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DC electric fields produce periodic bending of polyelectrolyte gels
Polymer 52 (2011) 2430e2436
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DC electric fields produce periodic bending of polyelectrolyte gels A.P. Safronov a, *, M. Shakhnovich b, A. Kalganov c, I.A. Kamalov a, T.F. Shklyar b, F.A. Blyakhman b, G.H. Pollack c a
Chemistry Department, Urals State University, 51 Lenin St., Yekaterinburg 620083, Russia Biomedical Physics Department, Urals State Medical Academy, 3 Repin St., Yekaterinburg 620219, Russia c Department of Bioengineering, Box 357962, University of Washington, Seattle, WA 98195, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 February 2011 Received in revised form 18 March 2011 Accepted 24 March 2011 Available online 31 March 2011
The periodic bending of polyelectrolyte hydrogels made of polyacrylamide, polyacrylic and polymethacrylic acids with 10% ionization under the DC electric field was observed in 0.8 mM CaCl2. When the field with intensity 13.5 V/cm was applied perpendicular to the longitudinal axis of the gel sample, the gel first bent to cathode, then more substantially to anode, then to cathode again and so on with damping amplitude. Within experimental error up to two periods of such oscillations were observed. The maximum amplitude of bending was approximately 30% of sample length. After 150e200 s, the gel sample finally reached a steady state slightly bent to anode. During these oscillations the volume of the sample gradually decreased by 10e30% depending on the gel. Kinetics of displacement of the free end of the gel sample could be fitted by a damped sine wave function, depending initial amplitude, final displacement, wave period, and decay time. All parameters except wave period depended on sample cross-section. The amplitude, wave period and decay time decrease with the increase of initial degree of gel swelling. The physical basis of the periodic bending is discussed based on the theoretical approach of Doi, Matsumoto and Hirose, although that theory can describe only initial cathodic and successive anodic displacement of gel. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Hydrogels Polyelectrolytes Swelling
1. Introduction When a polyelectrolyte gel is placed in an electric field, free ions that are present in the gel and surrounding solution begin moving to the oppositely charged electrode. Consequently, ionic distribution inside and outside the gel becomes non-uniform. As ionic concentration is one of the major repulsive factors that affects gel volume, its variation inevitably results in volume changes and hence the mechanical response of the gel. As easy as it may be to formulate the principal idea that polyelectrolyte gel will mechanically respond to the electric field, it is less easy to predict a priori which way it will respond. Experiments show that predicting gel behavior in electric fields is far from trivial. The first observation of a field-induced deformation of a partly hydrolyzed polyacrylamide gel was made in the early 80-ies by Tanaka et al. [1], who found that when a rodlike specimen is placed between electrodes in close contact with them, the anodal side of the gel shrinks proportionally to the voltage applied. A similar
* Corresponding author. E-mail addresses: [email protected] (A.P. Safronov), Felix.bljakhman@ usu.ru (F.A. Blyakhman), [email protected] (G.H. Pollack). 0032-3861/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2011.03.048
effect was observed as well by other workers [2,3]. The initial interpretation was based on the mechanical stress that squeezed the gel at the anodal side due to the attraction of the negatively charged network to anode. Later, however, this interpretation was questioned when it was found in several works [4,5] that, if the same specimen is placed at a fixed position separated from the electrodes, the anodal side of the gel swells. In some gels the swollen anodal part later began to shrink as the electric field was maintained. Shiga et al. [4] pointed out that these phenomena might be induced by the change in the ionic distribution under the electric field. These and other experimental results [6] obtained in the 90-ies provided the background for research on polyelectrolyte gels as electroactive smart materials. The review by Shahinpoor and Kim [7] for example, focused on polyelectrolyte actuators, sensors, and transducers which basically are made of metal-plated gel strips, bending as voltage is applied to metal films on both sides of the strip. When the gel is anionic then the strip bends toward the anode; when the gel is cationic the bending occurs toward the cathode. The principle of such devices is based on the early results of Tanaka as bending occurs due to the shrinking of the strip side adjacent to certain electrode. Another extensively studied field of application is electro-responsive drug delivery from hydrogels. One
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may address the review by Murdan [8] for details. Generally, such applications are based on the overall contraction of the gel under the influence of a steady electric field. If some therapeutic agent is incorporated inside the gel network, then the contraction of gel will cause exudation of the drug into target tissues. Its worth mentioning the opposite influence of the electric field upon anionic hydrogels found in Ref. [9] where it was shown that poly(acrylic acid) gels substantially swell when placed in phosphate buffer saline between electrodes sealed in polyethylene to avoid direct contact with solution. The swelling reached saturation during ca 100 h, and besides this the dependence of swelling on the distance between gel and electrode was also demonstrated. Theoretical interpretations of mechanoelectric effects in gels may be placed in one of the three categories: physical models, black box models, and gray box models [7]. Physical models are based on detailed consideration of underlying physical mechanisms believed to govern electromechanical response. For black box (empirical) models physical features are only a minor consideration and model parameters are based solely on system identification. Gray box models are suitable combinations of the first two. Objectives of practical applications better match two last categories of models as they are specially designed to obtain quantitative results important for practical use based on empirical tunable parameters. One may find the examples of such theoretical approaches in the aforementioned reviews [7,8]. However, these models are limited to the systems with well-defined and predictable behavior. Physical models generally are not as distinct in quantitative predictions but they are more fruitful in maintaining understanding of specific and controversial features of gel behavior. It looks that up to now the most realistic and flexible physical model of electromechanical effects in polyelectrolyte gels is the one introduced by Doi, Matsumoto, and Hirose [10] and developed for the most common anionic poly(acrylic acid) gels. Basically, all physical models of polyelectrolyte gel take into account the following: (i) volume interactions between polymer network and the solvent; (ii) elastic entropic deformation of macromolecular coils between crosslinks; (iii) translational entropy of free counterions; (iv) DebyeeHuckel electrostatic interactions, which, however, in most cases are not taken into account as negligible [11]. Doi and co-authors [10] restricted their consideration solely to the osmotic pressure of mobile ions which depended on the difference of concentration inside and outside the gel. Therefore they defined their theory as qualitative. However, this theory correctly predicts qualitative tendencies in gel volume changes as the increase or decrease in osmotic pressure will inevitably result in corresponding gel swelling or contraction. At the same time the theory includes all possible contributions to the ionic concentration. In addition to commonly considered counterions inside gel network that compensate charged monomer units and external salt ions, Doi and coauthors [10] also took into account self-dissociation of water and dissociation of acidic monomer units. Due to these extra variables of the theory ionization degree of the network and its total electric charge became the function of ionic concentration. As a result, Doi, Matsumoto, and Hirose theory successfully described both the shrinkage of the gel in contact with anode and the swelling of the anodal side if separated from anode. The theory predicted as well that this swelling might switch to contraction when the field was kept applied for a longer time. However, it was not tested experimentally. Based on theoretical predictions and published experimental data we intended to model in the present study the mechanical response of the living cell to the applied electric field with the use of synthetic polyelectrolyte gels. As it was shown in the book by one of the authors [12] many biophysical phenomena including muscle contraction and propagation of nerve excitation can be the result of
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phase transition in cell gel structure accompanied with electromechanical effects. We believe that synthetic polyelectrolyte gels of partly neutralized polyacrylic and polymethacrylic acids could be a suitable model for this. Then our objective was to study the dynamics of mechanical response of the rodlike polyelectrolyte gel samples placed in DC electric field across the field lines apart from the electrodes in the presence of mono and bivalent ions typical for living systems. Below we will present experimental data which will show that at the early stage the mechanical response of the gel closely follows the predictions of the theory [10] but further behavior strongly deviates from it. We have found that bending of polyelectrolyte rod in DC electric field is periodic, which we believe is completely new phenomenon never reported before.
