Mesoscale Phenomena in Fluid Systems - ACS Publications

Chapter 3

Characterization Mesoscale Structure and Phenomena in Fluids Using NMR

Downloaded by UNIV OF SYDNEY on November 22, 2016 | http://pubs.acs.org Publication Date: August 17, 2003 | doi: 10.1021/bk-2003-0861.ch003

Peter Stilbs Physical Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden

N M R techniques can provide valuable insight into the structure and dynamics of mesoscale structures. Line broadening and spin relaxation effects, which researchers interested in small molecule N M R often work hard to eliminate, can yield detailed information about molecular motion, particularly reorientation processes. They have been used to characterize molecular dynamics and order in alkyl chains, water, or counter-ions participating in mesoscale structures, and to study protein dynamics. Multi-component self-diffusion techniques (such as FT-PGSE) provide information on molecular displacements over longer time scales (picoseconds to microseconds). The self-diffusion rate of a molecule can reveal its aggregation state (is it part of a larger structure?). Under carefully controlled conditions it can also reveal information about the medium through which it is diffusing (viscosity, concentration and structure of materials obstructing its path). Multi-component FT-PGSE has been used to characterize mixed micelles and to study polymer/ surfactant aggregates. Recent developments have extended the utility of these methods. Continued and expanded application to the study of mesoscale phenomena can be foreseen.

© 2003 American Chemical Society

Case and Alexandridis; Mesoscale Phenomena in Fluid Systems ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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Introduction As a concept, nuclear magnetic resonance (NMR) recently celebrated its 50year anniversary. In the continued development of N M R during the last decades the majority of new methods were in the field of multidimensional N M R , for the purpose of structural determination of organic compounds or biological macromolecules. We have also witnessed extensive new use of N M R in biomedicine, both as a spectroscopic method and as an imaging tool (MRI) that complements X-ray and positron emission tomograph (PET) methods. To a large extent, these new NMR-based procedures rely on the general developments in the field of electronics and, in particular, on that of digital computing. With regard to studies of mesoscopic structure and dynamics in solution, the main N M R 'tools' are quite different from those used in the determination of molecular structure. N M R offers many other experimental dimensions. The multinuclear detectability (protons ( H), deuterium( H), C , O , F , N a etc.) is of course one unique characteristic of 'Nuclear Magnetic Resonance'. Furthermore detailed and quantitative dynamic information that is often not accessible from other sources is available from either N M R spin relaxation data or from NMR-based, multi-component studies of molecular self-diffusion. These are the most valuable NMR-tools in the present context. Here the basic spin relaxation approach(i) may provide detailed information on local molecular dynamics (picosecond to microsecond) and order of alkyl chains, water or counter-ions in the system. In principle, it can be based on data for any N M R accessible type of nuclei in the system, at any location in a molecule. The multi-component self-diffusion technique(2) (Fourier transform pulsedgradient spin-echo: FT-PGSE or just PGSE) provides information on overall molecular displacements on a much longer timescale (typically the order of 5 to 500 milliseconds, depending on experimental conditions and the instrumental set-up. The two families of methods are both complementary and highly selective and applicable to very complex systems. Isotopic labeling can sometimes be applied to further enhance the selectivity and sensitivity of either of the methods in question. Particularly common in the present context is selective deuterium labeling for the purpose of studying deuterium spin relaxation at a particular location, at a high sensitivity and spectral selectivity. This strategy provides quantitative information on the reorientation and order of a particular C - H bond vector, in a very unambiguous and quantitative way. Application examples in this paper are from studies of polymer or surfactant systems in aqueous solution. 1

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n

1 9

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Intrinsic Problems in NMR Investigations of Complex Fluids

Polymers or surfactants in solution do not really have well-resolved N M R spectra to begin with - a problem that becomes amplified in mixed systems. This is not only because of added signal overlap, but also because of line-broadening and faster spin a relaxation rate that can occur as a direct result of enhanced aggregation and specific interactions. In general, line-broadening effects reduce sensitivity quite extensively in all types of N M R experiments, and they are normally the limiting experimental parameter. Going to higher magnetic field might seem like an obvious cure for the basic 'spectral resolution of peaks'-problem, since one would assume that N M R spectral dispersion should be linear with the applied magnetic field. However, for macromolecular systems this is only partly true, since the overall reorientation dynamics is normally at such a spectral range that bandwidths increase with magnetic field, and thereby do change 'unfavorably' from a mere resolution point of view. On the other hand, the line broadening and spin relaxation effects described actually do provide a rich source of detailed quantitative information about characteristics of the aggregates. Data on size, shape and local chain dynamics is accessible this way - provided a proper interpretation of the magnetic field-dependence and other experimental parameters is made. This was generally overlooked in early studies.

