T. Magn. Soc. Jpn. (Special Issues)., 3, 113-119 (2019)<Paper>Effect of Ionic Concentration on Dynamic Magnetic Susceptibility of Iron
Oxide Nanoparticles Embedded in Chitosan Hydrogel Matrix
M. E. Villamin, and Y. Kitamoto

Tokyo Institute of Technology, Department of Materials Science and Engineering, 4259 Nagatsutacho, Midori-ku, Yokohama,

Kanagawa, 226-8502

We investigate the effect of the ionic strength of surrounding NaCl solutions of an iron-oxide chitosan hydrogel (FeOxCH) on magnetic relaxation of the FeOx NPs. The magnetic relaxation of the FeOx NPs is examined using dynamic
magnetic susceptibility measurement. Swelling ratio (SR) is also measured after the FeOx-CH is immersed to various
NaCl concentrations. SR of the FeOx-CH decreases as the NaCl concentration increases. This trend is explained byconsidering the osmotic water flow in the FeOx-CH. The peak in frequency dependence of the imaginary part of thesusceptibility (χ ”) is found around 200 Hz. In addition, the position of the χ ” peak frequency shifts to lower frequencies
as the NaCl concentration increases. The observed frequency shift is inferred to be due to the suppression of the
Brownian relaxation caused by the decrease of SR of the FeOx-CH as the NaCl concentrations increases. An effective
viscosity change of 6.8% due to the change in the NaCl concentration is also estimated via analytical calculation.
Key words: biomagnetism, magnetic nanoparticles, magnetic biosensing, chitosan ferrogel, dynamic susceptibility,
1. Introduction
There is great research interest on the integration ofnanostructures with stimuli-responsive polymers for thedevelopment of multifunctional materials. One of these
multifunctional materials is a ferrogel that exhibits dualresponsiveness to both chemical and magnetic external
stimuli 1)-2). Such ferrogels are composed of magnetic
nanoparticles crosslinked (either via physical or chemical
crosslinking) with a stimuli-responsive polymer network.
Due to the dual-responsiveness to pH/magnetic orthermal/magnetic, these ferrogels are extensively
studied for many biomedical applications for stresssensors 3), controlled-release of drug 4), and externallycontrol microfluidics 5).
In particular, ferrogels are very useful for biosensing
applications. In a previous study, we have demonstrated
magnetic based pH-detection using an iron oxide –chitosan (FeOx-CH) ferrogel 6). This is achieved bycoupling the chemical-responsiveness (pH-sensitivity) of
the CH matrix to magnetic relaxation property of the
FeOx nanoparticles (NPs). That is a change in the pH(chemical stimulus) would cause a corresponding change
in the magnetic relaxation property of the embedded
FeOx NPs, which can then be measured by dynamic
magnetic susceptibility. This potentially paves the way
for non-contact magnetic-based chemical (pH) sensors
based on ferrogels. Note that different polymers may be
used to detect different chemical stimuli 7)-10). Hence,
ferrogel based biosensors are not limited to pH detection.
Potentially, ferrogel-based biosensors can be applied
to microarrays. Microarrays are used for simultaneous
analyses of different target molecules, such as in DNA
microarrays and in protein-based microarrays in a single
experiment run. In a conventional microarray, sensing
sites that have a unique target molecules are arranged in
an array or matrix. The surface of the sensing sites isfunctionalized so that the target molecules (and only thetarget molecules) bind to the sites. The bound target
molecules are then detected by labeling methods such theuse of fluorescent labels or isotopic labels, or non-labelingmethods such as mass spectrometry or micro-cantilevers11)-12). In commerciallyavailable microarrays, thefluorescent labeling detection method is dominantbecause of its high throughput and low cost 11). However,
fluorescent labels often chemically react to target
molecules that could potentially alter their intrinsic
property 3) and also sufficient time is required for thereaction to complete. These affect the reliability of thesignal detection, and prevent the real-time detection ofbinding events 11)-13). Alternative non-label methods, on
the other hand, are still under development.
Clearly, one possible alternative label-free method is
the use of a ferrogel based microarray, which utilizes
ferrogel sites instead of the functionalized surfaces. The
use of magnetic sensing offers potentially label-free, noncontact measurement at possibly real-time detection
speeds by using ferrogels. By choosing the appropriate
gel matrix material, target molecules could interact
directly to the gel without the need for further
functionalization. Furthermore, gels also potentiallyallow to increase the sensing part by using the wholevolume of the ferrogel instead of using two-dimensionalbinding surface.
As mentioned, magnetic based pH sensing has
already been previously demonstrated in FeOx-CH,
where changes in pH affected the magnetic relaxation of
the NPs, which was then detected by dynamic
susceptibility measurements 6). As pH changed from pH
1.95 (acidic) to pH 6 (neutral), the peak in the frequency
dependent imaginary part of the susceptibility shifted tolower frequency, from ~190 to ~170 Hz 6). This isaccompanied by a reduction in the swelling ratio (SR) of
ferrogel (i.e. the ferrogel reduced swelling and became

