Brushed Nano‐Stirbars for Measuring Viscosity in Microscopic Systems

Conventional methods for measuring viscosity rely on macroscopic device components, which are difficult to miniaturize. The magnetic nano‐stirbars are small enough to enter tiny spaces and can spin without precise installation, making them an ideal candidate for exploring new methods. It is shown that a dense layer of Au nanowires can be grown on the silica surface of the nano‐stirbars, as a means to modulate the viscous resistance during their spinning and to make them visible under an optical microscope. The uniform growth of Au nanowires and the slight fluctuation of the spinning rates are investigated. It is shown that the nano‐stirbars with the hairy layer of Au nanowires can be used to measure the viscosity in microscopic liquid systems, such as microfluidic chambers and capillary tubes, involving cell media and blood samples. It is believed that the success with the proof‐of‐concept tests will open a window for further miniaturization of the nano‐stirbars for measuring in ultrasmall systems.


Introduction
Viscosity defines the resistance of a liquid in response to movements and shape changes.It is a fundamental property of a DOI: 10.1002/admi.202300476liquid that affects our daily life as well as frontier research.From ships in the ocean, to colloidal nanoparticles, or ion movements in lithium battery, [1] viscosity plays a critical role in governing their behavior.
It is well known that liquids behave very differently in microscopic systems.For example, the Reynolds number becomes very small, and the influence of viscosity dominates over flow inertia, leading to laminar flows. [2]This is in contrast to the macroscopic system where the liquid domains moving at a moderate velocity could generate enough inertia to overcome the viscous resistance, leading to chaotic motions and random eddies.
Nanoparticles undergo random Brownian motion, as their collisions with solvent molecules at any instant are not balanced.As such, their motions are critically dependent on the temperature and inversely proportional to the viscosity of the solvent, as described by the Stokes-Einstein equation. [3]If you cannot measure it, you cannot manage it."The measurement of viscosity in microscopic systems is of critical importance, particularly for cellular environments that have large variations of local viscosity with biological impacts.
The conventional methods for measuring viscosity cannot be easily adapted for microscopic systems, because the critical component is often too large and requires precise assembly to operate.Most importantly, the liquid samples have to be isolated before they could be tested.One example is the Rotary Viscometer, where one cylinder (a few cm in size) is driven at a constant angular velocity and the other coaxial cylinder is suspended by torsion wire.Thus, the torsional force applied to the suspended cylinder at the equilibrium position reflects the viscous force transmitted through the liquid. [4]In Blood Viscometer, the liquid flows through a small tube of mm diameter, and the pressure differences at different flow rate are measured to obtain the fluid viscosity.
At the scale of 100 μm, micro-electro-mechanical system (MEMS)-based viscometers are being developed. [5]Such viscometers are integrated with microfluidics in a chip, thus requiring a much reduced volume of sample solutions.There are several detection schemes known, including oscillation, [6] acoustic, [7] cantilever, [8] and pressure-based methods. [9]For example, the device that integrates the magnetoelastic-sensor into microfluidic chip.It works by measuring the resonance of the sensor (2 mm × 400 μm × 30 μm) in an alternating magnetic field. [10]Another example exploits the propagation of acoustic waves in a microfluidic chamber (150 μm × 150 μm × 300 μm), where the sound velocity and decay rate are dependent on the liquid viscosity.7b] Hence, miniaturizing the critical mechanical component is the necessary step in pushing the limit of viscosity measurement in ultrasmall systems.
In recent years, magnetic stirbars as small mechanical devices have undergone rapid development.The capability of "remote" stirring driven by external magnetic field has proven useful in fields such as microfluidics, [11] biomedical engineering, [12] and heterogeneous catalysis. [13]Previously, our group reported the synthesis of magnetic nano-stirbars (MNS) by assembling colloidal magnetic nanoparticles followed by silica encapsulation [14] and by electrospinning. [15]In addition, several other synthetic methods also have been reported, for example, colloidal assembly of Fe 3 O 4 nanoparticles followed by polymer coating, [16] electrodepositing magnetic segments in AAO templates, [17] embedding Co nanoparticles in amorphous C nanorods via direct pyrolysis, [18] and cutting sheets of magnetic materials via laser micromachining. [19]Due to its size advantages, ease of manipulation, and rotation, the MNS could be viewed as an ultrasmall mechanical device capable of entering tiny spaces and spinning without the hassle of precise installation.
In this work, we report the growth of uniform vertical Au nanowires on the surface of MNS (the nano-brushes), as a means to modulate the viscous resistance during their spinning.The absorption and scattering from the metal layer also allow the direct observation by a microscope.As such, we show that the viscosity (1.19 -165 cP) of tiny systems (down to 50 nL) could be measured from the spinning rates of selected nano-brushes, driven by rotating external magnetic field.With the proof-of-concept established, we believe that there are great promises in further miniaturization for measuring viscosity in even smaller systems.

