Thermodynamic Properties of Crystalline Cellulose Allomorphs Studied with Dispersion-Corrected Density Functional Methods

Abstract

The phonon properties and thermodynamics of four crystalline cellulose allomorphs, Iα, Iβ, II, and III1, have been investigated using dispersion-corrected density functional theory (DFT). In line with experimental findings, the free energy differences between the studied cellulose allomorphs are small, less than 1 kJ/mol per atom. The calculated specific heat at constant volume (Cv) has been compared with the available experimental data in the temperature range 10-300 K. Quasiharmonic approximation has been employed to study thermodynamics and specific heat at constant pressure (Cp). For the studied temperature range of 10-400 K, the specific heat of all cellulose allomorphs shows very similar behavior. The calculated and experimental specific heat agree well at low temperatures below 100 K, but the deviation between theory and experiment increases with temperature. This may be due to increasing phonon anharmonicity as the temperature increases.

Keywords: cellulose; density functional theory; phonon properties; quantum chemical calculations; quasiharmonic approximation; thermodynamics.

Figure 1

(a) Chair conformation of $\beta$-D-glucose. (b) Two OH groups (inside the dotted boxes) are far apart and do not form a covalent 1,4 glycosysdic bond. (c) Chemical structure of cellulose ($\beta$-D-glucose in Haworth projection).

Figure 2

Illustration of interconversion of cellulose I and cellulose II into other cellulose allomorphs [5,6,7,8].

Figure 3

Harmonic phonon dispersion relations along high symmetry points (left) and phonon density of states (right): (a) cellulose I$\alpha$, (b) cellulose I$\beta$, (c) cellulose II, and (d) cellulose III${}_1$.

Figure 4

Temperature dependence of specific heat capacity at constant volume ($C_v$) and constant pressure ($C_p$), computed using harmonic and quasi-harmonic approximation for (a) cellulose I$\alpha$, (b) cellulose I$\beta$, (c) cellulose II, and (d) cellulose III${}_1$. Available experimental data are also plotted [12].

Figure 5

Temperature dependence of thermodynamic properties of cellulose allomorphs. (a) Specific heat capacity $C_v$ obtained with harmonic approximation. (b) Specific heat capacity $C_v$ obtained from quasi-harmonic approximation. Experimental $C_p$ is included for comparison [12].

Figure 6

Gruneisen parameter plotted as a function of temperature for cellulose allomorphs I$\alpha$, I$\beta$, II, and III${}_1$.