Langmuir 1995,11, 4196-4198
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Pulsed Laser Imaging Demonstrates the Mechanism of Current Rectification at a Hydrogel Interface Piotr E. Marszalek,? Vladislav S. Markin,$ Toyoichi Tanaka,§ Haruma Kawaguchi,” and Julio M. Fernandez*>’ Department of Physiology and Biophysics, Mayo Clinic, M S B 1- 11 7, Rochester, Minnesota 55905, Department of Cell Biology and Neuroscience, University of Texas Southwestern Medical Center, 5323 Harry Hines Boulevard, Dallas, Texas 75235, Department of Physics and Center for Materials Science and Engineering, Massachusetts Institute o f Technology, Cambridge, Massachusetts 02139, and Department of Applied Chemistry, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-Ku, Yokohama 223, Japan Received June 29, 1995. I n Final Form: September 1, 1995@ The accumulation or depletion of charge carriers at a p-n junction results in electronic rectification.’ Similarly, we show that accumulation or depletion of ions underlies ionic rectification at a single hydrogelelectrolyte interface. We monitored t h e rapid formation and collapse of ionic gradients at t h e hydrogelelectrolyte interface of n a t u r a P 3 and synthetic4 charged microparticles by the use of pulsed-laser m i c r o ~ c o p y . ~We , ~ conclude that the flow of t h e current is determined by the charge of t h e hydrogel and the geometry of the electric field applied to it. Our findings can be utilized to design hydrogel-based microswitches a n d “wet” integrated circuits.
Introduction We e x a m i n e a micrometer-sized electrical device that consists of a hydrogel microparticle a t t a c h e d t o a glass micropipette electrode (Figure 1A). This device w a s previously s h o w n to behave like a diode whose forward c u r r e n t was -100 times larger than the reverse current.2 The m e c h a n i s m b y which the hydrogel-pipette assembly rectifies the ionic c u r r e n t remained unexplained.2 We propose that the rectification c a n b e explained by considering the conduction m e c h a n i s m at the hydrogelelectrolyte interface. Due t o the fixed charges within the hydrogel particle the co-ions are excluded from the gel (Donnan exclusion7~*); the gel’s conductance is d o m i n a t e d b y mobile counterions, and t h e y become the majority carrier in the hydrogel. In comparison, both cations and a n i o n s contribute t o the conductance of the electrolyte s u r r o u n d i n g the hydrogel. In the transition region between the hydrogel and the electrolyte there is a change in the conduction m e c h a n i s m and we hypothesize that this interface resembles a junction between two semiconductors (i.e., a rectifying p-n junction). A voltagedependent accumulation (conducting s t a t e ) o r depletion (nonconducting s t a t e ) of charge carriers should thus be observed at the hydrogel-electrolyte interface (Figure 2). We model distribution of ions and ionic c u r r e n t s at the gel-electrolyte interface b y the use of the Nernst-Planck
* Author to whom correspondence should be addressed. Telephone: (507) 284-0423. Telefax: (507) 284-0521. E-mail:
[email protected]. ’ Mayo Clinic. University of Texas Southwestern Medical Center. Massachusetts Institute of Technology. I’ @
Keio University. Abstract published in Advance A C S Abstracts, November 1,
1995. (1)Kittel, C. Introduction to Solid State Physics, 5th ed.; John Wiley & Sons, Inc.: New York, 1976; p 242. (2)Nanavati, C.; Fernandez, J. M. Science 1993,259, 963. (3) Fernandez, J. M.; Villalon, M.; Verdugo, P. Biophys. J . 1991,59, 1022. (4) Kashiwabara, M.; Kasuya,Y.; Fujimoto,K.; Kawaguchi,H. Polym. Prepr. Jpn. 1993,42,4623. (5) Kinosita, K., Jr.; et al. SPIE 1988,909,271. (6) Monck, J. R.; Robinson, I. M.; Escobar, A. L.; Vergara, J. L.; Fernandez, J. M. Biophys. J . 1994,67,505. (7) Helfferich, F. Ion Exchange, 1st ed.; Mc Graw-Hill Book Company: New York, 1962. ( 8 ) Tam, P. Y.; Verdugo, P. Nature 1981,292,340. ~
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electrodiffusion formalism and monitor ionic gradients at t h i s interface with pulsed-laser m i c r o ~ c o p y . ~We . ~ compare the experimental current-voltage relationship with a theoretical model and suggest some applications of hydrogel-based micrometer-sized rectifiers.
