Influence of Nanoparticles on Miscibility of Polymer Blends. A Simple Theory

Abstract

We propose a simple theory describing the influence of nanoparticles on thermodynamics of binary polymer mixture. In particular, we consider the case in which nanoparticles preferentially segregate into one of the polymeric components. Depending on the particle radius R p and the polymer degree of polymerization N, addition of nanoparticles can either promote or hinder mixing of the polymers. We calculate how the addition of nanoparticles shifts the spinodal of the polymer blend. These results help to improve understanding of recent simulations on the dynamics of polymer/particle mixtures.

Determining the phase behavior of nanoparticle‐filled binary blends

“…We can, however, make a connection to the available experimental studies and point out the qualitative agreement between the latter findings and the trends obtained from these calculations. In the case of A-like particles, the previous theoretical predictions 17 showed good qualitative agreement with experimental studies on a PVA/PMMA blend filled with fumed silica. 16 In particular, the theory reproduced the experimental observation that at low PMMA content, the particles have an adverse effect on polymer miscibility, but for high PMMA content, they can actually compatibilize the two polymers.…”

“…As mentioned earlier, in previous studies, 17 it was assumed that v AB ¼ v BP and v AP ¼ 0. This assumption describes the scenario where the particles are inherently A-like or coated by an A layer.…”

“…19 The appearance of a particle size dependent prefactor, p R P r 0 , and its functional form was discussed in Ref. 17. We take the same functional form of p(x) ¼ max (tanh (x À 1),0) in this calculation.…”

“…[9][10][11][12][13][14][15][16] However, there have as yet been few systematic theoretical studies on the thermodynamic properties of mix- To address the aforementioned issue, Ginzburg recently carried out a thermodynamic analysis to determine the influence of nanoparticles on the miscibility of blends of A and B homopolymers. 17 The enthalpic interactions in the system are characterized by the FloryHuggins parameters, v AB , v AP , and v BP , where the first of these terms describes the interaction between the homopolymers and the latter two describe the interaction between the respective polymer and the particle. The latter study focused on the specific case where v AB ¼ v BP and v AP ¼ 0, implying that the nanoparticles are essentially A-like and, thus, are preferentially wet by the A domains.…”

Hybrid metal–polymer composites from functional block copolymers

“…Perhaps the most expedient method for the formation of metal-polymer composites is the direct mixing of preformed metallic species with block copolymers. Theoretical studies to outline both the positioning effects of the copolymer on the included nanoparticles and the effects of the nanoparticle size, shape, and surface chemistry on the copolymer morphology and properties have been undertaken, [53][54][55][56][57][58][59][60] and molecular dynamics simulations have agreed with some of these predictions. 61 Recent experimental results have confirmed that the simple mixing of trialkylphosphine oxide stabilized CdSe (or ferritin) nanoparticles with polystyrene-b-poly(2-vinylpyridine) copolymers in thin films results in the ordering of the nanoparticles by the phase-separated block copolymer film with concomitant alignment of the cylindrical phase-separated domains normal to the substrate upon which the film is cast by preferential interactions of one block of the copolymer with the nanoparticles.…”