Compositional relaxation on the approach to the glass transition in a model trehalose solution

Molecular dynamics simulation was used to study the temperature dependence of the mutual diffusion coefficient $D_m$ and the intermediate scattering function of equilibrium and metastable aqueous solutions of the cryoprotectant molecule trehalose at very low (2.2 and $9\mathrm{wt}.\%$) and very high (80 and $95\mathrm{wt}.\%$) concentrations. The simulations were conducted over a range of temperatures approaching the glass transition temperature $T_g$ for each concentration. Similar to a recent observation made on a glass-forming model polydisperse colloidal suspension [Hannam et al., Phys. Rev. E 96, 022609 (2017)], we confirmed by a set of independent computations that $D_m$ is responsible for the long-time decay of the intermediate scattering function. We observed that $D_m$ decreased on the approach to the glass transition temperature, resulting in an extremely slow long-time decay in the intermediate scattering function that culminated in the arrest of compositional fluctuations and a plateau in the intermediate scattering function at $T_g$. In both cases, crystallization requires a change in the composition of the solution, which is a process controlled by $D_m$. This transport coefficient can either increase or decrease as solidification is approached, because it depends on a product of thermodynamic and mobility factors. Our observations show that in both cases, for the glass-forming liquids, it is observed to decrease, while for a previously studied monodisperse colloidal suspension which crystallizes easily, it increases. The similarity in the behavior of these two very different glass-forming systems (the polydisperse colloidal suspension and the sugar solution) shows the importance of the mutual diffusion coefficient to our understanding of vitrification and suggests a possible distinction between between glass-forming and crystallizing solutions.

Figure 1

$\alpha ,\alpha$-Trehalose where hydrogen atoms have been omitted for clarity. All carbon and oxygen atoms have been labeled.

Figure 2

Plot of the constant pressure heat capacity $C_p$ as a function of temperature for trehalose wt.% concentrations shown in the legend.

Figure 3

Plot of the phenomenological coefficient $L_{11}$ calculated from Eq. (9) for (a) 2.2 wt.% and (b) 95 wt.% trehalose for temperatures approaching each concentration's corresponding glass transition temperature $T_g$. Note the $x$ axis scales differ.

Figure 4

Plot of the low-$k$ values of the static structure factors of a system at a concentration of 95 wt.% and temperature of $600\text{K}$. A fourth-order polynomial line of best fit was used to obtain the $S_{\alpha \beta }\left(0\right)$ values.

Figure 5

Plot of the thermodynamic factor $\partial {\mu }_1/\partial n_1$ calculated from Eq. (10) for (a) 2.2 wt.% and (b) 95 wt.% trehalose for temperatures approaching the corresponding glass transition temperature $T_g$. Note the $x$- and $y$-axis scales differ.

Figure 6

Plot of the mutual diffusion coefficient $D_m$ calculated from Eq. (8) for (a) 2.2 wt.% and (b) 95 wt.% trehalose for temperatures approaching the corresponding glass transition temperature $T_g$. Note the $x$- and $y$-axis scales differ.

Figure 7

Plot of the intermediate scattering function $F(k,\tau )$ of the water molecules at trehalose weight fractions of (a) 0 wt.%, (b) 2.2 wt.%, and (c) 9.0 wt.% at a low wave vector of $0.3372{\AA }^{-1}$ and temperature of 298 K. Also shown is the total multiexponential fit and the various mode contributions.

Figure 8

Plot of wave-vector-dependence of the long-time mode (a) decay coefficients $D_m\left(k\right)$ and (b) amplitudes $A_m\left(k\right)$. Data at trehalose concentration of 2.2 wt.% and temperatures shown in the legend. Independently calculated values of $D_m$ from Fig. 6 are shown as arrows and dotted line shows average of $D_m\left(k\right)$ taken over the $k$ range shown.

Figure 9

Plot of the water intermediate scattering function $F(k,\tau )$ at trehalose weight fractions of (a) 2.2 wt.% and (b) 9 wt.% at 298 K for wave vectors $k$ shown in the legend. Inset shows $S\left(k\right)$ at low wave vectors to help visualize the position of the wave vectors in the structure factor.

Figure 10

Plot of the water intermediate scattering function $F(k,\tau )$ at trehalose weight fractions of (a) 2.2 wt.% and (b) 95.0 wt.% at $k=0.33{\AA }^{-1}$ for temperatures leading down to the glass transition.