Unusual specific heat of almost dry L-cysteine and L-cystine amino acids

A detailed quantitative analysis of the specific heat in the 0.5- to 200-K temperature range for almost dry L-cysteine and its dimer, L-cystine, amino acids is presented. We report the occurrence of a sharp first-order transition at $\sim 76$ K for L-cysteine associated with the thiol group ordering which was successfully modeled with the two-dimensional Ising model. We demonstrated that quantum rotors, two-level systems (TLS), Einstein oscillators, and acoustic phonons (the Debye model) are essential ingredients to correctly describe the overall experimental data. Our analysis pointed out the absence of the TLS contribution to the low temperature specific heat of L-cysteine. This result was similar to that found in other noncrystalline amorphous materials, e.g., amorphous silicon, low density amorphous water, and ultrastable glasses. L-cystine presented an unusual nonlinear acoustic dispersion relation $\omega \left(q\right)=v{q}^{0.95}$ and a Maxwell-Boltzmann–type distribution of tunneling barriers. The presence of Einstein oscillators with ${\Theta }_E\sim 70$ K was common in both systems and adequately modeled the boson peak contributions.

Figure 1

Total and addenda heat capacity measurements for the $1.00$-mg L-cysteine sample in the 0.5- to 200-K temperature range. The inset shows the low-temperature $(\lesssim 3$ K) data.

Figure 2

(a) Relaxation data used to determine the specific heat $c\left(T\right)$ around $T_c\sim 76$ K. (b) $c\left(T\right)$ data close to the first-order transition obtained from Eq. (11).

Figure 3

The $c$ vs $T$ experimental data (open circles) and fitted curve to Eq. (12) for (a) L-cysteine (red dashed line) and (b) L-cystine (green dashed line) in Scenario II. The Ising contribution was not considered for L-cystine. Solid black lines show the individual contributions. The best fit parameters are shown in Table 1.

Figure 4

The $c/T^3$ vs $T$ data (open circles) for (a) L-cysteine and (b) L-cystine. The dashed blue lines correspond to best fit to Scenario I in the $0.5<T<T_{\min }$. $T_{\min }$ was 4 K and 8 K for L-cysteine (a) and L-cystine (b), respectively. Fitted curves to Eq. (12) for L-cysteine (red dashed line) (a) and L-cystine (green dashed line) (b) in Scenario II are also shown. Solid black lines show the individual contributions. The best fit parameters are shown in Table 1.

Figure 5

Low temperature specific heat contribution from $c_{\alpha }$ (solid lines) for $0.90<\alpha <1.10$ in the L-cysteine $[{\Theta }_D=268$ K (a)] and L-cystine $[{\Theta }_D=232$ K (b)] cases for Scenario II. The open circles are the experimental data.

Figure 6

The $c$ vs $T$ experimental data (open circles) and fitted curve to Eq. (12) (solid curves) for (a) L-cysteine and (b) L-cystine (Scenario III). The best fit parameters are shown in Table 1.

Figure 7

The $c/T^3$ vs $T$ experimental data (open circles) and fitted curve to Eq. (12) (solid curves) for (a) L-cysteine and (b) L-cystine (Scenario III). The best fit parameters are shown in Table 1.