Transaction of the Magnetics Society of Japan (Special Issues) Vol.3, No.1, 2019113

smaller). We attributed the shift in the peak of theimaginary part susceptibility to lower frequency due tothe change of Brownian relaxation time resulting fromthe reduced swelling of the CH. This can be interpreted
as a change in effective viscosity of CH. The viscosity of
the CH changed with pH due to the presence of NH2+ vs.
NH3+ causing the CH to decrease swelling in low pH. Thismechanism will be explained in more detail in a latter
section.
In this study, we utilize the same material systemand demonstrate magnetic-based ionic strength
detection. Similar to the previous study, the materials
used in this study are the following: CH as the stimuliresponsive polymer, and FeOx NPs as thesuperparamagnetic nanoparticles. We note that CH ischemically responsive not only to pH 14)-16),21) but also to
multiple chemicals, including ions (ionic strength
sensitivity) 15),17),18),20),22) and temperature 21). Other
advantages of using CH are its abundance 22)-23),
biocompatibility 14) - 22) and ease of functionalization 14), 21).
Hence, these make CH an ideal candidate for ferrogel
biosensors. Whereas, the merits of using FeOx NPs arebiocompatibility 24), strong magnetic property 24)-26) andlow toxicity 24), which makes them appropriate for many
biomedical applications. Here, we investigated the effectof the change in the ionic strength of the surrounding
solution to the magnetic susceptibility of the FeOx-CH
ferrogel, as measured by dynamic magnetic susceptibility.
2. Experimental Details
2.1 Synthesis and characterization of FeOx-CH
The chemicals used in the experiment are as follows:iron(III) chloride hexahydrate (FeCl3·6H2O) and iron(II)chloride tetrahydrate (FeCl2·4H2O) with 99.0 % purity
were bought from Wako Pure Chemical Industries, andchitosan powder with ~20000 – 50000 molecular weight,
was obtained from the Sigma Aldrich Company.
The synthesis process has been described in detail ina previous study 6). For convenience, here we describe theprocess briefly. First, FeCl3.6H20 and FeCl2.4H20 powder(Fe3+/Fe2+ ratio of 1/2) were added to a chitosan solution
using a magnetic stirrer. Next, the Fe3+/Fe2+/CH aqueous
solution was placed in an NH4OH coagulation bath until
the gelation is completed. Lastly, the resulting iron-oxidechitosan hydrogel (FeOx-CH), which has a distinctive
black color, was washed several times with purified
water. By measuring the height of the gel formed asfunction of time, we are able to estimate the gel formation
rate. Note that the FeOx NPs were not functionalized
before embedding into the gel. Thus, we assume that thenanoparticles are weakly bound to the chitosan matrix;
there is also a possibility that some FeOx NPs are freely
moving or completely not bound to the chitosan matrix.
The final structure of the FeOx-CH specimens was
confirmed by scanning electron microscopy (SEM). Prior
to SEM observations, the specimens were coated with
osmium. Moreover, the ferrogel formation and FTIR