2. Experimental part Gels of poly(acrylic) (PAAc) and poly(methacrylic) (PMAc) acid and their copolymers with 90% (mol) of acrylamide were prepared by free-radical polymerization with N,N0 -methylene-diacrylamide as a cross-linker in aqueous solution. All reagents were purchased from Merck (Schuchardt, Hohenbrunn). Each gel had 10% of ionized monomer units. In order to achieve this, 10% of acid monomer were neutralized by the required amount of potassium hydroxide or magnesium oxide before polymerization, which gave fully dissociating acrylate or methacrylate units in the gel network. In each case the overall monomer concentration was 2.7 M, while the cross-linker to monomer concentration was set at 1:100. Ammonium persulphate (0.5 g/l) was used as initiator. Polymerization was carried out in PE probe tubes 10 mm in diameter for 1 h at 80 C and then 3 h at 50 C. After polymerization, gel samples were washed in distilled water to remove the sol fraction and free salts. Water was renewed every day for 2 weeks. The degree of swelling of gel samples was determined by measuring the net weight of the residue after drying. Notification, composition and equilibrium degree of swelling in water at 25 C for all gels under study are given in Table 1. Gel samples for electromechanical experiments were cut by a razor blade. Their dimensions were ca 10 mm in length and 1 1 mm in cross-section. The schematic picture of the experimental design is presented in Fig. 1. The cell was made of a Teflon ring 5 mm in height and 20 mm in inner diameter mounted upon a glass plaque. Two 5 5 mm Ag foil electrodes were placed at the opposite walls of the cell. All experiments were performed under constant voltage conditions at 27 V DC. The gel sample was positioned in the center of the cell between electrodes with its longer axis across field lines. One end of the sample was fixed in a gap in the wall of the cell, while the other end was left free to move in the applied field. During the experiments the cell was filled with 7 ml of 0.8 mM CaCl2 to cover on electrodes and the gel sample. Computerized optical system of laboratory design was used for the video
Table 1 Composition of gels. Notification PAAc/KA
Acid monomer
Acrylic acid 90% (mol) PMAc/KM Methacrylic acid 90% PMAc/MgM Methacrylic acid 90% PAAm/MgM e
Ionized monomer
Acrylamide Counterion Degree of monomer swelling
Acrylate 10%
e
Methacrylate e 10% Methacrylate e 10% Methacrylate 90% 10%
Kþ
66.9
Kþ
28.1 2þ
14.6
Mg2þ
40.1
Mg
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Fig. 1. Schematic of experimental setup: 1 e experimental cell; 2 e gel sample; 3 e electrodes; 4 e video camera; 5 e computer.
recording of gel sample bending in the applied DC field. A video camera was placed beneath the transparent bottom of the cell. A combination of red and green optical filters was used to enhance the contrast of transparent gel sample in water. Bitmap video files were analyzed by specially written computer program to digitize the movement of any particular point on the sample image and the time-dependent changes of the total area of the sample. Supplementary video related to this article can be found at doi: 10.1016/j.polymer.2011.03.048. 3. Results and discussion As the general framework of the study was the search for approaches to model electromechanical excitation of living matter, all experiments were performed in weak (0.8 mM) solution of CaCl2 which is the typical Ca2þ concentration outside cell in vivo. Thus, we intended to provide the possibility of Kþ/Ca2þ exchange in synthetic gels which might take place in the cell’s electromechanical activity. As such Ca2þ concentration is lower than the threshold of gel contraction under divalent/monovalent ionic exchange [13], the degree of swelling in this solution remains the same as in water. Fig. 2 presents a sequence of images taken from the video file recorded in a typical experiment when the DC electric field was applied to a gel sample in 0.8 mM CaCl2. At the beginning of the experiment the gel sample remains straight (t ¼ 0). When DC field is applied, the sample starts to bend toward cathode (Fig. 2b). This result is consistent both with earlier experimental data [4,5] and theoretical considerations [10]. Such bending implies that the anodal surface of the sample swells and the sample begins bending toward the cathode. After 15 s bending to cathode stops and the direction reverses; after 30 s the sample almost straightens (Fig. 2c) and then proceeds bending toward the anode (Fig. 2d). As one can see from Fig. 2b and d, “anodal” bending is more substantial than “cathodal” bending. “Anodal” bending is also consistent with the theory: as shown by Doi and co-authors [10], when the electric field is kept on, the anodal surface of the gel begins to contract and forces the gel to bend toward the anode.
The physical reason for two first stages according to the theory [10], are the changes in ionic concentration inside the gel. As it increases, two possible regimes of gel volume changes may take place. In low pH (acidic regime) the increase in ionic concentration results in permanent contraction of the gel. In neutral and basic conditions, however, contraction occurs only at relatively high ionic concentration, but if ionic concentration increases from ca 107 up to ca 105 M its addition causes extra swelling of the gel. The physical reason for such swelling is additional ionization of carboxylic acidic groups in the network due to the substitutions of protons by alkali metal ions, which happens not only in basic conditions but in neutral as well. As it was numerically shown by Doi and co-authors [10] when DC field was applied, concentration of cations and anions decreased at the anodal side of the gel and increased at the cathodal side with time. As the ionic concentration increases at the cathodal side of the gel, it results in the increase of the effective screening of electrostatic forces and the gel network tends to contract. For the same reason the decrease of ionic concentration at the anodal side results in its swelling. While the diminishing ionic concentration at the anodal side remains higher than 105 M the anodal side swells. However, when DC field is kept on for longer time, almost all counterions leave anodal side of the gel and the concentration of ions descends under 105 M. Then the remaining carboxylate monomer units absorb protons from the water solution and reassemble into carboxyl residues, which are non-dissociating, that results in the decrease in gel network ionization and consequent contraction of the anodal side. This speculation is qualitatively consistent with our results. Quantitative comparison with the theory is surprisingly fair. Estimation of the time of the reversal from swelling to contraction at anode side given in Ref. [10] was about 250 s for the gel sample 5 mm in length placed 2.5 mm apart from both electrodes at field intensity 10 V/cm. At almost the same field intensity 13.5 V/cm we have experimentally obtained about 15 s for the sample 1 mm thick 10 mm from each electrode. It is quite reasonable that thinner gel samples more rapidly respond to the effects stemming from ionic migration.
