2 Measurements of Self-Diffusion in Colloidal Systems by Magnetic-Field-Gradient, Spin-Echo Methods JOHN E. TANNER
Downloaded by UNIV OF ROCHESTER on January 19, 2018 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0034.ch002
Naval Weapons Support Center, Applied Sciences Department, Crane, Ind. 47522
A very useful application of NMR methods to colloidal systems is the measurement of translational self-diffusion coefficients in the fluid (usually liquid) components. Rates of diffusion indicate the restrictions to mobility due to adsorption or due to physical barriers. In many cases, one may also obtain information on the dimensions of the barriers or other inhomo geneities. Types of systems which have been or might be studied by these methods include biological cells and tissues, porous rocks and minerals, emulsions, liquids adsorbed on fibers, polymer solutions, and the synthetic and natural adsorbent materials used for various types of chromatography. NMR Methods of Measuring Diffusion There are two distinct NMR methods used for measuring translational diffusion. In one method the nuclear spin-spin (T ) and spin-lattice (T ) relaxation times due to random motions over distances of a few Angstroms are measured by cw or pulse methods. By repeating the measurements over a range of tempera tures and/or resonance frequencies, and/or degrees of isotopic substitution, and by the use of other information about the system it is frequently possible to analyze these motions in terms of molecular rotations and translations. The simpler the experimental system, the easier the analysis, and the less ambiguous are the results. With certain metals and plastic crystals the measurement of spin relaxation is the preferred method of determining translational self diffusion. A somewhat different application of spin-relaxation measure ments to determine diffusion coefficients involves the determi nation of exchange times between spatial regions which have different spin relaxation rates. Exchange times may be determined if the spin relaxation function can be resolved into two (or more) components, and if independent knowledge of the relative spin populations or of the relaxation rates in the 1
2
1
2,3
4
5
16
Resing and Wade; Magnetic Resonance in Colloid and Interface Science ACS Symposium Series; American Chemical Society: Washington, DC, 1976.
TANNER
2.
17
Self-Diffusion in Colloidal Systems
Isolated regions 1s available. I f the dimensions of the regions are also known, then the diffusion coefficients or the barrier permeabilities may be calculated from the dimensions and the exchange times. This method has recently been applied to measure i n t r a c r y s t a l l i n e diffusion of butane i n z e o l i t e and the permeability of human red c e l l s to water. The other NMR method measures the loss of phase coherence of a set of precessing nuclear spins due to their random motion over a gradient in the magnetic f i e l d . " This method (MFGNMR) i s the subject of the present paper. Numerous applications of this method to c o l l o i d a l systems have been made in the past decade. A part of this has been reviewed by S t e j s k a l . The emphasis here w i l l be on more recent experimental results and developments of methods. 6
Downloaded by UNIV OF ROCHESTER on January 19, 2018 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0034.ch002
8
1 0
11
The MFG-NMR Experiment The magnetic-field-gradient, spin-echo experiment has been well described In many places (see e.g. r e f . 8-10); only an outline w i l l be given here. B r i e f l y , the sample i s placed in a high magnetic f i e l d which creates a small net magnetization among the nuclear and electronic spins present. A small o s c i l l a t i n g f i e l d of appropriate duration and magnitude ("ΘΟ") at the resonance frequency of the nuclear spins of interest (usually in the radio frequency, r f , range) rotates this magnet ization into a plane perpendicular to the s t a t i c f i e l d , about which i t then precesses, producing a detectable signal. This signal decays as the spins in their precession lose phase coherence due to various energy transfer processes (time constant T ) and due to inhomogeneities 1n the magnetic f i e l d . Magnet ization reappears in the direction of the s t a t i c f i e l d . The time constant for t h i s , L , gives the upper l i m i t of T . To the extent that tne spins remain i n place, the loss of phase coherence due to f i e l d inhomogeneities can be reversed by applying a second r f pulse of appropriate magnitude ("ΙδΟ "), which causes the spins to b r i e f l y regain phase coherence forming an increased s i g n a l , the "spin echo". Any displacement of the nuclear spins after the 180° pulse from their position before the 180° pulse lessens this signal recovery, so that the spin echo i s attenuated. This attenuation of the echo can be amplified by a r t i f i c i a l l y increasing the magnetic f i e l d inhomo geneities already present, applying a (linear) f i e l d gradient. In the e a r l i e r experiments, a steady f i e l d gradient was applied. ' More recently i t has become common to apply the gradient in two pulses, one before and one after the 180° r f pulse. For experimental reasons, a much larger gradient can be applied in this manner, and thus lower diffusion coefficients can be measured. If the pulses are short compared to their separation, the diffusion time of the experiment i s well defined and i s the pulse separation i n t e r v a l . This experiment 1s 0
2
2
0
8
9
10
Resing and Wade; Magnetic Resonance in Colloid and Interface Science ACS Symposium Series; American Chemical Society: Washington, DC, 1976.
18
MAGNETIC RESONANCE
Illustrated schematically in Figure 1(b). For the shortest diffusion times, i t i s necessary to multiply the effect by repeating the gradient pulses a number of times before observing the echo. One means of doing this i s to apply trains of gradient pulses of alternating s i g n . For the longest diffusion times, i n cases where T , » ^ , which i s typical f o r c o l l o i d a l systems, a three-rf pulse sequence, with observation of the "stimulated echo" i s advantageous. ' These variations are also i l l u s t r a t e d i n Figure 1. Special methods have been developed to help overcome problems associated with the short T of certain types of s o l i d systems. Pines and Shattuck have demonstrated the long T of naturally abundant C i n a p l a s t i c c r y s t a l , using a special r f sequence designed to impart a high degree of spin magnetization to these nuclei. As they imply, i t should be possible to use long enough gradient pulses so that the diffusion coefficient can be measured. Blinc and c o - w o r k e r s have performed experiments i n which a Waugh-type r f sequence was combined with pulsed gradients, with the object of measuring s e l f diffusion of l i q u i d crystals in nematic and smectic phases. This method i s useful where T >>To, where T i s the rotating frame T Where nuclei of the same type but belonging to different molecular species contribute to the observed s i g n a l , the i n d i vidual signals may in principal be resolved by means of d i f f e r ences i n the T, or To spin relaxation times, by differences in the chemical s h i f t s (using Fourier transformation of the echo), or by differences in the diffusion coefficients themselves. Naturally a higher i n i t i a l signal strength i s required so that each component w i l l be measurable, and to compensate f o r losses in the resolution process. 1 2
Downloaded by UNIV OF ROCHESTER on January 19, 2018 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0034.ch002
8
13
2
14
2
13
15,16
lP
1P
v
17
Diffusion Time and Distance Ranges With the best of presently developed magnetic-field-gradient techniques, and with simple systems where only one component contributes to the s i g n a l , i t should be possible to measure diffusion coefficients with at least 20% precision (and usually better) over a range of diffusion times, 10"
