where I(t) is the signal intensity at time t. Usually the largest local fields encountered in hydrogen NMR originate from magnetic dipolar interactions between neighbouring magnetic nuclei, followed by much smaller electron nuclear interactions responsible for chemical shifts. Variations in magnetic field brought about by variations in susceptibility are also important. For hydrogen in solids, dipolar field strengths are of order a milli Tesla and the corresponding spin-spin relaxation time is a few micro seconds, say 10-30 |a.s. The dipolar interaction tends to swamp all others. In liquids, the much greater molecular mobility ensures that dipolar interactions are effectively averaged to zero on the timescale of the experiment. In consequence, dipolar interactions do not contribute significantly to spin-spin relaxation and other effects are seen. The spin-spin relaxation time may be a few seconds in a very pure liquid but more typically values in the range 5-500 ms are observed. Between these limits (10 us - 500 ms) is a whole continuum of relaxation times reflecting a continuum of degrees of mobility and interaction strengths. Multiple component exponential decays are usually observed from heterogeneous solids. Table 1 gives an indication of the range of spin-spin relaxation times commonly encountered in food science.

Another major source of apparent spin-spin relaxation is inhomogeneity of the applied magnetic field. This leads to signal loss in a characteristic time T2*, so that

rp obs rp sample rji *

If T28ample is much greater than T2* then T2obB, the observed value, is independent of the sample and is only a measure of the quality of the magnet. In order to remove systematic errors resulting from a measurement of T2\ it is usual to observe long ip^sampie pjj-j C0mp0nents jn the form of a spin echo train. So called 180° pulses are applied at regular intervals after the initial 90° pulse throughout the decay. The additional pulses serve to refocus dephasing due to the magnetic field inhomogeneities but not BIoc. The CPMG (Carr and Purcell, 1954; Meiboom and Gill, 1958) pulse sequence for this is well established, experimentally robust and straightforward to implement.

Table 1

Typical 'H low resolution NMR T2 relaxation times of food constituents.

Constituent T2

Solid protein / carbohydrate 10-20 (is

Solid / semi solid / liquid lipid 10-20 us / 100-200 (a.s / 10-20 ms

Edible oils 100-200 ms

Ice / bound moisture / free water 10 |is / 500 (is / 500 ms


A common bench top low resolution NMR measurement is a solid to liquid ratio determination. Figure 1 illustrates the general concept. It is drawn for a hypothetical two phase system with a solid (66.6%) with a T2 of 20 (is and a liquid (33.3%) with a T2 of 1 ms. The magnetisation intensity immediately following the 90° pulse, at time t=0, is proportional to the total number of hydrogen atoms in the sample (Iq) and is therefore a measure of the solid plus liquid content. The signal due to the solid part of the sample (S) decays rapidly whereas the signal due to the liquid part (L) does not. The intensity S+L is measured as quickly as possible. The magnetisation intensity remaining, say, 70 (is after the pulse originates only from the liquid. If the liquid decay time is sufficiently long so that negligible decay occurs during the 70 (is then the ratio of these signals is proportional to the fractional liquid content as follows:

The calibration factor, f, accounts for decay of the solid signal occurring in the spectrometer dead time, shown hashed in figure 1, between the pulse and the first measurement opportunity, typically 5-10 (is, and also the difference in the number of hydrogen atoms per unit mass in the two phases. If a detailed hydrogen atom count per unit mass in the two phases is known as is the solid phase relaxation time then a precise ratio can be calculated from S and L. Often, however, it is sufficient merely to calibrate the liquid content measured some other way (say drying) against this NMR parameter with f set empirically. In practice, it is often preferable to measure L from a spin echo intensity. The method is adaptable to the measurement of water, oil and fat. A related method involves observation of just the liquid signal, at say 100 (is and comparison of its intensity against a known standard. It has been pointed out that low magnet homogeneities can be an advantage in this measurement since the dominant cause of spin-spin relaxation for the liquid may be the magnet, T2*, and not the sample so that variations in liquid T2 are unimportant (Tiwari et al, 1974).

Figure 1. A schematic LR NMR signal showing the solid (S) and liquid (L) intensities (main figure) used to determine the solid / liquid ratio of foodstuffs. The inset shows the full signal.


Figure 1. A schematic LR NMR signal showing the solid (S) and liquid (L) intensities (main figure) used to determine the solid / liquid ratio of foodstuffs. The inset shows the full signal.

In simple systems in which there is rapid exchange averaging of nuclei between free and bound liquid phases, the observed relaxation rate is given by

1 = Pb ^ Pf rp obs rp b rp f where Pb and Pf are the fractional contents of bound and free liquid respectively and T2b and T2f are the individual relaxation times of the bound and free liquids (Zimmerman and Brittin, 1957). Hence, T2obs increases with the free liquid content. The relaxation time can be rapidly and accurately measured in a low homogeneity magnetic field using a CPMG sequence. However, most food systems are not as simple as this and the reader is referred to the work of Belton and co-workers (Belton et al, 1992 and references therein) for a more complete discussion.

3.2. Applications

Laboratory low resolution NMR measurements have been carried out on a wide variety of systems, including many food systems and the results reported in the literature, (Padua et al, 1991; Lazaros et al, 1990; Guillou and Tellier, 1988, Rutledge et al, 1988; Defour, 1985; Tiwari and Burk, 1980). An excellent review of NMR applied to food systems in general and including low resolution measurements has been made by Belton, Colquhoun and Hills (Belton et al, 1992). As an example, Nicholls and De Los Santos have used low resolution NMR to study moisture content in corn gluten (Nicholls and De Los Santos, 1991). Figure 2, taken from their work, shows the ratio of the second echo intensity of a CPMG echo train (the liquid signal) to the full FID intensity immediately following the 90° pulse (the liquid plus solid signal) against moisture content determined from oven drying. An excellent correlation, typical of low resolution NMR moisture determinations is observed.

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