Content uploaded by Mikkel Fougt Hansen
Author content
All content in this area was uploaded by Mikkel Fougt Hansen
Content may be subject to copyright.
On-chip measurements of Brownian relaxation of magnetic beads with
diameters from 10nm to 250nm
Frederik Westergaard Østerberg, Giovanni Rizzi, and Mikkel Fougt Hansen
Citation: J. Appl. Phys. 113, 154507 (2013); doi: 10.1063/1.4802657
View online: http://dx.doi.org/10.1063/1.4802657
View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v113/i15
Published by the American Institute of Physics.
Additional information on J. Appl. Phys.
Journal Homepage: http://jap.aip.org/
Journal Information: http://jap.aip.org/about/about_the_journal
Top downloads: http://jap.aip.org/features/most_downloaded
Information for Authors: http://jap.aip.org/authors
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
On-chip measurements of Brownian relaxation of magnetic beads
with diameters from 10 nm to 250 nm
Frederik Westergaard Østerberg,
a)
Giovanni Rizzi, and Mikkel Fougt Hansen
b)
Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech, Building 345
East, DK-2800 Kongens Lyngby, Denmark
(Received 16 January 2013; accepted 4 April 2013; published online 19 April 2013)
We demonstrate the use of planar Hall effect magnetoresistive sensors for AC susceptibility
measurements of magnetic beads with frequencies ranging from DC to 1 MHz. This wide
frequency range allows for measuring Brownian relaxation of magnetic beads with diameters
ranging from 10 nm to 250 nm. Brownian relaxation is measured for six different magnetic bead
types and their hydrodynamic diameters are determined. The hydrodynamic diameters are found to
be within 40% of the nominal bead diameters. We discuss the applicability of the different bead
types for volume-based biosensing with respect to sedimentation, magnetic trapping, and signal per
bead. Among the investigated beads, we conclude that the beads with a nominal diameter of 80 nm
are best suited for future on-chip volume-based biosensing experiments using planar Hall effect
sensors. V
C2013 AIP Publishing LLC [http://dx.doi.org/10.1063/1.4802657]
I. INTRODUCTION
Magnetic beads have proven to be a promising ingredi-
ent in future biosensors.
1–4
Since most biological samples
are non-magnetic, the readout will not be disturbed by chem-
ical or biological components of the sample. Magnetic beads
also have the advantage that they can be manipulated mag-
netically and are generally well dispersed in a liquid sample
such that diffusion times can be significantly reduced.
Finally, the presence and properties of magnetic beads can
be detected by magnetic field sensors to directly provide an
electrical signal.
Connolly and St Pierre
5
first proposed to use Brownian
relaxation measurements of magnetic beads for biosensing.
Brownian relaxation is the physical rotation of a bead in
response to an oscillating magnetic field and it is character-
ized by the Brownian relaxation frequency, which is inver-
sely proportional to the hydrodynamic volume of the bead.
Using functionalized magnetic beads, it is possible to bind a
target analyte to the beads to obtain a detectable increase of
their hydrodynamic size.
The simplest assay is to directly detect a hydrodynamic
size change of the free beads in suspension due to bound ana-
lytes. However, as most analytes are typically much smaller
than the beads, this will only give rise to a limited change of
hydrodynamic size.
6
Moreover, the change may be difficult
to resolve due to the inevitable bead size distribution. A
more effective assay strategy is to use the target analyte to
form clusters of beads and hence induce bead agglutination.
7
Yet another strategy is to use amplification of the target ana-
lyte to form substantially larger entities, e.g., by forming
large DNA coils by a rolling circle amplification.
8,9
Such
coils have the advantage of both changing the hydrodynamic
size of single beads significantly and that each coil can bind
multiple beads.
10
The drawback is that the rolling circle
amplification requires additional sample preparation.
Brownian relaxation of magnetic beads can be measured
with various techniques including inductive methods,
6
flux-
gates,
11
superconducting quantum interference device
(SQUID) magnetometers,
12
and magnetoresistive sen-
sors.
13,14
Particularly magnetoresistive sensors are promising
in future lab-on-chip devices as they are small, potentially
inexpensive, require small sample volumes, and can be inte-
grated with sample preparation in a microfluidic device.
The frequency range in which a given technique oper-
ates determines the bead sizes for which Brownian relaxation
can be measured. Thus, it is advantageous to have a detec-
tion system that can operate at frequencies spanning many
orders of magnitude.