Experimental Section Hydrogel. Natural anionic heparin proteoglycan hydrogel microparticles were extracted from the giant secretory granules of beige mouse mast cells. Isolated secretory granules were prepared by sonication of purified beige (bgj/bgJ)mouse mast cells obtained by peritoneal l a ~ a g e The . ~ synthetic amphoteric microspheres (-6 ,um) were prepared by copolymerization of methacrylic acid (MAC)and p-nitrophenyl acrylate (NPA) with methylenebisacrylamide (MBAAm) as a crosslinker and 2,2’azobisisobutyronitrile (AIBN) as an i n i t i a t ~ r The . ~ particles were modified for 48 h at room temperature in the presence of ethylenediamine (particle/ethylenediamine= lequiv/100 equiv). Electrical Measurements. The arrangement used to apply an electric field to a micrometer-sized (1-6um) hydrogel particle is outlined in Figure 1A. A pipette was filled with an electrolytic solution identical to the bathing medium, and the hydrogel was placed a t the tip of a glass micropipette electrode. The conical angle ( 8 ) was on average lo”, and the ratio of the solid angles of the pipette (0utside:inside)was -130. Silver/silver chloride electrodes were inserted into the pipette and placed in the bathing medium. They were connected to a variable voltage source via a current-voltage converter that was controlled by a computer interface. Imaging. The distribution of anionic fluorescein was determined by ratiometric pulsed-laser imaging microscopy.6 Briefly, an inverted epifluorescence microscope was coupled to a high intensity pulsed coaxial flash lamp dye laser which provided short (350 ns) pulses of illumination. Image pairs were taken by a CCD camera. The procedure involves acquiring an image of the gel when no voltage pulse (control) was applied and then capturing an image of the gel during a voltage pulse (stimulus). The fractional change in fluorescence was calculated from the ratio of the stimulus image divided by the control image. This procedure was repeated several times at different points along the voltage pulse. The bathing medium contained (in mM): histamine, 15; and HEPES, 10 (pH 7.3). The pipette solution was the same except for the addition of fluorescein (100 uM).
Theoretical Considerations The hydrogel a t t a c h e d t o the pipette has t w o rectifying interfaces (external bathing medium-microparticle and (9) Monck, J. R.; Oberhauser, A. F.;Alvarez de Toledo, G.; Fernandez, J. M. Biophys. J . 1991,59, 39.
0743-7463/95/2411-4196$09.00/0 0 1995 American Chemical Society
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Langmuir, Vol. 11, No. 21, 1995 4197
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Figure 1. Experimental demonstration of the mechanism of current rectification by a gel-electrolyte interface. (A)The arrangement used to apply an electric field to a micrometer-sized (1-6 pm) hydrogel particle. (B) Steady-statecurrent-voltage relationship for a natural anionic hydrogel microparticle. The electrolyte contained 25 mM histamine dihydrochloride and 5 mM citric acid buffered at pH 3.5. The solid line is a least squares fit of eq 4 to the experimental data (filled circles) with R,, found to be 0.72 MQ. Prior to insertion of the gelRp0was measured to be 4.311152. The dotted line represents the current-voltage relationship for the micropipette alone. (D) A sequence of pulsed-laser snapshots captured during the experiment shown in C. The time at which the laser pulses were fired and the images captured (white numbers in each image) correspond to the arrows marked in C (at 1,4,9, 15, and 30 ms). The orientation of the pipette and the localization of the gel particle (natural)is as shown in A. The color bar represents the linear gradation in fluorescence intensity (0, low; and 3, high). The images captured at 4 and 9 ms are saturated in this scale; the increase in the fluorescence intensity in the image captured at 4 ms was at least 6-fold.
