Material- and size-selective separation mechanism of micro particles in frequency-modulated dielectrophoretic particle chromatography

Separation of (biological) particles ( (cid:28) 10µm ) according to size or other properties is an ongoing challenge in a variety of technical relevant ﬁelds. Dielectrophoresis is one method to separate particles according to a diversity of properties, and within the last decades a pool of dielectrophoretic separation techniques has been developed. However, many of them either suffer selectivity or throughput. We use simulation and experiments to investigate retention mechanisms in a novel DEP scheme, namely, frequency-modulated DEP. Results from experiments and simulation show a good agreement for the separation of binary PS particles mixtures with respect to size and more importantly, for the challenging task of separating equally sized microparticles according to surface functionalization alone. The separation with respect to size was performed using 2µm and 3µm sized particles, whereas separation with respect to surface functionalization was performed with 2µm particles. The results from this study can be used to solve challenging separation tasks, for example to separate particles with distributed properties.


Introduction
1 Re(CM) > 0, particles experience positive dielectrophoresis (pDEP) and move towards local field maxima, when Re(CM) < 0, particles experience negative dielectrophoresis (nDEP) and are repelled from field maxima. The frequency where Re(CM) equals zero is called crossover frequency. At this frequency, the particles do not experience a dielectrophoretic force. Due to 23 its dependency on field frequency and medium properties, Re(CM) can change its value or sign during an experiment, which 24 can result in a movement direction change of target particles. The net conductivity of a microparticle of non-conducting bulk 25 material in an electrolyte suspension can be calculated as 16, 23 26 σ p = σ bulk + 2K s r p . ( The conductivity is composed of the bulk material conductivity, σ bulk , and a part caused by the intrinsic double layer that forms 27 around suspended particles. The surface conductance K s comes from the ions in the electric double layer of the particle and can 28 increase the overall conductivity 16 . As a consequence, even particles with negligible bulk conductivity, such as the polystyrene 29 (PS) particles used in this work, can show pDEP.

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Equations (1), (2) and (3) show that the dielectrophoretic motion depends on material (e.g. conductivity and permittivity), 31 process parameters (e.g. medium conductivity, field strength and frequency) and size. The diversity of influencing variables 32 provides the opportunity to address different separation tasks. Depending on the process design, even specific multidimensional 33 tasks could solved in one set-up. Simultaneously, DEP-based separation requires careful design to enable a functioning 34 separation processes.

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In its 50 years of existence, many different techniques and designs have been established to perform a dielectrophoretic 36 separation of particles. One way to categorize the existing DEP techniques is whether a continuous or a chromatographic 37 separation is performed. Whereas continuous separation methods often focus on spatial separation or selective trapping 17, 24-26 , 38 chromatographic methods are usually batch or semi-batch processes and result in particle type-dependent residence times in 39 a separator. They are a promising approach to achieving separation of high purity or adjustability 27,28 . In this work, we use  Once per experiment a particle suspension is injected. The device is used for two different types of experiment. I) The crossover frequency of particles is determined using field-flow fractionation (FFF) at a fixed frequency f by comparing the elution profiles with and without applied voltage (V 0 ) (panel C). The obtained particle characteristics where used as input parameters for a full-scale simulation model realized in COMSOL Multiphysics to find suitable process parameters (panel D). II) Eventually, the set of process parameters is used as starting point for experiments to achieve a chromatographic separation by using frequency-modulated ( f = f (t)) dielectrophoretic particle chromatography (DPC) (panel E).
results against experiments. We will further capitalize on the simulation to predict parameters for separating polystyrene 73 particles of equal size based only on their surface conductance. Finally, we will compare the simulated and experimental results 74 of this separation. According to equation (3), the conductivity and thus crossover frequency of polystyrene particles depends 75 on their size and the yet unknown surface conductance K s . Thus, to perform a simulation we need to determine the crossover 76 frequency and the particle's K s -value. To do this, we use a fixed-frequency method (figure 1 C), which is explained in detail in 77 section 4.2: Here, the frequency is kept constant per particle injection (but is changed between experiments) and the particle 78 residence time is observed as a function of applied frequency. When the applied voltage is chosen careful, particles will either 79 be retarded by positive or negative DEP, or, in case the applied frequency closely matches the crossover frequency, particles 80 will not be retarded. Thus, by comparing the elution time as a function of frequency and comparing it against the elution time 81 without superimposed electric field, it is straight-forward to determine the crossover frequency. The determined K s -value can be 82 adjusted slightly to improve the match between experiments and simulation. To summarize our approach: 83 i. Find the crossover frequency and K s of the particles by performing fixed-frequency experiments (figure 1 C).

