Toward nanoscale multiferroic devices: Magnetic field-directed self-assembly and chaining in Janus nanofibers

Nanofibers have unique properties and potential application in photonics, nanoelectronics, biosensors, and optoelectronics.^1–3 Specifically, multiferroic Janus nanofibers have been of interest recently because their predicted and measured magnetoelectric coupling is higher than bulk thin films.^4–6 These fibers couple piezoelectricity and magnetostriction, allowing electrical control of magnetism and vice-versa.^4,7–9 Janus fibers consist of two materials with the interface along the length of the fiber.¹⁰ Self-assembly of nanofibers into structured devices is a potential means to leverage their enhanced properties, and include electric- and magnetic-field-assisted alignment, and Langmuir-Blodgett film-formation.^3,11 In particular, in magnetic-field-driven assembly, when a magnetic field is applied to a suspension of magnetic particles their moments align with the external magnetic field and experience an attractive dipolar interaction. This kind of chaining has been studied extensively in nanoparticle systems.^12–20 One recent experiment studied dynamic assembly of isolated clusters of ferromagnetic rods in aqueous solutions at small fields ∼ 1 mT.²¹ In this article we present optical microscope observations of chaining in Janus BaTiO₃: CoFe₂O₄ nanofibers (Fig. 1a) colloidally suspended in polyvinyl alcohol(PVA)/water solutions, and analyze the assembled structures using standard models for dipolar chaining.

While kinetic growth of colloidal small particle ( < 1 μm diameter) chains is well-modeled using a dynamic scaling power law called diffusion-limited cluster aggregation(DLCA),^{13–15,19,22–24} there has been concern about its applicability to suspensions of larger particles. However because of the quasi-2D aspect of thin spin-coated suspensions, DLCA’s scaling theory has been applied to describe growth of suspensions with larger particles( > 1μm).^12,19,25

DLCA is applied by first determining the average chain length (〈L(t)〉) and the weighted chain length (〈S(t)〉) which are given as follows,

Here n_s is the number of chains with length s.^22–24 At long times, 〈L(t)〉 and 〈S(t)〉 follow dynamic scaling theory such that $⟨L(t)⟩∼tz′$ and 〈S(t)〉 ∼ t^z. $z′$ and z are the dynamic scaling exponents for 〈L(t)〉 and 〈S(t)〉 respectively and are normally assumed to be equal and independent of concentration and magnetic field strength. For nanoparticles, a scale parameter, $z′$⁠, of 0.5 with respect to time and 4/3 for magnetic field, was observed for diffusion limited chaining.¹⁴ For isotropic diffusive aggregation the scaling factor has been reported to be ∼1.4.¹⁹ Models of both mass independent and diffusion limited chaining found scaling parameters of z = 1 and z = 0.5 respectively.²³ 

The power scaling law for aggregation is,

where $w$ is a scaling exponent that describes the reduction of n_s, τ is a static exponent that describes the relation between cluster size and cluster density, and the function f(s/t^z) approaches 1 when s < < t^z and 0 for s > > t^z. At long times Equation 2 simplifies to n_s ∼ $t−w$⁠.²⁴ Thus a crossover parameter, Δ = $w$/z, can be calculated, which helps in identifying the type of aggregation that is occurring.^12,18,24 The crossover parameter is defined as,

where CC is dominated by chains aggregating with chains and fibers, and FC is dominated by chains aggregating with “individual” fibers or small chains.¹² For diffusion limited chaining, if Δ > 1 then z = $z′$ and if Δ < 1 then $z′$ =$w$⁠.^16,18 The crossover exponent has been used to analyze chaining of 10 μm non-magnetic particles in ferrofluids and the scaling exponents changed as a function of concentration and magnetic field.¹² Following this approach, we used the three different scaling exponents and the crossover parameter extracted from optical images to characterize our system.

PVA/water/fiber solutions are spin coated onto clean circular glass wafers, leaving a thin quasi-2D polymer layer, that is dried in a uniaxial magnetic field. To measure chaining in situ a microscope was incorporated into an electromagnet, as shown in Figure 1b, which allowed for real-time videos of assembly. After the samples were fully dried they were imaged separately to obtain the final length and angular distribution. To obtain length and orientation data, the images and videos are processed using software from NIH called ImageJ.²⁶ 

Our Janus nanofibers consist of two hemi-cylinders produced by electrospinning together sol-gel solutions of BaTiO₃ (62% mass) and CoFe₂O₄(38%).¹⁰ The electrospun fibers have an average diameter of 1μm and are ground with mortar and pestle producing fibers of various lengths. To obtain a colloidally stable solution the fibers are coated with citric acid. In order to increase electrostatic repulsion, the pH was increased using 0.1M NaOH to ∼10. The fibers are suspended in a solution of polyvinyl alcohol and water to slow aggregation, sedimentation and to provide a curable medium to immobilize the chains once formed. Due to the size of the fibers significant sedimentation occurs in ∼45 minutes, so the solutions are sonicated before being spin coated onto glass wafers(VWR VistaVision^TM Cover Glasses). Three different concentrations of fibers (0.25, 0.18, 0.083 mg mL⁻¹) and a range of magnetic fields were used to study nanofiber chaining.

