RU2517762C2 - Pulse sequence to measure parameters of self-diffusion by method of nuclear magnetic resonance - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: usage: for measurement of substance characteristics by NMR method. Substance: consists in the fact that to determine parameters of self-diffusion of the investigated sample they use a cycle of pulse sequence, made of the specified quantity of gradient pulses, duration, shape, amplitude and intervals between which are permanent, and two radio frequency pulses - 90-degree and 180-degree with the interval t between them, sent in the intervals between the third from the end and the last but one gradient pulse and between the last but one and the last gradient pulse, accordingly. Amplitude of the echo signal is measured at the moment of its maximum - via time t after 180-degree pulse or is produced by averaging by interval of time around this moment. To produce a diffusion drop, the cycles of measurement are repeated to change one of cycle parameters - amplitude of the gradient, duration of gradient pulses or interval between gradient pulses. The repetition period is determined by time of sample relaxation. Positive effect is achieved by setting a quasi-stationary condition in the series of gradient pulses, as a result of which the last pair of pulses in the measurement cycle of the sequence becomes close to equivalence.

EFFECT: higher accuracy of diffusion drop production and determination of self-diffusion coefficient, expanded range of its measurement.

8 dwg

Description

The invention relates to the field of methods for measuring the characteristics of a substance by the method of nuclear magnetic resonance (NMR) and can be used to increase accuracy and expand the measurement range of diffusion attenuation, diffusion decay and determination of the self-diffusion coefficient (CSD) of substances.

Modern methods of measuring CSD using NMR are based on recording the behavior of the spin-system of atomic nuclei of the investigated substance in an inhomogeneous magnetic field. The best characteristics are those using a pulsed magnetic field gradient (IGMP) [1], which have advantages in sensitivity and measurement range over techniques using a constant gradient. Consider the most common method for determining CSD with IGMP, in which the diffusion attenuation is measured using a pulse sequence [2], the cycle diagram of which is shown in Fig. 1.

This method uses two gradient pulses of the same amplitude and duration with an inverting RF pulse between them. The first pulse dephases the spin packet, and the second returns it to the initial phase. The movement of spins in the packet in the interval between pulses leads to the fact that some of the spins do not restore their phase, due to which the amplitude of the echo decreases. The calculation of the echo amplitude is performed according to the formula

называется диффузионным спадом (ДС). В случае свободной диффузии однокомпонентного вещества график должен быть линейным, а КСД определяется по наклону графика ДС. На рис.2 показан ДС для тестового раствора CuSO₄ в воде. Диффузионный спад для образца CuSO₄ в воде, параметры последовательности: t_g= 0.5мс, t_d= 5мс. По горизонтали - параметр, пропорциональный квадрату g. Величина КСД, вычисленная по наклону ДС = 2700 мкм²/с. По вертикали - условная амплитуда эха.where A (g) is the amplitude of the echo signal at the gradient amplitude = g, A (0) is the amplitude of the echo at zero gradient amplitude, γ is the gyromagnetic ratio, t _g is the duration of the gradient pulses, t _d is the diffusion time interval, D is the self-diffusion coefficient . The relative decrease in the echo amplitude in the presence of IGMP is called diffusion attenuation (RS). KSD is measured in the SI system in units of m ² / s; its value for water at room temperature is 2.5 · 10 ^-9 m ² / s (2500 μm ² / s). To determine the CSD, the dependence of the echo amplitude on the gradient value is removed, and a plot of the logarithm of the amplitude on the square of the gradient is constructed. In the sequence cycle, the diffusion interval t _d and the gradient pulse duration f _g can also vary. The dependence of the logarithm of the amplitude of the echo signal on the effective parameter

called diffusion recession (DS). In the case of free diffusion of a single-component substance, the graph should be linear, and the CSD is determined by the slope of the DS graph. Figure 2 shows the DS for a test solution of CuSO ₄ in water. Diffusion drop for a CuSO ₄ sample in water, sequence parameters: t _g = 0.5ms, t _d = 5ms. Horizontal - a parameter proportional to the square g. The KSD value calculated by the slope of the DS = 2700 μm ² / s. Vertical - the conditional amplitude of the echo.

The disadvantage of this method is its high sensitivity to the non-identity of gradient pulses, which leads to incomplete restoration of the phases of the spin groups located in different parts of the sample. The measurement of the CSD of low-viscosity samples (the value of the CSD> 1000 μm ² / s) is not difficult, especially with not very short relaxation times T2 (more than 10-20 ms). The diffusion decay plots are linear in a wide range of amplitudes, therefore, the measured values of the CSD are quite accurate. Small KSD values (less than a few hundred μm ² / s) are much more difficult to measure, especially in the presence of short-term components of the relaxation decline. This is due to the fact that obtaining a diffusion decay in a sufficient range of amplitudes requires large amplitudes and durations of gradient pulses and a longer diffusion interval, the choice of which is limited by the relaxation time of the sample. Using these sequence parameters, a diffusion decline with distortion is obtained (see Fig. 3, DS for a vacuum oil sample, parameters: t _g = 4ms, t _d = 10ms, calculated KSD = 36.8 μm ² / s).