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ii.a. Use the obtained K s -value to determine suitable frequency ranges and perform frequency-modulated DPC experiments to 85 separate particles by size (figure 1 E).

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ii.b. Simulate the particles movement and compare the elution profiles of the experiment and the simulation. Apply moderate 87 changes to the simulation (e.g. simulated particle polarizability) to increase match with experiment (figure 1 D).

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iii Use simulation to design a different separation task: 89 iii.a. Find crossover frequency of polystyrene particles with different surface functionalization but same size. iii.b. Input crossover frequency into the simulation to find suitable center frequencies for separation in the experiment. iii.c. Perform the separation experimentally with optimized parameters from iii.b.

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2 Results and discussion 93 We first determine the surface conductance for the size-selective separation using fixed-frequency experiments (figure 1 C).

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Based on these results, we perform DPC experiments using the frequency-modulation technique (figure 1 E). We will then 95 perform simulations, using the same process parameters, to see how the simulation matches the experiments. Finally, we use 96 the simulation to find process parameters to separate a binary mixture of particles according to their surface modification.

Size-selective separation
Two monodisperse PS particle suspensions with diameters of 3.1 µm and 2.12 µm without an additional surface functionalization 99 were selected for generating experimental data to compare with the simulation. Since the surface conductance is an important 100 yet unknown characteristic of the particles, it was measured using fixed-frequency field-flow fractionation (see section 4.2).
Choosing the right voltage for the experiments is important, as a too high voltage would cause immobilization and too low 102 voltage would result in only slightly differences in the residence time distribution. For the larger particles a voltage of 120 V pp 103 was selected. The smaller particles required a higher voltage of 160 V pp , since the DEP force scales with particle volume.

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Frequencies between 180 kHz and 310 kHz were tested. Figure  residence time around 290 kHz. Since the dielectrophoretic mobility for smaller particles is lower, the crossover is less clear.

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Nevertheless, knowing the crossover is close to this value, a surface conductance of 0.9 nS was assumed for further steps.

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Now that we know K s and crossover frequency of both particles, we can select suitable frequency ranges for separation.   Overall, the simulation gives valuable insight into the particle behaviour and trajectories in the channel and is able to 183 support the process design. Additionally, it can be used to study the impact of side effects, since the simulation is able to isolate 184 the movement due to drag, gravitation and dielectrophoresis and therefore a significant divergence between experiment and 185 simulation suggests the presence of side effects. In this section, we will demonstrate the separation of polystyrene particles of almost equal size based on their surface 188 functionalization. Firstly, we determine the crossover frequency using fixed-frequency experiments. Then, we input the 189 crossover frequency into the simulation to find ideal separation parameters. Finally, we will use these parameters to separate 190 the particles efficiently in an experiment. The separation was conducted using the already characterized 2.12 µm PS particles 191 without surface functionalization (plain) and 2 µm carboxy functionalized PS particles (COOH).

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The fixed-frequency experiments (see SI figure 1) suggest a crossover close to 210 kHz for the carboxylated particles, 193 resulting in a surface conductance of K s =0.6 nS, significantly lower compared to K s of the plain particles (K s =0.9 nS). The 194 voltage for separating theses two particle types was fixed at 160 V pp because this voltage showed the highest separation To conclude, we have used simulation and experiments to demonstrate three different particle behaviors in frequency-modulated 227 chromatography, i.e., retardation due to nDEP or pDEP-dominated behavior or a balanced behavior leading to no retardation. 228 We have firstly addressed size-selective separation of two different PS particles to investigate the particle retention mechanisms.

