Boltzmann polarization

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

ESR observations were conducted at 9.5 GHz, using a Varian E-line ESR spectrometer with variable temperature capabilities from 90K-300K. The g value was determined using a Varian pitch standard with a g-value of 2.00302 + 0.00005. The integrated intensity was also calibrated to a Varian pitch standard. The parameters g, AH u, AH-p and the radical density were determined for each sample. Saturation measurements were made on a selected subset of samples. Low temperature runs at 125 K were made for all inertinite samples, as well as for selected samples of the other maceral types. Little temperature variation in g value, linewidth, or lineshape, was seen in any sample. The integrated intensity varied approximately as 1/T, suggesting Boltzmann polarization of the spins at lower temperatures. 

Much of the technical development of NMR over the past half century has focused on improving sensitivity. The fundamental problem is the low starting Boltzmann polarization that arises from the low energies of nuclear spin transitions. Several methods have been developed to improve the sensitivity or S/N in NMR. One major approach is through pulse sequence development to optimize the efficiency and information content of NMR spectra through manipulating the spin physics some of the more important experiments for small molecules were described above. 

Despite considerable progress in the field, NMR spectroscopy still has two significant limitations the intrinsically low sensitivity, due to the low Boltzmann polarization of nuclear spins in thermal equilibrium, and the low dispersion of observed frequencies, due to small differences in nuclear shielding by surrounding electrons for nuclei of the same kind. The first problem is continuously... 

The recent renaissance of dynamic nuclear polarization (DNP) provides an extremely promising approach for sensitivity enhancement [87—89]. It borrows the large Boltzmann polarization from unpaired electron spins of free radicals to boost the NMR signal. DNP experiments have been performed on quadrupolar nuclei such as [90], " N [91], [92,93],... 

Hyperpolarization is a term which collects a set of dilferent signal-enhancement techniques in NMR spectroscopy. They have in common that they create population differences (polarizations) of the nuclear spin, which are far larger than the thermal equilibrium value (Boltzmann polarization). Following a proposal by Overhauser in 1953, which was experimentally verified by Carver and Slichter Dynamic Nuclear Polarization (DNP) schemes were developed. These techniques employ an auxiliary reservoir of fast and effectively polarizable spins to generate spin order which is subsequently transferred to the spin system of interest. In case of DNP experiments the strong polarization of electron spins is transferred to the nuclear spins by means of microwave irradiation. In the early days DNP experiments were restricted to relatively low fields ( H-frequency below 60 MHz) due to the technical limitations of klystrons used as microwave sources. 

Fig. 13 (shuttle) DNP enhancement reported by Reese et al. [56] of C-chloroform in water with 25 mM D- N-TEMPONE. The enhanced signals are compared with the Boltzmann polarization at 14 T. Reprinted with permission from [56]. Copyright 2009 American Chemical Society... 

LW) interactions refer to the purely physical London s (dispersion), the Keesom s (polar) and Debye s (induced polar) interactions and correspond to magnitudes ranging from approximately 0.1 to 10 kJ/mol (but in rare cases may be higher). The polar forces in the bulk of condensed phases are believed to be small due to the self-cancellation occurring in the Boltzmann-averaging of the multi-body... 

Clearly, if a situation were achieved such that exceeded Np, the excess energy could be absorbed by the rf field and this would appear as an emission signal in the n.m.r. spectrum. On the other hand, if Np could be made to exceed by more than the Boltzmann factor, then enhanced absorption would be observed. N.m.r. spectra showing such effects are referred to as polarized spectra because they arise from polarization of nuclear spins. The effects are transient because, once the perturbing influence which gives rise to the non-Boltzmann distribution (and which can be either physical or chemical) ceases, the thermal equilibrium distribution of nuclear spin states is re-established within a few seconds. 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

The basic principles are described in many textbooks [24, 26]. They are thus only sketchily presented here. In a conventional classical molecular dynamics calculation, a system of particles is placed within a cell of fixed volume, most frequently cubic in size. A set of velocities is also assigned, usually drawn from a Maxwell-Boltzmann distribution appropriate to the temperature of interest and selected in a way so as to make the net linear momentum zero. The subsequent trajectories of the particles are then calculated using the Newton equations of motion. Employing the finite difference method, this set of differential equations is transformed into a set of algebraic equations, which are solved by computer. The particles are assumed to interact through some prescribed force law. The dispersion, dipole-dipole, and polarization forces are typically included whenever possible, they are taken from the literature. 

I In this chapter we use notations generally accepted in theoretical physics instead of those used in other chapters of this book the Boltzmann constant instead of the gas constant R, the elementary electrical charge e (in Chapter 1 denoted Q ) instead of the Faraday constant F (obviously, k T/e = RTIF). Electrode polarization (overvoltage) AE is denoted T. For all reactions we assume that n = 1. 

---