Synthesis of the Nano-Brushes
The synthesis of the MNS is adapted from our previous methods. [14]More specifically, the 22 nm oleic acid-stabilized Fe 3 O 4 nanoparticles [20] (Figure S1a, Supporting Information) were purified to remove the excess oleic acid, and then ligand was exchanged with citrate acid.They were assembled into chains with the help of an external magnetic field, and simultaneous silica encapsulation was used to preserve the magnetic chains.The resulting silica shell was ≈60 nm (Figure S1b, Supporting Information), and it was further expanded by multiple cycles of silica deposition, to push the MNS diameter to 0.8-1 μm for easy observation (Figure S1c, Supporting Information).
As shown in Figure 1a, the surface Au nanowire arrays (NWAs) were grown by adapting our previous method for bulk oxide substrates. [21]More specifically, the MNS were functionalized with amine groups by reacting with 3aminopropyltriethoxysilane (APTES), purified and then coated with a layer of citrate-stabilized 3-5 nm Pt nanoparticles as seeds (Figure S2a,b, Supporting Information).A growth solution was prepared by mixing the ligand 3-mercaptobenzoic acid (3-MBA), the Au precursor HAuCl 4 , the reductant L-ascorbic acid, and the surfactant PVP for preventing aggregation.
As shown in Figure 1b, the MNS before the growth of Au NWAs are straight with a smooth surface.After the growth, a hairy layer formed on their surface (Figure 1c) and upon close inspection in the scanning electron microscopy (SEM), the Au NWAs are found to stand vertically on the MNS surface.They were roughly parallel to each other with slightly curved tips.The layer of Au NWAs was 1.1 ± 0.21 μm in thickness (Figure 1d).Under transmission electron microscopy (TEM), the constituent Au nanowires were ultrathin with a diameter of 6.4 ± 1.0 nm and their roots are tethered to the silica surface (Figure 1e,f).
As shown in Figure 2a, the growth solution turns from colorless to greyish brown with the increasing length of the Au NWAs.The weak absorption peak at 515 nm in the UV-vis spectrum (Figure S2c, Supporting Information) could be assigned to the transverse absorption of the Au nanowires. [22]After magnetic attraction to isolate the nano-brushes, the supernatant appeared colorless and transparent, indicating that there are barely any Au nanoparticles formed by homogeneous nucleation in the solution.That is, most of the Au participated in the growth of the Au NWAs.
Under an inverted microscope equipped with CCD camera (Figure 2d), the Pt-seeds@MNS cannot be seen, despite the large diameter of the MNS (0.8-1 μm).With the growth of Au NWAs, the nano-brushes gradually appeared as black rods and the changes could be monitored in situ.The lengthening Au NWAs would enhance light absorption and scattering from the nano-brushes, making them visible.As shown in Videos S1 (Supporting Information), the nano-brushes with 1.1 μm Au NWAs as suspended in the colloidal solution instantaneously aligned with the external magnetic field and rotated with the field.14b]

