The measured S/Vp represents an average of water confined within the triple and two grain junctions. In the long displacement time, Δ ≫ lp2/Do, D (Δ)/Do asymptotes to 1/α, where α is geometric tortuosity. Tortuosity is the ratio of the path length a molecule travels in a porous media to the geometric length traversed

α = lpath/lgeom and is a measure of inter-connectivity of the pore space [28]. Here we are limited to observing the approach to asymptotic diffusion, out to Δ ∼ 1000 ms due to NMR signal loss via T1 magnetic relaxation , and therefore measure an effective α. Fig. 3 shows displacement time dependent diffusion evolution with ice aging for the ice control lacking protein, ice with ECP, ice with rIBP(2) and ice with rIBP(4). The short time slope of the Ganetespib solubility dmso D (Δ)/Do curve for the ice control yields an effective diffusion distance lp that increases from 2.5 ± 0.1 μm at t = 25 h to 4.2 ± 0.1 μm at 790 h, consistent with ice crystal growth and subsequent larger elongated liquid veins (lp = dvein/4) and planar junction thicknesses (lp = dplane). AZD5363 D (Δ)/Do of the ice control at t = 790 h approaches a larger asymptotic value, or smaller effective tortuosity α. A Padé approximation can be used to interpolate between the short and long time [29] and [30], resulting in an estimation of tortuosity [29] and [31]. The Padé fit includes a fitting parameter θ with units of time that represents the time

for a particle to diffuse the distance needed to reach the tortuosity limit. For the ice control at t = 25 h, α is 4.2, while at t = 790 h it decreases to

3.7, consistent with ice crystal coarsening. Ice with BSA (not shown) exhibited similar behaviour to the Amino acid control sample that lacked protein. The D (Δ)/Do behaviour for the ice with rIBP(4) remained stationary over 1000 h. This lack of ice microstructural evolution is evidence of irreversible IBP binding [32], and the longevity of the effect indicates microbial activity is potentially a factor for consideration in ice rheology models where ice structure is a parameter. Ice with rIBP(4) also had the smallest effective diffusion length, lp = 1.0 ± 0.5 μm, and largest tortuosity, α = 47.0, at t = 819 h, therefore providing direct experimental evidence of smaller ice crystal structure and smaller liquid veins. Ice with rIBP(2) had lp = 1.5 ± 0.5 μm and α = 12.2 at long times (t = 810), while ice with ECP had lp = 3.0 ± 0.5 μm and α = 8.9 at long times (t = 933 h). This trend suggests that larger overall crystal sizes and diffusion lengths correlate with decreasing IBP concentration. The D (Δ)/Do data asymptotes to larger diffusion values (a smaller tortuosity) with decreased IBP concentration, again indicative of larger ice crystals and larger more elongated liquid veins. Despite microstructural differences due to IBP, water content measured from the liquid state 1H NMR signal [33] was stable between 2 and 2.