Physics of Directional Polymer Crystallization.

It has been proposed that the nonisothermal directional crystallization of a polymer driven by a moving sink has an exact analogy to an equivalent isothermal crystallization protocol. We show that this is substantially true because polymers are poor thermal conductors; thus, polymer crystallization occurs over a relatively narrow spatial regime, while the thermal gradients created by this freezing occur over a much broader scale. This separation of scales allows us to replace the crystallization process, which is spatially distributed, with an equivalent step. The temperature at this step, which corresponds to the desired equivalent isothermal crystallization temperature, scales linearly with sink velocity. However, a few metrics, such as the Avrami exponent characterizing the kinetics of crystallization are very different in the two cases. These findings provide new insights into the physics of these spatially varying crystallization protocols and should inspire new experiments to probe the underlying equivalences more deeply.

Local Structure of Polymer-Grafted Nanoparticle Melts.

Polymer-grafted nanoparticle (GNP) membranes show unexpected gas transport enhancements relative to the neat polymer, with a maximum as a function of graft molecular weight (MWg ≈ 100 kDa) for sufficiently high grafting densities. The structural origins of this behavior are unclear. Simulations suggest that polymer segments are stretched near the nanoparticle (NP) surface and form a dry layer, while more distal chain fragments are in their undeformed Gaussian states and interpenetrate with segments from neighboring NPs. This theoretical basis is derived by considering the behavior of two adjacent NPs; how this behavior is modified by multi-NP effects relevant to gas separation membranes is unexplored. Here, we measure and interpret SAXS data for poly(methyl acrylate)-grafted silica NPs and find that for very low MWgs, contact between GNPs obeys the two-NP theory─namely that the NPs act like hard spheres, with radii that are linear combinations of the NP core sizes and the dry zone dimensions; thus, the interpenetration zones relax into the interstitial spaces. For chains with MWg > 100 kDa, the interpenetration zones are in the contact regions between two NPs. These results suggest that for MWgs below the transition, gas primarily moves through a series of dry zones with favorable transport, with the interpenetration zone with less favorable transport properties in parallel. For higher MWgs, the dry and interpenetration zones are in series, resulting in a decrease in transport enhancement. The MWg at the transport maximum then corresponds to the chain length with the largest, unfavorable stretching free energy.

Boundary layer description of directional polymer crystallisation.

Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger-Gryte ansatz.

Tuning Selectivities in Gas Separation Membranes Based on Polymer-Grafted Nanoparticles.

Polymer membranes are critical to many sustainability applications that require the size-based separation of gas mixtures. Despite their ubiquity, there is a continuing need to selectively affect the transport of different mixture components while enhancing mechanical strength and hindering aging. Polymer-grafted nanoparticles (GNPs) have recently been explored in the context of gas separations. Membranes made from pure GNPs have higher gas permeability and lower selectivity relative to the neat polymer because they have increased mean free volume. Going beyond this ability to manipulate the mean free volume by grafting chains to a nanoparticle, the conceptual advance of the present work is our finding that GNPs are spatially heterogeneous transport media, with this free volume distribution being easily manipulated by the addition of free polymer. In particular, adding a small amount of appropriately chosen free polymer can increase the membrane gas selectivity by up to two orders of magnitude while only moderately reducing small gas permeability. Added short free chains, which are homogeneously distributed in the polymer layer of the GNP, reduce the permeability of all gases but yield no dramatic increases in selectivity. In contrast, free chains with length comparable to the grafts, which populate the interstitial pockets between GNPs, preferentially hinder the transport of the larger gas and thus result in large selectivity increases. This work thus establishes that we can favorably manipulate the selective gas transport properties of GNP membranes through the entropic effects associated with the addition of free chains.

High-Frequency Mechanical Behavior of Pure Polymer-Grafted Nanoparticle Constructs.

Polymer-grafted nanoparticle (GNP) membranes show increased gas permeability relative to pure polymer analogs, with this effect evidently tunable through systematic variations in the grafted polymer chain length and grafting density. Additionally, these materials show less deleterious aging effects relative to the pure polymer. To better understand these issues, we explore the solid-state mechanical properties of GNP layers using quartz crystal microbalance (QCM) spectroscopy, which operates under conditions (≈5 MHz) that we believe are relevant to gas transport. The GNP's high-frequency storage moduli exhibit a characteristic increase with increasing nanoparticle (NP) core loading, consistent with past work on the reinforcement of polymers physically well mixed with bare NPs. However, these GNPs show a substantial, nonmonotonic decrease in loss as a function of chain length (at fixed grafting density), with the loss minimum corresponding to the chain length with the maximum gas permeability. We speculate that this feature corresponds to a dynamical transition, where the GNP membranes go from a jammed solid (colloid-like) to liquid-like (polymer-controlled) behavior with increasing chain length.

