The Transport Properties of Sodium Atoms and the Heat Capacity of Sodium Dimers at High Temperatures

Abstract

Including the contribution of excited state atoms can improve calculations of dilute gaseous transport properties at high temperatures. For sodium, experimental and/or theoretical information is available about the potential energy curves associated with each of ten low-lying states of the sodium dimer. These include the X 1 g + and 3 u + states that dissociate to two ground state 2 S sodium atoms and the four 3 g,u + , 1 g,u + , 1 g,u , 3 g,u gerade/ungerade pairs of states that dissociate to a ground state 2 S atom and an excited state 2 P atom. Nine of these are bound states and have been fitted with the Hulburt-Hirschfelder potential, a very good general purpose atom-atom potential. The 3 g state is not bound and has been fitted with the exponential repulsive potential. We have used these potentials to calculate viscosity collision integrals as a function of temperature, and employed degeneracy-weighted averaging to determine the viscosity and translational contribution to the thermal conductivity of the sodium atoms. These same potentials have been used to calculate the heat capacity, C o p , of the sodium dimer using an approach that depends on the second virial coefficient and its first two temperature derivatives. Again, the inclusion of molecular states that dissociate to an excited state atom allows C o p to be determined with improved accuracy at higher temperatures. Thus, thermophysical property calculations for sodium have been extended to 25,000 K. These results are compared with previous results, including heat capacities given in the NIST-JANAF Thermochemical Tables.

High-temperature ideal-gas partition function of the ${{\rm{H}}}_{2}^{+}$ molecule

“…However, in recent years interest in this topic has grown. The molecules (diatomics) to which it has been applied are Na 2 [9][10][11], N 2 [12], O 2 [13], MgH [3] and BBr [14].…”

High-Temperature Heat Capacity of the $${\text {Na}}_{2}$$ Molecule

“…The bound (excluding the negative contribution) and unbound versions of heat capacity are compared in Table 4. The NIST [1] data and Biolsi's results for the ground and first excited state are also displayed [9]. Inclusion of the first excited state changes all the results especially those with all unbound states (C U p ) even at the lowest temperature of 2000 K which is actually not surprising because it is a low excited state dissociating to the same limit as the ground state.…”

“…As discussed later the accuracy of the PECs at low and high inter-atomic distances is crucial so it is important to use ab initio PECs fitted to actually calculated energies as in Zhang et al [13], not ones which are based only on spectroscopic constants (which describes best the vicinity of the PEC minimum and are often empirical) as in Biolsi [9] and Song et al [4].…”

“…The unbound states (both metastable and scattering) also significantly influence thermodynamic quantities; the heat capacity is again the most sensitive. The recent tendency is to use all the unbound states in thermodynamic calculations [7][8][9]. Fortunately, in the case of the classical approach, it is the simplest option available but at high temperatures one also needs to know the purely repulsive PECs (potential energy curves) to describe all the interactions between the atoms.…”

The Ideal Gas and Real Gas Heat Capacity of Sodium Atoms

“…When a ground state atom interacts with an atom in the first excited ( 2 P) state, they can interact along eight potential energy curves, the 1 + g,u , 3 + g,u , 1 g,u , and 3 g,u gerade/ungerade pairs of states [31]. Interactions between two excited 2 P atoms become important [32] above ∼20 000 K but, as discussed below, non-ideal effects have essentially vanished below 10 000 K.…”