Two-step build-up of a thermoreversible polymer network: From early local to late collective dynamics

We probe the mechanisms at work in the build-up of thermoreversible gel networks, with the help of hybrid gelatin gels containing a controlled density of irreversible, covalent crosslinks (CLs), which we quench below the physical gelation temperature. The detailed analysis of the dependence on covalent crosslink density of both the shear modulus and optical activity evolutions with time after quench enables us to identify two stages of the physical gelation process, separated by a temperature-dependent crossover modulus: (i) an early nucleation regime during which rearrangements of the triple-helix CLs play a negligible role, and (ii) a late, logarithmic aging one, which is preserved, though slowed down, in the presence of irreversible CLs. We show that aging is fully controlled by rearrangements and discuss the implication of our results in terms of the switch from an early, local dynamics to a late, cooperative long-range one.

Figure 1

Evolution of the shear modulus of a 5 wt % gelatin gel in water at $T={20}^{\circ }\text{C}$, vs logarithm of time after quench. The dashed line fits the late aging behavior. The double bar indicates the crossover region as deduced from optical data (see Sec. 3a). Inset: same data in the lin-log representation.

Figure 2

(a) Shear modulus dependence on time after quench to $T={20}^{\circ }\text{C}$ of a set of hybrid gels with various densities of covalent crosslinks. The labels indicate the values of the shear modulus $G_{ch}$ of the corresponding chemical networks. (b) Evolution of the renatured collagen fraction $\chi$ for the same gels. Data from the $G_{ch}=1480$ Pa gel have been discarded due to the smallness of the corresponding signal-to-noise ratio.

Figure 3

Early evolution of the excess shear modulus $\Delta G\left(t\right)=G\left(t\right)-G_{ch}$. Same data as in Fig. 2.

Figure 4

Same data as in Fig. 2: each hybrid gel curve has been shifted along the time axis so as to allow comparison with the purely physical gel one $G_{ph}\left(t\right)$ (black curve, solid dots). $t_0\left(G_{ch}\right)$ is the time at which $G_{ph}=G_{ch}$. The hatched strip indicates the end of the early regime. The double vertical bar indicates the crossover range as obtained from $\chi \left(G\right)$ data (see Sec. 3a).

Figure 5

(a) Helix fraction $\chi$ vs shear modulus $G$ for the physical gel at $T={20}^{\circ }\text{C}$. The thick dashed line is the linear fit to the initial regime ending at $G=G_{\chi }^{☆}$. Inset: Inverse of the linear regime slope, $dG/d\chi$, vs reduced departure from gelation temperature $T_g={30}^{\circ }\text{C}$. (b) Helix fraction vs shear modulus for a hybrid gel with $G_{ch}=253$ Pa at $T={20}^{\circ }\text{C}$. Inset: End of linear regime $G_{\chi }^{☆}$ vs chemical modulus $G_{ch}$ at the same temperature.

Figure 6

Logarithmic slope $\Gamma =dG/d\left({log}_{10}t\right)$ vs $G_{ch}$ for hybrid gels at $T={20}^{\circ }\text{C}$. Solid line: best fit $\Gamma =Aexp(-G_{ch}/\mathcal{G})$ with $\mathcal{G}=685$ Pa. The purely physical gel data point (solid dot) has been excluded from the fit (see text). Inset: $\Gamma$ vs $G_{ch}$ at different temperatures below $T_g$.

Figure 7

Modulus build-up curves $G_{ph}\left(t\right)$ at different temperatures. The circles indicate the crossover modulus ${\overline{G}}_{\chi }^{☆}$. The squares indicate the modulus $\mathcal{G}$ characteristic of the sensitivity of gel aging to $G_{ch}$ (see Table 1).