Assessing the Impact of Polydispersity on the Thickness of Polystyrene Thin Films to Adapt a Monodisperse Polystyrene Machine Learning Model

Spin-coated polystyrene (PS) thin films have many industrial applications including biomedical devices, photonics, organic electronics manufacturing, and nanomaterial synthesis. The thickness of these thin films determines their mechanical, electrical, and thermal properties. A previous study by Wang et al. utilized a curve-fit machine learning model to produce a 3D manifold relating molecular weight (MW), solution concentration, and film thickness of spin-coated monodisperse PS samples [1]. However, the curve-fit model’s applicability to polydisperse PS, which has greater industrial applications due to its ease of production and affordability, has yet to be fully assessed. This study aims to evaluate the accuracy of the model when applied to spin-coated polydisperse PS thin films. In this case, we simulated polydispersity by forming solutions of monodisperse PS polymers of different MW compositions. We examined the relationship between the weighted average MW and total polymer concentration of the solutions to the film thickness. The results were then used to determine the extent to which the curve-fit model is able to predict this relationship as a function of polydispersity and average MW.<br/><br/>First, binary PS solutions of MWs 30k/50k, 30k/200k, 30k/311k, 30k/650k, and 30k/2000k were dissolved in toluene and combined at concentrations of 10, 15, 20, 25, and 30 mg/mL. The solutions were made at ratios of 1:9, 1:3, 1:1, 3:1, and 9:1. Polished silicon wafers [1,0,0] were cleaved and particulates were removed under nitrogen gas flow. The native oxide layer was removed using diluted hydrofluoric acid. Three wafers were then spin-coated for each PS solution for 30.0 seconds at a fixed rate of 2500 rpm and acceleration of 1000 rpm/s. Ellipsometry was conducted to determine the thickness of the PS films, which were averaged and used for further data analysis.<br/><br/>Initially, the average film thickness and the weighted average of the MWs in each solution were used as inputs to the model used by Wang et al. [1]. The model consistently predicted lower concentrations for each thickness than the actual experimental values. The graphs of thickness vs. concentration for each MW combination showed that thicknesses for a given ratio were consistently shifted towards the predicted thickness of the 30k MW. By assessing the ratio of the thickness difference between the sample and the lower bound MW over the thickness difference in higher and lower monodisperse bounds, a linear relationship was determined at each concentration for each ratio. For instance, the 30k/2000k combinations had an R2 value of 0.9991 for a linear curve-fit. As such, error can be quantified and the monodisperse model can be adjusted for any binary polydisperse PS samples, given sufficient experimental data. van Ruymbeke et al. proposed the theory of constraint release on long chains being driven by quicker relaxation times of short chains, leading to tube dilation [2]. Their physical model provides a reasonable explanation for our observed data, since their model predicts lower viscosity for binary solutions with large MW differences in solution; moreover, we observed a decrease in error of the model used by Wang as the MW difference in solution decreases. Future research will involve gathering more data to empirically model the larger impact of the lower MW in a polydisperse sample on film thickness. Furthermore, testing polymers below entanglement weight would prove valuable in determining the reasoning behind the disproportionate impact based on weight. Testing the thickness of polydisperse solutions with more than two different MWs would be necessary to draw broader conclusions on the effects of polydispersity on the characteristics of thin films.<br/><br/>Work supported by the Louis Morin Charitable Trust.<br/><br/>[1] Wang, A.C., et al. MRS Communications 14, 230–236 (2024).<br/>[2] Van Ruymbeke, et al. Macromolecules 47 (21), 7653–7665 (2014).