Ferromagnetic Nanorods in Applications to Control of the In ...u Y Gu and Konstantin G. Kornev * Ferromagnetic nanorods play important roles as active ﬁ llers in multi-functional

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nanorods as the fi llers are believed to be the best candidates for materials working in extreme environment and hence they are on demand in aerospace and space exploration applications. [ 39–43 ] In com-posite fi lms needed for inductor and antennae applications, the alignment of magnetic particles is required to increase the high frequency permeability and to lower the hysteresis losses. [ 44–47 ] In appli-cations to manufacturing of high density recording fi lms and discs, spin alignment is required to carry the recorded informa-tion when spins in magnetic nanorods are prone to align parallel to the nanorod axis. [ 37,48–50 ] In optical applications, magnetic liquid crystals are attractive candidates for making reconfi gurable

magnetooptical devices with the fast time response measured in milliseconds. [ 11–18,51–53 ]

In all these applications, one needs to control the align-ment of magnetic nanorods in liquid medium. Therefore, this problem is actively discussed in the literature; however, the general strategy for making macroscopic samples with ordered nanorods has not been developed yet and it remains the main challenge of materials engineering [ 32–35,39–42,54 ] Processing of multifunctional coatings and thin fi lms require many steps and hence one needs to control the fi lm properties at each step.

Rheological properties of the fi lms at each stage of their pro-cessing play the most important role in nanorod ordering and keeping nanorods in place. Characterization of thin coating fi lms during composite manufacturing remains challenging. Different experimental methods have been proposed and devel-oped for in situ characterization of rheological properties of thin fi lms and coatings. [ 20,25–27,55–60 ] It appears that unique features of rotation of ferromagnetic nanorods can be used for char-acterization of very thin fi lms when other methods fall short. Recently introduced magnetic rotational spectroscopy (MRS) with nanoparticles and nanorods allows one to probe fl uid rhe-ology in very thin fi lms and nanoliter droplets. [ 12,20,22,25,60,61 ] MRS takes advantage of a distinguishable behavior of rotating magnetic tracers as the frequency of applied rotating fi eld changes. Unlike many methods based on the analysis of small oscillations, which are diffi cult to interpret when the fi lm is very thin, MRS with magnetic nanorods enjoys analysis of full revolutions of magnetic tracers. [ 20,22,24,25,60,62,63 ]

Understanding of the characteristic features of rotation of a single nanorod in complex fl uids and alignment of an assembly

Ferromagnetic Nanorods in Applications to Control of the In-Plane Anisotropy of Composite Films and for In Situ Characterization of the Film Rheology

Yu Gu and Konstantin G. Kornev *

Ferromagnetic nanorods play important roles as active fi llers in multi-functional composite fi lms. Many composite fi lms used as inductors and antennae, as recording media, or electromagnetic (EM) fi lters and polar-izers, require the nanorod alignment in a certain direction. The strategy for the in-plane alignment of nanorods has not been established yet. Since the composite assumes a multistep processing when the material rheological properties change in time, in situ characterization of the fi lm is required. Magnetic rotational spectroscopy (MRS) with ferromagnetic nanorods offers fl exibility and accuracy providing desired spatial and temporal resolution in characterization of submicron thick fi lms. Herein, recent progress in under-standing of the basic physical principles is presented guiding the nanorod alignment in thin fi lms by external magnetic fi eld and characterization of these fi lms by MRS.

DOI: 10.1002/adfm.201504205

Dr. Y. Gu Institute of Optoelectronic and Nanomaterials College of Materials Science and Engineering Nanjing University of Science and Technology Nanjing , Jiangsu 210094 , P. R. China Prof. K. G. Kornev Department of Materials Science and Engineering Clemson University Clemson, SC 29634 , USA E-mail: [email protected]

1. Introduction

Progress in nanotechnology offers new exciting prospects on making colloids with shaped magnetic nanoparticles. [ 1–4 ] The rod-like ferromagnetic nanoparticles deserve a special atten-tion because of their specifi c anisotropic interactions favoring uniaxial magnetic anisotropy of alignment of spins along the nanorod axis. [ 4,5 ] This type of anisotropic ordering is attrac-tive for the different high-tech applications, in particular, in medical, [ 6,7 ] sensoric, [ 8–10 ] optofl uidic, [ 11–18 ] and microrheolog-ical [ 19–27 ] engineering.

Ferromagnetic nanorods bring about a new feature of the in-plane magnetic ordering in thin composite fi lms when all mag-netic moments of the nanorods are pointing in the directions of nanorod placement. [ 4,9,11,12,15–17,28–31 ] This makes them unique candidates for manufacturing multifunctional composites with unprecedented magnetic and mechanical properties. [ 10,32–38 ] Ceramic matrix nanocomposites (CMNCs) with nanofi bers or

Adv. Funct. Mater. 2016, DOI: 10.1002/adfm.201504205

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of nanorods is necessary for future progress in this fi eld. In this review, we cover the recent progress in understanding of the role of different materials properties on kinetics of in-plane rotation and ordering of magnetic nanorods by magnetic fi eld.