Controlled Synthesis of Au Nanowire Arrays
The Au NWAs are more densely grown on the MNS than in our previous works (Figure 2b,c). [21]The difference was that 3-5 nm Pt nanoparticles were adsorbed on the MNS surface as the seeds, as opposed the 3-8 nm Au nanoparticles (Figure S4a,b, Supporting Information).The former was prepared by quick NaBH 4 reduction of H 2 PtCl 4 in the presence of citrate.In the field of electroless plating, it is well known that Pd and Pt seeds could form a denser layer on the amine-functionalized surface, likely due to their higher affinity and smaller charge repulsion. [23]At least in our hands with extensive trials, the Pt seeds always gave denser NWAs.
The surface density of Au NWAs could be modulated by the amount of Pt seeds.More specifically, 1, 5, 10, 20, 40, and 160 μL of the stock seed solution were used to treat a same amount of the amine-functionalized MNS, followed by purification to remove the excess seeds.As shown in Figure 2e, there is a general trend that the density of Au NWAs increases with the seed It should be noted that the SEM images only show the samples after drying.At the last minute of drying, it is expected that the soluble nanowires would be pushed together by the residual solution (the capillary effect).That is why the NWAs are typically pushed to the two sides of the MNS showing a butterfly shape.Judging from the roots, there are uniform NWAs in all directions of the MNS.Thus, it is likely that in solution the NWAs are waving around the MNS and the butterfly shape in the SEM images are only formed as a result of drying effects.
As in all seeded growth, the length of the NWAs depends inversely on the amount of growth sites.It is reflected in the above discussion where longer NWAs were obtained with sparser seeds.Another approach is to change the amount of the Ptseeds@MNS in the colloidal solution.Since their absolute concentration is difficult to measure, we used the relative amounts: 8000, 2000, 1000, 500, 250, 125, and 50 μL of the Pt-seeds@MNS stock solution were used for the growth, after isolation to remove the excess solvent.The resulting NWAs on the MNS were 0.092 ± 0.021, 0.54 ± 0.14, 1.1 ± 0.21, 1.9 ± 0.35, 3.4 ± 0.51, 6.2 ± 1.8, 10.1 ± 2.8 μm, respectively (Figure 2f; Figure S6, Supporting Information), roughly consistent with an inverse dependence.The nanowire width is quite uniform (6.4 ± 1.0 nm) among the samples.In Figure S7 (Supporting Information), the less than expected length (plateauing) with the lower seed concentrations is likely due to the homogeneous nucleation that gives free nanoparticles competing for the growth materials.
Figure 3a shows the elemental analysis via Energy Dispersive Spectroscopy (EDS).O is mostly associated with the Fe 3 O 4 nanoparticles and the silica shell, and it is clearly at the center taking the shape of the MNS.The distribution of Au and Pt are roughly overlapping at the position of the NWAs.Fe and Si could be distinguished in the HAADF images of the thin MNS, where a clear core-shell distribution was observed (Figure S8, Supporting Information).In high-resolution TEM (HRTEM), middle sections of the Au nanowires were studied, showing crystalline regions as well as complex Moiré patterns.Fourier transformation shows that the crystalline regions (Figure 3c) gave orderly diffraction patterns.The characteristic spacing of 0.237 and 0.202 nm in Figure 3e-f could be assigned to the Au (111) and (200) planes.That is, the Pt-seeded nanowires are in general consistent with the previous works that their rapid growth leads to occasional random defects. [21]In X-ray diffraction (XRD), the peaks of the Fe 3 O 4 nanoparticles and the Pt seeds are too weak to be seen, giving only the peaks of Au (Figure S9a, Supporting Information).
The ligand 3-MBA plays an important role in the growth of AuNWs on the MNS.When the [3-MBA] in the standard condition (0.7 mm, with all other conditions kept unchanged) was increased to 1.4 mm, the resulting AuNWs remained the same width of 6.4 ± 0.83 nm (Figure S10b, Supporting Information).At 2.8 mm, 3-MBA formed complexes with Au ions leading to insoluble floccules (Figure S10a, Supporting Information). [24]On the other hand, when the [3-MBA] was reduced to 0.35 mm, the AuNW width increased to 7.8 ± 1.2 nm (Figure S10c, Supporting Information), because the dynamic competition between ligand adsorption and Au deposition moved to the side of slower ligand inhibition. [21]In the absence of 3-MBA, there was no active surface growth.As a result, the seeds simply grew larger into appendant nanospheres of 77 ± 20 nm diameter (Figure S10d, Supporting Information).
The ligand 3-MBA was replaced by other thiolated ligands with aromatic backbone, including 4-mercaptobenzoic acid (4-MBA), 4-mercaptophenylacetic acid, 2-naphthalenethiol, and 1-mercapto-4-methylbenzene.As shown in Figure S10e-h (Supporting Information), dense NWAs were also formed on the MNS, consistent with the previous work on the generality of the ligands. [25]e need a control sample of MNS (non-brushed MNS) without the resistance from the Au NWAs.Because the MNS with only silica shells are nearly invisible under the microscope, a layer of Au nanospheres coating is desirable to improve light absorption and scattering.To this end, the above synthesis of appendant 77 nm Au nanospheres was modified with the higher amounts of Pt-seeds@MNS and a lower amount of Au precursor.The nonbrushed MNS (Figure S11, Supporting Information) with smaller appendant Au nanospheres (37 ± 7.2 nm) were obtained.

