^{1}, Alexey Aprelev

^{2}, Mikhail N. Zakharov

^{2,3}, Guzeliya Korneva

^{4,5}, Yury Gogotsi

^{4}and Konstantin G. Kornev

^{1,a)}

### Abstract

We report on the development of a multifunctional magnetic rotator that has been built and used during the last five years by two groups from Clemson and Drexel Universities studying the rheological properties of microdroplets. This magnetic rotator allows one to generate rotating magnetic fields in a broad frequency band, from hertz to tens kilohertz. We illustrate its flexibility and robustness by conducting the rheological studies of simple and polymeric fluids at the nano and microscale. First we reproduce a temperature-dependent viscosity of a synthetic oil used as a viscosity standard. Magnetic rotational spectroscopy with suspended nickel nanorods was used in these studies. As a second example, we converted the magnetic rotator into a pump with precise controlled flow modulation. Using multiwalled carbon nanotubes, we were able to estimate the shear modulus of sickle hemoglobin polymer. We believe that this multifunctional magnetic system will be useful not only for micro and nanorheological studies, but it will find much broader applications requiring remote controlled manipulation of micro and nanoobjects.

We thank Gelester Baskett for the assistance with the synthesis of Ni nanorods, and David White for his help at different stages of this project. The authors thank Professor F. A. Ferrone for suggesting to study hemoglobin rheology and for general advice during the project. The authors are grateful for the financial support of National Science Foundation, Grant EFRI 0937985 and National Institutes of Health Grants R01HL057549 and P01HL058512.

I. INTRODUCTION

II. DESIGN OF THE MAGNETIC ROTATOR

III. MEASURING A TEMPERATURE-DEPENDENT VISCOSITY OF A MICRODROPLET

A. Theory of nanorod rotation in liquids with constant viscosity

B. Experiments and discussion

IV. MEASURING THE MICRO RIGIDITY OF SICKLE HEMOGLOBIN POLYMER

V. CONCLUSIONS

##### B81B

##### B82B1/00

##### F15D

## Figures

(a) Circuit of magnetic rotator. (b) Circuit of the voltage-current converter. (c) An example of magnetic rotator. (d) Experimental measurements of the magnetic field in the middle of the two face-to-face placed coils as a function of applied current.

(a) Circuit of magnetic rotator. (b) Circuit of the voltage-current converter. (c) An example of magnetic rotator. (d) Experimental measurements of the magnetic field in the middle of the two face-to-face placed coils as a function of applied current.

A uniform magnetic field **B** rotates in a plane of this figure making angle α(t) with the reference X-axis. Magnetic moment of the nanorod, **M**, makes angle θ (t) with the field direction. Magnetic moment forms angle φ(t) with the reference X-axis.

A uniform magnetic field **B** rotates in a plane of this figure making angle α(t) with the reference X-axis. Magnetic moment of the nanorod, **M**, makes angle θ (t) with the field direction. Magnetic moment forms angle φ(t) with the reference X-axis.

Integral curves of Eq. (4) showing the solution behavior for different parameters *V*(*l*, *d*, η, *B*, *m*, *f*) at different initial conditions θ_{0}. (a) V<1. (b) V>1.

Integral curves of Eq. (4) showing the solution behavior for different parameters *V*(*l*, *d*, η, *B*, *m*, *f*) at different initial conditions θ_{0}. (a) V<1. (b) V>1.

(a) The φ-solutions of Eq. (4) for different driving frequencies of magnetic field. The upper straight lines correspond to the change of alpha-angles with frequencies f = 1 Hz (straight solid line), f = 2 Hz (straight dashed line), and f = 3 Hz (straight dotted line). The corresponding φ-solutions are marked with different symbols. The nanorod rotates synchronously with magnetic field at these frequencies. (b) The φ-solution of Eq. (4) for different driving frequencies of magnetic field. The upper straight lines correspond to the change of alpha-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 marked with different symbols.

(a) The φ-solutions of Eq. (4) for different driving frequencies of magnetic field. The upper straight lines correspond to the change of alpha-angles with frequencies f = 1 Hz (straight solid line), f = 2 Hz (straight dashed line), and f = 3 Hz (straight dotted line). The corresponding φ-solutions are marked with different symbols. The nanorod rotates synchronously with magnetic field at these frequencies. (b) The φ-solution of Eq. (4) for different driving frequencies of magnetic field. The upper straight lines correspond to the change of alpha-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 marked with different symbols.

Dependence of dimensionless critical frequency f_{d} on nanorod aspect ratio.

Dependence of dimensionless critical frequency f_{d} on nanorod aspect ratio.

(a) Viscosity of the viscosity standard liquid S600 measured by rotation of the nanorods with different aspect ratios; squares and blue line show the table values of the viscosity; open circles show measured viscosity from 5 independent experiments with nanorods of different aspect ratios. A data point corresponding to the 927.5 mPa·s viscosity was used to obtain constant χ = 290. (b) Two sinusoidal signals sent to two coils at the time moments (c)–(f). Following the generated rotating field, the Ni nanorod rotates counterclockwise at 2 Hz frequency.

(a) Viscosity of the viscosity standard liquid S600 measured by rotation of the nanorods with different aspect ratios; squares and blue line show the table values of the viscosity; open circles show measured viscosity from 5 independent experiments with nanorods of different aspect ratios. A data point corresponding to the 927.5 mPa·s viscosity was used to obtain constant χ = 290. (b) Two sinusoidal signals sent to two coils at the time moments (c)–(f). Following the generated rotating field, the Ni nanorod rotates counterclockwise at 2 Hz frequency.

(a) Schematic of the setup for measurements of shear modulus of polymeric filaments. (b) Schematic of a carbon nanotube embedded into the column of sickle cell hemoglobin. (c)–(e) Three images showing the growth of sickle hemoglobin domain initiated by the laser pulse. The black spot corresponds to the cross-section of a nucleating polymerized domain which is almost circular in the cross-section. The nanotube is directed parallel to the coverslips. One end of the nanotube is fixed by the polymerized domain and the rest of the nanotube is exposed to non-polymerized fluid. As the polymerized domain expands, it creates the side dendrites and the column is no longer circular in cross section.

(a) Schematic of the setup for measurements of shear modulus of polymeric filaments. (b) Schematic of a carbon nanotube embedded into the column of sickle cell hemoglobin. (c)–(e) Three images showing the growth of sickle hemoglobin domain initiated by the laser pulse. The black spot corresponds to the cross-section of a nucleating polymerized domain which is almost circular in the cross-section. The nanotube is directed parallel to the coverslips. One end of the nanotube is fixed by the polymerized domain and the rest of the nanotube is exposed to non-polymerized fluid. As the polymerized domain expands, it creates the side dendrites and the column is no longer circular in cross section.

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