114

results are also presented.
2.2 Swelling ratio
Swelling ratio (SR) is generally used to evaluate theamount of water absorption of hydrogels. SR values of
FeOx-CH are calculated using equation (1) 27).
SR % = [(Ws - Wd) / Wd] × 100%,(1)where Ws is the specimen’s weight when swollen aftersubmerging to the solution, and Wd is the specimen’s
weight after freeze drying for two hours. The sample was
immersed in the solution with different NaCl
concentrations (10 mM, 100 mM and 500 mM) prior to SR
measurements. Note that the sample was washed after
each measurement, and then, the same sample was usedin the next measurements.
2.3 Dynamic Magnetic Susceptibility Measurement
For the magnetic characterization, we measured
dynamic magnetic susceptibility (sometimes referred toas the AC susceptibility or frequency dependent
susceptibility) under alternating fields of the FeOx-CH
using a Physical Property Measurement System(Quantum Design Corp.: PPMS). The dynamic
susceptibility represents dynamic magnetic responses of
the FeOx NPs inside the CH. Susceptibility is simply theslope of the magnetization (M) with respect to appliedmagnetic field (H). In the dynamic susceptibility
measurement, we measured the two parts ofsusceptibility, the real (χ’) part and imaginary (χ”) partof susceptibility 29)-32). Theoretically, the two parts are
expressed as follows;χ’(ω) = χ0 / [1+ (ωτeff)2],
χ”(ω) = χ0 · (ωτeff) / [1 + (ωτeff)2],

(2)
(3)

χ0 = (μ0nm2) / (3kBT) .

(4)

τeff = (τB · τN ) / (τB + τN ) .

(6)τB = [ η·(dh)3 ] / (2kBT) .

(7)

where ω = 2πf is the angular frequency with f thefrequency, τeff the effective relaxation time, and χ0 is thestatic susceptibility (ω = 0) described bywith vacuum permeability μ0, thermal energy kBT,
magnetic moment m, and particle number density n. In
this study, the point of interest is the imaginary part ofthe susceptibility χ”, which can be used to estimate theeffective magnetic relaxation time τeff. At the frequency
where χ” is maximum, the following relation 29)-32) is true:
2πfpeak · τeff = 1,
(5)where the fpeak is the frequency at χ” maximum. Therefore,
we can calculate τeff from fpeak. The effective relaxation
time τeff is the combination of the two magnetic relaxation
processes: Brownian relaxation and Néel relaxation. The
Brownian relaxation is due to the physical rotation of
nanoparticles, whereas Néel relaxation is from theinternal rotation of a magnetic moment of nanoparticles.
In general, the faster relaxation mechanism is dominantand τeff is given by the equation 29)-32)
The Brownian relaxation time (τB) is given by thefollowing equation 26), 29)-32),

where η is the viscosity of the suspension and dh is theTransaction of the Magnetics Society of Japan (Special Issues) Vol.3, No.1, 2019

hydrodynamic particle diameter. From equation (7), it
can be noted that the τB is dependent on thehydrodynamic size of the nanoparticle. The Néel
relaxation time τN is described by 29)-32)

τN = τ0 · exp [(κπdc3) / (6kBT)] .

(8)