Studies of local and global dynamics in fluids through nuclear spin relaxation rates Due to the low energy difference between nuclear spin states, the equilibrium Boltzmann distribution between them only differs by an order of 1 in 10 . A t the low spectral frequencies of N M R (1-1000 M H z , depending on nucleus and magnetic field) spontaneous emission is a totally ineffective mechanism for establishing an equilibrium Boltzmann distribution. Instead the pathway is via fluctuations of spin interactions, originating from molecular reorientation processes. There are several mechanisms for achieving spin state equilibrium this way, and the establishment and loss of phase coherence between individual nuclei is also a component here. The detailed theory is complex, and is far outside the scope of this overview. Its fundamentals can be found in classical textbooks on NMR(3,4). A n excellent educational review on spin relaxation in liquids recently appeared.(5j The useful consequence of spin relaxation rate information in the present 5



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context is that it contains detailed information about molecular motion, in particular reorientation processes. A specific overview with reference to complex surfactant systems was given some years agofij. It should be consulted for a fuller treatment of the subject, together with some key references given in that review (pp 447-451 of (1)). Random molecular reorientation processes (overall reorientation of molecules, aggregates and macromolecules, and local chain motion) are modeled in terms of a correlation function for motion. This quantity is not determined directly. Instead one determines the Fourier transform at a limited number of frequencies. As a consequence one has to invoke models to proceed from the spectral densities (the intensity of reorientational fluctuations at a given frequency) to the correlation functions. Needless to say, such models should be chosen with care. Fortunately, the dynamics of polymer or surfactant systems in solution occur on timescales that are well matched to the frequencies of commonly available N M R spectrometers. Two such models have become popular and are extensively used today i) the 'two-step model' ((6,7), mainly for surfactant systems) and ii) the 'modelfree model' or Lipari-Szabo model ((8,9) for motional dynamics of proteins in solution). Both imply a global 'slow' motion of an aggregate or macromolecule (for example overall tumbling and diffusion on a surface, characterized by a correlation time T i ), order parameters (S) that quantify how rigidly a particular moiety (e.g. a -CH -group) is coupled to that 'slow' motional process, and a second correlation time Tf , characterizing the rate of local motions within that moiety. Mathematically, both approaches lead to the same type of expression. The somewhat subtle differences between the two, their parameters as well as their applicability to particular chemical systems are discussed in ref. (1). Experimentally, one needs access to spectrometers operating at several magnetic fields to gather the required spin relaxation information, and a computer program to carry out a global fit of x i and the individual S and modeling parameters. Meaningful experiments that can actually be evaluated must be designed so that only one intramolecular spin relaxation mechanism operates on the studied nuclei. Feasible approaches include studies through C spin relaxation (normally feasible without isotopic enrichment above the natural abundance of 1%) and/or deuterium N M R studies on selectively labeled alkyl groups. Protein backbone dynamics is normally quantified through spin relaxation studies on uniformly N labeled molecules. Such isotope enrichment is made through modern biotechnology techniques. Typical examples of surfactant studies (through the two-step model) are in references (7,10-14) and of protein studies (through the 'model-free' approach) are in references (15-17). s

ow

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asl

s

ow

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PGSE-based studies of organization and dynamics in fluids through multi-component self-diffusion rates A proven method for quantifying 'free/bound' situations and 'binding isotherms' is NMR-based multi-component self-diffusion monitoring by the FTP G S E method (Fourier Transform Pulsed-Gradient Spin-Echo) (2,18,19). In a chemical sense this approach relies on the often vastly different self-diffusion rates for the same molecule in 'free' or 'bound/aggregated' state. The basic (la) P G S E experiment(20) uses pulsed linear magnetic field gradients (of amplitude 'g', duration '8' and separation ' A ' ) that are applied during a so-called spinecho experiment(2i), involving two or more radio frequency pulses (in the simplest case separated in time by 'x' - see Figure 1).

