Thermoporoelastic Moduli from Molecular Fluctuations and Application to Moisture Effect on Amorphous Cellulose

Although imperceptible at the macroscale, fluctuations of physical properties are ubiquitous at the nanoscale because of thermal agitation. While fluctuations are detrimental to the accuracy of molecular simulations, their magnitude is actually a great source of information since it quantifies the elasticity of the system with respect to any evolution of the control variables. Fluctuation formulas are well known for fluids or solids but have not yet been derived for porous media. In this article, we derive fluctuation formulas for all the moduli involved in thermoporoelasticity. These fluctuation formulas are applicable even for adsorbing media and can be used for poroelasticity extended to adsorption, whereas usual poroelasticity assumes a bulk fluid in the pores. Moreover, the practical application of the fluctuation formulas in molecular simulation is straightforward, as one only needs to collect extensive quantities readily accessible and at almost no additional computational cost. The application of these fluctuation formulas is illustrated by considering a typical example of mechanosorption coupling, namely, amorphous cellulose submitted to moisture at various relative humidities. The thermoporoelastic behavior is fully characterized from the fluctuations computed during molecular simulation of amorphous cellulose. Some peculiarities of moisture-induced behavior of cellulose are discussed, such as the high Biot coefficient, the negative Biot modulus, the negative thermal expansion, and the high heat capacity. This work investigates only the case of a pure fluid in the pores with volumetric deformations but can be easily extended to fluid mixture and shearing effects.