A.P. Safronov et al. / Polymer 52 (2011) 2430e2436
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Fig. 2. Sequential images of PAAc/KA gel bending in DC electric field: a e 0, b e 15, c e 30, d e 60, e 90, f e 150 s from the beginning.
However, as one can see from Fig. 2e and f experimental behavior appears more complicated than predicted by Doi, Matsumoto, and Hirose theory [10]. After having bent toward the anode, the gel does not stop its movement, but begins to straighten back again (Fig. 2f). The amplitude of back movement is lower than during two first phases but it certainly can be observed. Further analysis of video records which will be presented below revealed that the third stage of second “cathodal” movement is followed by fourth stage of second “anodal” movement with decaying amplitude. Thus, we have observed at least two periodic cathode/anode swings of the gel samples without any changes in the polarity and intensity of the applied DC electric field. This result to the best of our knowledge has never been reported before. For now, we know of no theoretical physical interpretation of this result; hence, we will limit ourselves to analysis of the formal wave characteristics of the periodic motions we have found. Fig. 3 presents the kinetics of the displacement of the free end of the gel sample PAAc/KA under DC electric field. Positive shift corresponds to “cathode” and negative to “anode” bending. Three curves corresponding to the samples with the same length (8 mm)
but different width are similar in shape but do not coincide. In each case, the first maximum lies in the positive range of shift values, which means that the gel sample first bends toward cathode. The second maximum and both minima lie in the negative range, which means that after the first displacement toward the cathode the gel sample bends toward anode and its further periodical bendings take place in the “anodal” hemicycle and are in fact periodic changes in sample curvature. The shape of the curve is typical of wave-like kinetics with decaying amplitude, according to which free-end displacement to cathode y(t) can be described by the following function:
t þ t0 t þ t0 sin 2p yðtÞ ¼ yN þ A exp s B
(1)
where A e is the initial amplitude of the wave, s e is the decay time, B e is the period of the wave, t0 e is the time (phase) shift of the wave, yN e is the asymptotic position of the free end with respect to the center of the cell.
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Fig. 3. Time dependence of free-end displacement upon bending of PAAc/KA gel sample in DC electric field. Positive values correspond to cathode shift, negative to anode shift from the initial position. Sample length is 8 mm, width is 1.01 (1), 1.38 (2), 1.42 (3) mm.
Parameters of Eq. (1) for all gels were determined by fitting procedure applied to plots of free-end displacement obtained from bitmap video files. The best-fit values of the parameters for the plots presented in Fig. 3 are given in first three rows of Table 2. Although basic physical interpretation is lacking, formal analysis of the parameters in Table 2 yields the following information on the influence of sample geometry on the damped wave kinetics. As the width (the cross-section area) of the sample increases,
Initial amplitude decreases; Final displacement to anode (negative values) increases; Decay time increases; Wave period does not changes; Time shift increases.
The decrease of the initial (cathodic) amplitude with the thickening of PAAc/KA gels seems reasonable. It might be simply the result of the increase in the tensile strength of the sample due to the increase in its cross-section area. However, comparing Fig. 3 and Table 2 one may notice that A values in Table 2 differ less than positive maxima on corresponding curves in Fig. 3. This is because the height of maximum equals A þ yN, and the actual initial displacement depends not only on the initial amplitude and tensile strength of the sample but also on yN. The increase in negative yN values for the final anodic displacement of the free end can be understood if we refer to the common interpretation of bending as the result of the ionic concentration gradient along the field. It seems reasonable that at long durations some steady ionic distribution will be established. This distribution will be characterized by the certain gradient for each ion present in the gel. For one and the same value of gradient the actual difference in ionic concentrations at the opposite sides of the thick sample will be larger than that for
the thin sample simply because of being proportional to the product of gradient and the distance. Therefore, osmotic pressures at the anodic and cathodic sides for the thick sample should differ more than that for the thin sample and so the first one will be more bent to anode asymptotically. Another group of parameters consist of s, B, and t0, which are “dynamic”. Decay time is basically the characteristic time of ionic transport toward some steady state corresponding to the final displacement yN. Therefore it looks rather reasonable that s follows the same trend as yN, i.e. it increases with sample width as it takes more time to establish a steady ionic distribution across thick sample. Wave period B and time shift t0 are directly attributed to the periodic nature of sample bending. At this moment we can say nothing about the probable driving forces of such periodicity. It is quite clear that the mechanisms included in the Doi, Matsumoto, and Hirose theory [10] provide no basis for periodic bending. From a general point of view there should be some positive feedback mechanism to provide any kind of oscillatory behavior in chemical system. Periodic changes in chemical composition and responding activity are typical for biological systems, but such ability is provided by very complex metabolic sequences including enzymes and other systems. None of this is present in the gels, which basically consist of polymeric stochastic network and several common ions. Therefore, we can only formulate the trends in B and t0 behavior, leaving them without any reasonable comment for now. We were pleased to find that the wave period B does not depend on geometry, being the only such parameter. So, probably, the wave period is exclusively a function of gel structure. Time shift t0 increases with the width of the sample. It is worth mentioning that according to the trend in t0 there could be no initial “cathodic” bending of the gel sample if it were thick enough and t0 were more than a quarter of wave period. Although all parameters except B are geometry dependent, it does not necessarily mean that they do not depend on gel structure. Damped wave behavior was found for all the gels involved in the present research. The time plots of free-end displacement in all cases were similar to those presented in Fig. 3. All these plots were fitted by a damped wave function (Eq. (1)) and the best-fit parameters are given in the last rows in Table 2. Among all the data obtained in the present study we have listed those corresponding to gel samples with close width values to minimize the influence of geometry. One can see from the data presented in Table 2 that wave period B is the most sensitive to the chemical nature of polymer network and the counterion. Wave period increases twice when the hydrophilic polyacrylic network is changed to more hydrophobic polymethacrylic (samples PAAc/KA and PMAc/KM). When Kþcounterion is replaced by Mg2þ (samples PMAc/KM and PMAc/ MgM) the wave period additionally increases by almost twice. Substitution of polymethacrylic acid monomer units by hydrophilic acrylamide results in two-fold decrease in wave period (samples PMAc/MgM and PAAm/MgM). Based on these few examples we may suppose that the wave period increases as the network
Table 2 Parameters of periodic displacement of the free end of the gel sample in DC electric field. Gel sample
Width of the sample, mm
Initial amplitude A, mm
Final displacement yN, mm
Decay time s, s
Wave period B, s
Time shift t0, s
PAAc/KA PAAc/KA PAAc/KA PMAc/KM PMAc/MgM PAAm/MgM
1.01 1.38 1.42 1.40 1.46 1.56
2.62 1.86 1.82 3.0 3.41 2.85
0.27 0.62 1.09 0.94 1.14 0.91
27.7 60.3 68.3 77.1 136 70.8
121 121 124 269 456 249
2.3 9.1 24.9 22.4 33.5 16.8
A.P. Safronov et al. / Polymer 52 (2011) 2430e2436
becomes more hydrophobic and monovalent counterions are replaced by divalent. However, this conclusion should definitely be justified in more extended further study. As for the other damped wave parameters, it is difficult to figure out any clear trend as their values fall within the same range for all the gels under study. However, we have found correlations of these parameters with the initial swelling of the gels, which are given in Table 1. Fig. 4 presents the dependence of “spatial” parameters A and yN on the initial degree of swelling which is basically the inverse density of gel network. Fig. 5 gives the same for “dynamic” parameters s, B, and t0. According to the plots, final displacement yN and time shift t0 are practically independent on the degree of swelling. All other damped wave parameters decrease with an increase of the degree of swelling and a corresponding decrease in network density. The decrease in the initial amplitude at first sight does not correlate with the arguments given above, which were based on the tensile strength of the sample. The tensile strength should obviously be lower for the less dense (more swollen) gels and so the amplitude of the displacement should be larger. However, one should take into account that dense gels contain more electric charges per unit volume than weak gels. This results in stronger interaction with the applied electric field. The decrease of the decay time may be related to the increased mobility of ionic species in weak networks. The decrease in wave period is difficult to interpret as we are still missing general understanding of the underlying mechanism of periodic bending of gel sample. Based on the result that the degree of gel swelling is strongly affecting the damped wave parameters, we suppose that gel volume changes might play the role of feedback mechanism providing the possibility of periodic bending. Fig. 6 presents the changes in the total volume of the gel sample during the application of DC electric field. One may see, that in addition to their bending gel samples contract in the DC electric field which is basically consistent with numerous applications of gels as drug-delivery agents [8]. Such contraction is not taken into account in the Doi, Matsumoto, and Hirose theory [10], but might still be an important feedback mechanism, which provides the periodic swelling and contraction of the gel network. For now we can only give an idea in very general and qualitative way of how it may happen.
