Magnetophoretic long jump of magnetic microparticles in an engineered magnetic stray field landscape for highly localized and large throughput on-chip fractionation

Abstract

A common issue faced by magnetic particle-based Lab-on-a-chip systems, e.g, for medical diagnostics, is the intrinsic fabrication-related polydispersity in particle sizes and magnetic properties. Therefore, to reduce this variation, it is prudent to integrate a pre-separation procedure for the particles into the overall workflow of the system. In this work, a concept for the controlled on-chip fractionation of micron-sized superparamagnetic beads (SPBs) is introduced, which is applicable for sorting magnetic particles according to their properties in a continuous operation mode. A specifically designed magnetic domain pattern is imprinted into an exchange-biased thin film system to generate a tailored magnetic stray field landscape (MFL), enabling lateral transport of SPBs when superposing the MFL with external magnetic field pulses. The domain pattern consists of parallel stripes with gradually increasing and decreasing width, resulting in a step-wise jumping motion of SPBs with increasing/decreasing jump distance. SPBs with different magnetophoretic mobilities, determined, among others, by the particle size and magnetic susceptibility, discontinue their lateral motion at different jump distances, i.e., different lateral positions on the substrate. Thorough analysis of the motion using optical microscopy and particle tracking revealed that an increasing stripe width not only leads to a larger jump distance but also to a lowered jump velocity. As a consequence, particles are spatially separated according to their magnetic and structural properties with a large throughput and time efficiency, as simultaneous sorting occurs for all particles present on the substrate using a constant sequence of short external field pulses.

Figures (9)

• Figure 1: Schematic concept for the spatial fractionation of MPs in a microfluidic environment based on their directed transport above a magnetic stripe domain pattern with gradually increasing stripe width. MPs of varying characteristics (size, magnetic content distribution, surface properties) are expected to be immobilized at a locally different position along the domain pattern, depending on the respective stripe width. In this work, we experimentally demonstrate the feasibility of the fractionation concept by separating differently-sized MPs. The domains are magnetized as indicated by the grey arrows, resulting in a head-to-head (hh)/tail-to-tail (tt) magnetization configuration. A periodic sequence of trapezoidal magnetic field pulses in the vertical $z$-direction (solid, orange line) and the lateral $x$-direction (blue, dashed line) with a fixed alteration frequency is applied to achieve MP separation.
• Figure 2: Optical analysis for the motion behavior of SPBs dispersed in water on top of a magnetic stripe domain pattern with gradually varied stripe width. Shown are single optical microscope images (a)-(e) obtained at different recording times $t$ of a video recording taken with a frame rate of 25 fps. For the recorded experiment, a periodic sequence of trapezoidal magnetic field pulses with $T/4$ = 0.1s and $\mu_{0}H_{\mathrm{max,x}}~=~\mu_{0}H_{\mathrm{max,z}}~=~1mT$ was applied. The stripe domain pattern within the underlying substrate is indicated in each displayed frame by black dashed lines. For frames (a) and (b), SPBs (black spots) are transported from left to right across the substrate (see green arrows), leading eventually to immobilization at a lateral $x$-position of ca. 100µm, prominently visible in (c). Here, the external field sequence was stopped and paused for 8s, resulting in a halted SPB motion. Upon re-initialization of the external field sequence with inverted phase relation between field pulses in $z$- and $x$-direction, SPBs are transported into the opposite direction, emphasized in (d) and (e) by the green arrows. Frame (e) highlights the immobilization of SPBs this time around ca. 200µm $x$-position. Lateral particle density profiles, averaged along the $y$-dimension, are included as brown-filled curves in each frame.
• Figure 3: Motion behavior of SPBs dispersed in water on top of a magnetically patterned substrate with increasing stripe domain width for two different external magnetic field amplitudes in $z$-direction. A qualitative impression of the SPB transport is given by presenting averaged lateral intensity profiles of each recorded image frame as a function of recording time. The color scale indicates the image intensity; high intensity represents the background and low intensity the presence of SPB rows. For weak external magnetic field pulses of $\mu_{0}H_{\mathrm{z,ext}}~=~\mu_{0}H_{\mathrm{x,ext}}~=~1.0mT$ magnitude (a), fractions of mobile and immobile SPBs were distinguishable in dependence on the substrate position. The immobilization of SPBs occurred at a substrate area between $\approx60µm$ and $\approx200µm$ lateral $x$-position (marked by dashed white lines), coinciding with the substrate region of largest stripe domain width. Mobile SPBs were initially transported from left to right until immobilization. After a pause, the external field sequence was modified so that SPB transport from right to left was initiated. Most of the previously mobile SPBs regained their mobility by this. Stronger field pulses of $\mu_{0}H_{\mathrm{z,ext}}~=~2mT$ magnitude (b) lead to mobilization of SPBs even for the region of largest stripe domain width.
• Figure 4: Quantitative analysis of SPB motion dynamics in water above a magnetically patterned substrate with increasing stripe domain width. Starting from the evolution of averaged lateral intensity profiles acquired from each recorded image frame during the experiment (a), three SPB row trajectory snippets highlighted with white-framed rectangles were picked as examples for the identification of maximum particle velocity in (b) - (d). The period of the external magnetic field pulse sequence was chosen to be $T~=~0.8s$ with pulse magnitudes of $\mu_{0}H_{\mathrm{z,ext}}~=~\mu_{0}H_{\mathrm{x,ext}}~=~1mT$ to initiate SPB transport from left to right throughout all domain widths present in the underlying substrate (no immobilization). Maximum SPB row motion velocities, as a measure for their averaged mobility, were determined for the transport step initiated after changing the sign of the external field in $z$-direction. The red-marked areas for the exemplary trajectory data $x(t)$ in (b) - (d) were considered for the velocity calculation by fitting a Gaussian error function to the marked data and subsequently obtaining the velocity as the maximum of the fit's time derivative. Each velocity is assigned a transport step distance $\Delta x$, which corresponds to the difference between two consecutive plateaus in the trajectory data (see further explanation in the text). Plotting the obtained velocities as a function of the respective transport distance for the two SPB row trajectories that contain the exemplary steps of (b) - (d), a decreasing tendency for the velocity with larger transport steps (larger domain width) is observable (e).
• Figure 5: Fractionation of differently sized SPB populations on top of a magnetically stripe domain patterned substrate with increasing stripe width. (a) All SPBs are assembled on the left edge of the microscope's field of view, resembling minimal stripe domain width in the underlying substrate. (b) Upon application of an external magnetic field pulse sequence of constant frequency, all SPBs are transported to the right side of the field of view. (c) After a short time, the SPBs are immobilized (oscillatory motion) at specific locations. Statistically, smaller SPBs ($d~=~1µm$) are immobilized earlier (at lower lateral $x$-position) than larger SPBs ($d~=~2.8µm$). The two SPB populations were spatially separated into distinguishable fractions. Averaged intensity profiles (brown-filled curves) indicate the lateral extent of each fraction above the substrate surface.