Constrained nonlinear optimization for solubility parameters of poly(lactic acid) and poly(glycolic acid)—validation and comparison

An optimization technique has been proposed to determine Hansen solubility parameters (HSP) and radius of interaction (R) of PLA and PGA; objective function to be minimized being radius of interaction (R), and the constraints being that the solvents should be within and nonsolvents outside the interaction sphere. The proposed method has been validated and found to be most reliable. The values of HSP (δd, δp, δh) and R for PLA have been obtained as ((18.50, 9.70, 6.00) and 10.50) (J/cc)0.5 at 25 °C; and those of PGA as ((17.70, 6.21, 12.50) and 1.92) (J/cc)0.5 at 80 °C. For formulating the nonlinear inequality constraints known HSP data for 20 solvents and seven nonsolvents have been used for PLA at 25 °C; similarly HSP data for three newly found solvents (phenol, m-cresol and 4-chlorophenol), and five nonsolvents have been used for PGA at 80 °C. Established methods have been used for comparison. HSP and R have been directly compared using the 3D intrinsic viscosity and classical methods. Indirectly the total solubility parameter δ has been compared with the values obtained from the intrinsic viscosity 1D approach and group contribution method using Fedors and van Krevelen correlations. The 1D approach has led to an empirical correlation for intrinsic viscosities of PLA and PGA.