Nanoscale water-polymer interactions tune macroscopic diffusivity of water in aqueous poly(ethylene oxide) solutions

Abstract

The separation and anti-fouling performance of water purification membranes is governed by both macroscopic and molecular-scale water properties near polymer surfaces. However, even for poly(ethylene oxide) (PEO) - ubiquitously used in membrane materials - there is little understanding of whether or how the molecular structure of water near PEO surfaces affects macroscopic water diffusion. Here, we probe both time-averaged bulk and local water dynamics in dilute and concentrated PEO solutions using a unique combination of experimental and simulation tools. Pulsed-Field Gradient NMR and Overhauser Dynamic Nuclear Polarization (ODNP) capture water dynamics across micrometer length scales in sub-seconds to sub-nanometers in tens of picoseconds, respectively. We find that classical models, such as the Stokes-Einstein and Mackie-Meares relations, cannot capture water diffusion across a wide range of PEO concentrations, but that free volume theory can. Our study shows that PEO concentration affects macroscopic water diffusion by enhancing the water structure and altering free volume. ODNP experiments reveal that water diffusivity near PEO is slower than in the bulk in dilute solutions, previously not recognized by macroscopic transport measurements, but the two populations converge above the polymer overlap concentration. Molecular dynamics simulations reveal that the reduction in water diffusivity occurs with enhanced tetrahedral structuring near PEO. Broadly, we find that PEO does not simply behave like a physical obstruction but directly modifies water's structural and dynamic properties. Thus, even in simple PEO solutions, molecular scale structuring and the impact of polymer interfaces is essential to capturing water diffusion, an observation with important implications for water transport through structurally complex membrane materials.

Fig. 1. Distinct experimental and computational techniques probe small molecule diffusion processes occurring over vastly different length and time scales. Techniques such as MD simulations and ODNP can uncover molecular-scale dynamic behavior of small molecules in polymers or polymer solutions while tools like PFG-NMR and membrane permeation experiments reveal macroscopic transport phenomena.

Fig. 2. (A) Comparison of water self-diffusion coefficients in aqueous PEO solutions at room temperature (21 °C) from PFG-NMR (filled blue circles) with system-average water diffusivities (D_H2O, filled red triangles) and local water diffusivities (D_local, unfilled red triangles) from MD simulations. (B) Comparison of PFG-NMR water diffusivities in aqueous PEO solutions (black circles) with model fits for Stokes–Einstein (blue dashed curve), Mackie–Meares (red dotted curve), free volume theory (green solid curve), and Yasuda's free volume approximation (purple dashed/dotted curve). PEO overlap concentration (c*) is marked in both figures by a dashed black line (see ESI for c* derivation).

Fig. 3. Free volume model for water self-diffusion coefficients in PEO determined by PFG-NMR using fractional free volume (FFV) values derived from experimental solution densities (black circles and solid green line) compared to free volume model fit for system-average water self-diffusion coefficients determined by MD simulations using FFV values derived from MD simulations (black triangles and dashed green line).

Fig. 4. Comparison of PFG-NMR water diffusivities in aqueous glycerol solutions (black circles) with model fits for Stokes–Einstein (blue dashed curve), Mackie–Meares (red dotted curve), free volume theory (green solid curve), and Yasuda's free volume approximation (purple dashed/dotted curve).

Fig. 5. (A) Comparison of water diffusion coefficients in PEO solutions determined by PFG-NMR (filled blue circles), ODNP with PEO-tethered spin labels (unfilled gold squares), and ODNP with free TEMPOL spin labels (filled gold squares). PEO overlap concentration (c*) is marked by a dashed black line. (B) MD snapshots illustrating first hydration waters around TEMPO spin label on PEO chain end for 5 and 20 wt% aqueous PEO solutions. Orange molecules represent PEO chains, grey circles represent water molecules beyond first hydration layer, and cyan surface represents volume enclosing first hydration shell waters.

Fig. 6. (A) Radial distribution functions of water molecules near PEO chains maintain similar shapes with increasing PEO concentration from 0.5 to 50 wt% with a systematic increase in the 1st and 2nd peak heights (darker colors correspond to higher concentrations). (B) MD-derived local and system-averaged water self-diffusivities in PEO solutions generally correlate with the coordination number of the first hydration shell. (C) Three-body angle distributions show enhancement in the tetrahedrality of water (109.5°) in the hydration layer near PEO chains with increasing PEO concentration from 0.5 to 50 wt% (darker colors correspond to higher concentrations). (D) The integral over the tetrahedral region of the three-body angle distributions P(θ), indicated by the shaded region in part A, correlates with both local and system-averaged water self-diffusivities in PEO solutions derived from MD simulations.