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J. Phys. Chem. B 2010, 114, 13718–13725
Micropatterned Polyvinyl Butyral Membrane for Acid-Base Diodes La´szlo´ Roszol,† Thuy Lawson,† Vikto´ria Koncz,† Zolta´n Noszticzius,† Maria Wittmann,*,† Tama´s Sarkadi,‡ and Pa´l Koppa‡ Department of Physics, Budapest UniVersity of Technology and Economics, 1521 Budapest, Hungary, and Department of Atomic Physics, Budapest UniVersity of Technology and Economics, 1521 Budapest, Hungary ReceiVed: July 21, 2010; ReVised Manuscript ReceiVed: September 1, 2010
Until now, polyvinyl alcohol (PVA) gel cylinders have been used in electrolyte diodes as a connecting element between the acidic and alkaline reservoirs. In this paper, a new connecting element is reported: a breath figure templated polyvinyl butyral (PVB) membrane prepared with dip-coating from a dichloromethane solution of the polymer in a humid atmosphere. The procedure gives a 1.5-2 µm thick membrane with a hexagonal pattern, the average characteristic length of which is 1 µm. After an acidic etching, it was found to be a good connecting element. The voltage-current characteristics and dynamic properties of PVA and PVB were measured and compared. The PVB membrane has a faster response to voltage changes than the PVA gel, but in both cases, there was a slow drift in the current that prevented it from reaching a steady state. Reproducible characteristics can be obtained, however, after the current reaches a well-defined quasi-steady state. Introduction Concept of an Acid-Base Diode. The scheme of an acid-base (or electrolyte) diode, a special system with engineered complexity,1-3 is shown in Figure 1a. As can be seen, the system has three major parts: an alkaline and an acidic reservoir and a connecting element. To maintain constant and homogeneous concentrations within the reservoirs, both are fed continuously with fresh chemicals (here with aqueous potassium hydroxide and hydrochloric acid solutions), while the connecting element (indicated by a blue rectangle in Figure 1a) is an unstirred zone, free of any advection or convection. Thus, within this zone, the transport of the chemical components takes place only by diffusion and by ionic migration as described by the Nernst-Planck equations.4 When electric voltage is applied between the reservoirs, the voltage-current characteristic (VCC) obtained for this system resembles that of a semiconductor diode (see Figure 1b). This is because in the forward direction (polarity: the alkaline reservoir is positive with respect to the acidic one) potassium and chloride ions migrate into the connecting element forming a well-conducting salt solution there. On the other hand, in a reverse biased diode with an opposite polarity, the electric field drives hydroxide and hydrogen ions into the connecting element. These ions form water there, and thus a layer characterized by low mobile ion concentration and high resistance (ion depleted zone) appears in the connecting element. Electrolyte diodes were studied first in the seventies,6,7 but the majority of the papers5,8-21 was published in the last 15 years. Acid-base diodes are interesting from the point of complex systems (“systems chemistry”22) and nonlinear chemistry2 as reaction-diffusion and ionic migration occur here simultaneously. Simultaneous potential and pH gradients also occur in biological systems, for example, in the inner mitochondrial * To whom correspondence should be addressed. E-mail: wittmann@ eik.bme.hu. Phone: +36-1-4631897. Fax: +36-1-4631896. † Department of Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary. ‡ Department of Atomic Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary.
Figure 1. (a) Schematic view of an acid-base diode: an alkaline reservoir containing an aqueous KOH solution is attached to an acidic one containing HCl via a connecting element (blue rectangle). The arrows indicate flows of fresh solutions to maintain constant concentrations in the reservoirs. If ∆φ < 0, the diode is forward biased. (b) Calculated voltage-current density characteristic (V ) -∆φ). The calculation5 was based on the Poisson-Nernst-Planck equations ([KOH] ) [HCl] ) 0.1 M; concentration of the fixed acidic groups, 4 × 10-3 M; see other details in ref 5).
membrane of the cell.23 In recent experiments, the connecting element was always a polyvinyl alcohol (PVA) based hydrogel cross-linked by glutaraldehyde.5,8-13,17-21 The gel was applied in a form of a cylinder connecting the two reservoirs, as shown schematically in Figure 2a. A hydro-gel (like a liquid) allows diffusion and electric migration of the mobile ions, but it suppresses any disturbing advection or convection which would occur in a free liquid.
