# Computational protocol for heat capacity and thermal conductivity of nanofluids

MaX researchers at ICN2 in Barcelona have developed a new computational protocol to understand thermal energy storage in molten salts and nanofluids. The protocol, in the form of a ready-to-use workflow, will be soon publicly available and will permit to calculate the heat capacity and the thermal conductivity of nanofluids. The protocol has been tested in the case of a particular nanofluid consisting in carbon graphene nanoflakes dispersed in DMF.

Ionic liquids and molten salts are used by the industry for many thermal applications, including the storage and transport of thermal energy in solar energy plants. A more efficient heat storage and transport media can be obtained by introducing nanoparticles dispersed in the liquid to create a so-called nanofluid. The determination of thermo-physical properties such as heat capacity, self-diffusion and heat conductivity as a function of the nano-scale structure of the nanofluids is a fundamental step both experimentally and theoretically. The newly developed protocol permits to determine these properties and to address their dependence on the composition and concentration of the nanoparticles in nanofluids of organic solvents, ionic liquids and molten salts.

The method, that implements the 2PT approach [1-3] in a post-processing code, takes as input the classical MD trajectories and permits to partition atomic velocities into translational, rotational, and vibrational contributions, to compute the velocity autocorrelation functions (VACF) and the density of states (DoS), and finally to calculate thermal properties, in particular the quantum and the classical heat capacities as weighted integrations of the DoS.

Nanofluid Test Case: Graphene Nanoflakes dispersed in DMF

Fig.1: Graphene nanoflakes of different sizes dispersed in DMF. In all the systems, the proportion of the number of carbon atoms to DMF molecules is constant (0,24), although the size of the particles varies, increasing from left to right, and the number of DMF molecules increases proportionally. From left to right, the number of carbon atoms and DMF molecules in the simulation cell are: 24/100, 54/225, 138/575, 348/1450, 942/3925, 2022/8425.

An interesting application is the calculation of graphene nanoflakes dispersed in DMF, that represent a model for a nanofluid. As a first step we calculated the isobaric heat capacity of a pure dimethylformamide (DMF) solvent by combining OPLS/A forcefield and the 2PT method. The result obtained, Cp=149.2 J/mol/K, is in excellent agreement with the experimental value (148.3 J/mol/K).  We moved then to analyse our organic nanofluid. To establish the convergence of the heat capacity with flake size, we performed a series of simulations of nanoflakes  ranging from 24 to 2011 carbon atoms at a fixed concentration of DMF (see Fig.1); we  demonstrated that our protocol works well for obtaining the isochoric heat capacity, even for much larger nanoflakes that can now be simulated at the atomistic level. Our preliminary results show an increase in Cv of the nanofluid compared to the pure DMF solvent, although so far less pronounced than has experimentally been reported [4].

For the same systems we calculated the heat flux autocorrelation function by implementing the Green-Kubo relation, and then after integration on time, the thermal conductivity. Results obtained for different configurations (from 24 to 942 carbon atoms diluted in DMF) are reported as a function of the correlation time (see Fig.2). For all the considered systems, the integral converges to a plateau value after 20-50 ps.

Fig 2: Thermal conductivity obtained with the Green-Kubo equation as a function of the upper integration limit. The lower set of lines show the convection part of the conductivity, obtained from the first term in equation for the flux, J(t), which converges to a plateau value after 20-50 ps (see also the inset using a linear time scale). The plateau value for the total conductivity (convection + vibrational/phononic parts) is noisier.

[1] S-T. Lin, P. K. Maiti, and W. A. Goddard III. J. Phys. Chem B, 114:8191, 2010. DOI: 10.1021/jp103120q
[2] T. A. Pascal, S.-T. Lin, and W. A. Goddard III. Phys. Chem. Chem. Phys., 13:169, 2011. DOI: 10.1039/c0cp01549k
[3] R. Hentschke. Nanoscale Research Letters, 11:88, 2016. DOI: 10.1186/s11671-015-1188-5
[4] R. Rodriguez and P. Gomez, to be published.