where κ is the anisotropy constant, dc is the magnetic core
diameter of the nanoparticle, and τ0 is the intrinsic
relaxation time with a typical value of 10-9 s 29),31). Fromequation (8), it can be noted that τN is dependent on themagnetic core size.
Dynamic susceptibility measurements were madewith a magnetic field strength of 10 Oe and frequency
range of 10 Hz to 10 kHz. The sample was immersed indifferent NaCl concentrations (10 mM, 100 mM and 500mM) before the PPMS measurements. Note that the
sample was washed after each measurements and thenthe same sample was used in the next measurements.
3. Results and Discussion
3.1 Formation of ferrogel
The formation of ferrogel is discussed in this paper
to elucidate how the ferrogel have become a porous
structure. The actual image of the ferrogel during thegelation time of 1 hour is shown in Fig. 1. The region witha black color is ferrogel, that above the ferrogel is the
NH4OH solution, and that below the ferrogel (coloredorange) is the unreacted Fe3+/Fe2+/CH solution. To
monitor the height of the ferrogel, photos of specimens
were taken with the gelation time. There were 8 photos
taken during the 6 hour-observation of the ferrogel.
Using an image editor software, the vertical height of theferrogel was measured in pixels. The height of thecontainer was used as the calibration height to convert
the height in pixels to mm. Thus, we are able toaccurately estimate the height of the gel via image
processing.

Fig. 2 Measured height of the ferrogel (left y axis, open
circles) and the calculated rate of gelation (right y axis,
filled circles) are plotted as a function of gelation time.
The calculated ferrogel heights are shown in Fig. 2(left y axis, open circles). From the figure, it can beobserved that the height of the ferrogel monotonicallyincreases with the gelation time. This implies that theferrogel is porous because it allows the NH4OH topenetrate into the bottom of the container in order toreact and form the additional ferrogel.
The rate of the ferrogel formation is also shown in
Fig. 2 (right y axis, filled circles). From the figure, it canbe seen that the rate of gelation is decreasing with time.
It is also evident from the plots that the calculated initialrate is very high (>1 mm/min) from time = 0 to 30
minutes. Immediately after the initial stage, the rate
gradually decreases from time = 30 to 150 min; the rate
becomes very slow (<0.1 mm/min) from time = 150 to 350
min. From these data, we can observe that the gelformation rate continuously decreases. This nonlinear
gelation behavior suggests that the ferrogels might havedifferent layers within the hydrogel 33) due to thedifference on the rate of diffusion of the OH- from the top
to the bottom of the container. Furthermore, this trend isconsistent with the idea that as the gel becomes thicker,
the diffusion rate naturally becomes slower, leading to
the decrease in gel formation rate with time.

Fig. 1 Actual image of ferrogel. Fe2+/Fe3+/CH solution
inside the bottle is submerged in NH4OH solution. WhenFe2+/Fe3+/CH combines with NH4OH, ferrogel is formed.
This image is taken half way thru the synthesis, thus theunreacted Fe2+/Fe3+/CH solution, initially formed ferrogel,and NH4OH solution are all present. Here, ferrogel
membrane separates the two solutions.

Fig. 3 FTIR spectrum of FeOx-CH.

Transaction of the Magnetics Society of Japan (Special Issues) Vol.3, No.1, 2019115

Fig. 4 SEM image of FeOx-CH at 25Kx magnification.
Blue arrows point to some of the FeOx NPs clusters
within the ferrogel.
3.2 FTIR and SEM results
Fig. 3 shows the FTIR results of the FeOx-CH. For
CH, the characteristic bands of the asymmetricstretching of the C-H bond appeared around 2876 cm-1.
The N-H and C-N vibrations of the amino group present
in chitosan is evident at 1633/1643 cm−1 and 1380 cm-1,
respectively. In addition, the band around 1159/1071 cm1 is from the C-OH stretching of the ester group inchitosan. More importantly, the absorption band ataround 600 cm-1 is from the Fe-O bond in the FeOx NPs.
From the FTIR data, it can be inferred that high quality
CH and FeOx NPs are present in the composite gels.
An SEM image of FeOx-CH is shown in Fig. 4. It canbe seen from the figure that the NPs (white areas) seemto be clustered and scattered along the striated wall of
the CH. The size of the clusters of NPs varies fromaround 50 nm to 500 nm, with an average of around 150
nm (from 30 sites within the SEM image). This confirms
the presence of FeOx NPs in the composite gel. The SEM
image also reveals the irregular/rough porous structureof the CH matrix. In particular, this rough structure
increases the surface area of the CH which is desirable toincrease sensitivity.
3.3 Swelling ratio at different ionic concentration
The swelling ratio (SR) is plotted as a function of theionic concentration of solutions in which the FeOx-CH
are immersed as shown in Fig. 5. The SR of the FeOx-CH
decreases as the ionic concentration of the solution
increases. As observed from the figure, it can beconcluded that the FeOx-CH is indeed sensitive tochanges in the salt concentration change. The degree ofswelling of hydrogels depends on the extent on the degreeof ionization of functional groups of the hydrogels and theionic strength of the external solution 23),33)-34).
One possible explanation on the reduced swelling of
the gel, when the surrounding solution of the CH has
high ionic strength, is the movement of the watermolecule from the lower osmotic pressure inside the CH
to the higher osmotic pressure outside the CH.

