Density as a Tool for Chemistry and Biology

Density, defined as the ratio of the mass and volume of an object, is a fundamental characteristic of all matter. In our lab, we have developed two density-based platforms—aqueous multiphase systems (AMPS) and magnetic levitation (MagLev)—that can be used to separate valuable materials, make medical diagnosis, enable self-assembly, probe chemical and biological binding events, and perform quality control.


Aqueous multiphase systems (AMPS) are aqueous mixtures of polymers, salts, and surfactants that spontaneously separate, like oil and water, into discrete phases having distinct densities (Figure 1).1 AMPS provide seven distinct advantages: (i) AMPS can be designed to have two to six phases (we have demonstrated over 300 different systems). (ii) The difference in density between the phases of an AMPS can be tuned to be very small (Δρ ~ 0.0003 g/cm-3). (iii) The molecularly sharp interfaces between the phases of an AMPS provide bins to separate and extract objects based on their densities. (iv) They can be made to be biocompatible and, because they have extremely low interfacial surface energy between the phases (nJ/m-2 to mJ/m-2), can be used to separate fragile objects, such as cells. (v) Unlike other density gradient systems, AMPS are thermodynamically stable: since the phases are immiscible, diffusional mixing of phases does not occur, and the steps in density reform following agitation. (vi) They are scalable—they can be used in a capillary tube for low-cost diagnostics, or in a Falcon tube for the large-scale separation of whole blood. (vii) The use of AMPS requires minimal training and only a benchtop centrifuge is necessary to perform an assay or separation.

Figure 1. (A) Beads of different densities in a mixture of five different phases. (B) Phases separate according to density after centrifugation; beads of intermediate density are trapped at interfaces between phases. (C) A plot of the distribution of densities of the phases.
Separations with AMPS


Many applications that exploit the unique properties of nanoparticles require particles (rods, spheres, etc.) having high purity. We have used AMPS as a means to separate nanoparticles based on their shape and size.2 When a particle is centrifuged in a viscous media (a process referred to as “rate-zonal centrifugation”), the hydrodynamic behavior of the particle depends on its shape and size. We exploit this behavior to enrich gold nanorods from 48% to 99% purity in less than ten minutes using a benchtop centrifuge (Figure 2).

Figure 2. (A) Microscope image of gold nanoparticles (NP) mixed with gold nanorods. (B) Phases separate according to density after centrifugation. (C) Microscope images of aliquots taken from each phase: [top] gold nanorods; [middle] gold NP; [bottom] high density clusters.

Using AMPS, we have created a simple method to enrich reticulocytes (immature red blood cells) that can be used to grow malaria species better than conventional reticulocyte purification methods.3

Diagnostics with AMPS

In certain cases, the ability to separate cells by density can provide a means to diagnose disease.4-6 For example, sickle cell disease is a genetic disease that approximately 300,000 children are born with each year. Most of these children are undiagnosed and at high risk for childhood mortality even though simple and effective interventions exist to manage the disease. The morphological changes in sickle cell disease lead to the formation of very dense erythrocytes that can be separated using AMPS. Using capillary tubes, AMPS, and portable centrifuges, we have created a low-cost, visual test for sickle cell disease that can be performed in ~15 minutes.6 After initial validation in the U.S., we worked with partners in Zambia to test the device in a larger population and to assess feasibility of the design in rural health centers.5



The second technique we developed to analyze density with minimal equipment is magnetic levitation.7-8 Using two magnets aligned with the like-poles facing, we create a magnetic field gradient, and we typically use a linear one. When a diamagnetic object is placed in a paramagnetic solution within the magnetic field gradient, the paramagnetic fluid will be attracted to the highest field (closer to the magnets) and will push diamagnetic object towards the point of lowest field (the midpoint between the two magnets). When the object has a different density than the solution, an additional buoyant force pushes the object away from the center, and towards the top (float) or bottom (sink) of the solution. The balance of the magnetic and buoyant forces results in a stable levitation height within the paramagnetic fluid that depends on the density (Figure 3). We have developed five major configurations of MagLev for density-based measurements and manipulations: (i) “standard” MagLev,8 (ii) “axial” MagLev (Figure 3b), (ii) “tilted” MagLev,9 (iv) MagLev optimized for high-sensitivity measurements,10 and (vi) MagLev optimized for high-throughput measurements.11 The paramagnetic fluid used in MagLev can consist of simple paramagnetic salts (e.g., MnCl2 or GdCl3) in water,8 biologically compatible paramagnetic chelates (e.g., Gadovist) in water,11-12 hydrophobic chelates (e.g., gadolinium(III) diethylenetriamine triacetic acid didecyldiacetamide) in hydrophobic solvents,13 paramagnetic ionic liquids,14 or paramagnetic AMPS.15