Role of PVP during the Growth of Au NWAs
In our synthesis, we found that the presence of polyvinylpyrrolidone (PVP, 58000 da) plays a significant role in the stability of the nano-brushes.More specifically, in the absence of PVP, black precipitates formed that were visible to the naked eyes (Figure 4b), whereas the same reaction with PVP gave stable colloid (Figure 4e).On the other hand, the initial MNS are stable in the absence of PVP, indicating that the instability should arise from the growth of Au NWAs.PVP probably plays a role in passivat-ing the Au NWAs and thus preventing aggregation of the nanobrushes.
In the absence of PVP, a prominent feature of the nanobrushes is that the Au NWAs are pushed to one side of the MNS (the over-turning, Figure 4d and Figure S12b, Supporting Information).After extensive experiments, we realized that the overturning was likely caused by the drag of the Au NWAs when the nano-brushes are in motion.Thus, the over-turning did not occur for the nano-brushes with shorter NWAs because they encounter less friction (Figure 4c; Figure S12a, Supporting Information).As illustrated in Figure 4a, for the PVP-stabilized nano-brushes, there was no over-turning when the Au NWAs were grown in a static solution (Figure 4f,g; Figure S12c,d, Supporting Information), whereas over-turning occurred when the nano-brushes were stirred by an external magnetic field during the growth of Au NWAs (Figure S13, Supporting Information).