Fig. 4. The dependence of the amplitude A (1) and final displacement yN (2) of the damped wave on the initial degree of gel swelling.
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Fig. 5. The dependence of the wave period B (1), decay time s (2), and time shift t0 (3) of the damped wave on the initial degree of gel swelling.
Let us return to the two phases of gel behavior in the applied field that are predicted in the theory. Both phases depend on the decrease of ionic concentration at the anodal side of the gel. When ionic concentrations fall into very low values, the gel at the anode side contracts due to de-ionization of the polymeric network. That is the final stage according to Doi, Matsumoto, and Hirose theory [10]. However, if the gel network gradually contracts as shown in Fig. 6, its volume decreases, and the concentration of ions per unit volume in the gel network increases just due to spatial reasons. This process is in principle favorable to the re-ionization of polymeric network and its re-swelling. Whether the re-swelling will take place or not will depend on local ionic concentration at different sections of the gel. We suppose that the conditions of such local reswelling are fulfilled at the anode side of the polyelectrolyte gel in the DC electric field during its gradual contraction. As a result, the gel network is balancing between swelling and contraction, which provides the driving force for swelling oscillations and the damped wave behavior we have observed. From this viewpoint, however, it is not clear whether the anodic contraction predicted by the theory corresponds to the first displacement of the free end to anode which is proportional to A, or to the final steady state proportional to yN.
Fig. 6. Time dependence of the volume of the gel samples in DC electric field. 1 e PAAc/KA, 2 e PMAc/KM, 3 e PMAc/MgM.
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4. Conclusions The physical reasons of the observed gel periodic bending are not yet clear. The most adequate theoretical approach that can describe at least two phases, the initial cathodal displacement and the next anodal one, is the theory of Doi and co-authors [10] based on the idea that the degree of gel network ionization is a function of the ionic concentration inside and outside the gel. We suppose that further development of this theory, which must take into account gel volume contraction, might be able to describe the damped periodic bending observed in our experiments. When ionic concentration in the anodal side becomes very low, and so does its degree of ionization, gradual contraction of the gel due to the imposed electric field superposes the effects of ionic transport and can cause local dynamic fluctuations of ionic concentrations and gel ionization. These processes result in dynamic oscillations of swelling and consequent damped wave of “swinging” of the free end of gel strip in DC electric field. Another, entirely different interpretational route is based on the presence of large interfacial zones recently found next to gels [14]. Because these extensive zones exclude particles and solutes, they have been termed “exclusion zones”. The effects of electric fields on exclusion zones have not been systematically explored, although preliminary data do show substantial impact. If changes in exclusion-zone size affect the mechanical properties of the respective gel surface, then there could be some contribution to bending. This hypothesis remains to be explored. The separate question that was not at all discussed above is the role of 0.8 mM CaCl2 concentration in the observed behavior. However, without extended research that we plan to do further it cannot be clarified with certainty. Meanwhile, the presence of low concentrations of divalent ions might be important for the periodic bending of the gel. From general point of view our results mean that under certain experimental conditions a relatively simple physico-
chemical process such as swelling of synthetic acrylic hydrogel can take place in periodic manner. In our earlier publication [15] we have presented general theoretical analysis of the possibility of swelling wave propagation along the gel, which may in principle model periodic excitations of biopolymers in cell membranes. However, no underlying physical mechanism was proposed at that time. Now we suppose that periodic swelling due to superposing of ionic transport and gel contraction might be such mechanism. Based on it we believe that our results will certainly extend the limits of biomimetic modeling by synthetic polyelectrolyte gels.
Acknowledgments Authors acknowledge the financial support of Russian Federation AVCP and FCP grants.
References [1] Tanaka T, Nishio I, Sun ST, Ueno-Nishio S. Science 1982;218:467e9. [2] Osada Y, Hasebe M. Chem Lett 1985;9:1285e8. [3] De Rossi DE, Chiarelli P, Buzzigoli G, Domenici C, Lazzeri L. Trans Am Soc Artif Intern Organs 1986;32:157e62. [4] Shiga T, Kurauchi T. J Appl Polym Sci 1990;39:2305e20. [5] Tomer R, Dimitrijevic D, Florence AT. J Control Release 1995;33:405e13. [6] DeRossi D, Kajiwara K, Osada Y, Yamauchi A, et al., editors. Polymer gels: fundamentals and biomedical applications. New York: Plenum; 1991. [7] Shahinpoor M, Kim KJ. Smart Mater Struct 2004;13:1362e88. [8] Murdan S. J Control Release 2003;92:1e17. [9] Jabbari E, Tavakoli J, Sarvestani AS. Smart Mater Struct 2007;16:1614e20. [10] Doi M, Matsumoto M, Hirose Y. Macromolecules 1992;25:5504e11. [11] Vasilevskaya VV, Khokhlov AR. Makromol Theory Simul 2002;11(6):623e9. [12] Pollack GH. Cells, gels and the engines of life. Seattle: Ebner and Sons; 2001. [13] Horkay F, Tasaki I, Basser PJ. Biomacromolecules 2001;2:195e9. [14] Zheng JM, Chin WC, Khijniak E, Khijniak Jr E, Pollack GH. Adv Colloid Interface Sci 2006;127:19e27. [15] Zubarev AYu, Blyakhman FA, Pollack GH, Gusev P, Safronov AP. Macromol Theory Simul 2004;13:697e701.
