Spin temperature

Consider a spin- system in a static magnetic field Hq. For each spin, we will denote the high and the low energy states by the labels b and a so that a spin in state b is antiparallel to the static field and vice versa. The difference in energy between the two states for one spin is AE=2 jHq. We sketch the spin population associated with the spin states in the following way where each x represents a spin. 

If the spin system is in thermal equilibrium with the surroundings (which we will call the lattice), the ratio of the populations in the two states will be given by the Boltzmann 

Suppose that the spin populations are now disturbed so that some additional nuclei in state a are promoted to state b. While the system may no longer be in thermal equilibrium with the lattice, we can still describe the populations by the Boltzmann relation provided that we change the definition of T to keep the relationship correct. Since the ratio is now 

If we have a system consisting of more than two energy levels per spin, there is no guarantee that the spins will be describable by a unique spin temperature. In the sketch below, system A might be characterized by a spin temperature but system B cannot be. 

For the remainder of this section, we will only consider 

---

The "decrease of the spin temperature means an increase of population difference between the upper and lower energy spin states and consequently an increased sensitivity of the NMR experiment. From Equation (25), the temperature of dilute spins has been lowered by a factor 7x/y1 h, that is, V4 when X = 13C. This means an increased sensitivity of the FID resonance experiment equal to about 4 for the 13C nuclei. Because the X signal is created from the magnetization of dilute nuclei, the repetition time of NMR experiment depends on the spin-lattice relaxation time of the abundant spin species, protons, which is usually much shorter than the spin-lattice relaxation times of the dilute nuclei. This, a further advantage of cross polarization, delay between two scans can be very short, even in the order of few tens of milliseconds. 

Wolf D (1979) Spin-temperature and nuclear-spin relaxation in matter basic principles and applications. Clarendon Press, Oxford... 

Table 10 Melting points and spinning temperatures of various polymers.

Typical melt spinning temperatures are given in Table 18.5. 

Relatively low spinning temperatures and pressures that are above the cloud-point pressure can be used. Microcellular foam fibers may be obtained rather than plexifilaments, even at spinning pressures slightly below the cloud-point pressure of the solution. 

Wolf, D. (1979) Spin Temperature and Nuclear-Spin Relaxation in Matter, Clarendon Press, Oxford Wysk, H, (1995) Ph.D.-Dissertation, Hannover University... 

The cross-polarization (CP), i.e. the transfer of I-spin polarization to the dilute spins (S), is a double resonance experiment in which the I and S spins are coupled by a certain interaction, determined by the cross relaxation time tb. From the dynamics of the CP process, usually described with the spin temperature concept, the following equation for the time dependence of S-spin polarization could be derived ... 

Consider the concept of spin temperature rs with reference to nucleus S of spin 2- The population ratio n J, /n f of S nuclei in the upper and lower energy state is... 

Figure 7.23. INS spectrum of solid methane phase II. (a) Spin temperature Ts <0.2 K. (b) Ts = 5K. (From Heidemann et al. [1984].)...

Goldman, M. 1970. Spin Temperature and Nuclear Magnetic Resonance in Solids. London Oxford University Press. 

---