Mathematical Modeling and Optimization of Poly(Ethylene Vinyl Alcohol) Film Thickness and Ethylene Composition Based on I-Optimal Design

Multilayer packaging is commonly used in the food industry to improve product preservation by combining materials with specific properties for optimal protection. Ethylene vinyl alcohol (EVOH) is highly valued for its barrier properties against air and moisture. The mechanical properties of EVOH films are influenced by both the ethylene content, which affects crystallinity and barrier performance, and the thickness of the EVOH layer, which affects the film's mechanical strength. This study develops mathematical models to explore the relationship between EVOH film thickness, ethylene content, and mechanical properties, such as tensile strength, elongation at break, and elastic modulus. Using RSM with I-optimal design, the optimal conditions for EVOH films are identified at a thickness of 0.03 mm and 48 mol% ethylene content. The model predicts values of 25.178% for elongation at break, 3077.865 MPa for elastic modulus, and 97.444 MPa for tensile strength. These predictions are validated through ANOVA, confirming the statistical significance of the model. Experimental results show achieved values of 27.119% for elongation, 3437.811 MPa for elastic modulus, and 107.308 MPa for tensile strength, demonstrating model accuracy. To further validate these findings, EVOH films are characterized by SEM, FTIR spectroscopy, and TGA, providing valuable insights into the structural and functional properties for food packaging.