Such distortions can be associated with the non-identity of two gradient pulses, as a result of which complete phase recovery does not occur. There can be several reasons for non-identity.

1. With an increase in the product of the gradient amplitude by the pulse duration, the heating of the reference resistor in the gradient current stabilization circuit increases, which leads to a change in its resistance, which manifests itself in a change in the amplitude of the second pulse.

2. The field of gradient coils affects the ferromagnetic pole pieces of the installation’s magnetic system, the magnetic parameters of which have their own relaxation properties. It can also lead to non-identical pulses.

Attempts to reduce the influence of these factors have already been undertaken [3] and led to improved measurement results, but did not give full compensation.

The aim of the invention is to increase the accuracy of obtaining diffusion decline and determine the coefficient of self-diffusion, expanding the range of its measurement.

The technical result is achieved by the fact that in order to ensure the identity of the effective action of the gradients, it is proposed instead of two to apply a series of gradient pulses with the same amplitude, duration and intervals between them, of which the last two will be included in the Han sequence cycle. In this case, the factors affecting the effective weight of the pulses will come into equilibrium, as a result of which the pair of working pulses will be close to identity, while the preliminary pulses will not affect the result, since they act on the unperturbed spin system.

The claimed technical solution is as follows.

The test sample is placed in a constant magnetic field inside the coil, which provides exposure to an alternating magnetic field in a direction perpendicular to the constant field vector. The same coil or another coil, also having an axis perpendicular to the constant field vector, is used to obtain the radio frequency NMR signal. The sample is exposed to radio frequency magnetic field pulses at a frequency close to the frequency of the Larmor precession of the spins of the nuclei under study:

,

,

where B ₀ is the magnetic field induction, γ is the gyromagnetic ratio for a given nucleus. For the nuclei of hydrogen atoms (protons) γ = 42.58 MHz / T.

In the pulse sequence, the amplitudes and durations of the radio frequency pulses are used, which rotate the magnetization vector of the spin system of the sample by 90 and 180 degrees from the initial state relative to the constant field vector. To obtain a spin echo signal, a sequence consisting of a 90-degree and 180-degree pulse with a time interval t between them is used, the amplitude of the echo signal is recorded 2 t after a 90-degree pulse. To measure the RS, identical pulses of the magnetic field gradient with amplitude g and duration t _g between the radio frequency pulses and before recording the echo signal with an interval t _d between them are used. To ensure the equal effect of gradient pulses before applying a 90-degree radio frequency pulse, a series of a given number of gradient pulses of amplitude g and duration t _g with intervals between them equal to t _{d is used} . The sequence with two preliminary pulses is shown in Fig. 4.

ось ординат градуируется в логарифмическом масштабе.To obtain a diffusion decline, the sequence cycles are repeated with a change in one of the sequence parameters: g, t _g , t _d . The intervals between cycles are selected taking into account the relaxation time of the sample. As a diffusion decline, a plot of the echo amplitude versus parameter is plotted

the ordinate axis is graduated on a logarithmic scale.

Figure 5-8 shows the diffusion decays obtained using sequences with different numbers of preliminary pulses. The sample and time parameters of the sequence are similar to Fig. 3. All measurements were performed on an NMR relaxometer with an operating frequency of 18.5 MHz, a duration of a 90-degree radio frequency pulse of 3.6 μs, and a free induction decay of about 500 μs.

The advantages of the proposed method are:

• Improving the shape of diffusion decline in the study of samples with low KSD values

• Reducing the requirements for temperature stability of gradient pulses and shielding of the magnetic system

• Extension of the range of measurement of KSD with a given accuracy

• Ability to select the number of preliminary pulses depending on the value of the measured KSD

Using the proposed method in NMR measurement techniques will improve the accuracy and repeatability of the measurement results of self-diffusion parameters while maintaining the hardware characteristics of the installation.

Used sources

1. J. Karger, W. Heing, Z. Exp. Technology. Phys., 1971, 19, 453.

2. E.O. Stejskal, J.E. Tanner, J. Chem. Phys. 1965, 42, 288.

3. A method for measuring the diffusion of adsorbed liquid molecules. Auth. testimonial. USSR No. 649996, publ. 02/28/1979, bull. No. 8.

Claims (1)

A method for determining diffusion attenuation, diffusion decay, and self-diffusion coefficient, including measuring the amplitude of the spin echo signal recorded at a time of 2 t or obtained by averaging over the time interval around this moment in a pulse sequence cycle consisting of a 90-degree pulse, a 180-degree pulse, fed through time m, including two identical gradient pulses applied between the radio frequency pulses and between the second radio frequency pulse and the recording echo amplitudes, characterized in that prior to the supply of a 90-degree pulse, a predetermined number of gradient pulses is formed with the amplitude, duration and shape of the pulse coinciding with the gradient pulses included in the measuring sequence cycle, the intervals between which and between the last of them and the first gradient pulse of the cycle coincide with interval between gradient pulses of the cycle.

Images