Here, we demonstrate on-chip measurements of
Brownian relaxation of magnetic beads with diameters rang-
ing from 10 nm to 250 nm using so-called planar Hall effect
bridge (PHEB) sensors
15,16
and that these sensors are feasi-
ble for dynamic magnetic measurements up to MHz frequen-
cies. Finally, we discuss the best choice of bead type and
size for future on-chip volume-based bioassays employing
these sensors.
II. THEORY
A. Brownian relaxation of magnetic beads
When a magnetic bead is placed in an external magnetic
field, the magnetic moment will align with the direction of
the applied field. The moment of the bead may relax by an
internal flipping of the moment (N
eel relaxation
17
) and by a
physical rotation (Brownian relaxation
18
). The N
eel relaxa-
tion may be relevant for magnetic nanograins smaller than
about 10–20 nm, when these form either a single magnetic
core or being part of a multigrain core. In this work, we will
for simplicity assume that N
eel relaxation can be neglected,
i.e., that the Brownian relaxation mechanism dominates.
Thus, when a bead is placed in a magnetic field oscillating at
a)
Electronic mail: Frederik.Osterberg@nanotech.dtu.dk.
b)
Electronic mail: Mikkel.Hansen@nanotech.dtu.dk.
0021-8979/2013/113(15)/154507/7/$30.00 V
C2013 AIP Publishing LLC113, 154507-1
JOURNAL OF APPLIED PHYSICS 113, 154507 (2013)
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
frequency f, the dynamic behavior is characterized by the
Brownian relaxation frequency
fB¼kBT
6pgVh
;(1)
where kBTis the thermal energy, gis the dynamic viscosity of
the liquid in which the bead is suspended and Vhis the hydro-
dynamic volume of the bead. The dynamic magnetic behavior
of a magnetic bead ensemble in response to an applied mag-
netic field is described by the complex magnetic susceptibility
v¼v0iv00,wherev0and v00 denote the in-phase and out-of-
phase magnetic susceptibilities, respectively. For ffB,the
beads rotate in phase with the applied field and for ffB
the field is oscillating too fast for the beads to respond. When
f¼fB, the component of the bead moment lagging behind the
applied field assumes its maximum, resulting in a peak in the
out-of-phase magnetic susceptibility. Cole and Cole
19
have
shown empirically that the complex magnetic susceptibility
due to Brownian relaxation for a polydisperse ensemble of
beads is often well described by
v¼v0v1
1þðif=fBÞ1aþv1;(2)
where v0and v1are the DC and high-frequency susceptibil-
ities, respectively. The parameter ais a measure of the poly-
dispersity of the bead ensemble and can assume values
between 0 and 1. For a monodisperse sample, a¼0 and the
Cole-Cole model reduces to the Debye model.
20
B. Sensor signal
The sensors used in this study are based on the aniso-
tropic magnetoresistance (AMR) effect.
21
The sensors are
structured in a bridge geometry as shown in Fig. 1. A bias
current Iis applied in the x-direction and the potential differ-
ence V
y
is measured across the y-direction. The signal from
the sensor bridge is the same as for cross-shaped planar Hall
effect sensors except for a geometrical amplification.
15
To
distinguish them from other AMR bridge geometries, we
have therefore named them PHEB sensors.
15
For low magnetic fields, the sensor signal is linear and
given by
15
Vy¼IS0Hy;(3)
where S
0
is the low-field sensitivity and H
y
is the average
magnetic field acting on the sensor area in the y-direction.
Our measurements of the magnetic bead susceptibility
are performed in nominally zero externally applied magnetic
field and the beads are magnetized by the magnetic field aris-
ing from the alternating bias current IðtÞ¼IAC sinð2pftÞ
passed through the sensors. We have previously shown
16
that the in-phase and out-of-phase components of the com-
plex second harmonic sensor signal V2¼V0
2þiV00
2meas-
ured using lock-in technique can be written as
V0
2¼23I2
ACS0c1v00 ;(4)
V00
2¼23I2
ACS0ðc0þc1v0Þ:(5)
Here, c0is a constant depending on the sensor stack and ge-
ometry that describes the sensor self-biasing and c1is a pa-
rameter depending on the sensor geometry and distribution of
beads that describes the magnetic field acting on the sensor
from magnetic beads magnetized by the sensor self-field. The
value of c1is positive in the presence of beads and zero in the
absence of beads.
22
Thus, the in-phase second harmonic sen-
sor signal is proportional to the out-of-phase magnetic bead
susceptibility and the out-of-phase second harmonic sensor
signal depends linearly on the in-phase magnetic bead suscep-
tibility. The term c0can be found from a measurement with-
out beads and subtracted from the out-of-phase sensor signal.