The real time measurements were taken with a Canon Rebel T2i EOS 550D over a time of 10 minutes with 24 frames per second. The videos were spliced into frames which are 5 seconds apart and processed with NIH software, ImageJ.²⁶ The videos consist of 1920x1080 pixels² with RGB color scale, and cover an area of 2991.36x1620.32μm². For this magnification one pixel was approximately equal to the fiber diameter which made it difficult to account for the smallest fibers but did not hinder measurement of the length distribution.

Post-curing, grayscale images were taken in bright field with a Nikon Eclipse LV150 microscope using a 5x Plan Fluor objective and a CCD camera(QImaging Exi Aqua, Monochrome) with an area of 1392x1040 pixels², i.e. a field of view of 1795.68x1341.6μm². To ensure consistency the images are taken at the center of the sample where it takes the longest time to cure. Thresholding is used to separate the fibers from the background. The image is then smoothed to limit noise due to small particles and optical artifacts. The thresholded pictures are compared with the original image. ImageJ’s particle analysis and directionality subroutines are used to obtain the chain length, orientation and angular dispersion. The angular dispersion is the standard deviation of the Gaussian distribution of fibers orientation, and allows us to measure how well aligned the chained fibers are with respect to the field. The real time chaining videos are processed in the same way except that n₁ is also extracted. n₁ is more difficult to extract since our fibers are of various length but we focus on the smallest fibers with aspect ratios less than 2. These particles are the smallest building blocks of chains and thus n₁ should decrease with time as the average chain length increases. The experiment was repeated three times at each field to make sure that the data were consistent and to average out optical abnormalities.

Figures 2a–b show representative images of chains for the highest and lowest concentrations, highlighting the significant difference in chain length for the two cases. Figure 2c plots average chain length for the three concentrations with respect to magnetic field. For the weakest concentration, the increase in chain length follows the same 4/3 power law that Fermigier et al. observed for nanoparticle chaining(dashed line).¹⁴ At twice and three times the concentration, chain length increases rapidly at low fields, but above 100 Oe also follows the chaining power law(dash dot and solid lines).¹⁴ We hypothesize that the rapid increase in chain length at higher fiber concentration is a field driven homogenization process where shorter fibers aggregate to form long fibers, then chain together in dipolar or tip-tip fashion at higher magnetic fields. The difference in average chain length for different concentrations is attributed to the increase in the amount of nanofibers available to form chains.

Figure 3 shows that as magnetic field increases the angular dispersion decreases. The longer the average chain length the more well aligned the sample is at higher magnetic fields. Below 100 Oe the dispersion is flat while the chain length increases rapidly and then starts to decrease monotonically as field increases. It should also be noted that the dispersion does not show drastically different dynamics as the concentration increases.

Chain length verses time is shown in Figure 4 for the middle concentration (volume fraction 3.0 * 10⁻⁵) and a range of magnetic fields to obtain the dynamic parameters. At long times the growth should be linear according to dynamic scaling theory, log₁₀(〈L〉) ∼ $z′$* log₁₀(t). To show this the data are transformed and fitted with a line where the slope is the dynamic exponent. To obtain $w$⁠, n_s is fitted at long times in the same way as for average chain length and 〈S(t)〉 to extract their scaling exponents respectively. To obtain n₁, we used ImageJ to extract the number of “individual” fibers by picking out the chains with aspect ratios of 2 or less.¹⁶ ImageJ’s circularity limits are used to count these objects. Chains will form from the smallest fibers, but we assume that if a chain has an aspect ratio larger than 2 it is not an individual fiber. This is reasonable because when n₁ is plotted we find a negative slope as expected for $w$⁠. The crossover exponent, Δ, is then calculated by dividing w by z.^12,18,24

Table I summarizes the dynamic parameters. At low fields the scaling parameter $z′$ does not follow either mass or diffusion limited aggregation, implying a change in diffusion dynamics. The scaling parameter(⁠$z′$⁠) does approach the ideal diffusion limited state at higher fields, and field dependence is also observed for $w$ and z. The crossover exponent(Δ) does show diffusion limited chaining in the regime where the fiber and chains are expected to aggregate simultaneously, and z and $z′$ show large deviations in their values even when Δ > 1 as do w and $z′$ when Δ < 1. The fluctuations in $w$ and Δ indicate that nanofiber chaining is not fully described by diffusion limited chaining. This may be due to the various sizes of the fibers with the smallest experiencing Brownian motion and the largest not.

In conclusion, we investigated chaining dynamics in multiferroic nanofibers and found significant deviations from the conventional DLCA model especially at higher nanofiber concentration. Neither the magnetic-field dependence of the dynamic scaling parameters, nor the rapid increase in chain length at low fields are expected from standard chaining models. In particular, the rapid increase in chain length at low fields and high concentrations suggests a field driven smoothing of chain length occurs prior to a transition to a standard chaining process at higher fields. Additional modeling to address the size and aspect ratio polydispersity in electrospun nanofibers, as well as the change in magnetic field profile during chain growth, especially for high fields and high concentrations, will be required to explain our observed assembly dynamics. The control of both alignment and chain length is integral to probing the magnetoelectric effect in these nanofibers. Future work will apply similar analyses to study the multiferroic coupling within assembled chains of nanofibers.

The authors acknowledge helpful conversations with Professor Randall Erb at Northeastern University, as well as with Annastasia Haynie. This work was supported by NSF under award number CMMI-1436560.