2. Nanorod Synthesis

There are several approaches for synthesis of magnetic nanorods which have been reviewed in the past. [ 64 ] Among them are the fi eld-directed assembly of magnetic nanobeads or electrostatic complexion between oppositely charged par-ticles, [ 65–70 ] method of fi lling and decorating nanotubes with magnetic nanoparticles, [ 11,12,71–73 ] template-based electrochem-ical deposition, [ 1,2,15,74 ] as well as template free wet chemical synthesis. [ 75–79 ] The template-based electrochemical growth of nanorods from magnetic metals and method of fi lling nano-tubes with magnetic nanoparticles appeared most attractive. [ 1,2 ] In this method, nanoporous alumina is used as a template and metal nanorods are electrochemically grown inside pores of this membrane. [ 2 ] The electrochemical growth of mag-netic nanorods enables one to precisely control the size of the nanorods: the nanorod/nanotube radius is set by the template pores and the length is controlled by the time of electrochem-ical deposition. [ 2,20,62,80,81 ] Magnetic nanorods of 100–200 nm diameter can be covered with polymers to prevent their agglom-eration. [ 15,80,82 ] One can generate Ni, Co, permalloy, and other metallic nanorods and nanotubes. [ 2,24,83,84 ] As an example, the Scanning Electron Microscope (SEM) image shown in Figure 1 shows nickel and cobalt nanorods produced in our laboratory.

The template grown nanorods and nanotubes exhibit fer-romagnetic order, with a distinguishable hysteresis loop ( Figure 2 ). The model of coherent rotation of magnetization vector associated with the rigid dipole model of the nanorod does not explain the hysteresis loops observed in experi-ments. [ 24 ] As evidenced from the analysis of magnetic micro-structure of nanorods with magnetic force microscopy and X-ray diffraction, the nanorods are composed of multiple

domains separated by grain boundaries. However, in a weak magnetic fi eld, the nanorods made of magnetic materials with weak crystalline anisotropy such as Ni, follow the rigid dipole model. [ 20,24,60,80 ] This behavior is favorable for easy alignment of magnetic nanorods during formation of thin coating fi lms. Magnetic behavior of nanotubes is more complex [ 4,83–85 ] and the methods of their processing for magnetic nanocomposites requires further investigation.

The nanorods of the microscopic size can be easily produced by the electroplating technique. [ 86–89 ]

The nanorods and nanotubes with magnetization vector parallel to the long axis are the most attractive candidates for making magnetic composites. When the magnetization vector is tilted with respect to the long axis, the nanorods are subject to complex instabilities and may tumble during their alignment in the fi eld. [ 90–93 ] Moreover, magnetic properties of the fi nal product may not follow the desired design performance; hence the nanorods with a complex magnetic microstructure may not be the best candidates in composite applications. We, therefore, limit ourselves to the analysis of characteristic features of rota-tion of nanorods following the rigid dipole model.

3. Control of Nanorod Alignment in Thin Films

3.1. The Rate of Nanorod Alignment with the Uniform Field: Newtonian Fluids

It is instructive to discuss fi rst the reaction of a ferromagnetic nanorod with magnetic moment m on the applied uniform magnetic fi eld B . We assume that the magnetic moment is coa-ligned with the nanorod axis so that the ends of the nanorod form the north and south magnetic poles. If the nanorod axis is tilted with respect to the applied magnetic fi eld, the latter exerts the magnetic torque m × B . This torque forces the nanorod to align parallel to the fi eld direction. However, if the nanorod is suspended in a liquid, the alignment is not instantaneous: viscous friction opposes the nanorod rotation. In Newtonian



Figure 1. SEM images (Hitachi S4800) and the length distribution of a) nickel and b) cobalt nanorods synthesized using electrochemical deposition method. Frequency of the histogram is defi ned as Δ N / N . Δ N is the number of nanorods in a certain length interval (e.g., 5–6 µm) and N is the total number of nanorods. The applied voltage was 1.5 V and duration of reaction was 12 min for both cases. c) Reaction time was 25 min and d) reaction time was 60 min. Reproduced with permission. [ 24 ] Copyright 2015, American Institute of Physics.

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fl uids, the viscous drag is linearly proportional to the par-ticle angular velocity, [ 94 ] provided that the Reynolds number Re = ρl 2 f / η is very small, where ρ is the fl uid density, l is the nanorod length, f is the rotation frequency of applied mag-netic fi eld, and η is the fl uid viscosity. In majority of applica-tions, the Reynolds number is small. For example, taking as an upper estimate for the nanorod length l = 10 µm and for the rotation rate f = 10 Hz, we have for water, Re = ρl 2 f / η = 10 3 × 10 −10 × 10/10 −3 = 10 −3 . More viscous fl uids will provide even smaller Reynolds numbers.

