Gases dilute polyatomic

A kinetic theory for dilute polyatomic gases has been developed by Wang-Chang and Uhlenbeck (W3, U3). No calculations have been made of the diffusion coefficients on the basis of this theory, however. For most polyatomic gases the results of the Chapman-Enskog monatomic gas theory seem to be adequate. 

The first Chapman-Cowling approximation to the thermal conductivity of a dilute polyatomic gas within the two-flux approach leads to a total value that is the sum of two contributions related to translational and internal degrees of freedom respectively ... 

Formally, the relationship between the coefficient of viscosity of a dilute polyatomic gas and the related effective cross section is identical to that for monatomic gases (Chapter 4). In a practical, engineering form it is given by... 

When treating polyatomics it is convenient to define an average molecular partition function, In = (lnQ)/N, for an assembly of N molecules. In the dilute vapor (ideal gas) this introduces no difficulty. There is no intermolecular interaction and In = (In Q)/N = ln(q) exactly (q is the microcanonical partition function). In the condensed phase, however, the Q s are no longer strictly factorable. Be that as it may, continuing, and assuming In = (In Q)/N, we are led to an approximate result which is superficially the same as Equation 5.10,... 

What quantity describes best the totahty of these solute-solvent interactions and how can the various contributions to them be estimated Let the pure solute B be vaporized in an imaginary process to a gas, and let this gas be very dilute, so that it obeys the ideal gas laws. In this condition each particle of the solute (molecule or ion) is very remote from any neighbor and has no environment with which to interact. If B is polyatomic, it does have its internal degrees of freedom, such as bond vibrations and rotation of the particle. 

Here, as earlier, we are restricting our attention to systems of pure monatomic gases. The theory as well as the comparison with experiment can be generalized to include dilute gas mixtures and dilute gases of polyatomic molecules (cf. Sections 2.4.4.1 and 2.4.4.2). 

The dilute-gas theory is presented here for the first time in terms of effective collision cross sections in a comprehensive readily usable form which applies to both polyatomic fluids and monatomic fluids. This description should now be used exclusively but, because it is relatively new, expressions are given for the macroscopic quantities in terms of these effective cross sections, and certain simple relationships between these effective cross sections and the previously used collision integrals are also described. 

The initial density dependence of the thermal conductivity of a polyatomic gas is given by expression (5.7). Neither the Rainwater-Friend model nor the modified Enskog theory accounts for the contribution of internal degrees of freedom, but it is assumed that this can be modeled as a purely diffusive process following an idea originally introduced by Mason Monchick (1962) for dilute gases... 

Calculation of the initial density dependence of the thermal conductivity for polyatomic gases requires knowledge of the translational and internal mode contributions to the dilute-gas thermal conductivity. Thus,... 

For the thermal conductivity of a polyatomic gas one further extension of the MET is necessary to account for the internal degrees of freedom of the molecule and the transport of internal energy. This is accomplished with the aid of the assumption that the transport of internal energy is diffusive and that there is no relaxation of internal energy. This approximation is similar to that discussed in Chapter 4 for dilute gases and enables one to write... 

As an example of the practical utility of MEMO simulations of the thermal conductivity, a summary of a calculation by Ravi et al. (1992) is given. The object was to explore the contribution of internal degrees of freedom to the conductivity of a polyatomic molecule. This contribution has not been quantitatively demonstrated until very recently (Murad et al. 1991). In fact, it is usually assumed that this contribution is independent of number density and is given by the dilute-gas value at the corresponding temperature. In the paper of Ravi et al. (1992), heat flow is discussed for a model benzene-like liquid with a six-centered Lennard-Jones pair potential. 

As outlined in Chapter 4, the thermal conductivity in the dilute-gas limit, is related to a number of effective cross sections, which are associated with the transport of translational and internal energy, and with their interaction. In principle, a similar analysis as given for nitrogen in Section 14.2 can be performed for polyatomic molecules. In practice, such an analysis is often hampered by a lack of experimental information and insufficient knowledge of the behavior of cross sections describing the diffusion of internal energy at high temperatures. 

KED using helium as the collision gas works very well when the interfering polyatomic ion is physically larger than the analyte ion. This is exemplified in Figure 10.4, which shows helium flow optimization plots for six elements in 1 10 diluted seawater. It can be seen that the signal intensity for the analytes—Cr, V, Co, Ni, Cu, and As—are all at a maximum, whereas their respective matrix, argon. 

Flow injection coupled to ICP-MS has shown itself to be very diverse and flexible in meeting the demands presented by complex samples, as indicated in the foregoing references. However, one of the most interesting areas of research is in the direct analysis of seawater by flow injection ICP-MS. Traditionally, seawater is very difficult to analyze by ICP-MS because of two major problems. First, the high NaCl content will block the sampler cone orifice over time, unless a 10-20-fold dilution is made of the sample. This is not such a major problem with coastal waters, because the levels are high enough. However, if the sample is open-ocean seawater, this is not an option, because the trace metals are at a much lower level. The other difficulty associated with the analysis of seawater is that ions from the water, chloride matrix, and the plasma gas can combine to generate polyatomic spectral interferences, which are a problem, particularly for the first-row transition metals. 

FIGURE 10.4 Helium cell gas flow optimization plots for Cr, V, Co, Ni, Cu, and As in 1 10 diluted seawater, showing that all polyatomic interfering ions are reduced to an acceptable level under one set of cell gas flow conditions. (Courtesy of Thermo Scientific.)... 

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