10.1021/jp106773y 2010 American Chemical Society Published on Web 10/08/2010
Polyvinyl Butyral Membrane for Acid-Base Diodes
J. Phys. Chem. B, Vol. 114, No. 43, 2010 13719 by its response time and a long-term drift. The response time can be determined assuming that the time evolution after a stepwise change in the boundary conditions starts first with a fast, close to exponential decay due to a rearrangement of the small mobile ions in the connecting element. Experiments show that this regime is followed by a much slower, nonexponential drift, reflecting the slow, creeping motion of some macromolecular ions in the viscoelastic polymer matrix. In the case of a connecting element with a length l (here we assume that the transport is roughly one-dimensional), the response time τD is proportional to the square of the length and inversely proportional to an average diffusion coefficient of the small mobile ions D in the connecting element
τD ∝ Figure 2. Cross-sectional view (not to scale) of the experimental apparatus made of Plexiglas with the acid and base reservoirs (c) and the two types of connecting elements (a) and (b): (a) Swelled PVA gel cylinder (blue) stuck in a PVC disk (red). (b) PVB membrane (blue) fixed between two PVC disks (red) with the help of self-adhesive tapes (double-sided tapes, yellow; single-sided tape, black). (c) The acidic and alkaline reservoirs are fed with 0.1 M HCl and 0.1 M KOH solutions through 2.5 mm diameter channels machined into the Plexiglas with a flow rate of 0.39 mL/min. The junction point of the tubings leading to the voltage sensing electrodes is about 1 cm from the connecting element, and thus the parasitic voltage drop appearing on this short distance is negligible provided that the connecting element has a high enough resistance. The Ag/AgCl voltage electrodes immersed in 1 M KCl solution are connected to the alkaline and acidic solutions via salt bridges containing 10 M NH4NO3 to suppress liquid junction potentials.
Motivation of the Research. It was found9 that although PVA-based gels are generally considered to be “charge-free” they still contain some fixed carboxylic acid groups, whose ionic dissociation leads to fixed negative ions. Model calculations and experiments show that these fixed ions modify somewhat the VCC of the diode9,17,18 compared to an “ideal” fixed-chargefree connecting element. A more problematic property is the long-term instability of the gel applied in the experiments. Namely, the following problems were observed: (1) To fix the gel cylinder between the reservoirs, it is placed into the hole of a polyvinyl chloride (PVC) disk in a dry form because it is the swelling caused by some water that keeps the gel in the hole (see Figure 2a). The swelling, however, is a slow process continuing even after the gel was already fixed in the hole, and a relatively stable VCC can be obtained only after a waiting period of 3-5 days. (2) The acetal bonds of the cross-links hydrolyze slowly in the acidic part of the diode. This leads to a slow but continuous swelling of the gel again and an associated drift in the VCC. To diminish this effect, the acidic medium should be applied during the experiments only, and the gel should be kept in water overnight. (3) There is another type of instability exhibited by the gel: the slope of its VCC in reverse direction grows slowly but steadily on the time scale of days. This indicates that the concentration of the fixed acidic groups increases with the aging of the gel. The above problems initiated our search to find a more suitable material for the connecting element of an electrolyte diode. Characteristic Properties of a Connecting Element. The dynamic behavior of a connecting element can be characterized
l2 D
(1)
Anothersand usually much shorterstime scale which can play a role here is the time scale of the ionic migration τm
τm ∝
l2 Du
(2)
where u is the dimensionless voltage which is in the order of 100 if the voltage is a few volts on the connecting element. So in our experiments, τm , τD, indicating that the “slowness” of the response is due to τD mostly. The above considerations suggest that a thin membranesinstead of a cylindersmade of a material ensuring high ionic mobility would be the ideal connecting element. This is not the case, however, because there is another, basically technical requirement for the resistance Rc of the connecting element
Rc . Rpar
(3)
where Rpar is the so-called parasitic resistance,18 i.e., the resistance of the acidic/alkaline solution between the voltage sensing electrode and the connecting element (Figure 2c). This condition should be met because the parasitic voltage drop Upar on Rpar modifies the measured voltage Um as Um ) Uc + Upar, where Uc is the voltage on the connecting element. If Rc . Rpar, then Uc . Upar, and consequently Um ≈ Uc. The resistance of the connecting element is proportional to its length and inversely proportional to its cross-sectional area A and to RD, the ionic permeability coefficient of the membrane material
Rc ∝