116

Fig. 5 Swelling ratio of FeOx-CH with different ionicconcentrations. Insets are photographs of actual FeOxCH used.
The additional osmotic pressure outside the CH is causedby the presence of cations (Na+) near the walls of the CH23)- 34). This is also known as the Donnan effect 23)- 34),
wherein, in this case, we consider that CH acts as a semipermeable membrane. To illustrate this, the schematic ofswelling mechanism of FeOx-CH at different ionicstrength is shown in Fig. 6. From the schematic diagram,the black arrows correspond to the amount and the
direction of the water flow from outside the gel into theinside the gel. When there is large water flow into the gel,the gel swelling is enhanced, whereas when there is asmall water flow into the gel, the gel swelling is reduced.
Figure 6 shows that when the NaCl concentration of thesurrounding CH is increased, the amount of the waterflow inside the CH is small, causing the CH to reduced
swelling. In contrast, when the NaCl concentration isdecreased, the water flow going to CH is large resulting
to an enhance swelling of the CH.

Fig 6. Schematic of FeOx-CH mechanism whensubmerged to increasing (left) or decreasing (right) ionicconcentration. Black arrows show the amount of waterflow inside the gel that causes the reduction andenhancement of the gel swelling. It also illustrates the
FeOx NPs rotation under these two ionic conditions.
3.4 Dynamic susceptibility as a function of ionic strength