Thus, a linear relation between the viscous torque and rota-tion rate of the particle should be expected. Balancing the mag-netic torque with the viscous torque, one obtains the governing equation describing the nanorod rotation in the fi lm plane [ 95–98 ]

γϕ α ϕ= −� mBsin( ) (1) where the angles α , ϕ are defi ned in Figure 3 , the drag co effi -cient γ for a magnetic chain of length l made of spherical

particles of diameter d is γ πη=−

≈l

l d AA

3 ln( / ), 2.4

3

, and for

an ellipsoidal particle of length l and maximum diameter d ,

l / d >> 2, A = 0.19.

Assuming that magnetic fi eld is directed along the x -axis, i.e., α = 0, and a nanorod forms angle ϕ 0 with the axis x at t = 0, one can solve Equation ( 1) analytically [ 80,95–98 ]

∫β

ϕϕ β

ϕϕ

ϕϕ

βγ

= − = −−

⋅ =⎛⎝⎜

⎞⎠⎟ϕ

ϕ1 dsin

1ln

1 cos1 cos

sinsin

, .000

tmB

(2)

This equation provides a metric for estimation of the time needed for a nanorod to coalign with the fi eld. The master curve in Figure 3 specifi es the dimensionless time T needed for a nanorod, which was initially oriented at angle ϕ 0 with the x -axis, to get coaligned with the fi eld. [ 80 ] For example, the nanorod making angle ϕ 0 = ± π /6 with the x -axis will take about t ≅ 4/ β seconds to reach the equilibrium orientation within the sector −0.01 < ϕ < 0.01; see the dashed lines in Figure 3 . The nanorods with magnetic moments antiparallel to the fi eld direction will experience the strongest effect of viscous drag: these nanorods will take about t ≅ 10/ β seconds to reach the equilibrium orientation. This time is about one order of magnitude longer relative to that of the nanorods whose mag-netic moments are initially oriented near the fi eld direction. This fact explains the challenge of alignment of an assembly

Figure 2. Theoretical hysteresis loops shown as the red solid curves obtained for an assembly of the single domain nanoparticles whose easy axes are randomly oriented. The blue dots are the experimental hysteresis loops. The theoretical curves were calculated using a uniaxial anisotropy with the easy axis coaligning with the rod’s long axis. a) Nickel b) cobalt. Adapted with permission. [ 24 ] Copyright 2015, American Institute of Physics. Experimental hysteresis loops obtained on c) FeNi alloy nanorods and d) FeNi alloy nanotubes. The red dots correspond to the measurements with the fi eld applied parallel to the nanorod/nanotube axes and the black dots correspond to the measurements with the fi eld applied perpendicular to the nanorod/nano-tube axes. Reproduced with permission. [ 84 ] Copyright 2013, Elsevier.



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of nanorods during the processing of magnetic fi lms subject to curing.

In order to analyze the kinetics of alignment of an assembly of nanorods, the probability P ( ϕ , t ) to fi nd the nanorods posi-tioned within a narrow angle, [ ϕ − Δ ϕ , ϕ + Δ ϕ ], was intro-duced. [ 80 ] When the concentration of nanorods is small and they do not magnetically interact with each other, this prob-ability P ( ϕ , t ) is calculated as

ϕπ

ϕβ=

′⎡⎣⎢

⎤⎦⎥

= −ϕ ϕ

ϕ ϕ

−Δ

+Δ

P tC t

t( , )1

arctantan( / 2)

( ), where C exp( )

(3)

Due to this defi nition, the probability P ( ϕ ,0) = Δ ϕ /2π cor-responds to the initial random orientation of nanorods. As time goes to infi nity, the probability goes to one, P (0,∞) = 1 meaning that all the nanorods can be found within interval [−Δ ϕ , Δ ϕ ]. Figure 4 demonstrates that the theory summa-rized by Equation ( 3) agrees fairly well with the experiments on dispersion of 4 × 10 −4 volume fraction of nickel nanorods of ≈200 nm diameter. The probability function P ( ϕ , t ) defi ned by Equation ( 3) has been used to construct the histograms by counting the number of nanorods N ϕ present in each sector ( ϕ − Δ ϕ , ϕ + Δ ϕ ) with Δ ϕ = π/36 and normalizing N ϕ by the total number of nanorods N t present in all fi ve pictures. [ 80 ]

This approach allows one to control the nanorod orienta-tion during processing of composite fi lms. It can be further developed for a practical case of liquids with a time-dependent viscosity.

3.2. The Rate of Nanorod Alignment with the Uniform Field: Fluids with Time-Dependent Viscosity

In applications to formation of nanocomposite coatings, the fi lm processing assumes either evaporation of the solvent or curing and cross-linking of the carrier fl uid. [ 99 ] The complexity of rheological behavior of the solidifying fi lm during the sol–gel processing makes the analysis and control of the nanorod align-ment into the fi eld direction challenging. The analysis can be signifi cantly simplifi ed by employing the following equation for viscosity



Figure 4. Orientation distribution for an assembly of nickel nanorods which are randomly distributed at the fi rst moment of time. The images of the nanorods were taken at t = 0, 1, 2, 3, and 4 s and then processed to obtain the histograms and to compare them with the theory (solid curves). Adapted with permission. [ 105 ] Copyright 2013, Wiley-VCH.