l ARD
(4)
Here, R is the average distribution coefficient of the ionic components between the membrane and the aqueous phase (for a hydro-gel like PVA R ≈ 1). Thus, to obtain a high resistance for thin membranes (small l) ARD should also be small. As the cross-sectional area cannot be smaller than a technical minimum, it is RD of the medium which should be small enough. Furthermore, to achieve better long-term stability in the harsh chemical environment of an electrolyte diode with a strong acid and base, a “tougher” polymeric network is required for the material of the connecting element. Such a densely cross-linked polymeric medium also has the advantage that at the same time ionic mobilities can be much lower. A further aspect is that
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physical cross-links seem to be preferable over chemical ones as they are less vulnerable for chemical attacks. We assumed that polyvinyl butyral (PVB) can meet the above requirements. It is not soluble in water: the interaction of the hydrophobic butyral groups of the polymer provides a physical cross-linking. At the same time, the polymer also contains some hydrophilic hydroxyl groups. (This is because when PVB is produced in a reaction of PVA with butyraldehyde the acetal ring formation requires two neighboring hydroxyl groups, and thus the remaining single isolated hydroxyl groups cannot react with the excess butyraldehyde.) We hoped that these hydroxyl groups might form hydrophilic regions, ensuring some ionic conductivity within the polymer. As the ionic conductivity of polyvinyl butyral was expected to be very low, we aimed to prepare thin membranes of the polymer. While developing the technique of producing such membranes, we rediscovered the breath figure method24 in a modified form. A microscopic view shows (see Figure 4) that with our technique hexagonal micropatterned membranes are formed. This is advantageous because in the middle of the hexagons the membrane can be much thinner than the average thickness without endangering the mechanical stability of the membrane. Furthermore, by chemical etching of the membrane, some of the butyral groups can be hydrolyzed to construct ionconducting “channels” at the bottom of the hexagonal pits, and the active cross-section of these channels is only a small fraction of the total membrane area. The aim of the present paper is to describe a method for the preparation of micropatterned polyvinyl butyral membranes and to compare the performance of these membranes with PVA gels as connecting elements in acid-base diodes. Experimental Section Chemicals. Polyvinyl alcohol (15 000, Fluka), polyvinyl butyral (MW 100 000-150 000, Polysciences), dichloromethane (Sigma Aldrich, puriss p.a.), 1 M hydrochloric acid (Fluka, analytical), and 1 M potassium hydroxide (Fluka, analytical) were used. PVA Gel Cylinder. The polyvinyl alcohol (PVA)-glutaraldehyde gel cylinder was prepared as described previously.18,20 The gel cylinder was inserted into a hole drilled in a PVC disk (Figure 2a). The gel was fixed with the same technique as before:18,20 first the gel was dried, and the shrunken dry gel cylinder was placed into the hole. Then, a droplet of water was put at both ends of the gel. When the water swells both ends, the gel is fixed tightly in the hole. The length (l) and the diameter (d) of the hole were l ) 0.5 mm and d ) 0.6 mm. The effective length of the gel18 was about 1 mm. (The actual length was about 2-3 mm.) The PVC disk with the gel cylinder was inserted into the apparatus as shown in Figure 2c. Preparation of the PVB Membrane. The membrane was prepared from 2.2% (w/w) polyvinyl butyral in dichloromethane as solvent. To prevent evaporation losses, the polymer solution was stored in a tightly closed glass bottle. To destroy polymer aggregates formed while storing, the solution was stirred magnetically in the closed bottle for at least 30 min before its use. Meanwhile two stripes of paper towel (width 2 cm) slightly wet with distilled water were pressed onto the inner surface of a glass cylinder (inner diameter 28 mm) in opposite positions (see Figure 3a). Next, the glass cylinder standing on a piece of dry paper towel in a Petri dish was placed into a thermostat set to 20 °C. Then, the lower two-thirds of a glass microscope slide (76 × 26 × 1 mm) was dipped into the PVB solution, and the
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Figure 3. Steps of the membrane-preparation process (not-to-scale cross-sectional views): (a) Making a thin membrane (blue) on a microscope slide in a glass cylinder having wet stripes of paper towel (brown) in opposite positions on the inner surface. A PVC disk (gray) at the top keeps the slide in a vertical position, but it does not close the glass cylinder: it is open to air during the process. (b) Separation of the thin membrane from the slide with the help of a single-sided adhesive tape (black). (c) Fixing the membrane between the PVC disks (red) with the help of double-sided adhesive tapes (yellow).
