Surfactant in a Polyol-CO2 Mixture: Insights from a Classical Density Functional Theory Study.

Silicone-polyether (SPE) surfactants, made of a polydimethyl-siloxane (PDMS) backbone and polyether branches, are commonly used as additives in the production of polymeric foams with improved properties. A key step in the production of polymeric foams is the nucleation of gas bubbles in the polymer matrix upon supersaturation of dissolved gas. However, the role of SPE surfactants in the nucleation of gas bubbles is not well understood. In this study, we use classical density functional theory to investigate the effect of an SPE surfactant on the nucleation of CO2 bubbles in a polyol foam formulation. We find that the addition of an SPE surfactant leads to a ∼3-fold decrease in the polyol-CO2 interfacial tension at the surfactant's critical micelle concentration. Additionally, the surfactant is found to reduce the free energy barrier and affect the minimum free energy pathway (MFEP) associated with CO2 bubble nucleation. In the absence of a surfactant, a CO2-rich bubble nucleates from a homogeneous CO2-supersaturated polyol solution by following an MFEP characterized by a single nucleation barrier. Adding a surfactant results in a two-step nucleation process with reduced free energy barriers. The first barrier corresponds to the formation of a spherical aggregate with a liquid-like CO2 core. This spherical aggregate then grows into a CO2-rich bubble (spherical aggregate with a vapor-like CO2 core) of a critical size representing the second barrier. We hypothesize that the stronger affinity of CO2 for PDMS (than polyether) stabilizes the spherical aggregate with the liquid-like CO2 core, leading to a lower free energy barrier for CO2 bubble nucleation. Stabilization of such an aggregate during the early stages of the nucleation may lead to foams with more, smaller bubbles, which can improve their microstrustural features and insulating abilities.

Competition between CO2-philicity and Mixing Entropy Leads to CO2 Solubility Maximum in Polyether Polyols.

In carbon dioxide-blown polymer foams, the solubility of carbon dioxide (CO2) in the polymer profoundly shapes the structure and, consequently, the physical properties of the foam. One such foam is polyurethane-commonly used for thermal insulation, acoustic insulation, and cushioning-which increasingly relies on CO2 to replace environmentally harmful blowing agents. Polyurethane is produced through the reaction of isocyanate and polyol, of which the polyol has the higher capacity for dissolving CO2. While previous studies have suggested the importance of the effect of hydroxyl end groups on CO2 solubility in short polyols (<1000 g/mol), their effect in polyols with higher molecular weight (≥1000 g/mol) and higher functionality (>2 hydroxyls per chain)-as are commonly used in polyurethane foams-has not been reported. Here, we show that the solubility of CO2 in polyether polyols decreases with molecular weight above 1000 g/mol and decreases with functionality using measurements performed by gravimetry-axisymmetric drop-shape analysis. The nonmonotonic effect of molecular weight on CO2 solubility results from the competition between effects that reduce CO2 solubility (lower mixing entropy) and effects that increase CO2 solubility (lower ratio of hydroxyl end groups to ether backbone groups). To generalize our measurements, we modeled the CO2 solubility using a perturbed chain-statistical associating fluid theory (PC-SAFT) model, which we validated by showing that a density functional theory model based on the PC-SAFT free energy accurately predicted the interfacial tension.

Effects of Confinement and Ion Adsorption in Ionic Liquid Supercapacitors with Nanoporous Electrodes.

We investigate the effects of pore size and ion adsorption on the room-temperature ionic liquid capacitor with nanoporous electrodes, with a focus on optimizing the capacitance and energy storage. Using a recently developed modified BSK model accounting for both ion correlations and nonelectrostatic interactions, we find that ion crowding proximate to the electrode surface induced by the spontaneous charge separation due to strong ion correlations is responsible for the anomalous increase in the capacitance with decreasing pore sizes observed in experiments. Reducing the strength of ion correlations increases the capacitance and suppresses the anomalous size dependence. For a given pore size, the capacitance peak diverges when the ion correlation strength α reaches a critical value, αsc,L. The capacitance peak shifts to smaller pore size as α decreases because of rapid decrease of αsc,L with decreasing pore size. Asymmetric preferential ion adsorption is shown to lead to significantly enhanced energy storage close to the transition point for any pore sizes. For a given correlation strength, the energy storage is optimal at a pore size where α = αsc,L.

Effects of Surface Transition and Adsorption on Ionic Liquid Capacitors.

Room-temperature ionic liquids (RTILs) are synthetic electrolytes with electrochemical stability superior to that of conventional aqueous-based electrolytes, allowing a significantly enlarged electrochemical window for application as capacitors. In this study, we propose a variant of an existing RTIL model for solvent-free RTILs, accounting for both ion-ion correlations and nonelectrostatic interactions. Using this model, we explore the phenomenon of spontaneous surface charge separation in RTIL capacitors and find that this transition is a common feature for realistic choices of the model parameters in most RTILs. In addition, we investigate the effects of asymmetric preferential ion adsorption on this charge separation transition and find that proximity of the transition in this case can result in greatly enhanced energy storage. Our work suggests that differential chemical treatment of electrodes can be a simple and useful means for optimizing energy storage in RTIL capacitors.

Field-Theoretic Simulations of the Distribution of Nanorods in Diblock Copolymer Thin Films.