The resulting corrected value V00
2;cor is proportional to the
in-phase magnetic bead susceptibility. In the data presentation
and analysis, it is convenient to use this to relate the corrected
second harmonic sensor signal V2;cor ¼V0
2þiV00
2;cor to the
Cole-Cole expression, Eq. (2),as
iV2;cor ¼V00
2;cor iV0
2¼V0V1
1þðif=fBÞ1aþV1;(6)
where V
0
and V1are defined as
V0¼23I2
ACS0c1v0;(7)
V1¼23I2
ACS0c1v1:(8)
We note that the value of c1cannot be determined unless the
bead distribution is known and that it is sensitive to changes
of the bead distribution and concentration near the sensor
surface over the duration of an experiment. Thus, the method
provides relative and not absolute values of the complex
magnetic susceptibility and care should be taken if beads
tend to sediment.
III. EXPERIMENTAL
The planar Hall effect bridge sensor used for the follow-
ing experiment consists of four segments arranged in a
Wheatstone bridge configuration as shown in Fig. 1, each
FIG. 1. Picture of a sensor with definition of dimensions. The bias current I
is applied through the arms in the x-direction, while the potential difference
V
y
is measured across the y-direction.
154507-2 Østerberg, Rizzi, and Hansen J. Appl. Phys. 113, 154507 (2013)
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
bridge segment has a length of l¼280 lm and a width of
w¼20 lm. The exchange-biased sensor stack consisting
of Ta(3 nm)/Ni
80
Fe
20
(30 nm)/Mn
80
Ir
20
(20 nm)/Ta(3 nm) has
been sputter-deposited in an applied magnetic field of 20 mT
to define an easy direction of magnetization along the posi-
tive x-direction. For further details on the fabrication, see
Ref. 16. The low-field sensitivity for this sensor was found
to S0=l0¼581 V=ðTAÞ, where l0is the permeability of
free space. The bridge resistance along the current was found
to 151.5 X.
Electrical contact to the sensor was made with a click-
on fluidic system,
14
which also defined the fluidic channel on
top of the sensor. The channel dimensions were length
width height ¼5mm1mm0.1 mm. During all
measurements, the temperature of the sensor mount was kept
constant at (25.00 60.01)8C using a proportional integral
differential (PID) controlled Peltier element. The sensor was
neither electrically nor magnetically shielded.
A. Brownian relaxation measurements
The second harmonic sensor signals were measured
using two different lock-in amplifiers depending on the
investigated interval of frequencies.
Frequency sweeps below 50 kHz were carried out
using a Stanford Research Systems model SR830 lock-in
amplifier. The alternating sensor bias current of amplitude
IAC ¼20 mA was supplied by a Keithley model 6221 AC
current source. The two instruments were synchronized via a
trigger link. The frequency of the current was swept from
f¼43.7 kHz to f¼1.88 Hz in 29 logarithmically equidistant
steps. After each measurement at frequency f, a reference
measurement was performed at a reference frequency fref
near the expected Brownian relaxation frequency of the
beads under investigation. A full frequency sweep consisting
of the measurements at 30 different frequencies and the 30
reference measurements took 3 min and 45 s.
Frequency sweeps extending up to 5 MHz were carried
out using a Zurich Instruments HF2LI lock-in amplifier. The
internal voltage output of the lock-in amplifier was used to
bias the sensors corresponding to a current of amplitude
20 mA. The frequency was swept from f¼5 MHz to
f¼37.7 Hz in 30 logarithmically equidistant steps. Also for
these measurements, reference points were measured
between each frequency. A full frequency sweep took 5 min
and 20 s.
Brownian relaxation measurements were performed for
six different bead types with nominal diameters Dnom rang-
ing from 10 nm to 250 nm. The following bead types were
studied: (1)–(3) iron oxide nanoparticles with nominal diam-
eters of Dnom ¼10 nm, 25 nm, and 40 nm and carboxylic
acid surface groups (cat. SHP) from Ocean Nanotech, USA,
suspended in MilliQ water; (4) plain bionized nano ferrite
(BNF)-starch beads with a nominal diameter of Dnom ¼80 nm
(cat. 10-00-801) from Micromod, Germany, suspended in phos-
phate buffered saline (PBS); (5)-(6) plain Nanomag-D beads
with nominal diameters of Dnom ¼130 nm (cat. 09-00-132)
and 250 nm (cat. 09-00-252) from Micromod, Germany, sus-
pended in PBS. Beads with nominal diameters from 10 nm to
40 nm were characterized using the high-frequency set-up, and
beads with nominal diameters from 80 nm to 250nm beads
were characterized using the low-frequency set-up. The bead
concentration was kept constant at 1 mg/ml for all six bead
types.