slide was put into the glass cylinder in a vertical position, parallel to the two wet paper stripes. This way the glass slide gets dipcoated with the PVB solution from which the solvent evaporates in a humid atmosphere. During the evaporation, the glass cylinder was kept opened at the top to the laboratory atmosphere. After complete evaporation of the dichloromethane (approximately 1 h), a thin layer of PVB membrane was left on the two sides of the slide. For the experiments, the upper middle part of the membrane was used where a white haze indicating pattern formation was intense and uniform. To fix the membrane between two 30 mm diameter PVC disks (Figure 2b), the following method was used. Both PVC disks have a concentric hole with a diameter of 4 mm. Onto both PVC disks, a ring-shaped double-sided adhesive tape (Tesa) was glued, having an inner diameter of 4 mm and an outer diameter of 22 mm. A 1 mm region at the upper part of the PVB membrane was separated a bit from the slide using a razor blade. Then, a ring-shaped single-sided adhesive tape (Tesa) having an inner diameter of 1 mm and an outer diameter of 22 mm was glued to the membrane close to the separated part. The membrane was pulled down from the slide with the help of this adhesive tape (see Figure 3b). Finally, the membrane was glued between the PVC disks (Figure 3c). This unit is placed into the apparatus, and this way the acidic and alkaline reservoirs are connected via the free, uncovered part of the PVB membrane with a diameter of 1 mm. To achieve appropriate ionic conductivity and high enough current, we found that etching of the membrane is useful. For this purpose the membrane was kept in 1% (w/w) PVA in 1 M HCl solution for 24 h at 20 °C. Before etching, the solutions together with the membraneswas deaerated with an aspirator for 5 min. The conductivity of the membrane was checked, and if it was not high enough, the procedure was repeated. During etching, some of the hydrophobic butyral groups in the PVB membrane are exchanged to hydroxyl groups providing a more hydrophilic membrane with higher ionic conductivity. Apparatus. The apparatus for measuring the current was the same as in our previous experiments.5 The alkaline and the acidic reservoirs contained solutions of 0.1 M KOH and 0.1 M HCl, respectively. To achieve constant ionic concentrations in the reservoirs, a continuous flow of the liquids was maintained
Polyvinyl Butyral Membrane for Acid-Base Diodes by a peristaltic pump as shown in Figure 2c. The flow rate was 0.39 mL/min. A Keithley 2410 sourcemeter was used as the voltage source in four-wire remote sensing mode. The voltage polarizing the membrane was measured close to the ends of the PVA gel or PVB membrane as shown in Figure 2c. In reverse mode, the resistance of the gel/membrane is large enough (compared to that of the free acid and alkaline solutions in the channels of the Plexiglas), and thus the potential drop between the electrode and the end of the gel/membrane (parasitic voltage) is negligible. This way the measured voltage equals the potential drop on the gel/membrane. In a forward biased diode, the parasitic voltage can be somewhat higher, but it is still not dominant. Electron Microscopy. A Jeol 840A scanning electron microscope was applied to disclose the structure of the PVB membrane. The accelerating voltage was 20 kV, and the electron current of the beam was 10-10 A. To raise the electric conductance of the samples, they got a thin gold coating. The thickness of this gold film was 20 nm. This thin film had no significant effect on the images because the resolution limit of our electron microscope was 50 nm on the surface.
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Figure 4. Electron microscopy image of the front side of the PVB membrane that contacts moist air during the membrane formation process. The white scale bar represents 10 µm.