Figure 1: The basic two-pulse PGSE experiment (a) and the stimulated-echo variant (b). Radio frequency (rf) pulse phase cycling is required (to suppress other echoes in (b)), the details of which also determine the resulting sign of the echo. Subsequent Fourier transformation of the 2 half of the echo produces a frequency-resolved NMR spin-echo spectrum (the individual traces in Figure 2) nd

Under these conditions the amplitude of the spin-echo (which occurs after a time 2T after the initial radio frequency pulse) attenuates from its full value (A(0)) according to the so-called Stejskal-Tanner relation(20): 2

A(2x) = A(0) exp(-2x/T ) exp(-D(yg8) (A-8/3)) 2


(la)

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T represents the (disturbing and experimentally limiting) transverse spin-spin relaxation rate of the nuclei in question, and y their magnetogyric ratio. As evident from this equation, protons are the easiest nuclei to study, owing to the high magnetogyric ratio. Applications to other nuclei are quite rare, due to a combination of instrumental factors, short T values and low sensitivity (another effect of a lower magnetogyric ratio). Tossible' nuclei include F , H , C and N a . P G S E experiments are always run at constant rf timing parameters (T), varying S, A or g only. This separates self-diffusion attenuation from spin relaxation attenuation, but does not eliminate the disturbing echo attenuation effect of transverse spin relaxation. For small molecules in solution at room temperature T i normally equals T , but in the presence of slower motional processes T i can become much longer than T (which decreases monotonically with slower motion). Then, the three-pulse stimulated echo PGSE variant (lb) becomes favorable from a detection point of view, despite the intrinsic 50% reduction in the effective echo amplitude(2i): 2

2

l 9

2

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2

2

A(T,+T ) = Vi A(0) e x p H v c O / T , ) exp(-2T,/T ) exp(-D (ygS) (A-8/3)) 2

2

]

H, 99.6 MHz PGSE/A I s A s U0 msec

2

(lb)

SDS+ tert-pentonol

6=110 msec Figure 2: A sequence of proton FT-PGSE 90-180 spin-echo spectra at sequentially increasing magnetic field gradient duration ('8' in Eqn. la) of partially solubilized neopentanol in sodium dodecyl sulfate (SDS) micelles in D 0 solution. The individual molecular *decay rates* translate into individual self-diffusion coefficients through Eqn. la. 2


33 Although more complex rf phase cycling schemes (typically 8 cycles) have to be applied in the stimulated-echo variant, it is almost always the preferred of the above two. Subsequent Fourier transformation of the composite echo in the time-domain separates the contributions at each frequency, just as in the normal basic pulsed F T - N M R experiment(2). Figure 2 illustrates a typical application of F T - P G S E N M R to a micellar system, in the context of solubilization.


FT-PGSE NMR self-diffusion studies for quantifying mesoscopic structure. Self-diffusion data in itself is a very direct source of information about aggregation processes. Fqr unrestricted diffusion during a selected time span the displacement probability in space of a given component 'k' (p (r,t)) is Gaussian and given by the equation: k

3/2

2

p (r,t) = const (l/8(7iD t) ) exp(-r /4D t) k

k

(2)

k

The characteristic self-diffusion coefficient (D) simply translates into a mean square displacement in space () during the observation time (At), through the Einstein relation: 2

2

= 6 D A t

(3)

The mean square displacement of even large macromolecules during the selected (method-dependent) time span of the experiment (At) is generally much larger than the average macromolecular diameter. Therefore the quantity () requires no further interpretation and becomes easy to visualize. In the case of restricted diffusion (for example in confined geometries) the situation will be different, but parameters like pore sizes and diffusion coefficients within porous structures are still accessible and quantifiable; see e.g. (22-25). One should note that self-diffusion coefficients are easily extracted from computer molecular dynamics simulation trajectories through the velocity autocorrelation function. This provides an easy path between theory and simulations and experimental self-diffusion data. A relatively recent study of this kind is (26). This is much more difficult with nuclear spin relaxation data. 2

Simple binding studies The self-diffusion approach to binding studies relies on a relative comparison of time-averaged self-diffusion rates between a 'bound' and 'free'


34 state. In the simplest two-state situation the effective self-diffusion coefficient D(obs) will be given by: D(obs) = p D(bound) + (1-p) D(free)

(4)

where the degree of binding (p) may assume values in the range 0

Mesoscale Phenomena in Fluid Systems - ACS Publications

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