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DC electric fields produce periodic bending of polyelectrolyte gels A.P. Safronov a, *, M. Shakhnovich b, A. Kalganov c, I.A. Kamalov a, T.F. Shklyar b, F.A. Blyakhman b, G.H. Pollack c a
Chemistry Department, Urals State University, 51 Lenin St., Yekaterinburg 620083, Russia Biomedical Physics Department, Urals State Medical Academy, 3 Repin St., Yekaterinburg 620219, Russia c Department of Bioengineering, Box 357962, University of Washington, Seattle, WA 98195, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 February 2011 Received in revised form 18 March 2011 Accepted 24 March 2011 Available online 31 March 2011
The periodic bending of polyelectrolyte hydrogels made of polyacrylamide, polyacrylic and polymethacrylic acids with 10% ionization under the DC electric field was observed in 0.8 mM CaCl2. When the field with intensity 13.5 V/cm was applied perpendicular to the longitudinal axis of the gel sample, the gel first bent to cathode, then more substantially to anode, then to cathode again and so on with damping amplitude. Within experimental error up to two periods of such oscillations were observed. The maximum amplitude of bending was approximately 30% of sample length. After 150e200 s, the gel sample finally reached a steady state slightly bent to anode. During these oscillations the volume of the sample gradually decreased by 10e30% depending on the gel. Kinetics of displacement of the free end of the gel sample could be fitted by a damped sine wave function, depending initial amplitude, final displacement, wave period, and decay time. All parameters except wave period depended on sample cross-section. The amplitude, wave period and decay time decrease with the increase of initial degree of gel swelling. The physical basis of the periodic bending is discussed based on the theoretical approach of Doi, Matsumoto and Hirose, although that theory can describe only initial cathodic and successive anodic displacement of gel. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Hydrogels Polyelectrolytes Swelling
1. Introduction When a polyelectrolyte gel is placed in an electric field, free ions that are present in the gel and surrounding solution begin moving to the oppositely charged electrode. Consequently, ionic distribution inside and outside the gel becomes non-uniform. As ionic concentration is one of the major repulsive factors that affects gel volume, its variation inevitably results in volume changes and hence the mechanical response of the gel. As easy as it may be to formulate the principal idea that polyelectrolyte gel will mechanically respond to the electric field, it is less easy to predict a priori which way it will respond. Experiments show that predicting gel behavior in electric fields is far from trivial. The first observation of a field-induced deformation of a partly hydrolyzed polyacrylamide gel was made in the early 80-ies by Tanaka et al. [1], who found that when a rodlike specimen is placed between electrodes in close contact with them, the anodal side of the gel shrinks proportionally to the voltage applied. A similar
* Corresponding author. E-mail addresses: [email protected] (A.P. Safronov), Felix.bljakhman@ usu.ru (F.A. Blyakhman), [email protected] (G.H. Pollack). 0032-3861/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2011.03.048
effect was observed as well by other workers [2,3]. The initial interpretation was based on the mechanical stress that squeezed the gel at the anodal side due to the attraction of the negatively charged network to anode. Later, however, this interpretation was questioned when it was found in several works [4,5] that, if the same specimen is placed at a fixed position separated from the electrodes, the anodal side of the gel swells. In some gels the swollen anodal part later began to shrink as the electric field was maintained. Shiga et al. [4] pointed out that these phenomena might be induced by the change in the ionic distribution under the electric field. These and other experimental results [6] obtained in the 90-ies provided the background for research on polyelectrolyte gels as electroactive smart materials. The review by Shahinpoor and Kim [7] for example, focused on polyelectrolyte actuators, sensors, and transducers which basically are made of metal-plated gel strips, bending as voltage is applied to metal films on both sides of the strip. When the gel is anionic then the strip bends toward the anode; when the gel is cationic the bending occurs toward the cathode. The principle of such devices is based on the early results of Tanaka as bending occurs due to the shrinking of the strip side adjacent to certain electrode. Another extensively studied field of application is electro-responsive drug delivery from hydrogels. One
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may address the review by Murdan [8] for details. Generally, such applications are based on the overall contraction of the gel under the influence of a steady electric field. If some therapeutic agent is incorporated inside the gel network, then the contraction of gel will cause exudation of the drug into target tissues. Its worth mentioning the opposite influence of the electric field upon anionic hydrogels found in Ref. [9] where it was shown that poly(acrylic acid) gels substantially swell when placed in phosphate buffer saline between electrodes sealed in polyethylene to avoid direct contact with solution. The swelling reached saturation during ca 100 h, and besides this the dependence of swelling on the distance between gel and electrode was also demonstrated. Theoretical interpretations of mechanoelectric effects in gels may be placed in one of the three categories: physical models, black box models, and gray box models [7]. Physical models are based on detailed consideration of underlying physical mechanisms believed to govern electromechanical response. For black box (empirical) models physical features are only a minor consideration and model parameters are based solely on system identification. Gray box models are suitable combinations of the first two. Objectives of practical applications better match two last categories of models as they are specially designed to obtain quantitative results important for practical use based on empirical tunable parameters. One may find the examples of such theoretical approaches in the aforementioned reviews [7,8]. However, these models are limited to the systems with well-defined and predictable behavior. Physical models generally are not as distinct in quantitative predictions but they are more fruitful in maintaining understanding of specific and controversial features of gel behavior. It looks that up to now the most realistic and flexible physical model of electromechanical effects in polyelectrolyte gels is the one introduced by Doi, Matsumoto, and Hirose [10] and developed for the most common anionic poly(acrylic acid) gels. Basically, all physical models of polyelectrolyte gel take into account the following: (i) volume interactions between polymer network and the solvent; (ii) elastic entropic deformation of macromolecular coils between crosslinks; (iii) translational entropy of free counterions; (iv) DebyeeHuckel electrostatic interactions, which, however, in most cases are not taken into account as negligible [11]. Doi and co-authors [10] restricted their consideration solely to the osmotic pressure of mobile ions which depended on the difference of concentration inside and outside the gel. Therefore they defined their theory as qualitative. However, this theory correctly predicts qualitative tendencies in gel volume changes as the increase or decrease in osmotic pressure will inevitably result in corresponding gel swelling or contraction. At the same time the theory includes all possible contributions to the ionic concentration. In addition to commonly considered counterions inside gel network that compensate charged monomer units and external salt ions, Doi and coauthors [10] also took into account self-dissociation of water and dissociation of acidic monomer units. Due to these extra variables of the theory ionization degree of the network and its total electric charge became the function of ionic concentration. As a result, Doi, Matsumoto, and Hirose theory successfully described both the shrinkage of the gel in contact with anode and the swelling of the anodal side if separated from anode. The theory predicted as well that this swelling might switch to contraction when the field was kept applied for a longer time. However, it was not tested experimentally. Based on theoretical predictions and published experimental data we intended to model in the present study the mechanical response of the living cell to the applied electric field with the use of synthetic polyelectrolyte gels. As it was shown in the book by one of the authors [12] many biophysical phenomena including muscle contraction and propagation of nerve excitation can be the result of
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phase transition in cell gel structure accompanied with electromechanical effects. We believe that synthetic polyelectrolyte gels of partly neutralized polyacrylic and polymethacrylic acids could be a suitable model for this. Then our objective was to study the dynamics of mechanical response of the rodlike polyelectrolyte gel samples placed in DC electric field across the field lines apart from the electrodes in the presence of mono and bivalent ions typical for living systems. Below we will present experimental data which will show that at the early stage the mechanical response of the gel closely follows the predictions of the theory [10] but further behavior strongly deviates from it. We have found that bending of polyelectrolyte rod in DC electric field is periodic, which we believe is completely new phenomenon never reported before.
