Digital Imaging of Colloidal Systems Manas Khan and A. K. Sood Department of Physics, Indian Institute of Science, Bangalore - 560 012, India. Abstract We propose a new algorithm to identify particles and extract quantitative information e.g. pair correlation function and structure factor from a colloidal image. The algorithm works for systems of spherical particles of different sizes and can be generalized to recognize non-spherical particles also. It can distinguish particles of different sizes in the case of a polydisperse system. The most noteworthy part is that the algorithm recognizes particles with cent percent accuracy even when the particles form aggregations. Here we present pair correlation functions evaluated using our algorithm for colloidal systems that under ac electric field show different phase behaviors. INTRODUCTION The use of digital image processing has greatly enhanced the utility of the optical microscope, permitted entire fields of study that were impossible earlier. Now there are many well-known techniques that improve the qualitative as well as quantitative aspects of using light microscopy. Finally it is the image processing part to extract the most useful information from the microscope images of the system. Extracting useful information from images of colloidal suspension needs only the detection of particle centers. To convert a microscope image into quantitative information three basic steps are followed: (1) reducing “noise”, (2) enhancing contrast and (3) quantifying intensity of an image. All these three steps are combined in a single technique to make popular and user-friendly particle detection techniques [1]. These regularly used particle detection techniques are not well suited for detecting colloidal particles from a image frame in many cases. Our new algorithm works accurately for all types of colloidal systems. THE PROPOSED ALGORITHM This algorithm uses a digital mask, usually called as filter to recognize a particle. Different filters are used for detecting different sizes of particles. Not only the elements but the size of the kernel also changes for a new filter. The first step is the algebraic manipulation of the image to enhance image contrast. Since different images are of different image contrast, the intensity and contrast are first normalized and then the same image manipulation can be employed to all the images. A filter is used to quantify the intensity pattern of the image. To make it more accurate, the same filter is used thrice on the same image with a intensity renormalization process after the application of the filter each time. Repetitive application of

filters makes the image more informative, but this noise reduction process saturates after the filter is applied for third time. Finally a intensity window is set such that every pixel which pass through that intensity window represents a particle center. For polydisperse systems, the process is a bit complicated. In this case the algorithm starts searching for the smallest particles, it recognizes the centers of the particles with smallest diameter and then deletes those particles. This process is repeated till the particles of all sizes are detected. EXPERIMENTAL DETAILS Electric field induced clustering has been studied by imaging. Colloidal suspensions of polystyrene particles (2µm) of required volume fraction are prepared using 1:1 mixture of deionized water and D2O and are kept in contact with ion-exchange resins. To study the effect of electric field (perpendicular to the electrodes), the sample is sandwiched between two glass-plates coated with conducting indium-tin oxide (ITO). The two plates are kept separated by insulating spacers and the cell is well sealed to prevent evaporation and flow of the suspension. A function generator combined with a potentiometer is used to regulate the applied sinusoidal varying voltage. Two multimeters are used to read the rms applied voltage and the current. We use conventional light microscopy for imaging of colloidal suspensions. One CCD camera and one VCR are used to record the observations on magnetic tape. Single image frames are grabbed from the video and processed to evaluate pair correlation function and structure factor. RESULTS Fig 1 shows the pair correlation function of colloidal suspension of 2µm particles with 0.2% volume fraction.

DISCUSSION In Fig 1, the pair correlation function shows the expected trends for a liquid system. Under the influence of external electric field the suspension form clusters of hexagonal crystal structure. So the pair correlation function should show the peaks for hexagonal crystal structures that override the smoothly falling first peak of liquid like pair correlation function. With increasing volume fraction, the size of the clusters increases which gives more prominent peaks for hexagonal structure on less dominant liquid like behavior. Fig 2 and Fig 3 are in complete agreement with the expected trend. In the case of hexagonal crystalline structure the evaluated pair correlation function gives position and intensities of the peaks accurately as shown in Fig 4. REFERENCES 1. John C. Crocker and David G. Grier, Journal of Colloid and Interface Science 179, 298-310 (1996) 2. F.Richetti, J.Prost and N.A.Clark, Physics of Complex and Supermolecular Fluids (Wiley, NY), 387 (1987) 3. M.Trau, D.Saville and I..Aksay, Science, 272, 706(1996)

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r/a Fig 3: Pair correlation function of a colloidal suspension forming bigger clusters in liquid phase. (averaged over 100 frames) 3.5

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Fig 2: Pair correlation function of a colloidal suspension forming small aggregations in liquid phase. (averaged over 30 frames)

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Without the application of any external electric field the suspension show liquid behavior. When electric field is applied along the perpendicular direction, the colloidal particles start aggregating [2]. The size of the clusters formed depends on the electric field intensity, frequency of the ac electric field and particle density [3]. Fig 2 and Fig 3 shows pair correlation functions of colloidal suspensions under ac electric field of 500 mV at 1 kHz for volume fraction 0.1% and 0.2% respectively. In the second case the size of the clusters are bigger than that of in the first case. Colloidal suspensions with volume fraction 0.1% form hexagonal crystals under ac electric field of strength 700 mV at 1 kHz. The pair correlation function for this case is shown in Fig 4.

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Fig 1: Pair correlation function of liquid phase (averaged over 50 frames)

Fig 4: Pair correlation function of colloidal suspension forming hexagonal crystalline phase (averaged over 40 frames). The starts (∗) show theoretically calculated peak positions and intensities.

Frequency dependent shape changes in electric field ...

particles of different sizes in the case of a polydisperse system. ... EXPERIMENTAL DETAILS ... mixture of deionized water and D2O and are kept in contact.

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