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Towards nuclear magnetic resonance m-spectroscopy and
m-imaging
P. J. M. van Bentum, J. W. G. Janssen and A. P. M. Kentgens*
Department of Physical Chemistry, NSRIM Center, University of Nijmegen, Toernooiveld 1,
6525 ED Nijmegen, The Netherlands. E-mail: Arno.Kentgens@nmr.kun.nl;
Fax: +31-24-3652112; Tel: +31-24-3652078
Received 24th March 2004, Accepted 14th June 2004
First published as an Advance Article on the web 5th August 2004
The first successful experiments demonstrating Nuclear Magnetic Resonance (NMR) were a spin-off from the
development of electromagnetic technology and its introduction into civilian life in the late forties. It was soon
discovered that NMR spectra held chemically relevant information making it useful as an analytical tool. By introducing
a new way of detection, moving away from continuous wave spectroscopy, Fourier Transform NMR helped to overcome
sensitivity problems and subsequently opened the way for multi-dimensional spectroscopy. As a result NMR has
developed into one of the most powerful analysis techniques with widespread applications. Still sensitivity is a limiting
factor in the applicability of NMR. Therefore we witness a renaissance of technique development in magnetic resonance
striving to improve its receptiveness. This tutorial review introduces the efforts currently made in miniaturizing inductive
detection by designing optimal radio-frequency microcoils. A second approach is to introduce a new way of detecting
magnetic resonance signals by means of very sensitive micromechanical force detectors. This shows that the detection
limits in terms of absolute sensitivity or imaging resolution are still open to significant improvements.
Introduction
Magnetic resonance spectroscopy (NMR) and imaging (MRI) have
had a tremendous impact on research in physics, chemistry, biology
and medicine. In chemistry and biology it has become the method
of choice for structure analysis because of the wealth of information
that can be obtained on a very local scale. For example it is possible
to extract inter-atomic distances and coupling strengths within a
molecule that can shed light on both the 3D configuration and
functional behavior. In materials science NMR is the method of
choice for analyzing materials with some inherent disorder present.
In medicine MRI has become the most prominent diagnostic tool
because of its versatility and non-invasive character. At present
there are no adverse effects known of the static magnetic fields or
the rf irradiation involved. This is mainly due to the low energy
scales involved. Even at the highest possible fields the nuclear
Zeeman splitting, and thus the electromagnetic radiation to pump
the transitions, remains much smaller than the thermal energy k
B
T
at room temperature. However this advantage also has an adverse
effect. The main limitation in NMR and MRI is the fact that these
low energy scales inevitably lead to a rather low sensitivity. Only
with the utmost care in noise reduction can the spectra or images be
accumulated in a reasonable amount of time. Even then, the
technique is only applicable for samples with relatively large
Jan van Bentum was born in the Netherlands, in 1953. He received
his PhD in Solid State Physics from the University of Nijmegen in
1986. In 1992 he joined the Dutch high magnetic field laboratory as
assistant professor in infrared and millimetre wave spectroscopy.
In 2003 he joined the Physical Chemistry Department of the NSRIM
research school of the University of Nijmegen, specializing in
NMR spectroscopy. His current research interests are very
high field NMR and general NMR methodology on a microscopic
scale.
Hans Janssen was born in The Netherlands, in 1966. He received
his engineer degree in Electronics from Den Bosch Polytechnic in
The Netherlands in 1991. In that year he joined The University of
Nijmegen as an Electronic Engineer at the Department of Physical
Chemistry. His current research interests are designing NMR
probeheads with solenoid coils and planar coils for research on
micro-scale.
Arno Kentgens was born in the Netherlands, in 1959. He received
his PhD in Chemistry from the University of Nijmegen, The
Netherlands, in 1987. In 1988 he
joined the Dutch High Frequency
NMR facility as supervisor for
solid-state NMR. Since 2000 he
has been Professor for Physical
Chemistry at the NSRIM centre of
the University of Nijmegen. His
current research interests are
devising new ways of detecting
NMR signals with enhanced sen-
sitivity, the development of tech-
niques for extracting structural
information from quadrupolar
nuclei and their application to
relevant problems in chemical
research and materials science.Jan van Bentum Hans Janssen Arno Kentgens
This journal is © The Royal Society of Chemistry 2004
DOI: 10.1039/b404497p
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/ Journal Homepage
/ Table of Contents for this issue
concentrations of spins. In spectroscopy typical sample sizes are of
the order of 10–100 mm
3
and in MRI one generally is very happy
to obtain a 1 mm resolution. In contrast to various other techniques
one typically requires of the order of 10
14
–10
16
nuclei in the
sample. In analytic chemistry, the sensitivity severely limits the
application as a routine in situ analysis tool.