2. Experimental part Gels of poly(acrylic) (PAAc) and poly(methacrylic) (PMAc) acid and their copolymers with 90% (mol) of acrylamide were prepared by free-radical polymerization with N,N0 -methylene-diacrylamide as a cross-linker in aqueous solution. All reagents were purchased from Merck (Schuchardt, Hohenbrunn). Each gel had 10% of ionized monomer units. In order to achieve this, 10% of acid monomer were neutralized by the required amount of potassium hydroxide or magnesium oxide before polymerization, which gave fully dissociating acrylate or methacrylate units in the gel network. In each case the overall monomer concentration was 2.7 M, while the cross-linker to monomer concentration was set at 1:100. Ammonium persulphate (0.5 g/l) was used as initiator. Polymerization was carried out in PE probe tubes 10 mm in diameter for 1 h at 80 C and then 3 h at 50 C. After polymerization, gel samples were washed in distilled water to remove the sol fraction and free salts. Water was renewed every day for 2 weeks. The degree of swelling of gel samples was determined by measuring the net weight of the residue after drying. Notification, composition and equilibrium degree of swelling in water at 25 C for all gels under study are given in Table 1. Gel samples for electromechanical experiments were cut by a razor blade. Their dimensions were ca 10 mm in length and 1 1 mm in cross-section. The schematic picture of the experimental design is presented in Fig. 1. The cell was made of a Teflon ring 5 mm in height and 20 mm in inner diameter mounted upon a glass plaque. Two 5 5 mm Ag foil electrodes were placed at the opposite walls of the cell. All experiments were performed under constant voltage conditions at 27 V DC. The gel sample was positioned in the center of the cell between electrodes with its longer axis across field lines. One end of the sample was fixed in a gap in the wall of the cell, while the other end was left free to move in the applied field. During the experiments the cell was filled with 7 ml of 0.8 mM CaCl2 to cover on electrodes and the gel sample. Computerized optical system of laboratory design was used for the video
Table 1 Composition of gels. Notification PAAc/KA
Acid monomer
Acrylic acid 90% (mol) PMAc/KM Methacrylic acid 90% PMAc/MgM Methacrylic acid 90% PAAm/MgM e
Ionized monomer
Acrylamide Counterion Degree of monomer swelling
Acrylate 10%
e
Methacrylate e 10% Methacrylate e 10% Methacrylate 90% 10%
Kþ
66.9
Kþ
28.1 2þ
14.6
Mg2þ
40.1
Mg
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Fig. 1. Schematic of experimental setup: 1 e experimental cell; 2 e gel sample; 3 e electrodes; 4 e video camera; 5 e computer.
recording of gel sample bending in the applied DC field. A video camera was placed beneath the transparent bottom of the cell. A combination of red and green optical filters was used to enhance the contrast of transparent gel sample in water. Bitmap video files were analyzed by specially written computer program to digitize the movement of any particular point on the sample image and the time-dependent changes of the total area of the sample. Supplementary video related to this article can be found at doi: 10.1016/j.polymer.2011.03.048. 3. Results and discussion As the general framework of the study was the search for approaches to model electromechanical excitation of living matter, all experiments were performed in weak (0.8 mM) solution of CaCl2 which is the typical Ca2þ concentration outside cell in vivo. Thus, we intended to provide the possibility of Kþ/Ca2þ exchange in synthetic gels which might take place in the cell’s electromechanical activity. As such Ca2þ concentration is lower than the threshold of gel contraction under divalent/monovalent ionic exchange [13], the degree of swelling in this solution remains the same as in water. Fig. 2 presents a sequence of images taken from the video file recorded in a typical experiment when the DC electric field was applied to a gel sample in 0.8 mM CaCl2. At the beginning of the experiment the gel sample remains straight (t ¼ 0). When DC field is applied, the sample starts to bend toward cathode (Fig. 2b). This result is consistent both with earlier experimental data [4,5] and theoretical considerations [10]. Such bending implies that the anodal surface of the sample swells and the sample begins bending toward the cathode. After 15 s bending to cathode stops and the direction reverses; after 30 s the sample almost straightens (Fig. 2c) and then proceeds bending toward the anode (Fig. 2d). As one can see from Fig. 2b and d, “anodal” bending is more substantial than “cathodal” bending. “Anodal” bending is also consistent with the theory: as shown by Doi and co-authors [10], when the electric field is kept on, the anodal surface of the gel begins to contract and forces the gel to bend toward the anode.
The physical reason for two first stages according to the theory [10], are the changes in ionic concentration inside the gel. As it increases, two possible regimes of gel volume changes may take place. In low pH (acidic regime) the increase in ionic concentration results in permanent contraction of the gel. In neutral and basic conditions, however, contraction occurs only at relatively high ionic concentration, but if ionic concentration increases from ca 107 up to ca 105 M its addition causes extra swelling of the gel. The physical reason for such swelling is additional ionization of carboxylic acidic groups in the network due to the substitutions of protons by alkali metal ions, which happens not only in basic conditions but in neutral as well. As it was numerically shown by Doi and co-authors [10] when DC field was applied, concentration of cations and anions decreased at the anodal side of the gel and increased at the cathodal side with time. As the ionic concentration increases at the cathodal side of the gel, it results in the increase of the effective screening of electrostatic forces and the gel network tends to contract. For the same reason the decrease of ionic concentration at the anodal side results in its swelling. While the diminishing ionic concentration at the anodal side remains higher than 105 M the anodal side swells. However, when DC field is kept on for longer time, almost all counterions leave anodal side of the gel and the concentration of ions descends under 105 M. Then the remaining carboxylate monomer units absorb protons from the water solution and reassemble into carboxyl residues, which are non-dissociating, that results in the decrease in gel network ionization and consequent contraction of the anodal side. This speculation is qualitatively consistent with our results. Quantitative comparison with the theory is surprisingly fair. Estimation of the time of the reversal from swelling to contraction at anode side given in Ref. [10] was about 250 s for the gel sample 5 mm in length placed 2.5 mm apart from both electrodes at field intensity 10 V/cm. At almost the same field intensity 13.5 V/cm we have experimentally obtained about 15 s for the sample 1 mm thick 10 mm from each electrode. It is quite reasonable that thinner gel samples more rapidly respond to the effects stemming from ionic migration.