For measurements with both lock-ins, reference fre-
quency sweeps without beads were measured with liquid in
the fluidic channel to correct for c0before injection of the
bead suspension. Then, 20 ll of bead suspension was
injected into the liquid channel on the chip at a flow rate of
13.3 ll/min for 1.5 min. This volume corresponds to 40 times
the channel volume. After injection of the bead suspension,
the beads were left for characterization in the fluidic channel
for about 60 min (Ocean Nanotech beads) or 240 min
(Micromod beads) before being washed out at flow rate of
300 ll/min. Measurements were also performed after wash-
ing to verify that the signals returned to their initial values.
Measurements on the same bead suspension using both set-
ups were found to give identical results in the overlapping
intervals, although with a slightly lower data noise at low
frequencies using the set-up for low frequencies (data not
shown).
B. Data treatment
First, the data were corrected for instrumental phase shifts
and offsets due to c0using the reference sweeps measured
without beads. Then, the data recorded at different frequencies
were corrected for the variation of the signal amplitude due to
bead sedimentation over the duration of a frequency sweep.
This was done by normalizing the measurement at each fre-
quency fwith the in-phase second harmonic sensor data
recorded at f¼fref . Finally, all data in the frequency sweep
were multiplied with the average value of the measurements
at f¼fref obtained during the frequency sweep. Bead sedi-
mentation over a single frequency sweep was mainly an issue
for the 250nm beads from Micromod. Subsequently, the
modified Cole-Cole model, Eq. (6),wasfittedtothecorrected
data with fB,a,V
0
,andV1as the four free fitting parameters.
The model was fitted to the in-phase and out-of-phase sensor
data simultaneously with a single set of parameters. The
hydrodynamic diameters were calculated from the obtained
Brownian relaxation frequency using Eq. (1) assuming that
the beads are spherical and that PBS has the dynamic viscosity
of water. The hydrodynamic diameters will be reported
instead of the Brownian relaxation frequencies.
IV. RESULTS
A. Signal vs. time at f5f
ref
The in-phase signals measured at f¼fref chosen near the
Brownian relaxation frequencies are plotted vs. time tafter
injection of the bead suspension in Fig. 2for all bead types.
The value of fref is indicated in the figure and listed in Table I
for each bead type. The signals from the Ocean Nanotech
beads (Fig. 2(a)) show a steep increase over the first few
minutes and become stable after 5–15 min. The signals
from the Micromod beads (Fig. 2(b)) show a steep initial
increase followed by a slow linear increase with time for at
154507-3 Østerberg, Rizzi, and Hansen J. Appl. Phys. 113, 154507 (2013)
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
least several hours. The initial signal increase takes place at a
higher rate for smaller beads than for larger beads. The transi-
tion to the region with a linearly increasing signal occurs at
t10 min, 15 min, and 45 min for the Micromod beads
with Dnom ¼80 nm, 130 nm, and 250 nm, respectively, and
the linear increase is significantly larger for the 250 nm beads
than for the other two bead sizes. From the figure it is also
seen that, except for the 130nm beads, the signal magnitude
increases with increasing bead size. It is also noted that all
signals return to their baseline level after washing.
From the reference measurements, the standard devia-
tion of the baseline in-phase sensor signal is estimated for
each of the six reference frequencies. This is done by finding
the standard deviation of the points measured without beads
present in the fluidic system (rNoBeads). This number repre-
sents the combined effect of the sensor and amplifier noise
and fluctuations of the ambient conditions (temperature,
magnetic, and electric fields) during an experiment and
defines the smallest signal change that can be resolved under
our experimental conditions. The six values are listed in
Table I. It is seen that the values of rNoBeads are constant at
5–6 nV for the frequencies between 226.67 kHz and
4.67 kHz measured with the HF2LI lock-in amplifier,
whereas they increase from 4 nV to 10.9 nV when decreasing
the frequency from 481.88 Hz to 42.67 Hz for the SR830
lock-in amplifier.
B. Brownian relaxation measurements with PHEB
In Fig. 3the in-phase (top) and out-of-phase (bottom)
second harmonic sensor signals are plotted as function of fre-
quency for measurements initiated at t¼20 min. The solid
lines are least squares curve fits of the Cole-Cole model to
the data. The model generally provides good fits to the data.