Figure 3. Dimensionless time needed for a nanorod to reach its equilib-rium orientation as a function of the initial orientation of the nanorod ϕ 0 . The dashed lines help to understand the meaning of this master curve explaining the meaning of the band. Inset: Basic vectors associated with magnetic nanorod and magnetic fi eld B . Adapted with permission. [ 80 ] Copyright 2013, Royal Society of Chemistry.

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η η τt t( ) = exp( / )0 0 (4)

where η 0 is the initial viscosity of the carrier, t is the time, and τ 0 is the characteristic time of polymerization or carrier evapo-ration. [ 99–101 ] This formula for the time-dependent viscosity has been used for many practically important carriers. [ 20,60,102–104 ]

Using this rheological equation of state, one can generalize the theory of nanorod rotation in a solidifying fi lm by replacing the constant viscosity in the drag coeffi cient γ with the expo-nentially increasing one. [ 20,105 ] The time τ 0 sets up a time scale for the nanorod rotation. Therefore, one can observe two dif-ferent regimes of the nanorod alignment into the fi eld direc-tion. For the suffi ciently fast rotating nanorods which are able to align into the fi eld direction within time τ 0 , the nanorods will stay parallel to the applied fi eld after fi lm solidifi cation t > τ 0 . For the slowly rotating nanorods, the nanorods will not be able to align into the fi eld direction after fi lm solidifi cation. The

quantitative analysis of these two cases given in ref. [ 105 ] leads to the phase diagram shown in Figure 5 . This diagram speci-fi es the conditions for the in-plane alignment of nanorods in solidifying fi lms. The diagrams help to determine the process parameters such as η 0 /( τ 0 B ) and l / d which would ensure the complete alignment of different ferromagnetic nanorods into the fi eld direction. [ 105 ]

3.3. The Rate of Nanorod Alignment with the Uniform Field: Viscoelastic Fluids

In viscoelastic fl uids, the rate of the nanorod rotation is infl u-enced not only by the fl uid viscosity but also by the fl uid elasticity. Many polymer solutions and ceramic precursors follow viscoelastic Maxwell or Kelvin–Voigt models. [ 100,106 ] In Figure 6 , the dash pot models the viscous reaction (viscosity η ) of the fl uid on the applied load and the spring models an elastic reaction (elastic modulus G ) of the fl uid on the applied load.

According to the Maxwell model, the viscous τ η = γ d ϕ η /d t and elastic τ G = γG ϕ G /η torques must be equal to the mag-netic torque, τ π θ= d lMBsinm 2 : τ η = τ G = τ m . The angular dis-placement satisfi es the relation: ϕ η + ϕ G = ϕ . Following these two relations, the equation governing the rotation of a rod-like particle reads [ 25 ]

ϕ ηγ

τ τγ

− =t G t

d

d

d

d.m m

(5)

According to the Kelvin–Voigt model, the torques satisfi es the relation: τ m = τ η + τ G , and the angular displacement satis-fi es the relation: ϕ η = ϕ G = ϕ . The basic dynamic equation is written as

ϕη

ϕ τγ

+ =t

Gd

d.m

(6)

Substituting the magnetic torque into these equations, one obtains the basic equations as follows [ 25 ]



Figure 5. Phase diagrams specifying the range of parameters leading to the complete ordering of nanorods in solidifying fi lms.

Figure 6. The Maxwell a) and Kelvin–Voigt b) models of the viscoelastic reaction of a rod-like magnetic particle subject to magnetic fi eld B .

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ϕ ωω

θ θ ω θ− =t t

d

dcos

d

dsin (Maxwell model)c

rc

(7)

d

dsin (Kelvin–Voigt model)r c

t

ϕ ω ϕ ω θ+ =

(8)

where ω c = MBV / γ is the critical frequency, V is the nanorod volume, and ω r = G / η is the reciprocal to the viscoelastic relaxa-tion time. In the Maxwell model, the ω r term accounts for the additive elastic resistance of the material to the rod rotation. As the viscoelastic relaxation time decreases (or ω r increases), ω r = G / η → ∞, the elastic resistance of the material to the rod rotation becomes much smaller than its viscous resistance. Consequently, the angle ϕ in Figure 6 changes mostly due to the dash pot movement and Equation ( 7) reduces to Equa-tion ( 1) for the Newtonian case. In the opposite limit when the viscoelastic relaxation time is large (or ω r is small) , ω r → 0, the second term on the left-hand side of the Maxwell model becomes singular implying that the model has to be augmented by the inertial terms. Furthermore, even if the inertial terms are insignifi cant, this singularity contributes to the rod dynamics at the short time scale. [ 107 ]

In the Kelvin–Voigt model, the second term on the left-hand side corresponds to the elastic torque. Since the spring and dash pot are connected in parallel, both elements have equal deformations. Therefore, the Kelvin–Voigt model reduces to the Newtonian case, i.e., Equation ( 1) , when the viscoelastic relaxa-tion time is large (or ω r is small), ω r → 0. Again, contrary to the Maxwell model, as the viscoelastic relaxation time decreases (or ω r increases), ω r = G / η → ∞, the elastic resistance of the material to the rod rotation becomes much stronger than the viscous resistance. This results in a singularity implying that the Kelvin–Voigt model also has to be augmented by inertial terms and some special care must be taken to analyze the rod dynamics in this case.