Spinning Nano-Brushes by External Magnetic Field
The nano-brushes of different sizes (1.3 -20.6 μm width, 3.3 -53.2 μm length) could be readily monitored under an inverted microscope equipped with CCD camera (500 times magnification).As shown in Figure 5a, the observed width is roughly proportional to the length of the Au NWAs.Unlike macroscopic magnetic stirrers, the nano-brushes with 1.1 μm Au NWAs stopped spinning as soon as the external stirring magnetic field stopped (Video S1, Supporting Information).2c,26] To study the effects of viscous forces, the nano-brushes were dispersed in sucrose solutions of increasing concentrations (0, 5.3, 10.3, 19.8, 36.9, and 64.9 wt%).As shown in Video S2 (Supporting Information) and Figure 5b, with the same spinning rate of the external magnetic field (500 rpm), the increase of solution viscosity caused an obvious reduction of the steady-state spinning rate for the nano-brushes.On the other hand, for each of the sucrose solution, there is a "volcano plot" for the rate of nanobrushes against the rate of external field, where the highest spinning rates occur in the middle.Basically, there are two scenarios (Figure 5c): When the viscous forces are small enough and the nano-brushes can catch up with the external field, the rate increases linearly with the latter; When the nano-brushes cannot catch up with the external field, the rate gradually slows down with the increase of the external field.Even with the lowest viscosity (0% sucrose), the nano-brushes cannot catch up when the external field exceeds 300 rpm, and their spinning rate gradually decreased with the increase of the external field, all the way to 1000 rpm (Figure 5c; Figure S14a and Video S3, Supporting Information).With more viscous solution, it becomes more difficult for the nano-brushes to catch up, so that the highest rate occurs earlier.One exception was when the 64.9 wt% sucrose solution was too viscous, so that the changes of the spinning rate (3.1-0.19 rpm) were too small to be shown (Figure 5c).
The long Au NWAs are the main source of viscous resistance, considering their enormous contact interface with the solution.As shown in Figure 5d and Video S4 (Supporting Information) (500 rpm external field), the nano-brushes spinning in water would quickly slow down with the lengthening of Au NWAs. Figure 5e shows the dependence of the steady-state spinning rate in water on the rate of external field.The highest spinning rate decreases with lengthening Au NWAs, and beyond the highest point, the spinning rate generally decreases with the increase rate of the external field.For the longest NWA length of 10.1 μm, the viscous resistance was too high, such that the spinning rate barely changed regardless of the external field (Figure 5e).
It should be noted that the above spinning rates were all measured at the steady state.The initial acceleration period (≈10 s) after turn-on of the external magnetic field is not uniform (Figure S14b, Supporting Information).Also, it is important to maintain a constant temperature because the solution viscosity changes dramatically with the temperature (Figure S14d, Supporting Information).
The aspect ratio of the nano-brushes is also of importance because the longer ones would have a higher linear velocity at the same angular velocity, and thus would experience higher viscous resistance and higher torque.Video S5 (Supporting Information) and Figure S14c (Supporting Information) show the dependence of nano-brushes on their aspect ratio (with 1.1 μm Au NWAs, 500 rpm external field).There is a general trend that the longer ones spin slower.Without the long NWAs, the control sample of the non-brushed MNS with 37 nm nanospheres would experience less viscous resistance.Their spinning rates are clearly faster as expected, and the relatively longer ones still spin slower.To normalize the length effects in our analyses, we tried to select the magnetic nano-stirbars (MNS) with a similar length (8 μm), by subtracting the nanowire length from the length measured from the microscope images.
The fluid environment for the nano-brushes is a typical Stokes flow, where the Reynolds number is small, and the viscous force dominates over inertia.The resistance torque along the nanobrushes is expected to increase with the distance from the center (Figure 6a), due to longer force arm and higher linear velocity.In our simplified model, the NWAs are treated as uniform and solid, and the nano-brushes are divided into 2N equal portions of Δl = L/2N.For high aspect ratio object with rotation axis perpendicular to its longitudinal axis, the resistance coefficient K can be expressed as: [27] K = 4L ln where  is the solution viscosity, and L and r are the length and radius of the nano-brush.Also, the linear velocity can be expressed as V w = l, where  is the angular velocity, and l is the force arm.Finally, the total resistance torque   along the nano-brush can be approximated as: [27b] the value of N must satisfy: L ≫ r.Hence, where the solution viscosity , the angular velocity  related to the external field, the model length L, and the radius r related to the length of the Au NWAs are all important parameters that influence the resistance torque.As demonstrated in the aforementioned experiments, variations in these parameters ultimately affect the spinning rate of the nanobrushes.
Obviously, when the nano-brushes cannot catch up with the rotating external magnetic field, its angular velocity cannot be uniform due to the changing attractive and repulsive forces.To understand the detailed process, we analyzed the video frameby-frame (15 frames s −1 ).At a low speed (100 rpm) in water, the observed change of angle is uniform for the nano-brush (8.9 μm length, with 1.1 μm Au NWAs) in each frame with 66.7 ms separation (Video S3 and Figure S15, Supporting Information).The plot of total rotation angle against time gives a straight line, indicating a perfect match with the rotating external magnetic field (Figure 6c).In another case, at a high speed (500 rpm) in 10.3 wt% sucrose solution, the nano-brush (16.1 μm length, with 1.1 μm Au NWAs) cannot catch up with the external field.The 46 rpm (expected value) is only a fraction of that of the external magnetic field (500 rpm), and it was averaged over two full cycles of the nano-brush.The observed change of angle is nonuniform for the nano-brush in each frame with 66.7 ms separation (15 frames s −1 , Video S5b (Supporting Information) and Figure 6b).As shown in Figure 6d, the frame-by-frame angular velocity fluctuates around the average rate, but not far off.While this is not surprising considering the push-pull forces from the external field with the mis-matched rates (Figures S16 and S17, Supporting Information), the small fluctuation is amazing and it could be attributed to the low Reynolds number of the system.In contrast, a macroscopic stirbar often "jumps" wildly when it cannot catch up with the external field.Thus, the negligible inertia of the nano-brushes is essential for their stable spinning as shown in Figure 5b-e, allowing the measurement of viscosity in the following studies.

