  Grad's method is used on the linearized Boltzmann collision operator to
derive the most general expressions for the collision coefficients for a
multi-component, multi-temperature plasma up to rank-2. In doing so, the
collision coefficients then get expressed as series sum of pure coefficients of
temperature and mass ratios multiplied by the cross-section dependent
Chapman-Cowling integrals. These collisional coefficients are compared to
previously obtained coefficients by Zhdanov et al [Zhdanov V.M., Transport
processes in multi-component plasma, Taylor and Francis (2002)] for 13N-moment
multi-temperature scheme. First, the differences in coefficients are compared
directly, and then the differences in first approximation to viscosity and
friction force are compared. For the 13N-moment multi-temperature coefficients,
it is found that they behave reasonably similarly for small temperature
differences, but display substantial differences in the coefficients when the
temperature differences are high, both for the coefficients and for viscosity
and friction force values. Furthermore, the obtained coefficients are compared
to the 21N-moment single-temperature approximation provided by Zhdanov et al,
and it is seen that the differences are higher than the 13N-moment
multi-temperature coefficients, and have substantial differences even in the
vicinity of equal temperatures, especially for the viscosity and friction force
calculations.