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Here, the simulation model supported our previous hypothesis. We then addressed the more challenging material-selective 230 separation of particles of equal size to show the power of the simulation method: We used the simulation to find suitable 231 operating parameters which allow a separation of two equally sized 2 µm PS particles with different surface functionalization.

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In the future, our simulation model can be used as a valuable tool to design operating schemes capable of addressing more 233 complex separation tasks, for example shape sensitivity or heterogeneous samples, or to study how a reduction of the applied  pDEP in one part of the frequency range and nDEP in another one. Consequently, three different particle behaviours can be 254 distinguished, as long as the crossover frequency is between the maximum and the minimum value of the modulation spectrum.

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Firstly, when particle shows more pDEP than nDEP in the applied frequency range, they tend to migrate towards the field with T max being the maximum of the residence time distributions and w x the full width at half maximum (FWHM). In 301 addition to the resolution the purity of each fraction can be used to describe the outcome of an separation, which here is defined by using t as time and I x (t) as fluorescence intensity at time t. This sum is normalized on its maximum cumulated intensity 304 and therefore always reaching 1 at the end of the experiment (t = 120 s).

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The electric field in experiment and simulation is generated by an electrode array. In these arrays an electrode with a 316 applied potential of V RMS is neighboured by two electrodes on GND (0 V) potential (figure 5). A thin PDMS layer is placed 317 on top of the electrodes. The thickness has not been determined experimentally but is significantly below 3 µm according to 318 literature 39 . It has been used as a fitting factor and the best match between experiment and simulation was achieved when using 319 h PDMS =1.75 µm. Placing PDMS as dielectric material on top of the electrode array generates a high-pass filter. The effect was 320 simulated and implemented into to the model (SI figure 3). Coupling of fluid field and electric field was not added, since the 321 experiments were conducted at low medium conductivity and sufficiently high frequencies. The first point does reduce the effect 322 of electrothermal movement (heat loss density= σ m E 2 ) whereas the latter suppresses the influence of AC electroosmosis 40, 41 .

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However, in microfluidics unspecific adhesion, (electro-)thermal flow, hydrodynamic lift, particle-particle interactions 324 and/or electrokinetic phenomena can play an important role, but are hard to quantify and therefore to implement. As a result, 325 experimental training data was used to get a good match by adjusting some parameters of the simulation in a reasonable range.

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The adjusted parameters were PDMS isolation thickness and the surface conductance (chapter 2.1) as well as the particle 327 release offset (see below).

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The second part of the simulation is the particle movement description. Particles are experiencing positive and negative 329 dielectrophoresis, viscous drag, and gravitation. All particles are assumed to be massless, which is reasonable given their small 330 stopping distance, to reduce the computational effort. Additionally, as soon as particles reach the ceiling or bottom they are 331 11/14 assumed to be trapped, which is not always true in reality. Once particles are trapped in the simulation they stay at their location. This is not valid for a DPC experiment, which leads to the third part of the model which is formed by the COMSOL-MATLAB 333 interaction.

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Using MATLAB, the movement of the particles through the channel is divided into multiple parts. In the experiment 335 the valve to inject the particles is opened for two seconds. In this time period, particles are entering the channel at different type are randomly placed at the beginning in a range of heights between 10 µm and 70 µm.

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After the particles are released they experience dielectrophoresis and may eventually reach a boundary where they freeze.

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Consequently, at sufficient high voltages no particles would exit the channel in the simulation. To overcome this issue, a 342 MATLAB script checks Re(CM) for changes of its sign and stops the simulation as the value reaches zero. At this point the 343 model checks for particles adhering to the wall and repositions them up to 10 µm orthogonal to the wall into the channel.

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The extend of the manipulation of the particles position is randomly chosen between 0 µm and 10 µm to incorporate the 345 inhomogeneous nature of particle-wall interactions, which effectively can lead to broader, less pronounced elution peaks.

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Particle positions are logged to calculate residence time distributions. Since the model contains random components multiple 347 runs are necessary to check for statistical validity (SI figure 6).

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Data availability 349 The datasets generated during and/or analyzed during the current study are available from the corresponding author on 350 reasonable request.