Measuring Solution Viscosity using the Nano-Brushes
Given their small size, the nano-brushes could rotate in a minimal volume of solution and reflect its viscosity.Thus, we developed a method to measure a few nL of solution with viscosity between 1.19 -148 cP (Figure 7a; Figure S18, Supporting Information).More specifically, a standard curve was obtained by observing nano-brushes of similar length (≈10 μm total length, with 1.1 μm Au NWAs) stirring in different sucrose solution under a 500 rpm external magnetic field, plotting the spinning rate against the sucrose concentration.In a different set of experiment, another standard curve was obtained by plotting the viscosity measured by a conventional method against the sucrose concentration.A straight line was found between the average spinning rate ( Vrpm ) and the average viscosity ( η) with a double logarithmic scale by the least square method (Figure 7d; Figure S19, Supporting Information).Then, an unknown solution was measured using the nano-brushes from the same batch.The average spinning rate was checked against the calibration curve to obtain the solution viscosity.
Similar experiments were carried out using the nano-brushes with shorter Au NWAs (92 nm), so that they could rotate in more viscous solutions (Video S6, Supporting Information), extending the viscosity range to 228 cP (Figure 7d; Figures S18 and S19, Supporting Information).As a proof-of-concept, we tested two readily available biological samples: A concentrated solution of the nano-brushes with 1.1 μm Au NWAs were dropped on a hydrophobic glass slide, wait until it is almost dried, and then added 1 μL of serum-free cell freezing medium (Figure S20b, Information).After mixing, the sample was stirred using 500 rpm external magnetic field and the spinning rate was determined to be 25 ± 5.8 rpm (Video S7a, Supporting Information), giving a viscosity of 3.73 ± 0.64 cP.For validation, large-scale measurement (8 mL) was carried out in the Rotary Viscometer, giving a viscosity of 3.50 ± 0.33 cP.
To test in flowing microfluidic chip (see the setup in Figure S20a (Supporting Information), with 200 μm × 50 μm × 20 mm channels), the nano-brushes with 1.1 μm Au NWAs were isolated from the solvent and then mixed with 500 μL DMEM medium.The suspension was then injected into the microchip at 100 nL/min flow rate using a microinfusion pump (Figure 7b).As shown in Video S8 (Supporting Information), the spinning nano-brushes flowed slowly with the solution in the microscopic channels.The spinning rate was determined to be 140 ± 25 rpm, corresponding to a viscosity of 1.19 ± 0.16 cP.For validation, large-scale measurement gave a viscosity of 1.35 ± 0.15 cP.A similar measurement was obtained from 10 μL of the static solution, and the spinning rate was basically the same (139 ± 39 rpm, Video S7b, Supporting Information).
Finally, the method was applied to measure blood samples obtained from the heart of an adult mouse.To minimize the non-specific binding of the nano-brushes, the quartz capillary tubes (with square cross-section of 300 μm × 300 μm) were pretreated with bovine serum albumin (BSA).The isolated nanobrushes were mixed with 100 μL of whole blood with anticoagulant (Figure 7c), from which an aliquot (estimated 54 nL) was obtained by tapping the capillary tube.The microscope shows an intense red color but the spinning nano-brushes could be easily recognized.The spinning rate was determined to be 19 ± 7.5 rpm (Video S9, Supporting Information), corresponding to an apparent viscosity of 4.58 ± 1.25 cP, within the range as previously reported. [28]or liquids with slightly higher viscosity, we also detected the 80 wt% and 88.5 wt% glycerol solutions by using the nanobrushes with 92 nm Au NWAs (Figure S21 and Video S10, Supporting Information).Control experiments show that the spinning rate of the nano-brushes (≈10 μm length, with 1.1 μm Au NWAs) is independent of the diameter and shape of the capillary tubes (Figure S20c,d; Video S11, Supporting Information).To examine the reproducibility of the method, the same batch of nano-brushes was separately used in 8 samples of DMEM medium, and the obtained spinning rates were consistent (Figure S22, Supporting Information).Furthermore, after the stirring, the nano-brushes were isolated and examined by SEM and TEM.The nanostructures are stable with no obvious sign of detached Au NWAs (Figure S23, Supporting Information).

Conclusion
In summary, we developed a method of using magnetic nanostirbars for measuring the viscosity in ultrasmall liquid systems.A dense forest of Au nanowires was grown on the silica-coated nano-stirbars, to modulate their viscous resistance upon spinning and to make them visible under an optical microscope.PVP plays a critical role for the colloidal stability of the nanobrushes and avoids over-turning of the nanowires.The spinning of the nano-brushes is typical of the microscopic system with low Reynolds number, so that they could spin stably with a small fluctuation of rates, even when it is highly mismatched with the spinning rate of the external magnetic field.As such, the nanobrushes could be used for measuring the viscosity in ultrasmall systems, as shown in our proof-of-concept demonstrations.The method is immensely promising, considering that the magnetic nano-stirbars could enter tiny spaces and rotate without precise installation.We envision that further miniaturization along with super-resolution techniques would allow viscosity measurement in cellular domains.

