Theoretical investigation of unimodal polydispersity effects on the cloud point behavior of polymer–solvent systems

Experimental investigations examining the influence of polymer polydispersity on liquid–liquid equilibrium (LLE) remain very scarce. The present study provides a theoretical investigation of the effect of polydispersity on the cloud-point behavior of polymer–solvent binary systems, offering a detailed analysis grounded in the characteristics of the polymer molecular weight distribution (MWD) profile. The approach is based on a discrete representation of the MWD through pseudo-components, combined with the PC-SAFT equation of state. The prediction of the polymer MWD is performed using the Hosemann–Schramek (HS) distribution model, which is defined by three key parameters: the number-average molecular weight M ¯ n , the weight-average molecular weight M ¯ w , and the Z-average molecular weight M ¯ z . The pseudo-components are defined using the moment approach as suggested by Tork et al. [Thomas Tork, Gabriele Sadowski, Wolfgang Arlt, Andre de Haan, Gerard Krooshof, Fluid Phase Equilibria 163 (1999) 79–98]. Under specific modeling assumptions, the results show that selecting moments covering the range from zero to three is recommended to reproduce the experimental moments and better capture the relevant MWD. Furthermore, the findings indicate that representing the polymer with 4, 5, or 7 pseudo-components yields comparable cloud point curves, whereas representations using two or three pseudo-components exhibit noticeable deviations, particularly at high polydispersity indices ( PD > 2). At low polydispersity index ( PD < 2), all representations (2, 3, 4, 5, or 7 pseudo-components) yield similar results. Regarding the specific impact of polydispersity on LLE, the results indicate that increasing polydispersity at constant M ¯ n shifts the MWD peak toward higher molecular weights, leading to a strong expansion of the demixing region. In contrast, when M ¯ w is kept constant, increasing polydispersity broadens the distribution toward lower molecular weights resulting in a slight reduction of the demixing region.