It is clear that there are many research topics that would benefit
from even a modest improvement in sensitivity or resolution. An
improvement in sensitivity by a factor of 10 would bring the data
acquisition times down from days to minutes and would allow for
example online quality control in chemical or pharmaceutical
production. Also, if the MRI resolution could be boosted to the
micron scale, it would be possible to perform functional studies on
the level of individual cells.
So far these expectations are far from being realised and in fact
there are firm physical laws that stand in the way of spectacular
short term improvements. Nevertheless, many research groups are
working towards gradual improvements and in retrospect we do
have seen an improvement of nearly such a factor of 10 in the last
decade, and there is no need to be pessimistic about the future. It is
therefore that we witness a renaissance of technique development in
magnetic resonance striving to improve the sensitivity. For
example there is a renewed interest in Dynamic Nuclear Polariza-
tion (DNP), the use of optically polarized Xe and
3
He, and
increasingly higher field strength using Bitter magnets or even
pulsed magnets. The options addressed in this contribution are to
improve sensitivity for mass-limited samples by using very small rf
coils (microcoils) which give a better absolute sensitivity for a
specific number of spins, and secondly, to move away from the
traditional method of inductive detection and use very sensitive
force detection sensors.
First we will shortly point to recent reviews in the literature on
both microcoils and force detected NMR microscopy. In the next
paragraphs we will discuss the issues at hand on an elementary level
and give some examples of recent developments in the field.
Webb has reviewed the essentials of solenoid microcoils.
1
Although this paper dates back to 1997, it contains most of the
important aspects including application for liquid chromatography
and electrophoresis. In a more recent paper by Ciobanu et al.
2
the
state of the art in MR spectroscopy is summarized with some
emphasis on biological problems. The impact of rf field in-
homogeneity with various imaging sequences is given with a
discussion on sensitivity and resolution.
The aspect of rf homogeneity and optimization of sensitivity for
microcoils is analyzed in detail by Minard and Wind.
3,4
These two
papers contain many useful guidelines for the design of solenoid rf
coils with specific optimization results for the number of windings
and wire diameter for either conducting and non-conducting
samples.
A theoretical analysis of the rf field homogeneity in high
frequency solenoid coils is given by Engelke.
5
The electromagnetic
field is derived analytically and used in numerical computations to
analyze the effect of dielectric sample materials, and standing
waves that may occur if the geometrical sizes are not small
compared to the wavelength of the rf radiation.
Eroglu et al.
6
reviewed the design and performance for spiral
surface coils in particular for micro fluidic applications. In general,
a good local sensitivity can be achieved at moderate spectral
resolution. Integration in micro fluidic devices is indeed possible,
although the close proximity of the rf coil degrades the field
homogeneity (and thus spectral resolution) because of susceptibil-
ity problems. The same group also reviewed the various applica-
tions of these surface coils in particular for biological samples.
7
A detailed description of the use of microcoils in micro fluidic
devices is given by Massin et al.
8
The achieved sensitivity for a test
sample of sucrose in D
2
O gives a proof of principle for ‘lab on a
chip’ analytic capabilities. Note, however, that these tests are done
at relatively high magnetic field values that require state of the art
superconducting magnet systems. For routine applications it will be
desirable to use permanent magnets, in order to make the
spectrometer compact and robust for in situ applications in e.g. a
production environment. At present it is not clear whether it is
possible to achieve the required resolution in magnet systems that
are not infinitely large compared to the size of the micro fluidic
devices.
The implementation of microcoils for solid state NMR is given
by Yamauchi et al.
9
They emphasize the use of microcoils to
generate very high rf fields that are needed to excite quadrupolar
nuclei where the spectral distribution can be as broad as several
MHz.
The limits of the attainable resolution in magnetic resonance
spectroscopy are discussed in a recent review by Glover and
Mansfield.
10
They give a detailed historical overview of the
developments in this field and re-examine the fundamental
principals of imaging and signal detection to evaluate the limits in
resolution, in particular for liquid, solid and gas-phase micros-
copy.