Figure 1 .
Figure 1.a) Schematic illustration of the synthetic route to the Au NWAs on MNS.b) SEM image of the initial MNS with 0.8-1 μm width.c) SEM image of the nano-brushes with 1.1 μm Au NWAs.d) A close-up view of Sample c. e) TEM image of the Au NWAs on the nano-brushes of Sample c. f) TEM image of the root region (the red circle in (e) showing the interface between the silica shell and the Au NWAs.

Figure 2 .
Figure 2. a) Photographs showing color changes of the solution during the growth of Au NWAs.TEM images of the nano-brushes synthesized by using b) Au seeds and c) Pt seeds.d) In situ monitoring of the nano-brushes during the growth of Au NWAs by an optical microscope.e) SEM images of the nano-brushes synthesized by using different amounts of Pt seeds, from left to right: 1, 5, 10, 20, 40, 160 μL.f) SEM images of the nano-brushes synthesized by using different amounts of Pt-seeds@MNS, from left to right: 2000, 1000, 500, 250, 125, and 50 μL of the stock solution.

Figure 3 .
Figure 3. a) SEM image and EDS elemental mapping of a typical nano-brush with 3.4 μm Au NWAs.b) HRTEM image of the Au NWAs on the nanobrushes.c) The Fast Fourier Transform of the selected region showing a single-crystalline segment.d) A close-in view of the blue box in (b).e) The characteristic 0.237 nm and f) 0.202 nm spacing corresponding to the (111) and (200) planes of the Au nanowires with face-centered cubic lattice.

Figure 4 .
Figure 4. a) Schematic illustration of the butterfly shape and the over-turned shape.Photographs showing the solution condition b) without or e) with PVP when the Au NWAs have grown for 10 min.SEM images of the nano-brushes grown without PVP c) with 3.4 μm Au NWAs and d) the over-turned nano-brushes with 10.1 μm Au NWAs.SEM images of the nano-brushes grown in static solution in the presence of PVP f) with 3.4 μm Au NWAs and g) with 10.1 μm Au NWAs.

Figure 5 .
Figure 5. a) Microscope screen captures showing the non-brushed MNS with 37 nm nanospheres and the nano-brushes with Au NWAs: 0.54 ± 0.14, 1.1 ± 0.21, 3.4 ± 0.51, 6.2 ± 1.8, 10.1 ± 2.8 μm in the water, respectively, as corresponding to Figure 2f.Scale bar: 10 μm.b) Dependence of the steady-state spinning rate of the nano-brushes with 1.1 μm Au NWAs on the sucrose concentrations, under 500 rpm external field.c) Dependence of the steady-state spinning rate of the nano-brushes with 1.1 μm Au NWAs on the rate of external field, for the sucrose solutions of different concentration.d) Dependence on the nanowire length, showing the steady-state spinning rate of the non-brushed MNS and the nano-brushes with 0.54, 1.1, 3.4, 6.2, 10.1 μm Au NWAs, under 500 rpm external field.e) Dependence on the nanowire length, showing the steady-state spinning rate in water, for the non-brushed MNS and the nano-brushes with 0.54, 1.1, 3.4, 6.2, 10.1 μm Au NWAs, against the rate of external field.

Figure 6 .
Figure 6.a) Schematics illustrating the viscous drag and the resistance torque: The nano-brush is treated as a rod and divided into 2N equal portions for the calculation of resistance torque.b) Photographs showing the rotation of a typical nano-brush (16.1 μm length, with 1.1 μm Au NWAs) in the 10.3 wt% sucrose solution under 500 rpm external field.Scale bar: 10 μm.c) Plot of the total rotation angle against time, showing that the nano-brush (8.9 μm length, with 1.1 μm Au NWAs) could catch up with the 100 rpm external field.d) Plot of the total rotation angle against time, showing that the 46 rpm nano-brush (16.1 μm length, with 1.1 μm Au NWAs) cannot catch up with the 500 rpm external field.The frame-by-frame changes are marked with alternating colors of grey and orange, and the relative rotation in each step is shown in the pie chart (inset).

Figure 7 .
Figure 7. a) Schematic illustration of the setup for observing the nano-brushes in a capillary tube.Photographs showing the nano-brushes in b) a channel of microfluidic chip and c) a blood sample in a quartz capillary tube.d) Plots showing the dependence of average spinning rate (lg Vrpm ) on the solution viscosity (lg η).