solution in the pipette-microparticle [internal])in series, but they are not equivalent. Due to the difference in the solid angles subtended by the pipette (on average the ratio 0utside:inside 130,Figure 1A)the hydrogel microsphere is subjected to a nonuniform electric field and approximately 99% of the applied voltage drops across the hydrogel and the internal gel-electrolyte interface. The voltage drop at the external interface is negligible. Therefore the voltage-inducedaccumulation and depletion of charge carriers at the internal interface controls the conductance of this device, i.e., it behaves like a single diode and not like two oppositelypolarized diodes in series. Rectificationwithin the hydrogel-pipette assemblywas modeled by use of the Nernst-Planck electrodiffusion equationlo assuming the solution contained one binary electrolyte. We also assumed that the hydrogel particle was spherical and the pipette had a conical shape, but neither the shape of the gel nor the shape of the pipette are critical for rectification provided the electric field is focused at one and dispersed at a second gel-electrolyte interface. Fluid convection was neglected in our derivation. At steady state, the current -voltage relationship is
--
q,=RH+-lnRT ZacP
[
l+-Z a c P R p O I ]
absolute temperature, and Zacc is the accumulation charge (negative and positive for anionic and cationic gels, respectively) which is defined _.
zacc -
a+z-DD-a+
+ a-z+D+ + D,a-
where a+and a- are the transference numbers, D+ and D- are the diffusion coefficients, and z+ and z- are the charge numbers for cations (+) and anions (-). Zacc accounts for the disparity between cationic and anionic transport when the gel is present. If most of the current is carried by the counterions, Zacc will approach the charge number of the impermeable co-ion, Le., Zacc -,Zco-ion. It is apparent from (1)that a negatively charged gel (zacc < 0) will cause the current to saturate at positive potentials. At the limit qp +=, zaccFRpo/RT - 1,and the expression for the saturation (reverse) current (Irev) becomes
-
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-
1
(3) Substituting eq 3 into eq 1the current-voltage relationship for the gel-pipette assembly can be written as
RT
where qpis the voltage applied between the interior of the pipette and the bathing medium (the current flowing out of the pipette is considered positive), Rpoand R, are the resistances of the pipette alone and the hydrogel alone, F is Faraday's constant, R is the gas constant, T is the (10) Bockris, J. O'M.; Reddy, A. K. N. Modern Electrochemistry, 1st ed.; Plenum Publishing Corp.: New York, 1977; Vol. 1, pp 394-399.
which is a typical current-voltage relationship of a diode in series with an ohmic resistance (R,).
Results and Discussion The hydrogels used in this study are the heparin sulfate proteoglycan core of the secretory g r a n ~ l eand ~ >synthetic ~ hydrogel micro sphere^.^ In the absence of the hydrogel
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4198 Langmuir, Vol. 11, No. 11, 1995 GEL
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Figure2. The origin of rectificationat the hydrogel-electrolyte interface. When the fixed charge on the gel is negative, the mobile anions are excluded from the gel (Donnan exclusion, upper panel) and a Donnan potential is established across the hydrogel-electrolyte interface.When the polarity of the applied voltage is opposite to the Donnan potential, the mobile anions are pushed toward and accumulate at the interface (middle panel). Due to the requirement for bulk electroneutrality the accumulationof anions is accompaniedby the accumulationof cations. The concentration of current carriers increases, and the conditions become favorable for the flow of current (mainly cationic).When the external voltage has the same polarity as the Donnan potential the mobile anions migrate away from the interface. Since the fixed negative charges of the gel do not participate in the current flow the interface becomes depleted of mobile anions, and due to the requirement for bulk electroneutrality the interface is also depleted of cations. This interface has a very low number of current carriers, and the conditions become unfavorable for current flow (lower panel). . When the fixed charge on the hydrogelis positive similar events occur at the hydrogel-electrolyte interface with the opposite voltage dependence.
