Glassy behavior of a percolative water-protein system

We show that is possible to look at the glass transition as a percolation transition in phase space. This study has been carried out on a hydrated globular enzyme for which the thermodynamic transition and the percolative transition could have a functional significance. The approach adopted is based on the identity of roles played respectively by the glass transition temperature $T_o$ and the critical hydration threshold $h_c$ for the percolation of protons on the surface and through the protein, given that dynamical arrest is observed at temperatures and hydration below $T_o$ and $h_c$. Theoretical predictions for temperature dependence of the nonexponentiality parameter, ${\beta }_{\mathrm{KWW}}$, appearing in the KWW relaxation function, indicate that at high temperatures, ${\beta }_{\mathrm{KWW}}$ remains insensitive to temperature changes, whereas in the vicinity of the glass transition, ${\beta }_{\mathrm{KWW}}$ is linearly increasing with temperature. The low temperature limit of ${\beta }_{\mathrm{KWW}}$ is about $1∕3$ and its temperature-independent behavior starts at $1.23T_g$: both predictions have been verified in the present study.

Figure 1

Angular frequency $\left(\omega \right)$ dependence of the real (left axis) and imaginary (right axis) components of the measured electric modulus for a lysozyme sample at $T=270\mathrm{K}$, $h=0.26\mathrm{g}∕\mathrm{g}$. The lines through the data are the result of a fit procedure that takes into account the complex admittance of low frequency dispersion and sample relaxations. The inset shows a detail of the low frequency peak due to sample conductivity.

Figure 2

Temperature dependence of the parameter $d$ appearing in Eq. (2).

Figure 3

Temperature dependence of the main relaxation time ${\tau }_{\text{main}}\left(T\right)$ (closed symbols). The solid line through the data represents the fit with a VFT equation ($T_0=193\mathrm{K}$, ${\tau }_0=1.33\times {10}^{-7}\mathrm{s}$, and $B_T=544\mathrm{K}$). On the right axis, the temperature dependence of the conductivity relaxation time ${\tau }_{\sigma }\left(T\right)$ is shown (open symbols). The conductivity relaxation time is defined as the inverse of the angular frequency where a maximum appears in the imaginary component of the electric modulus (see inset in Fig. 1). The limited data range for the conductivity relaxation time is due to the simultaneous presence in the measured spectra of sample dielectric relaxations, interfacial relaxation, and polarization electrode effects that at high temperature does not allow an easy and unambigous determination of the conductivity relaxation time.

Figure 4

Temperature dependence of the nonexponentiality parameter ${\beta }_{\mathrm{KWW}}$. The solid line is a linear fit of the data in the interval (1.0,1.2). Dashed vertical line is drawn at $T=1.23T_{g_D}$ representing the crossover temperature between two distinct dynamical regimes.