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

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.

FIG. 1.

Glass transitions indicated by T₁-T₂ 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 T₁ = T₂ for liquidlike behavior.

FIG. 2.

T₂-T₂ 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 T₂-T₂ mixing time. Exchange model fit (red;gray) between populations B and C with exchange correlation time τ_corr ~ 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 ~ 11 ms (95% C.I. [9.2,12.9]). Using the acetone diffusion coefficient D = 1.1 × 10^–12 m²/s measured for the sample at 22 °C gives a correlation length between populations B and C of l_corr ~ 250 nm and between populations A and C of l_corr ~ 270 nm.

FIG. 3.

T₂-T₂ 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 T₂-T₂ mixing time. Exchange model fit (red;gray) between populations B and C with exchange correlation time τ_corr ~ 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 ~ 46 ms (95% C.I. [23.8,69.1]). Using the acetone diffusion coefficient D = 3.5 × 10^–12 m²/s measured for the sample at 60 °C gives a correlation length between populations B and C of l_corr ~ 1.3 μm and between populations A and C of l_corr ~ 980 nm.

FIG. 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 μm and at 22 °C, (V_p/S) =590 nm. (b) Mean squared displacement of acetone $\langle z^2\rangle .$ Lines are power law fits of the form $\langle z^2(\Delta )\rangle ~{\Delta }^{\alpha }$ 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 $l_c~{\langle z^2\rangle }^{1/2}=710\text{nm}$ 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.