In order to better illustrate the shape of the curves and the
quality of the fits, the second harmonic signals have been
normalized to their maximum values and plotted in Fig. 4.
From the normalized plots, it is seen that the peaks in the in-
phase signals are comparatively narrow for the 10 nm,
40 nm, and 80 nm beads and wide for 25 nm, 130 nm, and
250 nm beads.
The values of the fitting parameters are shown in
Table II. The height of the peak in the V0
2data depends only
FIG. 2. In-phase second harmonic signal measured at the indicated values of
fref vs. time tafter injection of the bead suspension for (a) Ocean Nanotech
beads with nominal diameters of 10 nm, 25 nm, and 40 nm and (b) Micromod
beads with nominal diameters of 80nm, 130nm, and 250nm. In the final part
of each experiment, the bead suspension is washed out of the channel.
TABLE I. Standard deviation rNoBeads of baseline in-phase sensor signal at
f¼fref for the six values of fref used for the different bead types.
Dnom (nm) Lock-in fref rNoBeads (nV)
10 HF2LI 226.67 kHz 5.1
25 HF2LI 36.67 kHz 5.6
40 HF2LI 4.67 kHz 5.6
80 SR830 481.88 Hz 4.0
130 SR830 120.47 Hz 7.6
250 SR830 42.67 Hz 10.9 FIG. 3. In-phase (top) and out-of-phase (bottom) corrected second harmonic
sensor signals. The solid lines are fits of the Cole-Cole model to the data.
154507-4 Østerberg, Rizzi, and Hansen J. Appl. Phys. 113, 154507 (2013)
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
on V0V1and aand is given by V0
2;peak ¼Im½ðV0V1Þ=
ð1þi1aÞ. For a¼0;V0
2;peak ¼1
2ðV0V1Þ. From the table,
it is observed that the hydrodynamic diameters obtained
from the fits are all within 40% of the nominal bead sizes.
It is also seen that for the 10 nm-80 nm beads the value of
V0V1increases with the bead diameter. V1is found to be
close to zero for the beads from Ocean Nanotech.
1. Sensor signal vs. nominal bead concentration
From the measurements, it is possible to estimate the sig-
nal normalized with the bead molar concentration for the six
different bead types. This number is important when estimat-
ing the suitability of each bead type for volume-based bio-
sensing. The signal per bead molar concentration is
calculated by dividing the in-phase peak signal V0
2;peak with
the molar concentration cof beads. The in-phase peak signal
per concentration is listed in Table II. From this table it is seen
that, although the bead concentrationbymassisthesamefor
all samples, the samples with larger beads provide more signal.
Obviously, when the signal is normalized with the molar con-
centration of the bead suspension, the larger beads provide
substantially higher signals. For example, the normalized sig-
nal for the 250 nm beads is found to be 5 orders of magnitude
larger than that for the 10 nm beads. If the bead magnetizations
were the same, this difference would be anticipated to be
25
3
¼15 625, which is one order of magnitude smaller than
the observed ratio. However, it should be noted that the larger
beads also sediment such that the actual bead concentration
near the sensor surface is higher than the nominal one.
V. DISCUSSION
A. Brownian relaxation measurements
It is seen from the results that the planar Hall effect sen-
sor can be used to measure Brownian relaxation over the fre-
quency range 1 Hz–1 MHz. With this frequency range it is
shown that Brownian relaxation can be measured for beads
ranging in diameters from 10 nm to 250 nm and meaningful
hydrodynamic diameters can be extracted from the measure-
ments. The hydrodynamic diameters for the small beads
from Ocean Nanotech are within a few nanometers of their
nominal values. This is consistent with the assumption that
Brownian relaxation dominates for these particles. These dif-
ferences can be due to batch to batch variations. The hydro-
dynamic diameters found for the beads from Micromod are
found to be significantly larger than their nominal values. It
is expected that the hydrodynamic diameters are larger than
their nominal values, because the nominal diameters are
determined from transmission electron microscopy (TEM),
which measures the core size. However, the hydrodynamic
size obtained for the 250 nm beads is too large to be
explained by differences in measuring techniques alone.
Effects that could contribute to a higher measured hydrody-
namic size are trapping of beads by the magnetostatic field
from the sensor stack, interactions between the bead and the
sensor surface, and bead-bead interactions.
B. Signal vs. time at f5f
ref
In the experiments, we found a steep initial increase of
the signal followed by either a stable signal for the beads
that are smaller than 100 nm or a slowly increasing signal
for the beads that are larger than about 100 nm (cf. Fig. 2).
