Statistical Design of Experiments: Study of Cross-Linking Process through the Phase-Resolved Photoacoustic Method as a Multivariable Response

Abstract

This work presents an add-on result of cross-linking using photoacoustic spectroscopy (PAS) phases in a multivariable process using the phase-resolved photoacoustic (PRPA) method. The method is tested to separate contributions from groupings –OH, –CH2–, –CH3, and Si–OH overtones in the range from 700 to 2600 nm. Samples of the copolymers ethylene vinyltrimethoxysilane (EVS) and grafted vinyltrimethoxysilane (VTS) on low-density polyethylene (LDPE) were prepared having concentrations ( C) of 3, 5, and 7% of catalyst and temperatures ( T) of 70, 80, and 90 °C. By considering the condensation reaction, the reduction of –OH groups is monitored. The PRPA analysis was carried out using the surface response methodology and results indicated the optimum point for both answers (signal and phase-resolved) and for both factors of interest ( C, T). For the copolymers, it was found that C ≈ (5.00 ± 1.14)% and T ≈ (82.4 ± 4.3) °C, while for grafted LDPE PEg it was found that C ≈ (4.92 ± 0.85)% and T ≈ (80.8 ± 2.5) °C. These results agreed with the chemical analysis for gel content, which showed as the optimum point 5% of catalyst and temperature of 80 °C. Further, it is an advantage that the photoacoustic method allows one to perform a nondestructive analysis.