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Fig. 2. Sequential images of PAAc/KA gel bending in DC electric field: a e 0, b e 15, c e 30, d e 60, e 90, f e 150 s from the beginning.
However, as one can see from Fig. 2e and f experimental behavior appears more complicated than predicted by Doi, Matsumoto, and Hirose theory [10]. After having bent toward the anode, the gel does not stop its movement, but begins to straighten back again (Fig. 2f). The amplitude of back movement is lower than during two first phases but it certainly can be observed. Further analysis of video records which will be presented below revealed that the third stage of second “cathodal” movement is followed by fourth stage of second “anodal” movement with decaying amplitude. Thus, we have observed at least two periodic cathode/anode swings of the gel samples without any changes in the polarity and intensity of the applied DC electric field. This result to the best of our knowledge has never been reported before. For now, we know of no theoretical physical interpretation of this result; hence, we will limit ourselves to analysis of the formal wave characteristics of the periodic motions we have found. Fig. 3 presents the kinetics of the displacement of the free end of the gel sample PAAc/KA under DC electric field. Positive shift corresponds to “cathode” and negative to “anode” bending. Three curves corresponding to the samples with the same length (8 mm)
but different width are similar in shape but do not coincide. In each case, the first maximum lies in the positive range of shift values, which means that the gel sample first bends toward cathode. The second maximum and both minima lie in the negative range, which means that after the first displacement toward the cathode the gel sample bends toward anode and its further periodical bendings take place in the “anodal” hemicycle and are in fact periodic changes in sample curvature. The shape of the curve is typical of wave-like kinetics with decaying amplitude, according to which free-end displacement to cathode y(t) can be described by the following function:
t þ t0 t þ t0 sin 2p yðtÞ ¼ yN þ A exp s B
(1)
where A e is the initial amplitude of the wave, s e is the decay time, B e is the period of the wave, t0 e is the time (phase) shift of the wave, yN e is the asymptotic position of the free end with respect to the center of the cell.
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Fig. 3. Time dependence of free-end displacement upon bending of PAAc/KA gel sample in DC electric field. Positive values correspond to cathode shift, negative to anode shift from the initial position. Sample length is 8 mm, width is 1.01 (1), 1.38 (2), 1.42 (3) mm.
Parameters of Eq. (1) for all gels were determined by fitting procedure applied to plots of free-end displacement obtained from bitmap video files. The best-fit values of the parameters for the plots presented in Fig. 3 are given in first three rows of Table 2. Although basic physical interpretation is lacking, formal analysis of the parameters in Table 2 yields the following information on the influence of sample geometry on the damped wave kinetics. As the width (the cross-section area) of the sample increases,
Initial amplitude decreases; Final displacement to anode (negative values) increases; Decay time increases; Wave period does not changes; Time shift increases.
The decrease of the initial (cathodic) amplitude with the thickening of PAAc/KA gels seems reasonable. It might be simply the result of the increase in the tensile strength of the sample due to the increase in its cross-section area. However, comparing Fig. 3 and Table 2 one may notice that A values in Table 2 differ less than positive maxima on corresponding curves in Fig. 3. This is because the height of maximum equals A þ yN, and the actual initial displacement depends not only on the initial amplitude and tensile strength of the sample but also on yN. The increase in negative yN values for the final anodic displacement of the free end can be understood if we refer to the common interpretation of bending as the result of the ionic concentration gradient along the field. It seems reasonable that at long durations some steady ionic distribution will be established. This distribution will be characterized by the certain gradient for each ion present in the gel. For one and the same value of gradient the actual difference in ionic concentrations at the opposite sides of the thick sample will be larger than that for
the thin sample simply because of being proportional to the product of gradient and the distance. Therefore, osmotic pressures at the anodic and cathodic sides for the thick sample should differ more than that for the thin sample and so the first one will be more bent to anode asymptotically. Another group of parameters consist of s, B, and t0, which are “dynamic”. Decay time is basically the characteristic time of ionic transport toward some steady state corresponding to the final displacement yN. Therefore it looks rather reasonable that s follows the same trend as yN, i.e. it increases with sample width as it takes more time to establish a steady ionic distribution across thick sample. Wave period B and time shift t0 are directly attributed to the periodic nature of sample bending. At this moment we can say nothing about the probable driving forces of such periodicity. It is quite clear that the mechanisms included in the Doi, Matsumoto, and Hirose theory [10] provide no basis for periodic bending. From a general point of view there should be some positive feedback mechanism to provide any kind of oscillatory behavior in chemical system. Periodic changes in chemical composition and responding activity are typical for biological systems, but such ability is provided by very complex metabolic sequences including enzymes and other systems. None of this is present in the gels, which basically consist of polymeric stochastic network and several common ions. Therefore, we can only formulate the trends in B and t0 behavior, leaving them without any reasonable comment for now. We were pleased to find that the wave period B does not depend on geometry, being the only such parameter. So, probably, the wave period is exclusively a function of gel structure. Time shift t0 increases with the width of the sample. It is worth mentioning that according to the trend in t0 there could be no initial “cathodic” bending of the gel sample if it were thick enough and t0 were more than a quarter of wave period. Although all parameters except B are geometry dependent, it does not necessarily mean that they do not depend on gel structure. Damped wave behavior was found for all the gels involved in the present research. The time plots of free-end displacement in all cases were similar to those presented in Fig. 3. All these plots were fitted by a damped wave function (Eq. (1)) and the best-fit parameters are given in the last rows in Table 2. Among all the data obtained in the present study we have listed those corresponding to gel samples with close width values to minimize the influence of geometry. One can see from the data presented in Table 2 that wave period B is the most sensitive to the chemical nature of polymer network and the counterion. Wave period increases twice when the hydrophilic polyacrylic network is changed to more hydrophobic polymethacrylic (samples PAAc/KA and PMAc/KM). When Kþcounterion is replaced by Mg2þ (samples PMAc/KM and PMAc/ MgM) the wave period additionally increases by almost twice. Substitution of polymethacrylic acid monomer units by hydrophilic acrylamide results in two-fold decrease in wave period (samples PMAc/MgM and PAAm/MgM). Based on these few examples we may suppose that the wave period increases as the network
Table 2 Parameters of periodic displacement of the free end of the gel sample in DC electric field. Gel sample
Width of the sample, mm
Initial amplitude A, mm
Final displacement yN, mm
Decay time s, s
Wave period B, s
Time shift t0, s
PAAc/KA PAAc/KA PAAc/KA PMAc/KM PMAc/MgM PAAm/MgM
1.01 1.38 1.42 1.40 1.46 1.56
2.62 1.86 1.82 3.0 3.41 2.85
0.27 0.62 1.09 0.94 1.14 0.91
27.7 60.3 68.3 77.1 136 70.8
121 121 124 269 456 249
2.3 9.1 24.9 22.4 33.5 16.8
A.P. Safronov et al. / Polymer 52 (2011) 2430e2436
becomes more hydrophobic and monovalent counterions are replaced by divalent. However, this conclusion should definitely be justified in more extended further study. As for the other damped wave parameters, it is difficult to figure out any clear trend as their values fall within the same range for all the gels under study. However, we have found correlations of these parameters with the initial swelling of the gels, which are given in Table 1. Fig. 4 presents the dependence of “spatial” parameters A and yN on the initial degree of swelling which is basically the inverse density of gel network. Fig. 5 gives the same for “dynamic” parameters s, B, and t0. According to the plots, final displacement yN and time shift t0 are practically independent on the degree of swelling. All other damped wave parameters decrease with an increase of the degree of swelling and a corresponding decrease in network density. The decrease in the initial amplitude at first sight does not correlate with the arguments given above, which were based on the tensile strength of the sample. The tensile strength should obviously be lower for the less dense (more swollen) gels and so the amplitude of the displacement should be larger. However, one should take into account that dense gels contain more electric charges per unit volume than weak gels. This results in stronger interaction with the applied electric field. The decrease of the decay time may be related to the increased mobility of ionic species in weak networks. The decrease in wave period is difficult to interpret as we are still missing general understanding of the underlying mechanism of periodic bending of gel sample. Based on the result that the degree of gel swelling is strongly affecting the damped wave parameters, we suppose that gel volume changes might play the role of feedback mechanism providing the possibility of periodic bending. Fig. 6 presents the changes in the total volume of the gel sample during the application of DC electric field. One may see, that in addition to their bending gel samples contract in the DC electric field which is basically consistent with numerous applications of gels as drug-delivery agents [8]. Such contraction is not taken into account in the Doi, Matsumoto, and Hirose theory [10], but might still be an important feedback mechanism, which provides the periodic swelling and contraction of the gel network. For now we can only give an idea in very general and qualitative way of how it may happen.