FIG. 4. In-phase (top) and out-of-phase (bottom) corrected second harmonic
sensor signal from Fig. 3normalized to their respective maximum values.
The solid lines are fits of the Cole-Cole model to the data.
TABLE II. Values of D
h
,a,V0V1, and V1obtained from Cole-Cole fits to the frequency sweeps initiated 20 min after injection of the bead suspensions.
The numbers in parenthesis after the fitting parameter are 95% uncertainties. The last two columns list the molar concentration cof each bead type in nM and
the peak sensor signal normalized with the bead molar concentration V0
2;peak=c. LODtheory is the theoretical limit of detection calculated by rNoBeads =ðV0
2;peak=cÞ.
Dnom [nm] Producer Dh[nm] aV0V1[lV] V1[lV] c[nM] V0
2;peak=c[nV/nM] LODtheory [pM]
10 Ocean Nanotech 12.4(3) 0.08(5) 0.23(2) 0.05(18) 860 0.1 5:1104
25 Ocean Nanotech 21.6(4) 0.28(2) 0.56(2) 0.02(17) 58 3.0 1:9103
40 Ocean Nanotech 42.4(2) 0.06(1) 0.97(1) 0.03(15) 14 31.4 1:8102
80 Micromod 107.0(9) 0.20(1) 3.29(4) 0.4(7) 2.0 602 6.6
130 Micromod 155(2) 0.31(1) 0.99(2) 0.5(2) 0.48 622 12.2
250 Micromod 349(3) 0.43(1) 6.01(7) 5.2(5) 0.08 17:91030.6
154507-5 Østerberg, Rizzi, and Hansen J. Appl. Phys. 113, 154507 (2013)
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
The steep initial signal increase is due to the injection of the
bead suspension in the already liquid-filled fluidic system;
due to the parabolic velocity profile of the liquid during
injection, the liquid near the channel walls is replaced more
slowly than that in the center of the channel. This results in
an equilibration process, where the bead concentration at the
sensor surface increases due to continued injection of the
bead suspension as well as due to gravitational sedimentation
and diffusion of the beads.
The beads are subject to gravitational sedimentation at a
velocity u¼D2ðqbqfÞg=ð18gÞ,
23
where Dis the bead di-
ameter, qfand qbare the densities of the fluid and beads,
respectively, and gis the gravitational acceleration. Taking
D¼Dnom, we can find the characteristic time tsed for sedi-
mentation of the beads in the channel as h/u, where
h¼0.1 mm is the channel height. For the Micromod beads,
qb3g=cm3and we find tsed½min’25, 90, and 240 for
the beads with Dnom½nm¼250, 130, and 80, respectively.
The corresponding characteristic time tdif for diffusion
over the height of the liquid channel is estimated from the
Stokes-Einstein diffusivity Ddif ¼kBT=ð3pgDnomÞusing that
Ddif h2=tdif . For the Micromod beads with Dnom½nm
¼250, 130, and 80, we obtain tdif ½min’96, 50, and 31,
respectively. These simple arguments show that bead sedi-
mentation dominates over the random thermal motion of the
beads for the 250 nm beads that sedimentation and thermal
motion are comparable for the 130 nm beads and that thermal
motion dominates for beads with sizes of 80 nm and below.
Experimentally, we have observed an initial steep
increase of the signal measured vs. time at f¼fref in Fig. 2
upon injection of the bead suspension. As previously men-
tioned, due to the parabolic velocity profile and that liquid
without beads is already present in the channel during injec-
tion, the bead concentration near the bottom of the channel,
where the sensor is located, is therefore initially lower than
in the bulk of the bead suspension. This concentration
increases due to exchange of liquid in the channel, sedimen-
tation and equilibration of the bead concentration by diffu-
sion. For the 250 nm beads, this equilibration is dominated
by sedimentation and the estimated sedimentation time of
about 25 min is consistent with the observed time of about
45 min in Fig. 2(b). For the beads with sizes below 130 nm,
the equilibration time is mainly attributed to diffusion of the
beads. The beads from Ocean Nanotech are so small that the
equilibration takes place while the bead suspension is
injected. After the initial equilibration, the signals from all
bead types stabilize and remain essentially constant except
for the 250 nm Micromod beads, where the signal shows a
significant increase with time. We attribute this increase to
accumulation of beads near the sensor edges due to the mag-
netostatic field from the sensor stack. This accumulation was
clearly visible in micrographs of the sensor during the experi-
ments and was also visible in the frequency sweeps as a sig-
nal occurring at a lower frequency than that due to freely
rotating beads. For the other bead types, no bead accumula-
tion near the sensor edges could be observed visually and the
signal tail at low frequencies in the sensor measurements due
to immobilized or partially immobilized beads was signifi-
cantly smaller or negligible. Thus, the sedimentation and
trapping of the 250 nm beads results in a time dependence of
the signal due to the bead suspension itself, i.e., prior to
introduction of biomolecules, which is clearly undesirable.
