is affected more by the f -dependent arm packing than free chain ends. • PS stars have low free volume around their branch points, increasing with f .