Neutron reflectometry is the foremost technique for in situ determination of the volume fraction profiles of polymer brushes at planar interfaces. However, the subtle features in the reflectometry data produced by these diffuse interfaces challenge data interpretation. Historically, data analyses have used least-squares approaches that do not adequately quantify the uncertainty of the modeled profile and ignore the possibility of other structures that also match the collected data (multimodality). Here, a Bayesian statistical approach is used that permits the structural uncertainty and multimodality to be quantified for polymer brush systems. A free-form model is used to describe the volume fraction profile, minimizing assumptions regarding brush structure, while only allowing physically reasonable profiles to be produced. The model allows the total volume of polymer and the profile monotonicity to be constrained. The rigor of the approach is demonstrated via a round-trip analysis of a simulated system, before it is applied to real data examining the well characterized collapse of a thermoresponsive brush. It is shown that, while failure to constrain the interfacial volume and consider multimodality may result in erroneous structures being derived, carefully constraining the model allows for robust determination of polymer brush compositional profiles. This work highlights that an appropriate combination of flexibility and constraint must be used with polymer brush systems to ensure the veracity of the analysis. The code used in this analysis is provided, enabling the reproduction of the results and the application of the method to similar problems.
The temperature induced swelling/collapse transition of poly(oligoethylene glycol methacrylate) (POEGMA) brushes has been investigated in electrolyte solutions comprised of multiple anions.
Porous membranes coated with so-called
asymmetric polyelectrolyte
multilayers (PEMs) have recently been shown to outperform commercial
membranes for micropollutant removal. They consist of open support
layers of poly(styrene sulfonate) (PSS)/poly(allylamine) (PAH) capped
by denser and more selective layers of either PAH/poly(acrylic acid)
(PAA) or PAH/Nafion. Unfortunately, the structure of these asymmetric
PEMs, and thus their superior membrane performance, is poorly understood.
In this work, neutron reflectometry (NR) is employed to elucidate
the multilayered structure and hydration of these asymmetric PEMs.
NR reveals that the multilayers are indeed asymmetric in structure,
with distinct bottom and top multilayers when air-dried and when solvated.
The low hydration of the top [PAH/Nafion] multilayer, together with
the low water permeance of comparable [PAH/Nafion]-capped PEM membranes,
demonstrate that it is a reduction in hydration that makes these separation
layers denser and more selective. In contrast, the [PAH/PAA] capping
multilayers are more hydrated than the support [PSS/PAH] layers, signifying
that, here, densification of the separation layer occurs through a
decrease in the mesh size (or effective pore size) of the top layer
due to the higher charge density of the PAH/PAA couple compared to
the PSS/PAH couple. The [PAH/PAA] and [PAH/Nafion] separation layers
are extremely thin (∼4.5 and ∼7 nm, respectively), confirming
that these asymmetric PEM membranes have some of the thinnest separation
layers ever achieved.
M u l t i-s ti mu l u s r e spo ns iv e p o l y ( 2-( 2methoxyethoxy)ethyl methacrylate-co-2-(diethylamino)ethyl methacrylate) [P(MEO 2 MA-co-DEA)] 80:20 mol % copolymer brushes were synthesized on planar silica substrates via surface-initiated activators continuously regenerated via electron transfer atom transfer radical polymerization. Brush thickness was sensitive to changes in pH and temperature as monitored with ellipsometry. At low pH, the brush is charged and swollen, while at high pH, the brush is uncharged and more collapsed. Clear thermoresponsive behavior is also observed with the brush more swollen at low temperatures compared to high temperatures at both high and low pH. Neutron reflectometry was used to determine the polymer volume fraction profiles (VFPs) at various pH values and temperatures. A region of lower polymer content, or a depletion region, near the substrate is present in all of the experimental polymer VFPs, and it is more pronounced at low pH (high charge) and less so at high pH (low charge). Polymer VFPs calculated through numerical self-consistent field theory suggest that enrichment of DEA monomers near the substrate results in the experimentally observed non-monotonic VFPs. Adsorption of DEA monomers to the substrate prior to initiation of polymerization could give rise to DEA segment-enriched region proximal to the substrate.
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