Transaction of the Magnetics Society of Japan (Special Issues) Vol.3, No.1, 2019

Fig. 7 Dynamic susceptibility of the FeOx-CH (a), thezoomed in real (inset b, top values) and imaginary (inset
c, bottom values) parts of the susceptibility at 10mM ( ),150mM ( ), and 500mM ( ) NaCl concentrations.
As seen in Fig. 7a, the plot of the χ’ values are all
located in the top part of the plot with high susceptibility
values, whereas the plot of the χ” values are all located at
the bottom with low susceptibility values. The plots of thezoomed-in χ” and χ’ values are also shown in Fig. 7b andFig. 7c, respectively. We can observe from Fig. 7a that theχ” values are very small compared to χ’ values at lower
frequencies (χ” / χ’ ≈ 0.026), hence, it is expected that thearea inside M-H hysteresis curve at these frequencies
would be proportionally small (almost no hysteresis in MH curve is expected) which is a characteristic ofsuperparamagnetism. Further, as can be seen in the Fig.
7b (inset), it is evident that χ’ is decreasing as thefrequency increases. This decreasing behavior is a typicalsignature of the real part of the susceptibility forsuperparamagnetic nanoparticles 35) as the frequency
crosses the fpeak of the sample.
We can see in Fig. 7b (inset) that χ’ slightly decreases(shift downwards) with the increase of the ionicconcentration. This downward shift seems to be related
to the corresponding change in χ” with ionicconcentration. This is elucidated in the next paragraph.
Note also that the order of magnitude of the χ’ values
does not change, which suggests that the total moment of
the ferrogel sample did not change between
measurement, which is expected and a sign of goodexperimental reproducibility and reliability of the sample.
For all the ionic conditions, it can be observed in Fig.
7c (inset) that there is a clear χ” peak at around 200 Hz,
corresponding to an effective relaxation time of τeff ofaround 0.8 msec. Also, the χ” values are again increasingat >> 1 kHz which could correspond to another highfrequency peak. Moreover, the χ” plot shown in Fig. 7c(inset) are shifted to lower frequency with the increase of
the ionic concentration. This low-frequency shift of the χ”
would also cause a corresponding low-frequency shift inthe χ’. However, since there is no peak in the χ’, this low-frequency shift may appear as a downward shift, which
we see in the Fig. 7b results.
Shown in the inset of Fig. 8 is the plot of the zoomedin normalized χ” from the data in Fig. 7c. In thenormalization of χ”, the minimum χ” value (found at the
low frequency end) is set to 0, whereas the local
maximum χ” peak value (found around 200 Hz) is set to
1. Note that at the low frequency end, the value of χ” isvery much smaller than that of χ’ values and practicallyis zero. Also, in Fig. 8 inset, the normalized χ” values arevertically separated for visual clarity of the shift in fpeak.
It can be seen that the position of the maximum χ” shift
to lower frequency as the ionic strength increases. A plotof fpeak for different ionic strength are shown in Fig. 8.
These fpeak values are extracted from the fitted Gaussianfunction of the data from the inset of Fig. 8. It is evident
from Fig. 8 that there is a shift in the χ” peak position tolower frequencies from ~193 Hz to ~182 Hz upon increaseof the ionic concentration of the solution from 10 mM to
500 mM. We also note the strong correlation between the
SR in Fig. 5 to fpeak in Fig. 8, which clearly suggests thatthe reduced swelling of the ferrogel is related to the shift
in fpeak.
As previously mentioned in Section 2.3, the point ofinterest in this study is in the magnetic relaxation (τeff) of
the FeOx NPs in the ferrogel, we can estimate the τefffrom fpeak by applying Eq. (5). Here, we find τeff wasincreased from 0.874 msec to 0.825 msec as the ionicstrength increases from 10 mM to 500 mM.
In order to explain these results, we need todetermine the dominant magnetic relaxation mechanismin the present sample. We note that the Néel relaxation
time τN is not affected by changes in ionic concentration
or reduced swelling of the ferrogel, whereas the
Brownian relaxation time can be affected. When the
ferrogel reduced swelling, it likely becomes more difficult
for the FeOx NPs to rotate, especially if we consider
clustered NPs as suggested by the SEM imaging results.
This increased difficulty of rotation effectively
suppresses the Brownian relaxation of the NPs. This canbe interpreted as an increase in the effective viscosity ofthe surrounding gel. Therefore, the fact that a shift fpeak
was observed strongly suggests that in the sample in thecurrent study Brownian relaxation is dominant, as Néel
relaxation alone would not explain the fpeak.
Note that although the reduced swelling of the gelalso changes the spacing between NPs which can also
affect τeff, the trend, however, is opposite. If we consider
the spacing between NPs, the reduced swelling of the gel
would yield to the decrease in spacing between NPs,
which would enhance the dipolar interaction, whichshould in-turn decrease τeff 39)-40). That is when highdensity (small spacing) of NPs are present, relaxation isTransaction of the Magnetics Society of Japan (Special Issues) Vol.3, No.1, 2019117