the current-voltage relationship of the pipette is linear. This indicates that there are no detectable nonlinearities within the electrodes,at the liquid-liquid interfaces, and/ or arising from strong electric fields.ll When a charged gel microsphere was attached to the pipette diode-like rectification was observed (Figure lB, filled circles). The good fit between the predicted current-voltage relationship (eq4) and the experimental data (Figure 1B)supports our conjecture that rectification is caused by the accumulation and depletion of charge carriers at the hydrogel interface. To veri@ this hypothesis we used pulsed-laser fluorescence microsc0py~9~ to monitor the ionic gradients at the interface between a natural anionic gel and an electrolytic solution. The fluorescent anion, fluorescein, was used as (11)Onsager, L. J. Chem. Phys. 1934,2, 599.
an ionic probe. Anionic fluorescein was homogeneously distributed in the absence of an applied voltage. After applying a voltage pulse (-9V then +5 V, Figure IC) there was a redistribution of fluorescein, but there was no detectable penetration of fluorescein into the hydrogel. Although some penetration is required for entropicreasons it was not resolved by the instrument. The rearrangement ofions at the gel-electrolyte interface is not instantaneous (milliseconds, Figure 1D). It was recorded by firing the pulsed laser at various times during the buildup of an electrolyte gradient (1 and 4 ms after the onset of a -9 V pulse) and during its dissipation on reversing the polarity of the potential (9, 15, and 30 ms) (Figure 1D). This rapid appearance of the electrolytegradient parallels the increase in ionic current while the collapse of the ionic gradient is correlated with the decrease in the current. The snapshots at 9 and 15 ms show the expulsion and dispersion of the accumulated ions from the gel-electrolyte interface (observethe migrating band in the image taken at 15 ms). This is followed by the successive depletion of the ions from this interface (snapshots at 15 and 30 ms). Similar results were obtained with the synthetic amphoteric gel microspheres (6 pm). This indicates that the accumulation or depletion of charge carriers is a general property of the gel-electrolyte interface. In addition, the direction of the I,,, was reversed when the fixed charge of the hydrogel was titrated from net negative to positive values. This is consistent with the expression derived for the I,, (see above). It predicts that the reverse current should change direction upon reversing the sign of the accumulation charge. As expected the gel did not rectify the current when its fixed charge was titrated to zero.
Conclusions By the use of pulsed-laser fluorescent microscopy we observed the rapid formation and collapse of ionic gradients at a hydrogel-electrolyte interface. Pulsed-laser imaging should be ideal for examining ionic environments at a variety of interfaces as this technique measures ionic distributions with high spatial and temporal resolution. Our findings show that charged hydrogel microparticles will rectify ionic currents in systems in which the geometry of the electrical field produces an electrically dominant single gel-electrolyte interface as simply illustrated by attaching a hydrogel to a glass micropipette. A similar geometrical configuration consisting of a hydrogel microsphere immersed in electrolyte could be used as an electrical microswitch. An array of hydrogel microswitches could become a component of ”wet”integrated circuits capable of directing the flow of charged molecules,thereby controlling the course and localization of chemical reactions. This is yet another possible application for “smart” hydrogels.12-19
Acknowledgment. We would like to thank Brenda Farrell for helpful discussions and for suggestions on the writing of the manuscript. This work was supported by grants from the NIH and Tacora Co. to J.M.F. We acknowledge salary support for V.S.M. from the NIH grant to A. J. Hudspeth and for P.E.M. from Tacora Co. LA950524Q (12) Osada, Y.; Okuzaki, H.; Hori, H. Nature 1992,355,242. (13)Kajiwara, K.; Ross-Murphy, S. B. Nature 1992,355, 208. (14) Tanaka, T.; Nishio, I.; Sun, S.-T.;Ueno-Nishio, S. Science 1982, 218, 67. (15) Kwon, I. C.; Bae, Y. H.; Kim, S. W. Nature 1991,354,291. (16) Tanaka, T. Sei. Am. 1981,244, 124. (17) Kishi, R.; Osada, Y. J. Chem. Soc., Faraday Trans. 1 1989,85, 655. (18) DeRossi, D., Kajiwara, K., Osada, Y., Yamauchi, A,, Eds. Polymer Gels: Fundamentals and Biomedical Applications;Plenum Press: New York, 1991. (19) Steinberg, I. Z.; Oplatka, A.; Katchalsky, A. Nature 1966,210, 568.