Density-Fig-3 Figure 3 Overview of MagLev (A) The “standard MagLev” device comprises two like-poles facing, block magnets (NdFeB permanent magnets, W×L×H: 50.8 mm × 50.8 mm × 25.4 mm) positioned coaxially with a distance of separation of 45.0 mm. A standard cuvette (45 mm in height) is a common container used to levitate diamagnetic samples (represented by a 3-mm sphere) in a paramagnetic medium (e.g., aqueous solutions of MnCl2). The strength of the magnetic field is ~0.38 T at the center of the top face of the bottom magnet (N52 grade). (B) The “axial MagLev” device uses two like-poles facing ring magnets (NdFeB permanent magnets, OD×ID×H: 76.2 mm × 25.4 mm × 25.4 mm) positioned coaxially with a distance of separation of 15.0 mm. The same cuvette containing the 3-mm sphere in A is included to show the size of the devices. The strength of the magnetic field is ~0.33 T at the center of the top face of the bottom magnet (N45 grade).


Over a billion pounds of plastics are recycled each year. The value of recycled plastics is related to its final purity. MagLev is able to levitate several objects simultaneously at different levitation heights according to their densities.7 We have used MagLev to separate different grades of polymers (e.g., Nylon 6 and Nylon 6/6) or polymers having different stereochemistry (e.g., syndiotactic and atactic polystyrene).

Crystal Polymorphs

When organic molecules crystallize, they can produce a variety of different macroscopic structures (polymorphs), each having unique properties. Many small-molecule pharmaceuticals, for example, form several polymorphs and oftentimes only one structure possesses the desired properties. No convenient method for separating polymorphs exists. We have applied MagLev as a non-destructive tool to separate a variety of crystal polymorphs based on their density.16


Monitoring Polymerization and Solid-phase Chemical Reactions

MagLev can be used, as a simple analytical tool, to characterize the kinetics of free-radical polymerization17 and to monitor chemical reactions on a solid support.18 For example, we functionalized beads with ten derivatives of 4-benzyloxybenzaldehyde polystyrene, and monitored the extent and rate of reaction by measuring the densities of the functionalized polymer particles.


We developed MagLev as a simple, low-cost, broadly accessible tool with which to analyze trace evidence in a non-destructive manner.19 We determined the densities of a number of trace objects including glitter particles and smokeless gunpowder samples. Analysis by MagLev—even following repeated exposures to the paramagnetic medium—was not destructive to the sample, which may be re-used in tandem for alternative analyses.


Protein-Ligand Binding Assays

Bioassays frequently involve the use of proteins bound to beads to identify molecules of interest based on specific binding events. Most assays use labels (typically fluorescent) to detect and quantify binding events. While this approach is well studied and reliable, we sought to develop a label-free approach that may be particularly suitable for certain applications. We have used MagLev to measure the binding events between proteins and ligands by functionalizing small molecules (ligands) to diamagnetic beads.20-21As the protein-ligand binding progresses, the density of the beads increases; the process can be monitored, by eye, with high accuracy.

Immunoassays with MagLev

Using antigens immobilized onto the surface of polymeric beads, we have created a density-linked immunosorbent assays (DeLISA, analogous to the commonly used ELISA). When the beads are exposed to a sample, antibodies specifically bind the antigens. Anti-human antibodies conjugated with gold particles then bind to the captured antibody. We then chemically deposit silver or gold onto the beads. The deposition of metal leads to a change in density of the bead, which indicates the amount of antigen that was captured. Using parallel vials, we can perform a multiplexed DeLISA.22


Noncontact Orientation in MagLev

The manipulation and orientation of objects having irregular shape is a major challenge in advanced manufacturing; materials that are soft, sticky, or brittle are hard to manipulate no matter their shape. We have developed mathematical models that allow us to predict the height and orientation of an object levitating in MagLev.23 From this understanding, we have shown the ability of MagLev to manipulate objects by (i) rotating the MagLev device around an object suspended in paramagnetic solution, or (ii) using an external magnet to perturb the local magnetic field (Figure 4). We have used MagLev to manipulate hard plastics, soft elastomers, stick hydrogels, and fragile droplets of jammed particles.

Density-Fig-4 Figure 4. (A) Schematic of the experimental setup for controlling the orientation of a levitating object in laboratory space by rotating the MagLev device. (B) Experimental images taken along the y–z plane of a Nylon screw (8.5 mm in length) in the MagLev. We kept the cross in the background fixed relative to the laboratory. The white double-headed arrows indicate the orientation of the axis of the magnetic field gradient. (C) Similar rotations caused the screw to translate and contact the wall of the container when the density of the screw was greater than the density of the solution. Further rotations caused the screw to flip orientation. For scale, the horizontal line in the cross is 30 mm. (D) Schematic demonstration manipulation the orientation of an object in a MagLev device with an external magnet. (E) One of the orientations the screw adopts when placed in the device. (F) We moved an external magnet close to the screw to align the screw head along the red lines of the pattern. The brown square indicates the approximate position of the external magnet.
Self-Assembly using MagLev

Self-assembling objects on the mesoscale (mm to cm scale) is an unsolved challenge: structure tends to be dominated by gravitational forces rather than interactions between two assembling components. MagLev provides a buoyant force to counteract gravity, enabling objects to assemble based on size, shape, and density.24-25 Figure 5 illustrates a variety of self-assembled objects.

Density-Fig-5 Figure 5. (A, B) The self-assembly of multilayered structures of different densities by MagLev. Draining the paramagnetic medium from the container while the system remained in the applied magnetic field lowered the air-liquid meniscus and deposited the centered, correctly sized components at the bottom of the container. (C) Photographs demonstrating alignment and positioning of optical components levitating in an aqueous solution of MnCl2. Functionality of the optical system is illustrated by directing a laser at the assemblies.

Foods and Water

Density is commonly used in the food and beverage industries to obtain information about a substance. The alcohol content of wine, for example, can be inferred by measuring its density. Many tools exist to probe density of solids and liquids, but each has trade-offs between cost, ease of operation, and accuracy. MagLev provides a low-cost, simple, and rapid method to precisely assess the density of foods and water.13 Figure 6 shows several samples of milk levitating in a MagLev device—the levitation height is dependent on the fat content of the milk. MagLev can also be used to assess the density of small pieces of solids (string cheese) and pastes (peanut butter).

Density-Fig-6 Figure 6. Quality control of food items based on fat content. (A) Photographs of milk droplets levitating in Gd(DTAD) dissolved in 84:16 2-fluorotoluene/chlorobenzene. (B) Photographs of "string cheese" samples with different fat contents levitating in aqueous solutions of MnCl2. (C) Different kinds of peanut butter levitating in aqueous solutions of MnCl2.
Plastic Parts

Quality control is often the largest single cost in the manufacturing of small plastic parts. Visual evaluation, the most common form of quality control for plastic parts, cannot detect internal defects in opaque objects (i.e., the majority of plastic parts). Methods such as x-ray computed tomography and ultrasonic testing provide exquisite information on the structural characteristics of opaque parts, but they are generally slow and cannot be used to test a large number of parts without a prohibitive increase in cost and time for manufacturing. Many defects found in plastic parts (due to voids, cracks, unpolymerized material) have a different density than the bulk of the part. We have demonstrated the use of MagLev to rapidly and nondestructively assess injection-molded plastic parts for defects by monitoring, by eye, the orientation that a part adopts when levitating in the MagLev device (Figure 7).26

Density-Fig-7 Figure 7. Quality control of manufactured plastic parts (A) 3D schematic of an object with a hidden density defect. (B) Inside a MagLev device, the object tilts to an angle that depends on the mass and position of the hidden defect.



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3. Kumar, A. A.; Lim, C.; Moreno, Y.; Mace, C. R.; Syed, A.; Van Tyne, D.; Wirth, D. F.; Duraisingh, M. T.; Whitesides, G. M., Enrichment of reticulocytes from whole blood using aqueous multiphase systems of polymers. Am J Hematol 2015, 90 (1), 31-6.

4. Hennek, J. W.; Kumar, A. A.; Wiltschko, A. B.; Patton, M. R.; Lee, S. Y.; Brugnara, C.; Adams, R. P.; Whitesides, G. M., Diagnosis of iron deficiency anemia using density-based fractionation of red blood cells. Lab Chip 2016, 16 (20), 3929-3939.

5. Kumar, A. A.; Chunda-Liyoka, C.; Hennek, J. W.; Mantina, H.; Lee, S. Y.; Patton, M. R.; Sambo, P.; Sinyangwe, S.; Kankasa, C.; Chintu, C.; Brugnara, C.; Stossel, T. P.; Whitesides, G. M., Evaluation of a density-based rapid diagnostic test for sickle cell disease in a clinical setting in Zambia. PLoS One 2014, 9 (12), e114540.