Results and Discussion Structure of the PVB Membrane. It is known that PVB can form relatively strong films even in a thin layer. This property is widely applied in electron microscopy where 25-30 nm thick PVB membranes are often used as support films.25 These thin and transparent films are produced with a technique similar to our membranes (except the suggested chlorinated organic solvent is chloroform or ethylene dichloride, while in our case it is dichloromethane). There are two important differences, however, in the membrane making recipes. First, as we wanted to obtain a stronger membrane, a more concentrated PVB solution was applied than in electron microscopy. (2.2% PVB is dissolved in the organic solvent for our membrane, while it is only 0.3-0.5% for the support films.) It is a more important difference that we prepare our membrane in a humid atmosphere, while the transparent support films are made in a dry environment. This is because we have observed that hazy white membranes prepared in moist air have a much higher ionic conductivity than the ordinary transparent ones produced in a dry environment. Optical and electron microscopy was applied to disclose the structure of the hazy white membranes. A regular pattern could be realized already by an optical microscope, but the details of the structure could be seen well by an electron microscope only (Figures 4 and 5). The PVB membrane has two sides: a “front” side (Figure 4) where a honeycomb pattern is formed and a “back” side (Figure 5) which originally was contacting the glass microscope slide substrate. Figure 4 shows a hexagonal pattern where the regular structure is frequently interrupted by defects. The honeycomb pits (diameter 0.8-1.5 µm) are relatively close to each other: the thickness of the thin wall separating them is about 100 nm only. Figure 5 shows the back side of the membrane. (To study this side of the membrane, it was separated from the glass substrate with the technique described in the Experimental Section.) The back side pattern has a larger length scale than that of the front side one. The size of the structure units is 5-10 µm. The arrangement of these irregular spots is random, and it seems to be independent of the honeycomb structure of the front
Figure 5. Electron microscopy image of the back side of the PVB membrane that contacts the microscope slide during the membrane formation process. The white scale bar represents 10 µm.
side. These spots can be detected with optical microscopy even before removing the membrane from the glass surface. Figure 6 shows the “edge” and the back side of the membrane separated from the glass substrate. Unfortunately, this is a cut edge (the membrane was cut by a razor blade), and cutting obviously destroys the original structure of the membrane. Nevertheless, the thickness of the membrane can be measured this way, and it was found to be between 1.5 and 2 µm. Two fundamental questions arise regarding the patterns shown in Figure 4: (i) How these patterns were formed? (ii) Why the hazy patterned membranes work better as a connecting element in an acid-base diode than the transparent smooth ones? It was realized that the answer for the first question can already be found in the scientific literature: our patterns can be categorized as “breath figures”.24 These figures are formed if moist air is blown over a solution of a polymer, e.g., linear polystyrene (LPS)26 or carboxylate terminated LPS27 in an organic solvent such as carbon disulfide27 or chloroform.26 Then, evaporative cooling leads to the formation of water droplets on the liquid surface. The monodisperse droplets arrange into a hexagonal
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Figure 6. Electron microscopy image of the edge of the PVB membrane showing the thickness. The pattern from Figure 5 can be also seen. The white scale bar represents 5 µm.
Figure 7. Schematic imagined cross-sectional view of the breathfigure-patterned PVB membrane.
array andsas is usually assumedssink into the polymer solution. Finally, evaporation of the solvent and the water leaves an imprint of the water droplets as a hollow, air filled, hexagonally ordered bubble array in the thin polymer membrane. In our case, however, because of the vertical position of the glass slide and the liquid surface, sinking of the droplets cannot be a gravity assisted process. Also, an assumed levitation of the droplets above the liquid surface27 is not possible in a vertical position. It is more probable that the droplets touch the surface,28 and interfacial forces control the movement of the droplets and the polymer solution. It is important to mention that the ionic conductivity of the breath-figure-patterned PVB membranes is around 100 times higher than that of the smooth and transparent PVB membranes prepared with the same method but in a dry atmosphere. That increased conductivity is probably due to highly conductive spots at the bottom of the hexagonal pits. Here, the membrane can be much thinner (see Figure 7), and moreover, water condensation during the preparation of the membrane might orient the polar hydroxyl groups29 of the PVB, creating ion conducting “channels”. Comparing Voltage-Current Characteristics of Diodes with PVA Gel and with the PVB Membrane. To compare their performance as a connecting element, the VCC of the PVA gel cylinder and the PVB membrane has to be measured in an acid-base diode. To obtain reproducible data, however, first the problem of the drift should be addressed. As was already mentioned in the Introduction, the time evolution of the diode current after changing the applied voltage consists of a fast close-to-
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Figure 8. Voltage-current characteristics of a PVA gel and a PVB membrane. The red dashed line denotes the scaled current of the PVB with the ratio of the forward currents as the scaling factor (about 2.5). The concentrations in the reservoirs: [KOH] ) [HCl] ) 0.1 M.