These beads are, therefore, not suited for biosensing with the
present sensors.
1. Sensor signal vs. nominal bead concentration
From the value of signal per bead concentration listed in
Table II, it is clear that the choice of bead type will be very
important for the sensitivity of a volume-based biosensor.
For the beads investigated here, the peak signal normalized
with the nominal bead molar concentration varies over 5
orders of magnitude, which means that the choice of bead
type has a high impact on the sensitivity and dynamic range
of concentrations that can be detected. For instance, the bead
concentration of the 10 nm beads is 860 nM, which means
that, at least in principle, it will be possible to detect analyte
concentrations up to this value. The downside is a low signal
per bead which for the 10 nm beads is only 0.1 nV/nM.
Comparing to the baseline resolution from Table Iof 5.1 nV,
it implies that the theoretical limit of detection LODtheory is
expected to be higher than 51 nM. On the other hand, for
the 250 nm beads the theoretical dynamic range is 0.6–81
pM, the drawback of these beads is that they sediment, which
will make them difficult to use for biosensing. The sedimen-
tation of the 80 nm beads is limited and the signal is large.
Thus, these beads will be the best compromise for biosensing
to achieve a low detection limit. The theoretical dynamic
range for the 80 nm beads is 6 pM-2 nM. The upper sensitiv-
ity limit can be moved to higher concentrations by increasing
the bead concentration, but this will also increase the back-
ground signal and potentially make it more difficult to mea-
sure low concentrations. The lower limit of detection can be
decreased further by decreasing the bead concentration and/
or increasing the signal-to-noise ratio of the measurement
system. Currently most of the noise is induced by the lock-in
amplification, which means increasing the sensor signal will
increase the signal-to-noise ratio. This can be achieved by
using lower noise amplification electronics, increasing the
measurement time to reduce the effect of the noise or
improving the sensor design. One way of increasing the sen-
sor signal is to increase the length of each bridge segment,
which is the focus of future studies.
VI. CONCLUSION
It has been demonstrated that planar Hall effect bridge
sensors can be used to measure AC susceptibility of mag-
netic beads for frequencies spanning from DC to 1 MHz.
This wide frequency span allows for measuring Brownian
relaxation of beads with nominal diameters ranging from
10 nm to 250 nm. The hydrodynamic diameters obtained
from the measurement are all within 40% of the nominal di-
ameter supplied by the manufacturer. From the measure-
ments, it is also concluded that among the investigated beads
the 80 nm beads are most promising for volume-based bio-
sensing, because they provide the largest signal per bead
among the bead types that do not suffer from sedimentation
and magnetic trapping issues on the sensors.
154507-6 Østerberg, Rizzi, and Hansen J. Appl. Phys. 113, 154507 (2013)
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
ACKNOWLEDGMENTS
This work was supported by the Copenhagen Graduate
School for Nanoscience and Nanotechnology (C:O:N:T) and
the Knut and Alice Wallenberg (KAW) Foundation.
1
I. Koh and L. Josephson, “Magnetic nanoparticle sensors,” Sensors 9,
8130 (2009).
2
S. X. Wang and G. Li, “Advances in giant magnetoresistance biosensors
with magnetic nanoparticle tags: Review and outlook,” IEEE Trans.
Magn. 44, 1687 (2008).
3
N. Jaffrezic-Renault, C. Martelet, Y. Chevolot, and J.-P. Cloarec,
“Biosensors and bio-bar code assays based on biofunctionalized magnetic
microbeads,” Sensors 7, 589 (2007).
4
J. G€
oransson, T. Zard
an G
omez De La Torre, M. Str€
omberg, C. Russell, P.
Svedlindh, M. Strømme, and M. Nilsson, “Sensitive detection of bacterial
DNA by magnetic nanoparticles,” Anal. Chem. 82, 9138 (2010).
5
J. Connolly and T. G. St Pierre, “Proposed biosensors based on time-
dependent properties of magnetic fluids,” J. Magn. Magn. Mater. 225, 156
(2001).