Assume that a static magnetic fi eld is applied in the y -direction and the rod magnetic moment initially points in the x -direction. Substituting the relation θ ϕ π+ = / 2 into Equations ( 7) and ( 8) , one can infer the difference in nanorod behavior in the Newtonian, Maxwell, and Kelvin–Voigt fl uids ( Figure 7 ).

The angular time dependences of the nanorods rotating in the Maxwell and simple viscous fl uids are somewhat sim-ilar. However, due to the elasticity of the Maxwell fl uid, the nanorod takes more time to reach the equilibrium. Rotation of the same nanorod in a simple Newtonian fl uid with the same viscosity is faster. Experimental verifi cation of this theory has been done in ref. [ 25 ] using a rotating magnetic fi eld. We will discuss these experiments below. We are not aware of any experimental work on the analysis of nanorod align-ment in viscoelastic coating fi lms, neither the Maxwell nor the Kelvin–Voigt fi lms. Therefore, it would be very interesting to design these experiments and compare the results with these theories.

The theoretical analysis of The Kelvin–Voigt fl uid leads to a surprising result: the nanorod is not able to completely coa-lign with the applied fi eld. The Kelvin–Voigt spring tries to pull the nanorod back to its initial position hence the nanorod

is tilted by angle ϕ eq with respect to the original direction not reaching ϕ π= / 2 corresponding to the fi eld direction. The dependence of this fi nal confi guration of the nanorod on the physical parameters of materials is found by letting d ϕ /d t = 0 in Equation ( 8) and applying the relation θ + ϕ = π/2 as

ω ϕ ω ϕ= cosr eq c eq

(9)

This effect of incomplete alignment of nanorods into the fi eld direction may cause some diffi culties in processing nano-composites with the Kelvin–Voigt precursors. Because of the lack of experimental verifi cation of this conclusion, it is diffi -cult to judge whether or not the developed theory adequately describes the experiment.

In this paper we demonstrated that the fi lm rheology sig-nifi cantly affects the rate of nanorod alignment into the fi eld direction. Therefore, the analysis of the fi lm rheology during nanocomposite processing is critical for control of the nanorod ordering in the fi lm plane. It appears that one can use the same nanorods for rheological characterization of the fi lms undergoing different sol/get transitions or curing. The basic physical principles of nanorod rotation in viscous and non-Newtonian fi lms can be applied to develop a robust method-ology for monitoring physicochemical processes in thin fi lms. A review of the recent progress in this direction is given in the next section.

4. Characterization of Rheological Properties of Thin Films with Magnetic Nanorods

One can take advantage of the characteristic features of the nanorod rotation in thin fi lms to probe the fl uid viscosity. As shown in the literature, the wall effects in the fi lm can be safely neglected when the fi lm thickness is about ten times greater than the nanorod diameter. [ 20,22,24,60,62,80,108 ] Therefore, having nanometer thin nanorods, one can probe the fl uid viscosity of tens of nanometers thick fi lms!



Figure 7. Nanorod rotation in a uniform fi eld directed perpendicularly to the original confi guration of the nanorod.

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4.1. Newtonian Viscous Films

As fi rst shown by Frenkel, [ 109 ] rotation of a rigid magnetic dipole in a Newtonian fl uid has a very interesting “fi ngerprint” which can be used for probing fl uid viscosity. The dipole rotation changes from synchronous, when the dipole continuously fol-lows the rotating fi eld, to asynchronous, when the dipole period-ically swings back and forth. This transition occurs at a certain frequency of the rotating magnetic fi eld. The Frenkel effect was actively employed in the last century to study the rod-like poly-mers and liquid crystals. [ 95,106 ] Direct observations of the critical behavior of the rod-like particles, however, were lacking. The critical transition from synchronous to asynchronous rotation was fi rst visualized only in 2005 when carbon nanotubes fi lled with magnetic nanoparticles were used for these purposes. [ 12 ] In this paper, a transition from synchronous to asynchronous rotation of magnetic nanotubes was detected and used to esti-mate magnetic properties of composite nanotubes.

These experiments pushed forward the development of MRS as a new method to study rheological properties of nanoliter droplets and thin fi lms. [ 20,22,25,63,93,110–116 ] The idea of using the transition from synchronous to asynchronous rotation was imple-mented by several groups employing different magnetic probes.