NMR sensitivity and strategies for improvement
The basic expression that gives the NMR signal to noise ratio is
given by:
where k
0
is a scaling factor accounting for the rf inhomogeneity of
the coil, B
1
/i is the magnetic field induced in the rf coil per unit
current, V
S
the sample volume, N the number of spins per unit
volume, g the gyromagnetic ratio, I the spin quantum number, w
0
the nuclear Larmor precession frequency, T the temperature and Ó
and k
B
are Planck’s and Boltzmann’s constant, respectively. The
denominator describes the noise using the noise factor of the
spectrometer (F), conductive losses of the coil, circuit and sample
(R
noise
) and the spectral bandwidth (Df). In the derivation of this
expression it is assumed that the noise figures are dominated by the
coil resistance, including sample losses. An implicit assumption is
that the noise of the preamplifier is negligible. In this case, the Q-
factor of the resonant LC circuit drops out of the problem since
signal and noise are both amplified by the same amount. This
assumption may not be true any more if the noise is suppressed as
for example in cryo-cooled detector coils. From the above equation
it is clear that most of the parameters are constants of nature or
dictated by the sample properties or sample conditions such as
temperature. The basic strategy to optimize the NMR signal is to
choose the lowest possible temperature combined with the highest
magnetic field (and thus rf frequency) that is available. It has been
widely accepted that a cooling of the rf coil in so-called cryoprobes
is a sensible way to improve sensitivity. For pure metals, the
resistivity is more or less linear in temperature, so a reduction in
temperature by a factor of ten may lead to a factor of about three
reduction in the noise amplitude. Commercial instruments now
provide up to 900 MHz proton frequency in a 21 T static field.
Alternatively one can go to a resistive magnet or combined hybrid
magnet up to 45 T in one of the (inter)national high field magnet
facilities. Next, one wants to optimize the filling factor of the
specific rf coil, or maximize the V
S
N product. The only technical
design parameters of the rf coil and detection that can be
manipulated is in fact the term B
1
/i. In other words, one should
optimize the rf field that is generated per unit current. In addition,
one should minimize the total losses in the rf circuit to reduce the
noise. This translates to the question of choosing the proper coil
geometry for any given sample. Minard and Wind
3,4
have
summarized the basic guidelines for the most common coil
geometries. Note that for a uniform rf field the length of the wire
that forms the coil must remain short compared to the wavelength
of the rf frequency. For the highest frequencies this strongly
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restricts the number of windings in the coil. Also, most metals are
weakly diamagnetic and for example the copper wire that forms the
coil will lead to a (weak) distortion in the magnetic field and thus
will reduce the spectral resolution that can be obtained. In solid
state NMR the resonance lines are rather broad because interactions
do not average out as in solutions. For solid state samples the
requirement for the field homogeneity is therefore less stringent and
the coil can in general be designed to fit tightly around the sample
holder.
In the following we will describe some rather unconventional
approaches to achieve the best sensitivity for very small samples.
For these mass-limited samples the expected signals will be very
weak and one is forced to optimize the detection sensitivity as good
as possible. As a general design concept one can formulate the
following guidelines:
The volume in which the rf field is generated should be confined
in space to minimize the energy stored in the coil. This is equivalent
to minimization of the self inductance L. In this space the rf field
should be homogeneous and for optimum performance should be
completely filled with sample material. In the example of a
traditional helical solenoid roughly half of the magnetic field
energy is outside the coil and is wasted. Also, the field is linearly
polarized and for a circular polarized spin precession only half of
the signal is detected. Thus the effective efficiency of a helix is only
about 25% of the theoretical limit.
The resistive losses should be minimized. This translates to a
geometry where the surface current density is a constant and covers
(nearly) the entire surface of the sample volume. Eddy currents
should be avoided where possible. For this point, a conventional
helix is a good choice. Small improvements can be made by using
rectangular cross section wire, although the distance between the
windings should not be too small to prevent arcing when used at
high power levels.
Depending on the intended frequency range, one should be
careful to keep the total path length of the coil much smaller than
the rf wavelength. If this condition is not met, the self-capacitance
of the coil may lead to a current density that varies along the coil
axis, severely reducing the rf homogeneity. Also, one should realize
that the spins at the far end of the coil are excited at a later time than
the top end. During the detection cycle the currents should have the
same direction (phase). For example in a non resonant setup with a
50 ohm load connected in series with the coil this symmetry is
broken and in reflective detection the induction signals of the
beginning and end of the coil are no longer in phase and can partly
annihilate each other. A last problem with large wire lengths in the
coil is that heating may become a limiting factor. In good metals
most of the heat is carried away by the electrons and either
transferred to the environment or to the massive contact leads.
