Charge and Size of Molecules and Complexes in Solution
An Application of Pulsed Field Gradient NMR
- Credit: Alen Hunjet, freerangestock.com
- Fig. 1: Diffusion-ordered (DOSY) NMR spectrum of a solution of arginine, glutamic acid and PDADMAC recorded on a 500 MHz NMR spectrometer using a diffusion NMR probe head.
- Fig. 2: Electrophoresis NMR spectrum of a solution of arginine and glutamic acid, recorded on 300 MHz NMR spectrometer with microimaging accessory and a special electrophoresis NMR probehead.
- Fig. 3: Effective charge of poly(styrene sulfonate) in mixtures of water and methanol as a function of the mixing ratio.
The effect of magnetic resonance NMR is based on the interaction of the magnetic moment of nuclei with a strong external magnetic field which usually is established by superconducting magnets. Additional position-dependent magnetic fields, so-called magnetic field gradients, encode the space information or information on translation in the NMR signal. This provides information on the hydrodynamic size of molecules in solution. If in addition an electric field is applied in-situ, information the effective charge of molecules, complexes or aggregates is determined.
The magnetic field is coupled to the nuclear spin thus magnetic moments do not completely align in the external magnetic field they rather precess with a characteristic frequency, the so-called Larmor frequency around the external field. This Larmor frequency specific for each isotope and it is proportional to the external magnetic field which is the basis of the high selectivity of NMR. By irradiation with resonant high-frequency pulses the spins can be excited or selectively manipulated. Different sequences of such radio-frequency pulses define the large variety of different NMR experiments which is used to select or selectively average specific interactions in the NMR spectrum .
Structure Determination Based on Local Interactions
NMR provides local information, because of the local nature of the underlying interactions. NMR spectroscopy is thus ideally suited for the characterization of soft matter and disordered materials. It is indispensable for structure determination in solution and is today widely used in chemical industry and in materials research.
Space Encoding and Flow
Through the application of additional magnetic fields which depend on the spatial position, so-called magnetic field gradients spatial information can be encoded in the NMR signal which is the basis of a magnetic resonance tomography (MRT). In the pulsed-field gradient NMR experiment this principle is used to encode the position of molecules at two times. From the comparison of the encoding for the two times motion is measured . Pulsed-field gradient (PFG) NMR is widely used to measure diffusion in liquids.
From the self-diffusion coefficient via the Stokes-Einstein equation the hydrodynamic size is calculated, that is the size of a sphere exhibiting the same hydrodynamic resistance. Using a calibration based on standards of poly(styrene sulfonate) the molar mass of polyelectrolytes is determined from the self-diffusion coefficient. On the other hand the conformation of macromolecules in solution can be influenced by the quality of the solvent by pH, ionic strength or dielectric constant and thus impact the hydrodynamic size. The results compared nicely to those from dynamic light scattering. Dynamic light scattering is better suited for larger objects whereas pulsed-field gradient NMR is well-suited for small molecules which only exhibit a very small scattering intensity. In addition PFG NMR permits the detection of an additional spectral dimension thus the diffusion coefficients can be attributed to different chemical species. Figure 1 shows a so-called diffusion-ordered (DOSY) NMR spectrum of a mixture of glutamic acid and arginine and a long-chain polyelectrolyte. The large diffusion coefficients of the amino acids are well separated from the much smaller diffusion coefficient of the polymer. The same approach can be used to study the formation of complexes and aggregation.
In-situ Application of an Electric Field
Coherent motion like flow can be distinguished from incoherent motion like diffusion by pulsed-field gradient NMR experiments. Diffusion leads to signal attenuation, flow leads to a phase modulation . If one now applies an electric field in situ, charged species move coherently in this electric field. The motion is detected by pulsed-field gradient NMR  and appropriate data processing generates a two-dimensional correlation of chemical shift and electrophoretic mobility. Species can be identified by their chemical shift which is correlated with the electrophoretic mobility . Figure 2 shows an example of such an electrophoresis NMR spectrum from a solution of glutamic acid and arginine which can be identified by the chemical shift in the NMR spectrum at neutral pH. Arginine exhibits, because of its positive charge, a positive electrophoretic mobility and glutamic acid exhibits a negative electrophoretic mobility. In a separate PFG NMR experiment without electric field the diffusion coefficient and length scale is determined. On the timescale of the electrophoresis NMR experiment only is steady state, a constant velocity, is measured. From the combination of diffusion coefficient and electrophoretic mobility for each species the effective charge is calculated. This effective charge in macromolecular systems, polyelectrolytes and proteins is significantly smaller than the nominal charge because a significant fraction of the counterions condenses and thus lowers the effective charge of the macromolecule . Only this lowered effective charge is available for the interaction with other molecules or charged surfaces in the solution. The extent of condensation of counterions is strongly influenced by the surrounding medium by ionic strength, pH, and dielectric constant . Figure 3 shows and the effective charge of poly(styrene sulfonate) of a molar mass of 77 kg/mole in different mixtures of methanol and water which have been used to adjust the dielectric constant of the solution. It is clearly seen that even in pure water only roughly 1/3 of the total 350 charges are effective. Adding methanol lowers this number drastically. At the same time the polymer is much more the collapsed as is seen in the reduced hydrodynamic radius.
Based on a large variety of special and highly selective experiments proving the sensitivity of NMR spectroscopy to local interactions, the method is specifically suited for the investigation of soft matter like polymers and proteins. The only drawback, the limited sensitivity, nowadays is reduced by new developments and modern instruments. Pulsed field gradients enable measuring the translation of molecules in solution and assignment by their chemical shifts in the spectra. From the self-diffusion coefficient the hydrodynamic size is determined based on the Stokes-Einstein equation. Using a calibration with standards of poly(styrene sulfonate) the molar mass of polyelectrolytes is determined. The combination with the electrophoresis NMR experiment enables the direct determination of the effective charge of molecules, complexes, and aggregates.
Dr. Ulrich Scheler
Leibniz-Institute for Polymer-Research Dresden e.V.
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 Böhme, U. ; Scheler, U. Effective charge of polyelectrolytes as a function on the dielectric constant of a solution more Journal of Colloid and Interface Science 309 (2007) 231-235
 Böhme, U. ; Vogel, C. ; Meier-Haack, J. ; Scheler, U. Determination of charge and molecular weight of rigid-rod polyelectrolytes more Journal of Physical Chemistry / B 111 (2007) 8344-8347