In rotating magnetic fi eld, the angle α in Equation ( 1) depends linearly on time, α = 2 πft , where f is the frequency of the rotating magnetic fi eld. Substituting the defi nition of angle ϕ ( t ) through the angles α ( t ), and θ( t ), ϕ ( t ) = 2 πft − θ ( t ), Equation ( 1) is rewritten as

γ π θ θ−⎛⎝⎜

⎞⎠⎟ =f

d

dtmB2 sin

(10)

As illustrated in Figure 8 c, Equation ( 1) has a steady state solution where d θ ( t )/d t = 0. This implies that the nanorod rotates with the frequency of the applied rotating fi eld, but the



Figure 8. Schematic of a) synchronous and b) asynchronous regimes of the nanorod rotation. Adapted with permission. [ 24 ] Copyright 2015, American Institute of Physics. c) The solutions of Equation ( 10) for different driving frequencies of magnetic fi eld. The lines without any symbols correspond to the change of α -angles with frequencies f = 1 Hz (straight solid line), f = 2 Hz (straight dashed line), and f = 3 Hz (straight dotted line). The corre-sponding ϕ -solutions are marked with different symbols. The nanorod rotates synchronously with magnetic fi eld at these frequencies, d) illustration of asynchronous rotation showing drastic difference in behavior of the solutions to Equation ( 10) above the critical frequency f = 3 Hz. The straight lines correspond to the change of the α -angles with frequencies f = 4 Hz (straight solid line), f = 5 Hz (straight dashed line), and f = 6 Hz (straight dotted line). The corresponding ϕ -solutions are shown in the same color and the lines are not straight as opposed to those in (a). Parameters of numerical experiment: nanorod length l = 6.6 µm, fl uid viscosity η = 16 × 10 −3 Pa s, magnetization M = 2.25 × 10 −14 A m 2 and magnetic fi eld B = 0.0015 T. Adapted with permission. [ 62 ] Copyright 2012, American Institute of Physics.

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direction of magnetization vector does not necessarily coin-cide with the fi eld direction making a fi nite angle θ with the fi eld. However, if the frequency becomes greater than a certain critical frequency given by equation c cπ ω γ= =2 /f mB , this solution disappears and the particle cannot rotate in unison with the fi eld anymore. [ 109 ] One observes that the particle oscil-lates and the angle θ formed by the magnetization vector and the fi eld vector changes with time. Figure 8 d illustrates this behavior: periodic solutions correspond to asynchronous rota-tion of magnetic nanorods.

Expressing magnetic moment through the material mag-netization M , m rod = π Mld 2 /4, we notice that the dimensionless critical frequency, f d , introduced as

d

cπη= = ⎛⎝⎜⎞⎠⎟ −

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

−83ln

2

ff

MB

l

dA

l

d

(11)

does not depend on the particular size of the nanorod. For a rod-like particle, this frequency depends only on the length-to-diameter ratio l / d [ 20,22,63,80 ] ( Figure 9 b). This effect of the rod-shaped particle is explained as follows: the viscous torque in Equation ( 10) is proportional to l 3 , while the magnetic torque is proportional to d 2 l . These two torques compensate each other at the critical frequency, resulting in a universal depend-ence ( 11) . This dependence plays an important role when one needs to choose a particular magnetic probe. It appears that one can select either material magnetization ( M ) or the rod aspect ratio ( l/d ) and operate within a particular frequency band to enable measurements of viscosity of the wide range of fl uids. [ 20,22,24,25,60,63,80 ]

An experimental realization of MRS can be done with a microscope and a high-speed camera. A transparent cuvette containing the material under study with the dispersed mag-netic nanorods is placed on the stage of an up-right optical microscope. The microscope is coupled with a high speed camera connected to and controlled by a computer. Some groups employ permanent magnets fi xed on a moving stage that are spun to produce the AC fi eld. [ 21,117 ] Other groups utilize current carrying coils that generate magnetic fi elds with a broad frequency band. [ 12,20,22,25,62,63,113,114,118–121 ] Rotational behavior

of smaller nanorods which cannot be traced with a dark fi eld microscope can be studied using polarization methods as dis-cussed in ref. [ 27 ] . The MRS theory was confi rmed by using different fl uids and different magnetic materials. As an illustra-tion of the excellent agreement of the theory with experiment, we present Figure 9 a, where a standard liquid with a tempera-ture-dependent viscosity was used in the MRS experiments.

4.2. Films Thickening with Time

The characterization of thin fi lms where materials are subject to chemical reactions and transformations is a challenge. [ 20,25,57–60 ] MRS allows one to make a step forward and study polymeri-zation and sol/gel transitions in thin fi lms. The MRS theory for the fi lms following the rheological equation of state ( 4) has been discussed in ref. [ 20 ] . This theory was applied to study photopolymerization synthesis of 2-hydroxyethyl-methacrylate (HEMA)/diethylene glycol dimethacrylate (DEGDMA)-based hydrogel. [ 20 ]

Employing optical spectroscopy, one can study the mecha-nisms of viscosity change. For example, HEMA polymer-izes through the carbon–carbon double bonds and crosslinks through the two double bonds in DEGDMA. Therefore, fol-lowing the rate of decrease of the carbon–carbon double bonds in the system by measuring the rate of disappearance of the 1635 cm −1 peak corresponding to the carbon–carbon double bonds, one can monitor the crosslinking and correlate it with the rheological data [ 20 ] ( Figure 10 ).