As a last guideline one should match the coil geometry to that of
the sample. In the case of a cylindrical powder sample as is used in
a MAS experiment the natural coil geometry is that of the
traditional helix. However, in the case of thin films on a massive
substrate a helix is generally not the best option.
Similarly to regular NMR probes, cooling of the rf coil can
further improve sensitivity. In the case of microcoils the sample is
generally much closer to the coil, however, and it is not trivial to
obtain the proper thermal isolation over distances of 100 mm or less.
On the other hand, if one is allowed to cool the sample
simultaneously with the coil, a much bigger advantage is obtained
since the equilibrium magnetization of the sample itself is a nearly
linearly increasing function when going to lower temperatures.
Solenoid microcoils
The classical geometry to create a magnetic field with an electrical
current is the solenoid coil or helix. Even for a limited number of
windings this geometry provides a reasonable homogeneous B
1
field and a good filling factor is possible by winding the coil
directly onto a holder containing the sample. Miniaturization to a
scale of several hundred microns is not very difficult although the
wire diameter (typically 20 to 50 micron) becomes very small and
a freestanding coil is a very delicate object. For classical LC
resonant circuits one is tempted to use as many windings as possible
to get reasonable inductance values (of the order of 10–20 nH).
However the penalty one pays is that the maximum rf power that is
allowed without severely heating the sample may be rather low.
Fortunately a good B
1
/i field factor helps both to enhance the
detection sensitivity and to get high rf excitation fields even at
moderate power levels. A final point of attention should be toward
a minimization of the length of the electrical leads between
capacitor and inductor since this all adds to the electrical losses.
Although the length of wiring is strongly reduced by scaling down
the size of the helix, the effective resistance is nearly constant
because the diameter of the wire is scaled by the same amount. Note
that the rf currents flow only in a surface layer given by the
penetration depth near the inside of the helix. The field of a
cylindrical coil is at a maximum at the center and given by the
simple expression:
where m
0
is the permeability of free space, n the number of turns in
the coil, and r and l the radius and length of the coil. This shows that
the sensitivity increases with the inverse of the diameter for coils
with a fixed form factor l/2r, which is the basic rationale for using
microcoils to get NMR spectra from mass/volume-limited samples.
The B
1
field falls off to about half the center field near the ends of
the helix. This inherent inhomogeneity of the rf field is further
amplified by the fact that parallel currents repel each other, leading
to a redistribution of the current away from the axis for the
outermost windings. A final cause of rf field inhomogeneity is
related to the current leads that break the cylindrical symmetry. A
neat design to minimize most of these problems is sketched below
in Fig. 1. Here, the helix is embedded in the center of a custom-
made capacitor disk, which provides an LC geometry with very
short connections. Since the currents in the capacitor plates are
essentially radial, a minimum distortion of the rf field pattern is
achieved. The microcoil itself is wound on a vessel coil former with
a thread that is cut on a CNC lathe. In a later version of this design
we introduced a variable pitch in the coil to get optimum rf
homogeneity in the center half of the sample space (see Fig. 2 and
3). In principle this is similar to the classical trick of so-called “end-
compensated” rf coils in which the outermost windings were
squeezed to a slightly smaller pitch.
11
A reduction to below 100
micron diameter is possible but the machining and handling of such
coils will be rather tedious. For this reason various groups have
Fig. 1 Integrated solenoid microcoil and capacitor circuit. Top: actual
photograph to indicate the size. The microcoil has a free inner diameter of
300 mm, located in the centre of the image. Bottom: schematic representa-
tion to illustrate the integrated design with the solenoid embedded in the
centre of a tuned capacitor to provide an LC circuit with minimized
losses.
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explored the option to use planar lithographic methods to define the
coil shape.
For solenoid coils adding more turns to the coil will enhance the
B
1
/i ratio and thus both the inductance and the signal response. At
the same time the coil resistance will increase linearly, so the
improvement in sensitivity will be proportional to the square root of
the number of turns n. Note, however, that as soon as a packing of
one is reached, i.e. adjacent turns are in close contact, one can only
add more turns in a single layer if the wire diameter is reduced. This
will give a nearly quadratic increase in resistance as a function of n,
so the sensitivity will become independent of the number of turns.
