Angular Boltzmann factor

Besides, X is the Boltzmann factor related to the angular frequency of the H-bond bridge, that is,... 

The inversion population of the two spin-orbit states is also caused by the tilt geometry in the initial state. The principal axis of the NO 2tt orbital adsorbed in the tilt geometry is not parallel to the molecular axis due to a strong chemical interaction between the 2rr and the Pt 5d orbital. The population between the spin-orbit states of 12 = 1/2 and 3/2 is relevant to the ratio of these state densities in addition to the Boltzmann factor due to the energy difference. If the principal axis of the electronic configuration is not parallel to the molecular axis, the orbital angular momentum of the adsorbed molecule does not take a good quantum and the relation of the state density is broken. However, this simple consideration cannot interpret the experimental results. 

The effect of the three internal fields, at 0, ra and 2 , on one molecule is next treated, and after angular averaging the connection between the microscopic and macroscopic response functions established. The polarization of the dipole distribution by re-orientation of the molecules is induced by the static field. Introducing the Boltzmann factor and normalizing the distribution gives, for the number of molecules per unit volume with dipole moment inclined at an angle, 0, to the fields. 

Equation 58 can be interpreted as the Boltzmann factor for the perturbation averaged over the unperturbed (reference) system this is indicated in the expression on the left-hand side of the equation by the angular brackets with the subscript 0. Introducing Eq. 57 into Eq. 53, we obtain... 

Strength and the sample concentration, po is the permeability of free space, Q is the quality factor of the coil, coo is the Larmor angular frequency, K is the volume of the coil, F is the noise figure of the preamplifier, k is Boltzmann s constant, is the probe (as opposed to sample) temperature, and A/is the bandwidth (in Hz) of the receiver. It can be seen that the concentration sensitivity 5c (SIN per pM concentration of analyte) is poor for microcoils. This is due to the fact that microcoil probes have very small observation volumes and therefore contain a very small amount of analyte. However, if the sample can be concentrated into a small volume, then the microcoil can more easily detect the signal. This high mass sensitivity 5m (SIN per pmol of analyte) is characteristic of microcoil NMR probes. In essence, the use of microcoil probes enhances the mass sensitivity 5m at the expense of the concentration sensitivity 5c. To better understand the relationship between sensitivity and coil diameter, a detailed analysis was reported by Peck et Their results showed that mass sensitivity increases monotonically with decreasing coil diameter within the 1mm to 50 pm range they studied. However, the concentration sensitivity decreases, and therefore there is a trade-off between Sc and 5m that depends on coil diameter. 

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