In many applications, the fi lm thickens upon evaporation of the solvent. [ 99 ] In Figure 11 , we present the analysis of thickening of the aqueous solution of mullite (3Al 2 O 3 ·2SiO 2 ). [ 60,122 ] Applying the MRS analysis at different time moments during fi lm evapo-ration, one can infer an exponential dependence of viscosity on time. The phenomenological parameters of this complex liquid were measured by fi tting the experimental data points using this exponential approximation. Moreover, one can relate the change of viscosity with the mullite concentration. This information is very important for interpretation of the thickening mechanism in materials with a complex structural organization, where the gelation mechanism involves multiple bonds.



Figure 9. a) Viscosity of the liquid standard S600 measured by MRS with the nanorods with different aspect ratios; squares and blue line show the table values of viscosity; open circles show measured viscosity from fi ve independent experiments with nanorods of different aspect ratios. b) Theo-retical dependence of dimensionless critical frequency f d on the nanorod aspect ratio. Adapted with permission. [ 62 ] Copyright 2012, American Institute of Physics.

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4.3. Films from Viscoelastic Fluids

There is a very limited amount of works on characterization of viscoelastic fi lms. Following ref. [ 25 ] consider the specifi cs of the particle rotation when the applied magnetic fi eld revolves at angular frequency ω . In this case, the relation θ + ϕ = ωt holds true. Substituting this relation into Equations 7 and 8 , the evolution of the rod orientation under a rotating fi eld can be obtained.

Figure 12 demonstrates the angular dependence on time for a ferromagnetic rod rotating in three different fl uids under two different rotating frequencies. Two distinguishable syn-chronous and asynchronous regimes and transition between them are observed only in the Maxwell and Newtonian fl uids. While the rod behavior in these fl uids is somewhat similar, the rod trajectory in the Maxwell fl uid demonstrates a slight skew relative to the rod trajectory in a Newtonian fl uid. The transition occurs at the same frequency ω c for both fl uids. Therefore, the critical frequency ω c = 2π f c cannot be used for characterization of the fl uid elasticity. Moreover, as shown in ref. [ 25 ] the average frequency of nanorod rotation (averaged over the period of the nanorod swinging back and force in the asynchronous regime) in the Maxwell and Newtonian fl uids



Figure 10. The solid line illustrates the change of relative viscosity ( η 0 is the solution viscosity prior to polymerization) with time of photopolymerization of the 4.5 wt% crosslinker solution (the left vertical-axis) and the stars show the conversion of the double bonds during the photopolymerization (the right vertical-axis) and the dashed line is a trend line. The inset shows an Fourier Transfom Infared (FTIR) spectrum of the solution near 1635 cm −1 before (the solid line) and after 60 s of polymerization (the dashed line). Adapted with permission. [ 20 ] Copyright 2012, American Chemical Society.

Figure 11. A gallery of images showing oscillations of the nanorod inside evaporating mullite sol. a) The time evolution of the magnetization vector spinning inside evaporating mullite droplet. The angular frequency of the magnetic fi eld is ω = 2π s −1 . The blue circles are the experimental data points extracted from the video and the red lines are the theoretical curves. b) Viscosity of the mullite solution as a function of mass concentration of mullite. Adapted with permission. [ 60 ] Copyright 2014, American Chemical Society.

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is the same! The only distinguishable difference between rod rotations in the Maxwell and Newtonian fl uids in the asyn-chronous regime is that the backward rotation (d ϕ /d t < 0) in the Maxwell fl uid is faster due to the additional restoring force from the spring.

Due to the presence of a parallel spring in the Kelvin–Voigt fl uid, the rod will always oscillate during rotation. Therefore, it is easy to distinguish the Kelvin–Voigt fl uid from the other two.

Ref. [ 25 ] reports a detailed analysis of rotation of a para-magnetic rod in a surfactant wormlike micellar solution cetylpyridinium chloride (CP+; Cl−) and sodium salicylate

(Na+; Sal−) (abbreviated as CPCl/NaSal) dispersed in a 0.5 M NaCl brine. The 2 wt% CPCl/NaSal micellar solution was used for this analysis and all experiments were conducted at T = 27 °C. This solution follows the Maxwell rheological model with G = 9.4 ± 0.2 Pa, τ = G/n = 0.14 ± 0.03 s, and η = 1.3 ± 0.3 Pa s. The phase diagram ( Figure 13 ) is taken from ref. [ 25 ] . Although experiments were performed with paramagnetic nanorods, similar conclusions can be drawn for a ferromagnetic rod. This diagram shows different rotation regimes of a paramagnetic rod in a Maxwell fl uid. The ( ω c , ω ) plane corresponds to a Newtonian fl uid and the ( ω c / ω r , ω )



Figure 13. Phase diagram showing different rotational behavior of the nanorod. The black line is the trajectory of the nanorod and the red line shows the average angular velocity. Pictures a) and b) illustrate the transition between the two regimes in Newtonian fl uids. Pictures c) and d) correspond to the oscillations in the vicinity of the equilibrium position for an elastic material under a rotating fi eld. Pictures e) and f) help to distinguish the asynchronous rotation of a rod in a Maxwell fl uid showing a faster backward rotation compared to a Newtonian fl uid. Reproduced with permission. [ 25 ] Copyright 2013, American Physical Society.

