Solvent vapor annealing in block copolymer nanocomposite films: a dynamic mean field approach

Abstract

Polymer nanocomposites are an important class of materials due to the nanoparticles' ability to impart functionality not commonly found in a polymer matrix, such as electrical conductivity or tunable optical properties. While the equilibrium properties of polymer nanocomposites can be treated using numerous theoretical and simulation approaches, in experiments the effects of processing and kinetic traps are significant and thus critical for understanding the structure and the functionality of polymer nanocomposites. However, simulation methods that can efficiently predict kinetically trapped and metastable structures of polymer nanocomposites are currently not common. This is particularly important in inhomogeneous polymers such as block copolymers, where techniques such as solvent vapor annealing are commonly employed to improve the long-range order. In this work, we introduce a dynamic mean field theory that is capable of predicting the result of processing the structure of polymer nanocomposites, and we demonstrate that our method accurately predicts the equilibrium properties of a model system more efficiently than a particle-based model. We subsequently use our method to predict the structure of block copolymer thin films with grafted nanoparticles after solvent annealing, where we find that the final distribution of the grafted nanoparticles can be controlled by varying the solvent evaporation rate. The extent to which the solvent evaporation rate can affect the final nanoparticle distribution in the film depends on the grafting density and the length of the grafted chains. Furthermore, the effects of the solvent evaporation rate can be anticipated from the equilibrium nanoparticle distribution in the swollen and dry states.

Grafted polymer chains suppress nanoparticle diffusion in athermal polymer melts

“…It can be shown that the effective non-bonded interaction between the different components is given by a convolution of the shape functions, 36,37 which makes the non-bonded interactions non-local. We sample the model using a 3D version of dynamic mean field theory 38 that we have recently implemented, 39 which uses a particle-to-mesh scheme to evaluate the non-bonded interactions and is similar in spirit to singlechain in mean field 40 and related methods. 41 We note that although our implementation involves a dynamic mean-field approximation, thermodynamic fluctuations are accurately sampled.…”

“…41 We note that although our implementation involves a dynamic mean-field approximation, thermodynamic fluctuations are accurately sampled. 39 To map our Gaussian chain models onto the experimental PMMA polymers, we set up the number of segments in the Gaussian chain, N CG , and the statistical segment length, b, such that the unperturbed radius of gyration of the Gaussian chain, R g = N CG −1 6 b, matches the radius of gyrations of the real PMMA polymer, R g,exp = n−1 6 b exp , where n is the number of monomers and b exp is the experimentally measured statistic segment length in the real PMMA polymer. By adopting the experimentally measured b exp for PMMA at 0.66 nm 33 and choosing b at 1.96 nm, the grafted PMMA polymers with molecular weight, 16 and 21 kg/mol, are mapped to the Gaussian chains with N of 18 and 24 monomers, respectively.…”

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

“…Separately, Riggleman and co-workers showed that tuning the solvent evaporation rate relative to the particle diffusion rate can allow control over the NP distribution through a thin film. 231 These first studies opened up a number of questions that need to be answered. What is the relative role of the interactions between the solvent-NP-polymers and what is the interplay of these effects when the solvent evaporates?…”

Using reactive dissipative particle dynamics to understand local shape manipulation of polymer vesicles

“…Models of block polymer self-assembly are notoriously subtle, and a vast array of approaches for simulating polymer vesicles spanning length and times scale from atoms [49][50][51][52] to continuous fields [53][54][55] have been used. The timescale of atomistic simulations limit their applicability here, and though there are emerging field-based approaches of interest, [55][56][57][58] field theory-based simulations are typically challenging due to the need to capture both dynamics and the strong composition fluctuations present in micellar systems. 53 A mesoscopic particle model such as DPD is a practical alternative as it splits the difference between molecular dynamics (MD) and field-based methods, allowing for relatively fast relaxation times compared to MD and a facile incorporation of dynamics and fluctuations compared to field-based approaches.…”