Understanding the Molecular Weight Dependence of χ and the Effect of Dispersity on Polymer Blend Phase Diagrams

Abstract

Gibbs ensemble Monte Carlo simulations and cloud point measurements were performed to understand the molecular weight dependence of χ and the effect of dispersity on the phase behavior of polymer mixtures. Oligomeric blends consisting of poly­(ethylene-alt-propylene) (PEP) and poly­(ethylene oxide) dimethyl ether (PEO) were used as the model systems. First, the molecular weight dependence of χ for PEP/PEO mixtures was studied using simulations and experiments for PEP/PEO mixtures with various molecular weights. An empirical model with a single adjustable parameter k ij is used to quantify this molecular weight dependence, and it allows for the accurate prediction of χ of PEP/PEO mixtures with arbitrary molecular weights. Second, the effects of molecular weight distribution (MWD) and dispersity (Đ) of PEO on the PEP/PEO phase diagram were investigated via both simulations and experiments. When PEO is relatively monodisperse (Đ < 1.2), the phase diagram is found to be insensitive to either MWD or Đ, despite differentiation in molecular partitioning observed from simulations. However, the coexistence curve for mixtures containing PEO with a bimodal distribution and a large dispersity (Đ = 1.76) differs dramatically from that for mixtures containing low-dispersity PEO, which suggests that the former mixture can no longer be treated as a binary system. Furthermore, structural analysis was performed from simulation trajectories to probe microscopic heterogeneity and aggregation behavior in the liquid phases. The results in this work permit the accurate prediction of χ and the phase diagram of disperse binary polymeric mixtures.

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

“…In Figure we illustrate a spectrum of spatial length scales typically important for polymer systems: (i) atomistic structure is foundational to the chemical features and interactions in polymer systems; however, these are often coarse-grained to (ii) chain parameters (χ parameters − and Kuhn length − ) that describe an otherwise featureless polymer chain . (iii) Local chain conformations and architectural features give rise to overall chain dimensions, , and via (iv) interchain interactions, lead to self-assembled morphologies such as block copolymers. ,, Much of polymer physics revolves around understanding and manipulating these length scales, with a particular focus on universal properties at (or larger than) the chain conformational length scales .…”

Thermodynamic Modeling and Validation of the Temperature Influence in Ternary Phase Polymer Systems

“…In this section it is considered a negligible effect of the ternary interaction parameter on the phase diagram ( χ 123 = 0). This modeling approach has been the most widely reported in the literature [ 17 , 18 , 27 , 48 ]. Firstly, χ 13 and χ 23 parameters were calculated according to Equation (11) considering α 13 = α 23 = 1 ( Table 6 ).…”

“…Different aspects, such as the polymer having a broad molecular weight distribution, or swelling or plasticizing effects occurring between the polymer and the solvent for binary mixtures have been reported to alter significantly the values of the Flory–Huggins binary interaction parameters [ 48 , 49 , 50 ]. Previous works have reported the use of a correction factor α ij in the calculation of binary interaction parameters χ 13 and χ 23 , Equation (11), to amend the deviation observed between the modeled and experimental cloud points.…”

Molecularly Informed Field Theories from Bottom-up Coarse-Graining

“…The dependence of miscibility on the atomic charges is expected, because these directly modulate the strength of hydrogen-bonding in the AA model, with a less polar PEO ether-backbone entailing a weaker hydrogen-bond with water, a larger v pw , and phase separation at lower (higher) temperatures. Furthermore, the sensitivity to the AA force field is not unprecedented; for example, in a dodecane/ethanol system, a 1 kJ/mol difference in the transfer free energy (considered small during AA force field development) shifts the coexistence boundary by 50 °C. , Indeed, our CG model correctly captures trends in miscibility reflecting the changing solvent quality of the AA reference model, induced by changing PEO’s atomic charges.…”

“…Furthermore, the sensitivity to the AA force field is not unprecedented; 83 for example, in a dodecane/ethanol system, a 1 kJ/mol difference in the transfer free energy (considered small during AA force field development) shifts the coexistence boundary by 50 °C. 28,84 Indeed, our CG model correctly captures trends in miscibility reflecting the changing solvent quality of the AA reference model, induced by changing PEO's atomic charges.…”