Determining the phase behavior of nanoparticle‐filled binary blends

Abstract

Nanoparticle additives provide a means of imparting the desired electrical, optical, or mechanical properties to a polymeric matrix. The difficulty faced in creating these composites is determining the optimal conditions for forming a thermodynamically stable mixture, where the particles will not phase separate from the matrix material. This challenge is even more daunting when the polymeric matrix is itself a multicomponent mixture, as is often the case in advanced materials. Ideally, the nanoparticles would not only contribute the needed physical properties, but also stabilize the mixture so that the entire system forms a single-phase system. In this study, we use a free energy expression for a binary blend that contains nanoparticles and take the interaction parameters between the different species to be independent variables. Thus, the particles can have distinct enthalpic interactions with each of the polymeric components. Using this expression, we determine the conditions under which the mixture forms a stable, single-phase material. In particular, we isolate how variations in the system's parameters (e.g., polymer composition, particle volume fraction, particle size, interaction energies) affect the phase diagrams. The findings provide guidelines for creating effective formulations and can allow researchers to understand how choices made in the nature of the components affect the overall macroscopic properties.

Phase behavior of UCST blends: Effects of pristine nanoclay as an effective or ineffective compatibilizer

“…In spite of weak interaction of the used polymers with pristine nanoclay in comparison with the interaction between two phases (% AF and % BF >> % AB ), the addition of nanoparticles was observed to improve the compatibility of the virgin blends a little. According to the theoretical work of He et al [34], the intermixing of polymers can be promoted in the presence of nanofiller, even nanoparticles with relatively larger interaction parameters with polymer components than the interaction parameter of two polymers.…”

Fabrication of 3D‐Periodic Ordered Metallic Nanoparticles in a Block Copolymer Bulk Matrix via Oscillating Shear Flow

“…Recent theoretical work has already started to bring understanding on the thermodynamics involved in such complex systems. [13,14] Hybrid materials, based on self-assembled diblock copolymer and metallic nanoparticles, could be the key to develop novel functional materials with properties very different from its original constituents. [15] Diblock copolymers stand out as they spontaneously microphase separate leading to a variety of nanostructures (lamellae, cylinders and spheres), depending on the selected volume fraction of one of the blocks.…”

Nanoparticle/Polymer Blends: Theory and Modeling

“…To model such effects, Ginzburg [84], and He, Ginzburg, and Balazs [85] have formulated a simple theory that provides a description of the phase behavior of these three-component systems. This theory begins by writing a modified FloryHuggins [34, 35] free energy for the three-component system: Here, most definitions are the same as in Eq.…”

“…The function Y HS is the Carnahan-Starling [86] non-ideal con tribution to the free energy of hard spheres, given by: Finally, the term called entr deals with the changes in the conformational entropy of the polymers due to the presence of the particles. Mackay [26], and Ginzburg and coworkers [84,85], stipulated that entr was mainly due to chain stretching in the vicinity of the particles. In particular, Ginzburg and coworkers [84,85] used a simple scaling formula: 2 entr 3 P 1 7:7 j P 2 where B is the homopolymer chain length (assuming for simplicity that the lengths of the two homopolymers are equal).…”

“…Mackay [26], and Ginzburg and coworkers [84,85], stipulated that entr was mainly due to chain stretching in the vicinity of the particles. In particular, Ginzburg and coworkers [84,85] used a simple scaling formula: 2 entr 3 P 1 7:7 j P 2 where B is the homopolymer chain length (assuming for simplicity that the lengths of the two homopolymers are equal). Finally, the function ( ) serves to distinguish between a solvent ( P A , then 0) and nanoparticle ( P , then 1).…”