Fig 8. Peak frequency fpeak of χ” as function of ionicconcentration of the FeOx-CH. Inset: plot of thenormalized χ” as function of frequency at different ionicconcentrations, zoomed-in and vertically separated forvisual clarity of the position of fpeak.
enhanced. We note that this is in fact opposite the resultsof the present study, and is therefore unlikely. Moreover,since the NPs are arranged in clusters, the dipolarinteraction between individual particles is alreadypresent even without changing the ionic concentration.
Hence, changing the interparticle spacing due the ionicconcentration (and reduced swelling of the gel) is notexpected to increase the dipolar interaction significantly.
Furthermore, if we consider the only the effect ofionic concentration to NPs (the case without a CH gelmatrix), we expect that an increase in the ionicconcentration leads to the surface charges in the NPs,
which would prevent aggregation as well as increases
inter-particle spacing 41)-43). Again, this, however, is
opposite the results of the present study, where thepresence and reduction of swelling of the CH gel causes
the formation of clusters and the spacing between NPs todecrease. Therefore, the possibility that the ionicconcentration (chemical stimuli) is affecting the magnetic
properties NPs directly is unlikely, and that it is moreprobable that the ionic concentration directly interacts
with the CH gel and CH gel in-turn affects the magnetic
property of the NPs by suppressing the Brownian
relaxation.
After these considerations, we therefore infer thatfor the sample in the present study, Brownian relaxation
is dominant ( τeff ≈ τB 35)-37), and τB << τN ). This allows us
to estimate the hydrodynamic size dh. Using Eq. (7), we
estimated dh of around 130 nm for η = 1 mPa.s 44). We
note that this value agrees well with the clustered NPs
size showed in our SEM results. Whereas, we attributethe high frequency χ” peak (at >> 1 k Hz in Fig. 7c-inset)
to the non-clustered NPs in the ferrogel. Assuming thatthe high frequency peak is comparable to that of a similar
sample, it is expected to be in the order of 10 kHz, whichcorresponds to a τB ≈ 16 μsec and dh ≈ 34 nm. Note that118

the NPs dh and dc are of the same order of magnitude,
which is expected. Furthermore, this also allows us toestimate the minimum possible magnetic core size of theNPs. Since Brownian relaxation is dominant, τN >> τB ≈0.80 msec. Assuming τN is in the order of 8 msec, weestimate a magnetic core size of around 18.41 nm for κ =2 x 104 Joule·m-3 45)-46). This again fits well with the SEM
results, since the magnetic core size should be smaller
than the cluster size. Note that this is just the lower
bound for the magnetic core size of the NPs.
Similar to the analysis done in the previous study 6),
it is reasonable to assume that the Néel relaxation timeremains the same even if the ionic concentration changes.
Therefore, the presence of the experimentally observed
frequency shift suggests that Brownian relaxation isdominant in the present specimens. Ignoring thecontribution of Néel relaxation (i.e. 2πfpeak ≈ 1 /τB) 36)-38), we
can relate the change in the effective viscosity ∆η to theexperimentally observed shift in peak frequency, ∆fpeak,
due to ionic concentration change. This relation isanalytically written as∆fpeak ≈ (2 kBT∆η) / (πdh3η) = (∆η / η) × τB,(9)where the parameter ∆η/η is the fractional (or percent)change of the viscosity. Equation (9) is derived by taking
the derivative of the reciprocal of Eq. (5) with respect toη. From the experimentally measured frequency shift of∆fpeak ≈ 11 Hz due to ionic concentration change, a change
in the viscosity ∆η/η ≈ 6.13% is estimated. We estimatethat the viscosity change of the surrounding medium isincreased from 1 mPa.s to 1.0613 mPa.s when the ionicconcentration is increased. This is smaller compared toour previous result on the effect of pH. This signifies thatthe ferrogel is more sensitive to pH than to ionic strength
values used in the experiments.
4. Conclusion
In the present study, we experimentallydemonstrated the use of CH ionic strength sensitivity toaffect the magnetic relaxation properties of FeOx NPs.
The observed shift to lower frequency of the χ ” peak isdue to the reduced swelling of the hydrogel thatsuppresses the Brownian relaxation. The change ofeffective viscosity is also estimated by analytical
calculations. The results in this study is a promisingdemonstration of magnetic sensing of chemical stimuli
that may be useful for future bio-sensing applications.
Acknowledgements This work was partly supported by
the following foundations: Tokyo Ohka Foundation, Kato
Foundation and Murata Science Foundation.
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Received Oct. 16, 2018; Revised Dec. 27, 2018; Accepted Feb. 15,
2019Transaction of the Magnetics Society of Japan (Special Issues) Vol.3, No.1, 2019119