exponential change followed by a slow nonexponential drift. The drift persists for several hours: after the first 10 min, it is of the order of 0.1 µA/min, but later it decreases. So, to get reproducible results, the characteristics of the PVA gel and the PVB membrane shown in Figure 8 were measured by programming the Keithley instrument in the following way. The current was measured by setting the time delay to 9 s which means that the current was measured approximately every 9.5 s. The source voltage was set first to -10 V (reverse mode), and 180 data points were collected which covers about 29 min. Then the applied voltage was stepped through the sequence -8, -6, -4, -2, -1, 0.4, 0.8, 1.2, 1.6, and 2 V with 60 measurements covering 9.5 min in each point. At a certain voltage, the current is defined as the average of the last 12 points. This method ensures a good reproducibility because the applied waiting time is long enough to reach a quasi-steady-state current (see the subsection on the transient behavior). We have to mention that the acetal bonds in both polymers, especially in PVA and to a lesser extent in PVB, are vulnerable for an acid-catalyzed hydrolysis. This can be observed when these polymers are kept in the apparatus for a longer time where they are in a continuous contact with the acidic reservoir of the diode. After a few days, the VCC of these polymers changes: the absolute value of the current gradually increases. This effect is minor in the case of PVB membranes, but it is more pronounced for PVA gel cylinders. Furthermore, on the time scale of days and in the case of PVA only, the slope of the characteristic in reverse mode grows significantly. This indicates that the number of the fixed acidic groups is growing somehow in the gel. It is known that glutaraldehyde in solutions is susceptible to aerial oxidation to give the corresponding carboxylic acid. Thus, after an acidic hydrolysis of one of the two acetal bonds of the glutaraldehyde cross-linker, the aerial oxidation of the freed aldehyde group can lead to a fixed carboxylic group. Slope of the VCC in Forward Direction for PVA and PVB. For an acid-base diode with a strong acid (e.g., HCl) of concentration c0 and with a strong base (e.g., KOH) with the same concentration, the following formula can be applied for the slope of the VCC in forward direction9,12
s)
dI A ) F (DK + DCl)Rc0 du l
(5)
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where F is the Faraday constant; DK and DCl are the diffusion coefficients of the potassium and chloride ions, respectively; and u is the dimensionless voltage
u)
F U RT
(6)
Here, U is the voltage in volts; R is the gas constant; and T is the temperature. The original formula of eq 5 in refs 9 and 12 was extended here by adding the distribution coefficient R, as the R ≈ 1 approximation can be valid only for dilute hydrogels. Equation 5 can be applied for both PVA and PVB, and the following relationship between the parameters can be derived
(DK + DCl)PVBRPVB lPVB APVB sPVB ) (DK + DCl)PVARPVA lPVA APVA sPVA
(7)
On the basis of the geometrical data given in the Experimental Section, the following estimates can be applied
lPVB APVB ) 10-3 and ) 0.36 lPVA APVA
(8)
Furthermore, we can assume that RPVA ≈ 1, and according to Figure 8, the ratio sPVB/sPVA ≈ 0.4. This way, a rough estimate for the RD value in PVB can be obtained as
DPVBRPVB ∼ 10-4DPVA
(9)
where DPVA and DPVB are some kind of “average” diffusion coefficients (average of the diffusion coefficients of the potassium and chloride ions) in PVA and in PVB, respectively. Backward Intercept-Forward Slope Ratio of the VCC. The characteristics show that the current ratios of the PVB and PVA diode are different in reverse and forward mode. This effect is shown in Figure 8: the current of PVB scaled with the ratio of the forward currents (red dashed line) does not fit to the current of PVA in the reverse mode. To understand the reason for the above effect, the I0/s ratio was calculated for both the PVA gel cylinder and the PVB membrane where I0 is the intercept of the VCC diagram in the reverse direction. The intercept I0 can be expressed9,12 as
A I0 ) 2F (DH + DOH)Rc0 l
(10)
where DH and DOH are the diffusion coefficients of the hydrogen and hydroxide ions, respectively. Thus, the I0/s ratio is
I0 DH + DOH )2 s DK + DCl
(11)
which depends on the ratio of the diffusion coefficients in the connecting element only, and it is independent of other parameters. If we substitute the numerical values of the diffusion coefficients measured in dilute water30
