Elastic and Dynamic Heterogeneity in Aging Alginate Gels

Abstract

Anomalous aging in soft glassy materials has generated a great deal of interest because of some intriguing features of the underlying relaxation process, including the emergence of "ultra-long-range" dynamical correlations. An intriguing possibility is that such a huge correlation length is reflected in detectable ensemble fluctuations of the macroscopic material properties. We tackle this issue by performing replicated mechanical and dynamic light scattering (DLS) experiments on alginate gels, which recently emerged as a good model-system of anomalous aging. Here we show that some of the monitored quantities display wide variability, including large fluctuations in the stress relaxation and the occasional presence of two-step decay in the DLS decorrelation functions. By quantifying elastic fluctuation through the standard deviation of the elastic modulus and dynamic heterogeneities through the dynamic susceptibility, we find that both quantities do increase with the gel age over a comparable range. Our results suggest that large elastic fluctuations are closely related to ultra-long-range dynamical correlation, and therefore may be a general feature of anomalous aging in gels.

Keywords: alginate; dynamic heterogeneity; elastic heterogeneity; physical gels.

Figure 1

Torsional relaxation modulus vs. time for samples conditioned at different waiting times: 6 (blue), 9 (red), 12 (yellow), 24 (purple) and 48 h (green).

Figure 2

Average stress as a function of stretch ratio for samples conditioned at five different waiting times (increasing from bottom to top), as indicated. Each set of data were averaged over 12 tests. For the sake of clarity, the error-bars report only $$\frac{1}{5}$$ of the actual standard deviation. Inset shows the average initial compressive modulus and its actual standard deviation.

Figure 3

DLS measurements. Panels (a,b) report the intensity correlation function $$g_2\left(\tau ,q\right)-1$$ at different q-vectors for two samples, both conditioned for 6 h. From top to bottom, $$q$$ varies from 0.304 to 4.4 $${\mathsf{\mu }\mathrm{m}}^{-1}$$. Lines in panels (a,b) are single or double compressed exponential fits, respectively; see Equation (2).

Figure 4

(a) At increasing waiting times from bottom to top, 6 (blue), 9 (red), 12 (yellow), 24 (purple) and 48 h (green): late decorrelation times (circles) vs. q for the two replicas. For the four samples showing a two-step decay, early decorrelation times (squares) are also reported after being divided by a factor of 10. The line is a power law with exponent −1. (b) Wave-vector dependence of the height of the intermediate plateau in the double step functions of Figure 3b.

Figure 5

(a) An example of 2-D small-angle intensity scattering pattern for a sample at t_w = 6 h. Pixels corresponding to the same $$\left|\overrightarrow{q}\right|=3.28 \mu m^{-1}$$ have been highlighted by solid lines. Different line colors correspond to the different direction ranges used to evaluate the correlation functions reported in panel (b) as a function of time (colors in panel b correspond to those of panel a).

Figure 6

(a) Dynamic susceptibility $${\chi }_4\left(\tau ,q\right)$$ at $$q=3.3 {\mathsf{\mu }\mathrm{m}}^{-1}$$ and for different waiting times as indicated. (b) Maximum of the dynamic susceptibility $${\chi }_4^{*}$$ and standard deviation of the elastic modulus $$s_{E_0}$$, both normalized by their value at $$t_w=12 \mathrm{h}$$, as a function of the waiting time.

Figure 7

SEM of strontium alginate aerogels by sc-CO₂ drying at different magnifications: 40,000× (a) and 160,000× (b). The average size of the pores corresponds to the characteristic length-scale obtained comparing DLS and rheology ($${\lambda }_o\simeq 200\mathrm{nm}$$).