Using block copolymer microphases to guide the self-assembly of nanorods in thin films can give rise to polymeric materials with unique optical, thermal, and mechanical properties beyond those found in neat block copolymers. Often the design and manufacture of these materials require exquisite control of the nanorod distribution, which is experimentally challenging due to the large parameter space spanned by this class of materials. Simulation approaches, on the other hand, can access the thermodynamics that contribute to the nanorod distribution and hence offer valuable guidance toward the design and manufacture of the materials. In this work, we employ complex Langevin field-theoretic simulations to examine the thermodynamic forces that govern the assembly of nanorods in thin films of block copolymers with a particular focus on vertically oriented cylindrical and lamellar domains. Our simulations show that the nanorod geometry, the substrate selectivity for the distinct blocks of the copolymer, and the film thickness all play important roles in engineering both the nanorod orientation and spatial distribution in diblock copolymer thin films. In addition, we employ thermodynamic integration to examine how the nanorods alter the stability of vertical and horizontal domains in thin films, where we find that the tendency of the nanorods to stabilize a vertical orientation depends on both the film thickness and the nanorod concentration.

Grafted polymer chains suppress nanoparticle diffusion in athermal polymer melts.

We measure the center-of-mass diffusion of poly(methyl methacrylate) (PMMA)-grafted nanoparticles (NPs) in unentangled to slightly entangled PMMA melts using Rutherford backscattering spectrometry. These grafted NPs diffuse ∼100 times slower than predicted by the Stokes-Einstein relation assuming a viscosity equal to bulk PMMA and a hydrodynamic NP size equal to the NP core diameter, 2Rcore = 4.3 nm. This slow NP diffusion is consistent with an increased effective NP size, 2Reff ≈ 20 nm, nominally independent of the range of grafting density and matrix molecular weights explored in this study. Comparing these experimental results to a modified Daoud-Cotton scaling estimate for the brush thickness as well as dynamic mean field simulations of polymer-grafted NPs in athermal polymer melts, we find that 2Reff is in quantitative agreement with the size of the NP core plus the extended grafted chains. Our results suggest that grafted polymer chains of moderate molecular weight and grafting density may alter the NP diffusion mechanism in polymer melts, primarily by increasing the NP effective size.

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

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.

Dispersion and alignment of nanorods in cylindrical block copolymer thin films.

Although significant progress has been made in controlling the dispersion of spherical nanoparticles in block copolymer thin films, our ability to disperse and control the assembly of anisotropic nanoparticles into well-defined structures is lacking in comparison. Here we use a combination of experiments and field theoretic simulations to examine the assembly of gold nanorods (AuNRs) in a block copolymer. Experimentally, poly(2-vinylpyridine)-grafted AuNRs (P2VP-AuNRs) are incorporated into poly(styrene)-b-poly(2-vinylpyridine) (PS-b-P2VP) thin films with a vertical cylinder morphology. At sufficiently low concentrations, the AuNRs disperse in the block copolymer thin film. For these dispersed AuNR systems, atomic force microscopy combined with sequential ultraviolet ozone etching indicates that the P2VP-AuNRs segregate to the base of the P2VP cylinders. Furthermore, top-down transmission electron microscopy imaging shows that the P2VP-AuNRs mainly lie parallel to the substrate. Our field theoretic simulations indicate that the NRs are strongly attracted to the cylinder base where they can relieve the local stretching of the minority block of the copolymer. These simulations also indicate conditions that will drive AuNRs to adopt a vertical orientation, namely by increasing nanorod length and/or reducing the wetting of the short block towards the substrate.

Predicting the structure and interfacial activity of diblock brush, mixed brush, and Janus-grafted nanoparticles.

A modeling framework is developed to describe the structure and properties of fluid interfaces stabilized with grafted nanoparticles. The framework is demonstrated on nanoparticles functionalized with polymers of various grafting architectures; we find that the conformation of the grafted chains plays an important role in the interfacial tension.

Air-liquid interfacial self-assembly of conjugated block copolymers into ordered nanowire arrays.

The ability to control the molecular packing and nanoscale morphology of conjugated polymers is important for many of their applications. Here, we report the fabrication of well-ordered nanoarrays of conjugated polymers, based on the self-assembly of conjugated block copolymers at the air-liquid interface. We demonstrate that the self-assembly of poly(3-hexylthiophene)-block-poly(ethylene glycol) (P3HT-b-PEG) at the air-water interface leads to large-area free-standing films of well-aligned P3HT nanowires. Block copolymers with high P3HT contents (82-91%) formed well-ordered nanoarrays at the interface. The fluidic nature of the interface, block copolymer architecture, and rigid nature of P3HT were necessary for the formation of well-ordered nanostructures. The free-standing films formed at the interface can be readily transferred to arbitrary solid substrates. The P3HT-b-PEG films are integrated in field-effect transistors and show orders of magnitude higher charge carrier mobility than spin-cast films, demonstrating that the air-liquid interfacial self-assembly is an effective thin film fabrication tool for conjugated block copolymers.

Field theoretic simulations of polymer nanocomposites.

Polymer field theory has emerged as a powerful tool for describing the equilibrium phase behavior of complex polymer formulations, particularly when one is interested in the thermodynamics of dense polymer melts and solutions where the polymer chains can be accurately described using Gaussian models. However, there are many systems of interest where polymer field theory cannot be applied in such a straightforward manner, such as polymer nanocomposites. Current approaches for incorporating nanoparticles have been restricted to the mean-field level and often require approximations where it is unclear how to improve their accuracy. In this paper, we present a unified framework that enables the description of polymer nanocomposites using a field theoretic approach. This method enables straightforward simulations of the fully fluctuating field theory for polymer formulations containing spherical or anisotropic nanoparticles. We demonstrate our approach captures the correlations between particle positions, present results for spherical and cylindrical nanoparticles, and we explore the effect of the numerical parameters on the performance of our approach.