2
DH + DOH ) 7.2 DK + DCl
(12)
The measured I0/s value for the PVA gel cylinder is 8.2-8.5. Naturally, the diffusion coefficients in the gel are smaller than in water; however, one can expect that the medium in a hydrogel is mostly water-like, so the ratio of the diffusion coefficients should be the same in the gel and in water. This 15-20% deviation is probably due to the parasitic voltage which can play some role in the case of higher currents of the forward direction. This makes the measured slope smaller, and thus the I0/s ratio is higher than would be expected. The I0/s value for the PVB membrane is much smaller: it is only about 2.4. This large deviation indicates that the PVB membrane is qualitatively different from an aqueous medium. It is known that the unusually high diffusion coefficients of hydrogen and hydroxide ions in an aqueous medium compared to other ions are due to the Grotthus mechanism.31,32 It is rather obvious that in a nonaqueous medium like the PVB that this mechanism cannot help the diffusion of hydrogen and hydroxide ions. If all small ions would have the same diffusion coefficient in the PVB medium, then the I0/s value would be 2. The measured 2.4 is remarkably close to that value, especially if a correction due to parasitic voltage is also taken into account (like in the case of the PVA gel). Transient Behavior of the Diode. While recording the VCC, the quasi-steady-state current values were measured as described in the previous subsection. However, we also wanted to characterize the transient period to see if there is any difference between the PVA gel and the PVB membrane. Hence, to study the response of the diode to quick voltage changes, the following experiment was performed. The voltage was switched between forward (0.2 V) and reverse (-2 V) mode several times periodically. The voltage was kept at a fixed value for 10.25 min, and four periods were recorded. In each state, the current was measured with auto delay (∆t ≈ 0.07 s) in the first minute, then with a 2 s delay, and in the last five minutes with a 5 s delay. In Figure 9, the measured current is shown as a function of time in diodes based on the PVA gel and PVB membrane. As can be seen, both periodically forced dissipative systems (diodes) approach to limit cycle oscillations:33 the measured current-time curves are close to periodical except for the first cycle. It is interesting to see that when switching the diode from forward to reverse mode a great peak occurs, especially with the PVA gel. A similar rapid response was already observed by Slouka et al.34 where the system was set from 0 to -10 V. In Figure 10, the time evolution of the reverse current is compared for the last three periods. In this figure, the three periods are shifted to a common starting point, and the currents are scaled with the following method. In the case of PVA, the reverse current is scaled to the interval of -1 to 0 after subtracting the maximum value of the three periods (i.e., the approximate quasi-steady-state value). In the case of PVB, first the current is scaled to get approximately the same forward current as with PVA, and then the maximum value is subtracted and the same scaling factor as with PVA is used. This way, the three curves agree almost perfectly in the case of PVA, while with PVB there is a small deviation indicating that the approach to the full limit cycle is faster in the case of the PVA gel. (The difference between the average measured current in the last 100 s of the third and the fourth period is about 0.01 µA with PVA and 0.5 µA with PVB.)
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Roszol et al. segments they are attached to. As a consequence, the number of the fixed charges in that zone and the absolute value of the reverse current decrease. Since the changing of the polymer structure is a much slower process than diffusion and migration of free ions, it is observed on a different time scale and results in a slow drift. Conclusion
Figure 9. Switching the voltage between forward (0.2 V) and reverse (-2 V) mode periodically. The period time is about 20.5 min. The concentrations in the reservoirs: [KOH] ) [HCl] ) 0.1 M.
Figure 10. Scaled reverse current from Figure 9: the last three periods are shifted to a common starting point, and the currents are scaled. First, the current of PVB is scaled with the ratio of the forward quasisteady-state currents, and then both currents are scaled with the same factor.