6
A. P. Astalan, F. Ahrentorp, C. Johansson, K. Larsson, and A. Krozer,
“Biomolecular reactions studied using changes in Brownian rotation dy-
namics of magnetic particles,” Biosens. Bioelectron. 19, 945 (2004).
7
C. Hong, C. Wu, Y. Chiu, S. Yang, H. Horng, and H. Yang, “Magnetic
susceptibility reduction method for magnetically labeled immunoassay,”
Appl. Phys. Lett. 88, 212512 (2006).
8
A. Fire and X. Si-Qun, “Rolling replication of short DNA circles,” Proc.
Natl. Acad. Sci. U.S.A. 92, 4641 (1995).
9
D. Liu, S. L. Daubendiek, M. A. Zillman, K. Ryan, and E. T. Kool,
“Rolling circle DNA synthesis: Small circular oligonucleotides as efficient
templates for DNA polymerases,” J. Am. Chem. Soc. 118, 1587 (1996).
10
M. Str€
omberg, J. G€
oransson, K. Gunnarsson, M. Nilsson, P. Svedlindh,
and M. Strømme, “Sensitive molecular diagnostics using volume-
amplified magnetic nanobeads,” Nano Lett. 8, 816 (2008).
11
F. Ludwig, S. M€
auselein, E. Heim, and M. Schilling, “Magnetorelaxometry
of magnetic nanoparticles in magnetically unshielded environment utilizing
a differential fluxgate arrangement,” Rev. Sci. Instrum. 76, 106102
(2005).
12
H. Grossman, W. Myers, V. Vreeland, R. Bruehl, M. Alper, C. Bertozzi,
and J. Clarke, “Detection of bacteria in suspension by using a supercon-
ducting quantum interference device,” Proc. Natl. Acad. Sci. U.S.A. 101,
129 (2004).
13
B. T. Dalslet, C. D. Damsgaard, M. Donolato, M. Strømme, M.
Str€
omberg, P. Svedlindh, and M. F. Hansen, “Bead magnetorelaxometry
with an on-chip magnetoresistive sensor,” Lab Chip 11, 296 (2011).
14
F. W. Østerberg, B. T. Dalslet, D. Snakenborg, C. Johansson, and M. F.
Hansen, “Chip-based measurements of Brownian relaxation of magnetic
beads using a planar Hall effect magnetic field sensor,” AIP Conf. Proc.
1311, 176–183 (2010).
15
A. D. Henriksen, B. T. Dalslet, D. H. Skieller, K. H. Lee, F. Okkels, and
M. F. Hansen, “Planar Hall effect bridge magnetic field sensors,” Appl.
Phys. Lett. 97, 013507 (2010).
16
F. W. Østerberg, G. Rizzi, T. Zard
an G
omez de la Torre, M. Str€
omberg,
M. Strømme, P. Svedlindh, and M. F. Hansen, “Measurements of
Brownian relaxation of magnetic nanobeads using planar Hall effect
bridge sensors,” Biosens. Bioelectron. 40, 147 (2013).
17
L. N
eel, “Th
eorie du tra^
ınage magn
etique des ferromagn
etiques en
grains fins avec applications aux terres cuites,” Ann. G
eophys. 5,99
(1949).
18
W. Brown, “Thermal fluctuations of a single-domain particle,” Phys. Rev.
130, 1677 (1963).
19
K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics. I.
Alternating current characteristics,” J. Chem. Phys. 9, 341 (1941).
20
P. Debye, Polar Molecules (Chemical Catalogue Co., 1929).
21
W. Thomson, “On the electro-dynamic qualities of metals: Effects of mag-
netization on the electric conductivity of nickel and of iron,” Proc. R. Soc.
London 8, 546 (1856).
22
T. B. G. Hansen, C. D. Damsgaard, B. T. Dalslet, and M. F. Hansen,
“Theoretical study of in-plane response of magnetic field sensor to mag-
netic beads magnetized by the sensor self-field,” J. Appl. Phys. 107,
124511 (2010).
23
F. W. Østerberg, B. T. Dalslet, C. D. Damsgaard, S. C. Freitas, P. P.
Freitas, and M. F. Hansen, “Bead capture on magnetic sensors in a micro-
fluidic system,” IEEE Sens. J. 9, 682 (2009).
154507-7 Østerberg, Rizzi, and Hansen J. Appl. Phys. 113, 154507 (2013)
Downloaded 04 Jun 2013 to 192.38.67.112. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions
