Electrophoresis

Research in the field of electrophoresis

A part of the Liquid Crystals and Photonics Group is specialized in charge transport in display devices and in electrophoresis in general. For example, ion transport has important consequences in liquid crystal devices. Also, fundamental research is carried out on electrophoretic displays, a technology for electronic paper based on electrophoresis. Below some background information is given on the topic electrophoresis, and an overview is given of different research topics within our group. References of work published by our group can be found below.

What is electrophoresis?

"Electrophoresis" means motion due to an electric field. In general, the charged particles performing electrophoresis can either be charged molecules, charged colloidal particles (i.e. particles larger than 1 nm but smaller than a few micrometer), that are present in a gas, liquid or gel. Fig. 1 shows electrophoresis of a spherical particle with charge q. The particle velocity is the result of a balance between the electrostatic force and the friction force. In our group we are mainly interested in electrophoresis of molecules, micellar aggregates and solid colloidal particles in a liquid. The first studies of electrophoresis of colloidal particles are situated around the beginning of the 19th century, and are closely related to the development of the optical microscope at that time. For example, Reuss discovered in 1809 that colloids can naturally carry a charge, by observing the motion of clay particles in an electric field (F. F. Reuss, "Sur un nouvel effet de l'electricité galvanique", 1809). Since those early years, several theories were established (e.g. the standard elektrokinetic model) to explain various electrokinetic properties of colloidal particles. For example, electrophoresis of a charged particle in an electrolyte has been described by 4 contributions: the electrostatic force, the friction force, and forces due to retardation and relaxation caused by the countercharge in the electric double layer (see Fig. 2).

Principle of electrophoresis

Fig.1. Electrophoresis of a charged particle in a uncharged viscous medium.

electrophoresis in electrolyte

Fig.2. Forces on a charged particle in electrophoresis in an electrolyte. The gray zone represents the countercharge in the electric double layer.

Colloidal dispersions

Colloidal dispersions are mixtures of a disperse phase in a dispersing medium. In general, both the disperse phase and the dispersing medium may be solids, liquids or gases, as long as the particles of the disperse phase are much larger than the molecules of the dispersing medium. Fog is an everyday example of a colloidal dispersion in which water is dispersed in air. When solid particles are dispersed in a liquid, it is called a "sol". In the context of this thesis, the terms "colloid", "colloidal suspension", "colloidal particles" or just "particles" are used to refer to a sol. Typically the size of colloidal particles is smaller than a few micrometer and larger than 1 nm, so that a colloidal dispersion is distinguishable from true solutions. The first studies of colloidal particles are situated around the beginning of the 19th century, and are closely related to the development of the optical microscope at that time. A well known example is the experiment of Robert Brown in 1828 (R. Brown, Philos. Mag. 4, 161, 1828) in which he observed the random motion of microscopic pollen in water, later called "Brownian" motion (see Fig. 3). Another example is the discovery of Reuss in 1809 that colloids can naturally have a charge, by observing the motion of clay particles in an electric field. Those early observations triggered an expansion in the understanding of the properties of colloidal particles, and even led to important new physical insight. For instance, Brownian motion turned out to be hard evidence for the atomic structure of matter. In the years between 1800 and 1950 several theories were established to explain various electrokinetic properties of particles.

brownianmotion

Fig.3. Random fluctuating forces due to the liquid molecules (a) are causing the macroscopic Brownian motion of particles in a liquid.

Polar and nonpolar liquids

Polar and nonpolar liquids are distinguished by their ability to polarize in response to an electric field. Depending on their size and atomic structure, molecules in a liquid can have either a permanent dipole moment, attain a dipole moment in an external electric field, or just have no dipole moment at all. Dipole moments tend to align with an electric field, creating a field in the opposite direction and thereby reducing the original field. Molecules with no polarization do not align with the field and do not influence the field. The extent to which a material influences the electric field by its polarizability is described by the relative dielectric constant εr. Liquids are roughly classified as polar (εr > 40), weakly or moderately polar (5 < εr < 40) and nonpolar (εr < 5). Water is an example of polar liquid with εr = 80, dodecane is a nonpolar liquid with εr = 2. The polarity of a liquid has some important consequences (see Fig. 1.1). It explains the strong ability of polar liquids to dissolve salts, because the attractive field between oppositely charged ions is strongly reduced. The magnitude of the electrostatic force between two ions with charges q1 and q2 separated by a distance l in a liquid with dielectric constant εr and with vacuum permittivity ε0, is given by: F = q1q2/4πε0εrl2.



polar and nonpolar liquids

Fig.4. The electrostatic force between opposite charges in a polar liquid (left) and in a nonpolar liquid (right).




For example, in the case of the salt NaCl in water, the attractive force between the ions Na+ and Cl- is reduced 40 times in comparison to dodecane. Therefore, free ions can exist easily in a polar liquid, because the electric force trying to recombine opposite charges is strongly reduced (Fig.4 left). In contrast, in nonpolar liquids the electric force between opposite charges is strong, making it very difficult for ions to remain free in the solution (Fig.4 right). Another consequence is that the charge of colloidal particles in nonpolar liquids is typically low compared to particles in polar liquids. The explanation is similar: in polar media surface molecules can easily ionize, leading to a charged particle surface, while this is more difficult in nonpolar media.

A special intermediate case between polar and nonpolar suspensions arises when surfactant molecules, also known as amphiphilic molecules, are added to a nonpolar liquid. Surfactant molecules are characterized by having both a polar and a nonpolar part (see Fig.5a). In a liquid environment of nonpolar molecules, surfactant molecules spontaneously form energetically favorable aggregates called inverse micelles. In such an inverse micelle, tens to hundreds of surfactant molecules organize their polar parts together in the center, while the nonpolar parts stick out at the outside (Fig.5b). Typically inverse micelles
form around impurities, that can be an ion, traces of water or simply a surfactant molecule. Surfactant molecules also like to cover surfaces of colloidal particles and the walls of the suspension container, which is why they are called "surfactants". Inverse micelles can carry a charge, typically situated in the
polar micelle interior, but most inverse micelles are electrically neutral. The presence of surfactant molecules in nonpolar colloidal suspensions has a large effect on the charge of colloidal particles. Molecules on the surface of a colloidal particle can more easily ionize when a charged part of the surface molecule
can be transported away inside an inverse micelle. For this reason surfactant is also referred to as the "charging agent". In addition, the steric stabilization of the shell of surfactant molecules on the particle surface prevents agglomeration of particles.

micelle formation

Fig.5. Surfactant molecules in a nonpolar liquid (a) forming inverse micelles (b).

Electrophoretic displays



electrophoretic display

Fig.6. Schematic representation of a grayscale electrophoretic display.

In our group we are investigating fundamental properties of electrophoretic displays. Electrophoretic displays are reflective displays in the category "electronic paper", featuring paper-like readability, low power consumption, flexibility (just like printed paper) and all advantages of an electronic display. A typical electrophoretic display consists of a thin layer of "electrophoretic ink", sandwiched between two electrodes, of which one is transparant. Fig.6 shows a black and white, dual particle microencapsulated display, illustrating the basic display layout. The electrophoretic ink is a mixture of black and white colloidal particles, a clear nonpolar liquid and surfactant additives, all chosen in such a way that the white particles are positively charged while the black particles are negatively charged. By applying a positive or a negative voltage, a choice can be made to move the white particles to the upper, transparent electrode and black particles to the bottom electrode, or vice versa. Light is then respectively scattered on the white pigment particles, giving a light pixel, or
is absorbed by black pigment particles, giving a dark pixel. Switching many pixels arranged in a matrix is then used to show a page from a book, newspaper, or any type of image. In electrophoretic ink, typically a non-conductive dispersion liquid is chosen, such as a nonpolar liquid. In nonpolar dispersions, surfactant is usually added to increase the charge of the pigment particles and to stabilize them against agglomeration. Sometimes the ink is encapsulated in transparent polymer capsules (E Ink Corporation) or divided in compartiments by a microcup array (Microcup) to prevent the accumulation of pigments in parts of the display, for instance due to gravity. There are some important advantages of electrophoretic displays over other technologies such as liquid crystal displays. The reflection and absorption properties of the pigment particles are essentially the same as the pigments used in printing ink for newspapers and books. Therefore the electrophoretic display has a similar paper-like look, with excellent readability in both full sunlight and dim lighting and 180 degrees viewing angle. The power consumption is very low because there is no need for a backlight (light from the environment is used) and because power is only required to update an image but not no maintain it (bistability). This is especially interesting for mobile and handheld applications. And finally, the technology is compatible with many backplane types, even flexible substrates, paper or cloth. Flexible and rollable displays further increase the paper-like appearance. Currently much effort is being made to achieve full color, fast switching and flexible electrophoretic displays.

electrophoretic displays

Fig.7. Commercially available electrophoretic displays and some prototypes.

Currently, there is a whole range of commercially available electrophoretic displays (see Fig.7). The first electronic books launched in 2004 were the Sony Reader (Fig. 7a) and the Sony LIBRI´e, both quite expensive (±600 euro). The iRex iLiad (2006, Fig. 7b) has wireless networking, for instance for recieving a daily electronic newspaper, and a touchscreen allowing handwriting and sketching. More recently (in 2007) the Cybook was launched, selling for 350 euro (Fig. 7c). The Amazon Kindle (also 2007) costs 360 dollar, and has really opened up the market of e-book leasure reading, but is not able to read the pdf format. Other examples are the Motorola Motofone (Fig. 7d), smart cards (Fig. 7e), and segmented displays (Fig. 7f). These examples show that the technology for gray scale electrophoretic displays is getting mature. A prototype of a flexible display is the Readius from Polymer Vision (Fig. 7g). Fig. 7h shows the Plastic Logic Reader, to be launched in 2009. This is a very similar display to the iLiad, specifically designed for business readers. However, this is only a selection of the most important electrophoretic displays.

Charge in nonpolar liquids

More than fifty years ago, many people used to think that charges could not exist in nonpolar liquids, such as hydrocarbons. Even though charging effects were well understood in polar liquids such as water, this seemed physically impossible in nonpolar liquids. Fortunately (or unfortunately), explosions at an oil refinery in the fifties caused by buildup of electric charge revealed a more vivid picture of charges in nonpolar liquids (I. D. Morrison, Colloids and Surfaces A, 71, 1993, J. L. van der Minne and P. H. J. Hermanie, Elsevier publishing Co, 1958). From 1965 to now, the stability of nonpolar colloidal suspensions and electrical charging mechanisms were studied by Fowkes, Pugh, Kitahara, Morrison and many others. In recent years an increasing interest in nonpolar collodial suspensions has grown. Fundamental research has been carried out on colloidal crystals as model systems for atomic systems, on interparticle interactions and particle charging mechanisms. The most important application nowadays is perhaps the electrophoretic display. Other applications are for
example stabilization of soot in motor oil and electrodeposition of particles. However, there still remain many unanswered questions on fundamental principles of charging in nonpolar liquids. This is one of the problems addressed by our group (references). For example, the generation of charged inverse micelles (see Fig.8) was investigated by transient current measurements (see Fig.9) (F. Strubbe et al., JCIS, 300, 396, 2006).

formation of charged inverse micelles by disproportionation

Fig.8. The equilibrium between charged and uncharged inverse micelles by means of a disproportionation reaction mechanism.

transient current measurements

Fig.9. In a transient current measurement, the current due to electrophoresis of charged species is measured after application of a voltage step.

Optical tracking electrophoresis

Optical tracking electrophoresis is a method to measure the electrophoretic mobility of particles visible under the microscope (see Fig. 10). This method allows investigating properties of individual particles, which has the advantage that time-dependent changes and fluctuations of properties or position-dependent properties can be studied. The correlation between different particle properties such as charge, size, or even the shape and fluorescent wavelength, can be studied in polydisperse and heterogenous particle samples, which is difficult with existing methods that average the properties of many particles.

optical tracking electrophoresis setup

Fig.10. Typical optical tracking electrophoresis setup.

The particle position is determined using image analysis (see Fig.11).

image analysis

Fig.11 The particle position is determined in each image using software.

From the particle trajectories, for example the diffusion constant and the electrophoretic mobility can be determined. Fig.12 gives an example of Brownian motion of a particle in the x-direction (a), and the corresponding power spectrum of the position (b) and speed (c). For comparison, the same particle was measured in a sinusoidal electric field in Fig. 13. Here, the particle is moving sinusoidal, and a peak emerges in the power spectrum at the
frequency of the applied field.

analysis brownian motion

Fig.12 Brownian motion of a particle (a), power spectrum of the position (b) and power spectrum of the speed (c).

analysis sinusoidal motion

Fig.13 Motion of a particle in a sinusoidal electric field (a), power spectrum of the position (b) and power spectrum of the speed (c). The arrow shows the peak in the spectrum at the frequency of the applied field.




Not only the diffusion constant or electrophoretic mobility can be measured wit optical tracking electrophoresis.
It is also used to study particle trajectories when a DC voltage is applied (see Fig.14).

particle trajectories

Fig.14. Measurement (a,b,c,d) and simulations (e,f,g,h) of particle trajectories during a transient experiment, in 0, 0.01, 0.025 and 0.1% surfactant solutions.

Measuring the elementary charge on individual colloidal particles - the Millikan oil drop experiment in a
liquid.

The elementary charge e is a fundamental physical constant with a measured value of approximately 1.602176487(40)×10-19C. In 1909, Robert Millikan (with significant input of Harvey Fletcher) carried out the first measurement of the value of e by observing the motion of charged oil drops in air under the influence of an electric field (R. A. Millikan, Phys. Mag. XIX 6, 209 (1910), R. A. Millikan, Phys. Rev. 32, 349 (1911)). The experiment of Millikan and Fletcher demonstrates in a simple and elegant way that electrical charge is quantized and allows with a one man operated apparatus to calculate the value of the elementary charge with high precision. For that reason it is regarded by some as one of "the 10 most beautiful experiments" (G. Johnson, The Bodley Head London, 2008). The elementary charge is the smallest measurable value of the electric charge in stable matter, despite many recent attempts to measure fractional charges such as 1/3e and 2/3e of quarks (V. Halyo et al. Phys. Rev. Lett. 84, 12 (2000)).

elementary charge measurement on a colloid

Fig.15. Positively and negatively charged species interacting with a colloidal particle.

We demonstrated that it is also possible to measure of the elementary charge on individual solid particles in a liquid (F. Strubbe, F. Beunis, K. Neyts, Phys. Rev. Lett., 100, 21 (2008) (see Fig. 15). For example, Fig. 16 shows a histogram of the charge of colloidal particles, with peaks at multiples of the elementary charge. With our method the value of e was measured as (1.64 ± 0.05)×10-19C. This experiment is of course very related to Millikan's oil drop experiment, but -surprisingly- never carried out in the 100 years from his experiment. Recently, a measurement of the electrophoretic mobility distribution of a large collection of monodisperse particles with electrophoretic light scattering has also revealed charge quantization (E. V. Shevshenko et. al., Nature, 439, 55 (2006)). The new aspect here is that charge quantization is observed on individual particles, allowing e.g. to study dynamic fluctuations of the charge in time on polydisperse particle samples. Finding the elementary charge in a liquid is much harder than in air because of the higher viscosity, explaining the large error on our measured value of e. This reduces the motion of weakly charged particles in an electric field to a value which may be below the sensitivity of most measurement systems or difficult to separate from Brownian motion.

charge histogram showing elementary charge resolution

Fig.16. Charge histogram of colloidal particles showing peaks at multiples of the elementary charge.

Simulations with the Poisson-Nernst-Planck equations.

Simulations are carried out to compare measurements with approximate models. Drift and diffusion of charged species is often modelled by the Poisson-Nernst-Planck equations. We use these equations to model charge transport in electrophoretic devices in 1-dimensional (Fig. 17a) or 2-dimensional (Fig. 17b) device configurations.

simulations PNP equations

Fig.17. Examples of simulations based on the Poisson-Nernst-Planck equations in a 1D (left) and a 2D (right) electrophoretic device.

References

  • M. Marescaux, F. Beunis, F. Strubbe, B. Verboven and K. Neyts, "The impact of diffusion layers in strong electrolytes on the transient current", Phys. Rev. E, 79, 011502 (2009)
  • F. Strubbe, F. Beunis, M. Marescaux, B. Verboven and K. Neyts, "Electrokinetics of colloidal particles in nonpolar media containing charged inverse micelles", accepted to be published in Appl. Phys. Lett., December 2008.
  • A. R. M. Verschueren, P.H. L.Notten, L. J.M. Schlangen, F. Strubbe, F. Beunis and K. Neyts, "Screening and separation of Charges in Microscale Devices: Complete Planar Solution of the Poisson-Boltzmann Equation," J. Phys. Chem. B., 112(41), 303813050 (2008).
  • F. Beunis, F. Strubbe, M. Marescaux, J. Beeckman, K. Neyts and A. R. M. Verschueren, "Dynamics of charge transport in planar devices," Phys. Rev. E 78, 011502 (2008).
  • F. Strubbe, F. Beunis and K. Neyts, "Detection of elementary charges on colloidal particles," Phys. Rev. Lett. 100, 21, 2183011 to 2183014 (2008).
  • F. Beunis, F. Strubbe, M. Marescaux, K. Neyts and A. R. M. Verschueren, "Diffuse double layer charging in nonpolar liquids," App. Phys. Lett. 91(18), 82911/1182911/3 (2007).
  • F. Beunis, F. Strubbe, K. Neyts and A. R.M. Verschueren, "Power-law transient charge transport in a nonpolar liquid," App. Phys. Lett. 90(18), 182103/1182103/3 (2007).
  • F. Strubbe, F. Beunis, M. Marescaux and K. Neyts, "Charging mechanism in colloidal particles leading to a linear relation between charge and size," Phys. Rev. E 75 (3), 031405/1031405/8 (2007).
  • F. Strubbe, F. Beunis and K. Neyts, "Determination of the effective charge of individual colloidal particles," J. Colloid. Interf. Sci. 301, 302309 (2006).
  • F. Strubbe, A. R. M. Verschueren, L. J.M. Schlangen, F. Beunis and K. Neyts, "Generation current of charged micelles in nonaqueous liquids: Measurement and simulations," J. Colloid Interface Sci. 300, 396403 (2006).

More detailed information about the results we have obtained in our research can be found in our publications.

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