At the same time we will have a larger ohmic heating at the center
of the coil and an enhanced danger for arcing, so the optimum is
generally found for only a limited number of turns.
Besides rf performance, static field distortions due to susceptibil-
ity effects are an important factor in the design of microcoil
probeheads. The close proximity of the coil wires to most of the
sample will adversely affect the spectral resolution. As was
described by Webb,
1
possible workarounds are the immersion of
the coil in a material with a susceptibility similar to that of the coil.
In this way one mimics an infinite cylinder of given susceptibility
in which the static field will be homogeneous. Alternatively the coil
can be designed of multiple layers of different metals (e.g.
aluminium and copper) with compensating susceptibilities. In
solids samples magic angle spinning can (partly) average suscepti-
bility effects.
Planar microcoils
The most common geometry used in planar microcoils is based on
a spiral design with the center winding contacted to the outside
using a connection to another layer which is electrically isolated
with a thin oxide layer. A typical coil layout with the corresponding
rf field profile is shown in Fig. 4. Using standard lithography
techniques as used in the micro-electronics industry one can define
any structure with dimensions down to below a micron. Also the
fact that mass production is possible without the tedious procedure
of winding a wire onto a coil former is quite appealing.
Nevertheless, a detailed analysis shows that such a surface spiral
has some serious drawbacks, compared to a helical coil. First, the
outermost windings are much less efficient in the sense that they
contribute less to the centre axial field while they largely dominate
the resistive losses. Second, the fields produced by the outer
windings cause considerable eddy currents in the centre windings
adding additional losses and lowering the field homogeneity in the
centre region. For this reason the optimum is found for only a few
windings, and thus a rather low inductance. A third less advanta-
geous aspect of surface coils is that the conductance of the
connection to the bottom layer is not ideal. Using typical thin film
methods as is common in micro-electronics one ends up with
additional losses that can be comparable to the losses of the coil
itself.
One of the appealing aspects of lithographically produced rf coils
is that it may fulfil the promise of a ‘lab on a chip’ in which the
material synthesis and analysis is integrated on a single chip. An
example of such a probe is shown in Fig. 5. It is even conceivable
to integrate the NMR rf source and data acquisition electronics on
the same chip. The fast developments and miniaturization in the
cell-phone industry (working at rf frequencies in the same band as
employed in NMR) show that this is not unrealistic. In fact, a design
integrating coil and preamplifier module was developed using
CMOS technology by Boero et al.
12
A further possibility would be the use of microcoils for
performing solid-state NMR spectroscopy in very high field
Fig. 2 Cross section of the B
1
field for a solenoid coil with a variable pitch
to optimize the rf field homogeneity. In view of the cylindrical symmetry
only half of the cross section is given. The length of the coil is 1 mm and the
inner free diameter is 300 mm. The copper wire used to wind the coil has a
diameter of 50 mm. The colour scales indicate 10% levels with respect to the
maximum. For this optimized coil about 75% of the sample volume is
located in the homogeneous region. The graph on the right shows the rf field
strength along the axis. The red curve is an analytical calculation based on
the Biot-Savart law for a homogeneous current distribution in a simple
helical coil of length 1 mm. The black dashed curve is a numerical finite
element calculation that includes the effects of the finite penetration depth
and the induced Eddy currents. The blue curve (vertically displaced for
clarity) represents the finite element result for the coil with optimized pitch
shown on the left.
Fig. 3 Nutation spectrum for a 300 mm diameter solenoid microcoil with
a continuous pitch. The rf field in coil is 4.7 MHz (B
1
= 0.11 T) at a power
level of 270 W. Adapted with permission from ref. 9.
Fig. 4 Planar microcoil with 6 windings, inner diameter 300 mm, outer
diameter 1.4 mm. The B
1
field intensity is represented in a color map. The
most commonly used sample position is indicated in the red rectangle with
the rf field pointing in the axial direction. In this configuration the axis of the
rf coil will be oriented perpendicular to the external static field B
0
. An
alternative orientation is indicated in yellow for a thin layer sample. In this
case the in-plane (radial) component of the rf field can be used and the coil
must be oriented with the axis parallel to the external static field. In both
cases the rf field is not very homogeneous over the sample volume and
therefore multi-pulse excitation schemes are not very efficient.
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