Glass Dynamics and Domain Size in a Solvent-Polymer Weak Gel Measured by Multidimensional Magnetic Resonance Relaxometry and Diffusometry

Nathan H. Williamson, April M. Dower, Sarah L. Codd, Amber L. Broadbent, Dieter Gross, and Joseph D. Seymour

Phys. Rev. Lett. 122, 068001 – Published 12 February 2019

Abstract

Nuclear magnetic resonance measurements of rotational and translational molecular dynamics are applied to characterize the nanoscale dynamic heterogeneity of a physically cross-linked solvent-polymer system above and below the glass transition temperature. Measured rotational dynamics identify domains associated with regions of solidlike and liquidlike dynamics. Translational dynamics provide quantitative length and timescales of nanoscale heterogeneity due to polymer network cross-link density. Mean squared displacement measurements of the solvent provide microrheological characterization of the system and indicate glasslike caging dynamics both above and below the glass transition temperature.

Received 27 March 2018
Revised 7 November 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.068001

Physics Subject Headings (PhySH)

Anomalous diffusion Diffusion Rheology

Gels Glassy systems

Polymers & Soft Matter

Authors & Affiliations

Nathan H. Williamson¹, April M. Dower¹, Sarah L. Codd², Amber L. Broadbent³, Dieter Gross⁴, and Joseph D. Seymour^1,*

¹Department of Chemical and Biological Engineering Montana State University, Bozeman, Montana 59717-3920, USA
²Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, Montana 59717, USA
³Bend Research Incorporated, Lonza, Bend, Oregon 97701, USA
⁴Bruker Biospin Corp., 76275 Ettlingen, Germany

^*Corresponding author. jseymour@montana.edu

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Vol. 122, Iss. 6 — 15 February 2019

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Images

Figure 1
Glass transitions indicated by $T_{1} − T_{2}$ distributions of 45% wt acetone (column 1), 7% wt acetone (column 2), and 2.3% wt acetone SDD (column 3) at 60 (top row), 22 (middle row), and $- 18 ° C$ (bottom row). The glass transition temperatures for these concentrations are $- 131$ , 47, and $93 ° C$ , respectively. The dashed line is the parity line $T_{1} = T_{2}$ for liquidlike behavior.
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Figure 2
$T_{2} − T_{2}$ exchange distributions of the 7% wt acetone/HPMCAS sample at $22 ° C$ for two of the mixing times (a) $t_{m} = 1 ms$ and (b) $t_{m} = 100 ms$ . (c) Calculated mixing peak intensities as a function of $T_{2} − T_{2}$ mixing time. Exchange model fit (red;gray) between populations $B$ and $C$ with exchange correlation time $τ_{corr} \sim 9.5 ms$ (95% confidence interval [8.0, 10.9]). Exchange model fit (blue;black) between populations $A$ and $C$ with exchange correlation time $τ_{corr} \sim 11 ms$ (95% C.I. [9.2,12.9]). Using the acetone diffusion coefficient $D = 1.1 \times 10^{- 12} m^{2} / s$ measured for the sample at $22 ° C$ gives a correlation length between populations $B$ and $C$ of $l_{corr} \sim 250 nm$ and between populations $A$ and $C$ of $l_{corr} \sim 270 nm$ .
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Figure 3
$T_{2} − T_{2}$ exchange distributions of the 7% wt acetone/HPMCAS sample at $60 ° C$ for two of the mixing times (a) $t_{m} = 1$ and (b) $t_{m} = 100 ms$ . (c) Calculated mixing peak intensities as a function of $T_{2} − T_{2}$ mixing time. Exchange model fit (red;gray) between populations $B$ and $C$ with exchange correlation time $τ_{corr} \sim 75 ms$ (95% C.I. [44.1,105.9]). Exchange model fit (blue;black) between populations $A$ and $C$ with exchange correlation time $τ_{corr} \sim 46 ms$ (95% C.I. [23.8,69.1]). Using the acetone diffusion coefficient $D = 3.5 \times 10^{- 12} m^{2} / s$ measured for the sample at $60 ° C$ gives a correlation length between populations $B$ and $C$ of $l_{corr} \sim 1.3 μ m$ and between populations $A$ and $C$ of $l_{corr} \sim 980 nm$ .
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Figure 4
PGSE measurements of (a) the effective acetone self-diffusion coefficient plotted against the diffusive length scale. The slope of the lines were used to find the ratio of pore volume to surface area. At $60 ° C$ , $(V_{p} / S) = 1.4 μ m$ and at $22 ° C$ , $(V_{p} / S) = 590 nm$ . (b) Mean squared displacement of acetone $⟨ z^{2} ⟩$ . Lines are power law fits of the form $⟨ z^{2} (Δ) ⟩ \sim Δ^{α}$ to portions of the data. The MSD plateaus between 80–190 ms at $60 ° C$ and 40–130 ms at $22 ° C$ . The plateaus occur at a length scale of $l_{c} \sim {⟨ z^{2} ⟩}^{1 / 2} = 710 nm$ at $60 ° C$ and 320 nm at $22 ° C$ . The power law fits after the plateau region indicate subdiffusion with $α = 0.69$ (95% C.I. [0.63,0.75]) at $22 ° C$ and 0.71 (95% C.I. [0.61,0.81]) at $60 ° C$ .
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