Location of Imbibed Solvent in Polymer-Grafted Nanoparticle Membranes.

Membranes made purely from nanoparticles (NPs) grafted with polymer chains show increased gas permeability relative to the analogous neat polymer films, with this effect apparently being tunable with systematic variations in polymer graft density and molecular weight. To explore the structural origins of these unusual transport results, we use small angle scattering (neutron, X-ray) on the dry nanocomposite film and to critically examine in situ the structural effects of absorbed solvent. The relatively low diffusion coefficients of typical solvents (∼10-12 m2/s) restricts us to thin films (≈1 µm in thickness) if solute concentration profiles are to equilibrate on the 1 s time scale. The use of such thin films, however, renders them as weak scatterers. Inspired by our nearly two decades old previous work, we address these conflicting requirements through the use of a custom designed flow cell, where stacks of 10 individual ≈1 µm thick supported films are used, while ensuring that each film is individually exposed to solvent vapor. By using isotopically labeled solvents, we study the solvent distribution within the film and show surprisingly that the solvent homogeneously swells the polymer under all conditions that we examined. These results are not anticipated by current theories, but they suggest that, at least under some conditions, the free volume increases due to the grafting of chains to nanoparticles is apparently distributed isotropically in these materials.

Decoupling energetic modifications to diffusion from free volume in polymer/nanoparticle composites.

Diffusion coefficients of small molecules in a model composite of spherical nanoparticles and polymer with attractive interfacial interactions are reduced from that in the pure polymer, to a degree far below the level expected from geometric tortuosity arguments. We determine whether such dramatic reductions are due to modifications to the matrix polymer free volume near the nanoparticle surface, or alternatively are due to energetic attractions between the diffusants and nanoparticle surface. We performed ethyl acetate sorption experiments within the vicinity of the polymer glass transition (Tg ≤ T ≤ Tg + 25 K) for a model polymer/nanoparticle composite, silica-filled poly(methyl acrylate). By application of the Vrentas-Duda free volume theory of diffusion we have decoupled the energetic effects from those related to free-volume and segmental dynamics. While the latter is unaffected by addition of nanoparticles, the energy needed for the ethyl acetate diffusant to overcome neighboring attractive forces doubles after adding 40 vol% nanoparticles with a diameter of 14 nm. This is qualitatively consistent with hydrogen bonding interactions between the silica surface and ethyl acetate slowing its rate of diffusion. On the other hand for benzene, which does not hydrogen bond to the silica surface, diffusion coefficients that can be explained by tortuosity effects were obtained. This work provides quantitative evidence that the diffusant-filler energetic interactions and geometric blocking effects can be fully responsible for the substantially reduced diffusivity commonly observed in polymer/nanoparticle composite systems.

All-nanoparticle layer-by-layer surface modification of micro- and ultrafiltration membranes.

Layer-by-layer (LbL) deposition using primarily inorganic silica nanoparticles is employed for surface modification of polymeric micro- and ultrafiltration (MF/UF) membranes to produce novel thin film composite (TFC) membranes intended for nanofiltration (NF) and reverse osmosis (RO) applications. A wide variety of porous substrate membranes with different surface characteristics are successfully employed. This report gives detailed results for polycarbonate track etched (PCTE), polyethersulfone (PES), and sulfonated PES (SPEES) MF/UF substrates. Both spherical (cationic/anionic) and eccentric elongated (anionic) silica nanoparticles are deposited using conditions similar to those in prior works for solid substrates (e.g., Lee et al.). Appropriate selection of the pH for anionic and cationic particle deposition enables construction of nanoparticle-only layers 100-1200 nm in thickness atop the original porous membrane substrates. The surface layer thickness appears to vary linearly with the number of bilayers deposited, i.e., with the number of anionic/cationic deposition cycles. The deposition process is optimized to eliminate drying-induced cracking and improve mechanical durability via thickness control and postdeposition hydrothermal treatment. "Dead-end" permeation tests using dextran standards reveal the hydraulic characteristics and separations capability for the PCTE-based TFC membranes. The results show that nanoparticle-based LbL surface modification of MF and UF rated media can produce TFC membranes with NF capabilities.