Figure 12. Time evolution of the rod orientation for the Newtonian, Maxwell, and Kelvin–Voigt fl uids under a rotating magnetic fi eld. a) ω < ω c and b) ω > ω c .

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plane corresponds to a pure elastic material. Figure 13 a,b illus-trates the transition between the two regimes in Newtonian fl uids. Figure 13 c,d corresponds to the oscillations in the vicinity of the equilibrium position for an elastic material under a rotating fi eld. Figure 13 e,f depicts the asynchronous rotation of a rod in a Maxwell fl uid showing a faster backward rotation compared to a Newtonian fl uid.

The following major difference between the Maxwell and Newtonian fl uids was revealed. In a Maxwell fl uid (marked in Figure 13 b), the frequency ω keeps increasing while the ampli-tude of the backward rotation ϕ B reaches a plateau. In contrast, the angle ϕ B for a Newtonian fl uid keeps decreasing and fi nally reaches zero (see Figure 14 ).

The MRS experimental results from ref. [ 25 ] show excellent agreement with the measurements obtained from a cone-and-plate rotational rheometer. As such, MRS appears to be a prom-ising technique for characterization of viscoelasticity of these fl uids.

5. Conclusion and Outlook of Further Developments

We discussed the basic principles of the fi eld guided align-ment of ferromagnetic nanorods in thin liquid fi lms. The focus was given to the composite processing applications. As demonstrated, the fi lm rheology signifi cantly affects the rate of nanorod alignment. Different rheological models were sur-veyed and an analysis of the nanorod rotation in different fi lms was presented. The distinguishable features in behavior of these fi lm/nanorod pairs were revealed. In manufacturing of composite fi lms, the initial orientation of nanorods is typically random. Therefore, nanorods oriented parallel and antipar-allel to the fi eld direction will require different times to reach the equilibrium confi guration. When the fi lm material under-goes a sol/gel transition or is subject to curing, the drag force increases with time thus hindering the nanorod alignment into the fi eld direction. In an assembly of nanorods, some nanorods are able to keep up with the fi eld, but some nanorods are not capable of making a full revolution when the liquid is still thin.

This fl ock of nanorods will be frozen before they align into the fi eld direction. The aspect ratio of nanorods along with the ini-tial viscosity of a thickening fl uid can be used to construct a phase diagram classifying the cases of complete alignment from those of partial alignment of nanorods in the cured fi lms. We also discussed some implications of the outlined theory to practically important cases.

Ferromagnetic nanorods can do more than the passive fi llers. With ferromagnetic nanorods, one can monitor and probe the fl uid rheology in thin fi lms during composite processing. We demonstrated that behavior of ferromagnetic nanorod in a rotating magnetic fi eld has a characteristic feature that can be used to probe the fl uid rheology. As the rotation frequency of the applied fi eld increases, the nanorods fi rst rotate in unison with the fi eld (synchronous rotation) and then when the fre-quency of rotation of the external fi eld passes some character-istic frequency, the nanorod rotation undergoes a transition from synchronous to asynchronous motion. This transition depends on the nanorod drag coeffi cient, hence on the fl uid vis-cosity. This effect laid the ground for the development of a new method, MRS. In MRS, one studies the rotation of magnetic nanorods by scanning over the frequency of the applied rotating magnetic fi eld. MRS with ferromagnetic nanorods allows for the characterization of Newtonian viscous fl uids, fl uids with a time-dependent viscosity, and also viscoelastic Maxwell and Kelvin–Voigt fl uids. Remarkably, an increase of viscosity can be traced beyond the point when the material undergoes transition to a gel and the domains start to appear.

In summary, we believe that the outlined physical princi-ples of nanorod rotation in complex fl uids and thin fi lms can be used to control nanorod alignment during manufacturing of thin composite fi lms and coatings. Augmented with a mag-netic rotational spectrometer, the manufacturing process can be strongly controlled and the fi lm rheology and its physicochem-ical state can be monitored in real time.

In order to make a breakthrough in manufacturing of composites which require a high concentration of magnetic nanorods, one needs to understand the long range magneto-static interactions between them. This challenging problem requires an interdisciplinary approach. New synthetic pathways for formation of stable colloids of ferromagnetic nanorods need to be developed. Rheological behavior of ferromagnetic liquid crystals has to be investigated and reliable models have to be established. The nanorod- and nanotube-based ferromagnetic liquids will open new horizons in manufacturing of multifunc-tional materials and thin fi lms with unprecedented properties. This exciting perspective already sets the scene for the new developments in this fascinating fi eld of multifunctional col-loids and many surprises are expected to be discovered.

Acknowledgements The authors are grateful for the fi nancial support of the National Science Foundation Grant PoLS 1305338, the Air Force Offi ce of Scientifi c Research, Grant No. FA9550-12-1 and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

Received: October 1, 2015 Revised: November 8, 2015

Published online:



Figure 14. The frequency dependence of ϕ B for the Newtonian and Maxwell fl uids. Adapted with permission. [ 25 ] Copyright 2013, American Physical Society.

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