Fig. 4. The dependence of the amplitude A (1) and final displacement yN (2) of the damped wave on the initial degree of gel swelling.
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Fig. 5. The dependence of the wave period B (1), decay time s (2), and time shift t0 (3) of the damped wave on the initial degree of gel swelling.
Let us return to the two phases of gel behavior in the applied field that are predicted in the theory. Both phases depend on the decrease of ionic concentration at the anodal side of the gel. When ionic concentrations fall into very low values, the gel at the anode side contracts due to de-ionization of the polymeric network. That is the final stage according to Doi, Matsumoto, and Hirose theory [10]. However, if the gel network gradually contracts as shown in Fig. 6, its volume decreases, and the concentration of ions per unit volume in the gel network increases just due to spatial reasons. This process is in principle favorable to the re-ionization of polymeric network and its re-swelling. Whether the re-swelling will take place or not will depend on local ionic concentration at different sections of the gel. We suppose that the conditions of such local reswelling are fulfilled at the anode side of the polyelectrolyte gel in the DC electric field during its gradual contraction. As a result, the gel network is balancing between swelling and contraction, which provides the driving force for swelling oscillations and the damped wave behavior we have observed. From this viewpoint, however, it is not clear whether the anodic contraction predicted by the theory corresponds to the first displacement of the free end to anode which is proportional to A, or to the final steady state proportional to yN.
Fig. 6. Time dependence of the volume of the gel samples in DC electric field. 1 e PAAc/KA, 2 e PMAc/KM, 3 e PMAc/MgM.
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4. Conclusions The physical reasons of the observed gel periodic bending are not yet clear. The most adequate theoretical approach that can describe at least two phases, the initial cathodal displacement and the next anodal one, is the theory of Doi and co-authors [10] based on the idea that the degree of gel network ionization is a function of the ionic concentration inside and outside the gel. We suppose that further development of this theory, which must take into account gel volume contraction, might be able to describe the damped periodic bending observed in our experiments. When ionic concentration in the anodal side becomes very low, and so does its degree of ionization, gradual contraction of the gel due to the imposed electric field superposes the effects of ionic transport and can cause local dynamic fluctuations of ionic concentrations and gel ionization. These processes result in dynamic oscillations of swelling and consequent damped wave of “swinging” of the free end of gel strip in DC electric field. Another, entirely different interpretational route is based on the presence of large interfacial zones recently found next to gels [14]. Because these extensive zones exclude particles and solutes, they have been termed “exclusion zones”. The effects of electric fields on exclusion zones have not been systematically explored, although preliminary data do show substantial impact. If changes in exclusion-zone size affect the mechanical properties of the respective gel surface, then there could be some contribution to bending. This hypothesis remains to be explored. The separate question that was not at all discussed above is the role of 0.8 mM CaCl2 concentration in the observed behavior. However, without extended research that we plan to do further it cannot be clarified with certainty. Meanwhile, the presence of low concentrations of divalent ions might be important for the periodic bending of the gel. From general point of view our results mean that under certain experimental conditions a relatively simple physico-
chemical process such as swelling of synthetic acrylic hydrogel can take place in periodic manner. In our earlier publication [15] we have presented general theoretical analysis of the possibility of swelling wave propagation along the gel, which may in principle model periodic excitations of biopolymers in cell membranes. However, no underlying physical mechanism was proposed at that time. Now we suppose that periodic swelling due to superposing of ionic transport and gel contraction might be such mechanism. Based on it we believe that our results will certainly extend the limits of biomimetic modeling by synthetic polyelectrolyte gels.
Acknowledgments Authors acknowledge the financial support of Russian Federation AVCP and FCP grants.
References [1] Tanaka T, Nishio I, Sun ST, Ueno-Nishio S. Science 1982;218:467e9. [2] Osada Y, Hasebe M. Chem Lett 1985;9:1285e8. [3] De Rossi DE, Chiarelli P, Buzzigoli G, Domenici C, Lazzeri L. Trans Am Soc Artif Intern Organs 1986;32:157e62. [4] Shiga T, Kurauchi T. J Appl Polym Sci 1990;39:2305e20. [5] Tomer R, Dimitrijevic D, Florence AT. J Control Release 1995;33:405e13. [6] DeRossi D, Kajiwara K, Osada Y, Yamauchi A, et al., editors. Polymer gels: fundamentals and biomedical applications. New York: Plenum; 1991. [7] Shahinpoor M, Kim KJ. Smart Mater Struct 2004;13:1362e88. [8] Murdan S. J Control Release 2003;92:1e17. [9] Jabbari E, Tavakoli J, Sarvestani AS. Smart Mater Struct 2007;16:1614e20. [10] Doi M, Matsumoto M, Hirose Y. Macromolecules 1992;25:5504e11. [11] Vasilevskaya VV, Khokhlov AR. Makromol Theory Simul 2002;11(6):623e9. [12] Pollack GH. Cells, gels and the engines of life. Seattle: Ebner and Sons; 2001. [13] Horkay F, Tasaki I, Basser PJ. Biomacromolecules 2001;2:195e9. [14] Zheng JM, Chin WC, Khijniak E, Khijniak Jr E, Pollack GH. Adv Colloid Interface Sci 2006;127:19e27. [15] Zubarev AYu, Blyakhman FA, Pollack GH, Gusev P, Safronov AP. Macromol Theory Simul 2004;13:697e701.