Binding affinity of a small molecule to an amorphous polymer in a solvent. Part 2: preferential binding to local sites on a surface

Crystallization, a separation and purification process, is commonly used to produce a wide range of materials in various industries, and it usually begins with heterogeneous nucleation on a foreign surface in industrial practice and most other circumstances. Recent studies show that amorphous polymeric substrates are useful in controlling crystallization and selectively producing pharmaceutical polymorphs. In our previous publication, we investigated the possible correlation of the binding affinity of one molecule to key binding sites (local binding), and the possibility of using this binding affinity to guide the selection of polymers promoting heterogeneous nucleation. The studied systems were aspirin binding to four nonporous cross-linked polymers in ethanol-water 38 v% mixture. Cross-linked with divinylbenzene (DVB), these polymers were poly(4-acryloylmorpholine) (PAM), poly(2-carboxyethyl acrylate) (PCEA), poly(4-hydroxylbutyl acrylate) (PHBA), and polystyrene (PS). We discovered that the trend of the magnitudes of the average free energies of binding to the best sites is very similar to that of heterogeneous nucleation activities. This Article aims to investigate whether or not local binding to key sites is the important variable to describe heterogeneous nucleation as opposed to the overall/average binding affinity of molecules to a surface, and to investigate the possibility of using the overall binding affinity to guide the selection of polymers. We used the polymer surfaces generated from our previous study to calculate the overall binding affinity of aspirin molecules to the surface as measured by the preferential interaction coefficients of aspirin (1 m) to these polymers. We discovered that the trend of the average preferential interaction coefficients does not correlate as well to that of heterogeneous nucleation activities as the free energies of binding to the best sites. We also computed the average numbers of aspirin molecules associated with the areas of the surfaces' best binding sites and found that they correlate better to heterogeneous nucleation activities than the average preferential interaction coefficients. These results further support that local binding is indicative of heterogeneous nucleation. Moreover, we found a weak trend of the distance order parameters of the aspirin molecules to be similar that of heterogeneous nucleation activities. Our results from the two-part study suggest the importance of local binding to heterogeneous nucleation as well as the possibility of using the binding affinity to the local area (the free energy of binding to the best site and the number of nucleating molecules associated with the area of the best binding site) and the distance order parameters to guide the selection of polymers.