Because of the jump in the current appearing when the voltage is switched from forward to reverse mode (see Figure 9), the steady-state current is approached not from the smaller but from the higher absolute value with both materials. On the other hand, there is a qualitative difference between the PVA gel and the PVB membrane in the first seconds: with PVA the absolute value of the current still increases in the first 0.6-0.7 s, while with PVB the current decreases monotonically. In the case of the PVA gelsas one our reviewers pointed outsthe first 0.6-0.7 s is the time needed to remove (by migration) the potassium and chloride ions accumulated in the diode previously in an open mode. When H+ and OH- ions migrate into the gel to substitute the slower (less mobile) K+ and Cl- ions, the conductivity of the gel and consequently the current increases gradually until a point when the depletion zone starts to form. The estimated migration time (when OH- and H+ ion fronts meet in the gel) is in the order of 1 s. After that point, the current decreases due to the increasing resistance of the depletion zone. In the case of the PVB membrane, however, in the absence of the Grotthus mechanism all ionic mobilities are roughly equal. Consequently, substitution of K+ and Cl- ions by H+ and OHions, respectively, does not increase the ionic conductivity and the current. This explains the missing maximum in the case of PVB. In separate experimentssnot shown hereswe could observe that the slow drift of the current was going on also after an hour. A possible explanation for the drift in reverse mode can be the presence of fixed charges in the PVA and in the PVB: namely, the force acting on the fixed charges in the electric field can move them slightly since the structure of the polymer is not rigid. Thus, the “fixed” negative charges in the ion depleted zone of the diode are not really fixed, but due to the high electric field they move slowly together with the polymer
The aim of the research was to develop a connecting element for acid-base diodes which is better for this purpose than the traditional PVA gel cylinder. This aim was reached partially with the breath-figure-patterned PVB membrane. Namely: • The swelling problems typical for the PVA hydro-gel cylinders and hampering the measurements can be avoided by applying nonswelling PVB membranes. • The PVB membrane tolerates longer the acidic environment of an acid-base diode. This is because the penetration of the acid into the PVB is hindered, while it can diffuse more freely into a hydro-gel like PVA. As a result, the acidic hydrolysis of the acetal bonds is much slower in PVB than in PVA. • A gradual increase of the concentration of the fixed acidic groups due to aerial oxidation of the glutaraldehyde cross-links in the PVA does not occur in PVB. • The resistance of the PVB membrane in the forward direction is about 2.5 times higher than that of the PVA gel. This is remarkable because the PVB membrane is an about 3 orders of magnitude thinner connecting element than the PVA gel and also has a larger cross-section. The higher resistance results in smaller parasitic voltage (a deviation between the measured and the actual voltage on the connecting element). • The response time of the PVB membrane is much shorter than that of the PVA gel. • At the same time, a long drift of the backward current is observed for both connecting elements. In this respect, the performance of PVB is not better. To eliminate this problem, in the future we want to decrease the concentration of fixed acidic groups in the PVB membrane. Furthermore, it was found that the mechanism of ionic conduction in PVA and in PVB is somewhat different: • The conductivity of the PVB membrane is not only lower than that of the PVA gel but also “inhomogeneous”: the structure of the PVB membrane suggests that spots of higher conductivity can be present at the center of the hexagonal pits. • In the PVA gel, the ionic diffusion coefficients of the hydrogen and hydroxide ions are higher than that of the potassium and chloride ions, just like in free water. This is not the case with the PVB membrane: the diffusion coefficients are nearly equal to each other. This suggests that while diffusing through the membrane the ions are not in a true aqueous environment where the Grotthus mechanism can help the transport of the hydrogen and hydroxide ions. Acknowledgment. This work was supported by OTKA Grant Nos. 60867 and 77908 and by the Nanophysics Research Project of the Budapest University of Technology and Economics TAMOP-4.2.1/B-09/1/KMR-2010-0002. References and Notes (1) Kiss, I. Z.; Rusin, C. G.; Kori, H.; Hudson, J. L. Science 2007, 316, 1886–1889. (2) Grzybowsky, B. A. Chemistry in motion; Wiley: Chichester, 2009. (3) Makki, R.; Al-Humiari, M.; Dutta, S.; Steinbock, O. Angew. Chem., Int. Ed. 2009, 48, 8752–8756. (4) Rubinstein, I. Electro-Diffusion of Ions; SIAM: Philadelphia, 1990.
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