The developed single-particle microrheometer that combines the magnetic tweezers with TIRM. In this setup, two sets of four electromagnetic pole pieces are symmetrically arranged in the upper and lower planes of the sample cell in standard TIRM to achieve a three-dimensional position control. A top view is inserted which shows a probe microsphere from the CCD camera under the evanescent wave illumination surrounded by the tips of the eight magnetic poles.
Schematic drawing of the incorporated magnetic tweezers is shown on the left picture. The real instrument from the top view (upper picture) and side view (lower picture) is shown in the right picture.
The four core pieces of the upper set of magnetic poles under optical microscope. The tip of each pole is mechanically sharpened to less than ∼100 μm in size in order to optimize the generated magnetic driving force. The shape of the below four poles is similar, and placed with desirable distance to the sample stage.
Different modes are used to generate the upwards and downwards forces on the probe paramagnetic particle. The above three pictures are from the top view, and the below pictures are from the side view. From left to right: force towards the pole 0 is generated when pole 0 is turned on; a net upwards force is generated when pole 0 and 2 are turned on; and a net downwards force is generated by turning on poles 4, 5, 6, and 7 with proper voltages.
The typical displacement, h (-□-, left Y axis) and the original intensity I (-△-, right Y axis) of the probe particle under the alternative forces in upwards and downwards directions during the calibration. The experiments were performed in 40 wt. % sucrose solution containing 4.5 μm paramagnetic particles coated with PEG polymers. The red square wave indicates the direction of the generated magnetic force, with the starting upwards force by two-tips mode, following by downwards force by four-tips mode.
The applied voltage dependence of the upwards effective magnetic force, F net, generated on the 4.5 μm paramagnetic particle coating with poly(ethylene glycol) (PEG) (Mw = 1000 g/mol) polymers. The insets show F net in dependence of h under upwards drag at voltage = 0.8 V. The dashed line gives the averaged value. As h increases, noises increase, leading to a larger fluctuation of F net.
The applied voltage dependence of the downwards effective magnetic force, F net, generated on the 4.5 μm paramagnetic particle coating with PEG (Mw = 1000 g/mol) polymers. The inset shows F net in dependence of h under downwards drag at voltage = 4.0 V. The dashed line gives the averaged value.
Probe particle displacements, h(t), measured under oscillatory forces at 1 Hz (black), 2 Hz (red), and 5 Hz (blue) with the same force amplitude in gelatin aqueous solution.
The modulus G ″ of sucrose solution measured by our magnetic tweezers (MT) microrheometer under force amplitude = 1.14 pN (black solid circle). The solid line shows a linear fit, leading to the viscosity η = G ″/ω which is a constant in the measurable range.
The modulus G ′ and G ″ of 2 wt. % PEG solution measured by our MT microrheometer under force amplitude = 1.14/1.75 pN (G ′: -■-, G ″: -△-) and the bulk rheometer (G ′: -■-, G ″: -△-) with strain = 5%.
The elastic modulus G ′ at h c = 135 (-○-) and 17 nm (-△-) (upper figure); and the loss modulus G ″ at h c = 135 (-●-) and 17 nm (-▲-) (lower figure) measured at frequency = 0.1 and 0.2 Hz. The measurements were conducted in 4.5 wt. % PNIPAM microgel solution under force amplitude = 8.60 pN.
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