6. Kumar, A. A.; Patton, M. R.; Hennek, J. W.; Lee, S. Y.; D'Alesio-Spina, G.; Yang, X.; Kanter, J.; Shevkoplyas, S. S.; Brugnara, C.; Whitesides, G. M., Density-based separation in multiphase systems provides a simple method to identify sickle cell disease. Proc Natl Acad Sci U S A 2014, 111 (41), 14864-9.

7. Winkleman, A.; Perez-Castillejos, R.; Gudiksen, K. L.; Phillips, S. T.; Prentiss, M.; Whitesides, G. M., Density-based diamagnetic separation: devices for detecting binding events and for collecting unlabeled diamagnetic particles in paramagnetic solutions. Anal Chem 2007, 79 (17), 6542-50.

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9. Nemiroski, A.; Soh, S.; Kwok, S. W.; Yu, H. D.; Whitesides, G. M., Tilted Magnetic Levitation Enables Measurement of the Complete Range of Densities of Materials with Low Magnetic Permeability. J Am Chem Soc 2016, 138 (4), 1252-7.

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13. Mirica, K. A.; Phillips, S. T.; Mace, C. R.; Whitesides, G. M., Magnetic levitation in the analysis of foods and water. J Agric Food Chem 2010, 58 (11), 6565-9.

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15. Kumar, A. A.; Walz, J. A.; Gonidec, M.; Mace, C. R.; Whitesides, G. M., Combining Step Gradients and Linear Gradients in Density. Anal Chem 2015, 87 (12), 6158-64.

16. Atkinson, M. B.; Bwambok, D. K.; Chen, J.; Chopade, P. D.; Thuo, M. M.; Mace, C. R.; Mirica, K. A.; Kumar, A. A.; Myerson, A. S.; Whitesides, G. M., Using magnetic levitation to separate mixtures of crystal polymorphs. Angew Chem Int Ed Engl 2013, 52 (39), 10208-11.

17. Ge, S.; Semenov, S. N.; Nagarkar, A. A.; Milette, J.; Christodouleas, D. C.; Yuan, L.; Whitesides, G. M., Magnetic Levitation To Characterize the Kinetics of Free-Radical Polymerization. J Am Chem Soc 2017, 139 (51), 18688-18697.

18. Mirica, K. A.; Phillips, S. T.; Shevkoplyas, S. S.; Whitesides, G. M., Using magnetic levitation to distinguish atomic-level differences in chemical composition of polymers, and to monitor chemical reactions on solid supports. J Am Chem Soc 2008, 130 (52), 17678-80.

19. Lockett, M. R.; Mirica, K. A.; Mace, C. R.; Blackledge, R. D.; Whitesides, G. M., Analyzing forensic evidence based on density with magnetic levitation. J Forensic Sci 2013, 58 (1), 40-5.

20. Shapiro, N. D.; Mirica, K. A.; Soh, S.; Phillips, S. T.; Taran, O.; Mace, C. R.; Shevkoplyas, S. S.; Whitesides, G. M., Measuring binding of protein to gel-bound ligands using magnetic levitation. J Am Chem Soc 2012, 134 (12), 5637-46.

21. Shapiro, N. D.; Soh, S.; Mirica, K. A.; Whitesides, G. M., Magnetic levitation as a platform for competitive protein-ligand binding assays. Anal Chem 2012, 84 (14), 6166-72.

22. Subramaniam, A. B.; Gonidec, M.; Shapiro, N. D.; Kresse, K. M.; Whitesides, G. M., Metal-amplified Density Assays, (MADAs), including a Density-Linked Immunosorbent Assay (DeLISA). Lab Chip 2015, 15 (4), 1009-22.

23. Subramaniam, A. B.; Yang, D.; Yu, H. D.; Nemiroski, A.; Tricard, S.; Ellerbee, A. K.; Soh, S.; Whitesides, G. M., Noncontact orientation of objects in three-dimensional space using magnetic levitation. Proc Natl Acad Sci U S A 2014, 111 (36), 12980-5.

24. Ilievski, F.; Mirica, K. A.; Ellerbee, A. K.; Whitesides, G. M., Templated self-assembly in three dimensions using magnetic levitation. Soft Matter 2011, 7 (19), 9113-9118.

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26. Hennek, J. W.; Nemiroski, A.; Subramaniam, A. B.; Bwambok, D. K.; Yang, D.; Harburg, D. V.; Tricard, S.; Ellerbee, A. K.; Whitesides, G. M., Using magnetic levitation for non-destructive quality control of plastic parts. Adv Mater 2015, 27 (9), 1587-92.