Assessing the Impact of Polydispersity on the Thickness of Polystyrene Thin Films to Adapt a Monodisperse Polystyrene Machine Learning Model
Dhruva Bhat1*, Dvita Bhattacharya2*, Isabelle Chan3*, Aditi Kiran4*, Eli Krasnoff5*, Brenna Ren6*, John Jerome7, Miriam Rafailovich8
1Foothill High School, 2Kent Place School, 3Michael E. DeBakey High School for Health Professions, 4BASIS Independent Fremont, 5The Loomis Chaffee School, 6The Harker School
Spin-coated polystyrene thin films have a variety of industrial applications including biomedical device production, electronics manufacturing, and nanomaterial synthesis, with film thickness affecting their mechanical, electrical, and thermal properties [1]. A previous study by Wang et al. utilized curve-fit machine learning to produce a 3-dimensional manifold relating molecular weight (MW), solution concentration, and film thickness of spin-coated monodisperse polystyrene samples [2]. Although polydisperse polystyrene is more frequently utilized in industrial applications due to its ease of production and affordability, the curve-fit model’s applicability to polydisperse polystyrene has yet to be fully assessed. This study aims to evaluate the accuracy of the curve-fit model applied to polydisperse polystyrene thin films; examine the correlation between the ratio of monodisperse samples and thickness of the resultant thin-film; and adjust the curve-fit model to the polydisperse mixtures by relating the model’s prediction error to the ratio of the monodisperse samples.
Pure polystyrene stock solutions of MWs 30K, 50K, 200K, 311K, 650K, and 2000K were made at concentrations of 10, 15, 20, 25, and 30 mg/mL. Artificial polydisperse samples were then created by mixing the combinations 30K/50K, 30K/200K, 30K/311K, 30K/650K, and 30K/2000K for each of the following ratios: 1:9, 1:3, 1:1, 3:1, and 9:1. Silicon wafers were cleaved from 100 index silicon circles, cleaned under nitrogen gas, and dipped in hydrofluoric acid to ensure hydrophobicity. Three wafers were then spin-coated with polystyrene solution for 30.0 seconds at a rate of 2500 rotations per minute and acceleration of 1000 rotations per minute squared for each MW combination and ratio. In addition to the polydisperse samples, monodisperse control wafers were created for each of the MWs at 10 mg/mL and 30 mg/mL. Ellipsometry was conducted on each sample to determine the thickness in angstroms of the polystyrene film, and average thickness values for each ratio were plotted against concentration in comparison to control monodisperse.
The weighted average MW and film thickness for each sample were then inputted into Wang et al.’s model, which returned critical concentrations consistently lower than the actual concentration. The graph of thickness vs. concentration for each ratio was plotted, and the thicknesses were skewed more towards the lower MW of 30K (Fig. 1). A linear relationship was also determined between the percent of 30K MW in the polydisperse solution and the percent of the distance between the thickness of 30K to 2000K MW polystyrene at each concentration for each ratio, which had percentages significantly lower than the predicted relationship (Fig. 2). Future research will involve quantifying the correlation between the concentration of the lower MW in the polydisperse mixture and the impact on the polydisperse polystyrene thin film’s thickness, as well as determining the driving factor of this impact. Furthermore, it will be necessary to test the correlation of the concentration of the lower MW to the deviation in thickness in polystyrene solutions with more than two monodisperse MWs. Finally, once the requisite data is collected to determine each monodisperse polymer’s impact on film thickness, the curve-fit model must be adjusted for its error in predicted thickness based on pure weighted average MW rather than adjusted weighted average MWs.
[1]Kumar, S., & Aswal, D. K. (1970, January 1). Thin film and significance of its thickness. SpringerLink. https://link.springer.com/chapter/10.1007/978-981-15-6116-
0_1#:~:text=Thickness%20is%20one%20of%20the,electrical%2C%20etc.%2C%20depends.
[2]Wang, A.C., Chen, S.Z., Xie, E. et al. Utilizing machine learning to model interdependency of bulk molecular weight, solution concentration, and thickness of spin coated polystyrene thin films. MRS Communications 14, 230–236 (2024). https://doi.org/10.1557/s43579-024-00527-6