A Generalized Linear Mixed Models Inference Approach Based on Thermodynamic Compatibility Descriptors to Assess Electrospun Nanofiber Diameter

Electrospinning is an electrostatic technique for manufacturing polymeric fibers and membranes at the micro and nanoscale. It is widely used in textile, environmental, electronic, and tissue engineering to produce tissue scaffolds, drug delivery systems and specialized filters, whose performance is strongly determined by fiber diameter.

This study proposes the use of Generalized Linear Mixed Models (GLMMs) to determine the effect of design variables (X) on electrospun fiber diameter (Y) through inferential analysis, accounting for fixed and random effects. The database consisted of 228 electrospun fiber samples collected from 39 bibliographic sources. Fixed effect variables included solution and operating parameters, such as relative energy difference (RED) and the Flory Huggins interaction parameter (χ), used as thermodynamic descriptors of polymer solvent compatibility, as well as applied voltage, feed flow rate, tip to collector distance, and other fabrication variables, while random effects included bibliographic source and electrospun polymer.

GLMMs were fitted using Gamma, Gaussian, and inverse Gaussian distributions, combined with canonical and non-canonical link functions, to identify the statistical structure that best described electrospun fiber diameter. Model selection was performed using AIC, log-likelihood, deviance and DHARMa simulated residuals. Fixed effect significance was assessed using Wald and χ² likelihood ratio tests, whereas random effects were evaluated through intraclass correlation coefficients (ICC), and marginal and conditional R².

Among the three distribution candidates, the best performing GLMM was based on the natural logarithmic transformation of fiber diameter ln(Y), a Gamma distribution and an identity link function (μ). This model provided the best overall performance, with RMSE = 0.4276 ln-nm, Corr² = 79.34%, and MAPE = 8.22%. The model showed that solution parameters, especially concentration, RED and χ, had the strongest effects on fiber diameter. Regarding random effects, an ICC of 0.08 indicated measurable bibliographic source level and polymer level variability, supporting the use of GLMMs.