NMR diffusion experiments provide a way to separate the different compounds in a mixture based on the differing translation diffusion coefficients (and therefore differences in the size and shape of the molecule, as well as physical properties of the surrounding environment such as viscosity, temperature, etc) of each chemical species in solution. In a certain way, it can be regarded as a special chromatographic method for physical component separation, but unlike those techniques, it does not require any particular sample preparation or chromatographic method optimization and maintains the innate chemical environment of the sample during analysis.
The measurement of diffusion is carried out by observing the attenuation of the NMR signals during a pulsed field gradient experiment. The degree of attenuation is a function of the magnetic gradient pulse amplitude (G) and occurs at a rate proportional to the diffusion coefficient (D) of the molecule. Assuming that a line at a given (fixed) chemical shift f belongs to a single sample component A with a diffusion constant DA, we have
(1) S(f,z) = SA(f) exp(-DAZ)
where SA(f) is the spectral intensity of component A in zero gradient (‘normal’ spectrum of A), DA is its diffusion coefficient and Z encodes de different gradient amplitudes used in the experiment.
Depending on the type of experiment, there are various formulae for Z in terms of the amplitude G of the applied gradient and one or more timing parameters such as Δ (time between two pulse gradients, related to echo time) and δ (gradient pulse width). In the original Tanner-Stejskal method using two rectangular gradient pulses, for example,
(2) Z =γ2G2δ2(Δ-δ/3)
Eq. (2) holds strictly for simple PFG-NMR experiments, and is modified slightly to accommodate more complicated pulse sequences.
In practice, a series of NMR diffusion spectra are acquired as a function of the gradient strength. For example, the figure below shows the results of a series of 1H-NMR diffusion experiments for a mixture containing caffeine, 2-Ethoxyethanol and water.
It can be observed that the intensities of the resonances follow an exponential decay. The slope of this decay is proportional to the diffusion coefficient according to equation (1). All signals corresponding to the same molecular species will decay at the same rate. For example, peaks corresponding to water decay faster than the peaks of caffeine and 2-Ethoxyethanol
The DOSY transformation
As far as data processing of raw PFG-NMR spectra is concerned, the goal is to transform the NxM data matrix S into an NxR matrix (2D DOSY spectrum) as follows:
The horizontal axis of the DOSY map D is identical to that of S and encodes the chemical shift of the nucleus observed (general 1H). The vertical dimension, however, encodes the diffusion constant D. This is termed Diffusion Ordered Spectroscopy (DOSY) NMR. In the ideal case of non-overlapping component lines and no chemical exchange, the 2D peaks align themselves along horizontal lines, each corresponding to one sample component (molecule).
The horizontal cut along such a line should show that component’s ‘normal’ spectrum. Vertical cuts show the diffusion peaks at positions defining the corresponding diffusion constants.
The mapping S=>D will be henceforth called the DOSY transformation. This transformation is, unfortunately, far from straightforward. Practical implementations include mono and biexponential fitting, Maximum Entropy, and multivariate methods such as DECRA.
Recently, Mathias Nilsson and Gareth A. Morris have proposed the so-called ‘Speedy Component Resolution’ (Anal. Chem., 2008, 80, 3777–3782) as an improved variation of the Component Resolved (CORE) method (J. Phys. Chem, 1996, 100, 8180). This is a multivariate-based method and the examples used in the article show an excellent performance of the algorithm.
Following a different approach, we have recently developed a brand new method for DOSY processing which has been included in Mnova. I will leave the details (and how to get the program to try it out) for the next post. In the meantime, should you be interested, just drop me a line.
(1) S(f,z) = SA(f) exp(-DAZ)
where SA(f) is the spectral intensity of component A in zero gradient (‘normal’ spectrum of A), DA is its diffusion coefficient and Z encodes de different gradient amplitudes used in the experiment.
Depending on the type of experiment, there are various formulae for Z in terms of the amplitude G of the applied gradient and one or more timing parameters such as Δ (time between two pulse gradients, related to echo time) and δ (gradient pulse width). In the original Tanner-Stejskal method using two rectangular gradient pulses, for example,
(2) Z =γ2G2δ2(Δ-δ/3)
Eq. (2) holds strictly for simple PFG-NMR experiments, and is modified slightly to accommodate more complicated pulse sequences.
In practice, a series of NMR diffusion spectra are acquired as a function of the gradient strength. For example, the figure below shows the results of a series of 1H-NMR diffusion experiments for a mixture containing caffeine, 2-Ethoxyethanol and water.
It can be observed that the intensities of the resonances follow an exponential decay. The slope of this decay is proportional to the diffusion coefficient according to equation (1). All signals corresponding to the same molecular species will decay at the same rate. For example, peaks corresponding to water decay faster than the peaks of caffeine and 2-Ethoxyethanol
The DOSY transformation
As far as data processing of raw PFG-NMR spectra is concerned, the goal is to transform the NxM data matrix S into an NxR matrix (2D DOSY spectrum) as follows:
The horizontal axis of the DOSY map D is identical to that of S and encodes the chemical shift of the nucleus observed (general 1H). The vertical dimension, however, encodes the diffusion constant D. This is termed Diffusion Ordered Spectroscopy (DOSY) NMR. In the ideal case of non-overlapping component lines and no chemical exchange, the 2D peaks align themselves along horizontal lines, each corresponding to one sample component (molecule).
The horizontal cut along such a line should show that component’s ‘normal’ spectrum. Vertical cuts show the diffusion peaks at positions defining the corresponding diffusion constants.
The mapping S=>D will be henceforth called the DOSY transformation. This transformation is, unfortunately, far from straightforward. Practical implementations include mono and biexponential fitting, Maximum Entropy, and multivariate methods such as DECRA.
Recently, Mathias Nilsson and Gareth A. Morris have proposed the so-called ‘Speedy Component Resolution’ (Anal. Chem., 2008, 80, 3777–3782) as an improved variation of the Component Resolved (CORE) method (J. Phys. Chem, 1996, 100, 8180). This is a multivariate-based method and the examples used in the article show an excellent performance of the algorithm.
Following a different approach, we have recently developed a brand new method for DOSY processing which has been included in Mnova. I will leave the details (and how to get the program to try it out) for the next post. In the meantime, should you be interested, just drop me a line.
1 comment:
I'm interested in the processing of DOSY experiments using MestReNova, but I don't how it is. Could you help me with that?
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