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To the mechanism of polyelectrolyte gel periodic acting in the constant DC electric field
Sensors and Actuators A 229 (2015) 104–109
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
To the mechanism of polyelectrolyte gel periodic acting in the constant DC electric field F.A. Blyakhman a,b,∗ , A.P. Safronov c , T.F. Shklyar a,b , M.A. Filipovich b a b c
Biomedical Physics Department, Ural State Medical University, Yekaterinburg 620028, Russian Federation Physics Department, Ural Federal University Named After the First President of Russia B.N. Yeltsyn, Yekaterinburg 620083, Russian Federation Chemical Department, Ural Federal University Named After the First President of Russia B.N. Yeltsyn, Yekaterinburg 620083, Russian Federation
a r t i c l e
i n f o
Article history: Received 30 January 2015 Received in revised form 23 March 2015 Accepted 25 March 2015 Available online 3 April 2015 Keywords: Polyelectrolyte gels DC electric field Mechanical behavior
a b s t r a c t If the elongated filament of sodium polyacrylate gel immersed in 0.8 mM CaCl2 solution is placed in a DC electrical field across the field lines with one end affixed, up to four consequent sways of strip’s free end can be observed. This phenomenon is still not clear as it takes place in the constant electric field with the constant polarity. To disclose underlying mechanism of the periodic bending, angle of the gel free end displacement (inclination) from the vertical (initial) position, the apparent area and the lengths of the cathodal and anodal borders of the projective image of the gel stripe were monitored. It was found, both the cathodal and the anodal sides of the stripe followed the trend of the gel shrinkage, but with a substantial time lag between them. The misbalance between the cathodal and the anodal contraction of the gel resulted in the strip periodic acting. The underlying mechanism of this phenomenon based on ionic diffusion and ionic exchange due to oriented ionic flux in a DC electric field is proposed. © 2015 Elsevier B.V. All rights reserved.
1. Introduction One of the interesting features of polyelectrolyte gels is their sensitivity to external electrical fields [1]. In this respect they might be undoubtedly referred to as electroactive smart materials, the most promising application of which relates to the biocompatible electromechanical actuators, sensors, and transducers [2–4]. Furthermore, the use of gels as a smart polymeric scaffold to optimize the cells’ growth and differentiation demonstrates prospects of success in the field of tissue engineering [5–8]. The main underlying principle of gel-based devices functioning is to obtain the mechanical response of the gel due to its volume changes under an applied electrical field. The essential part of the known prototypes [9] is the sandwich metal-plated gel stripe, which bends as a voltage is applied to the metal films on its sides. This effect is based on early results of Tanaka et al. [10], who found that if a partly hydrolyzed polyacrylamide gel specimen was placed between electrodes in close contact with them, the anodal side of the gel shrank proportionally to the voltage applied. Consequently,
∗ Corresponding author at: Biomedical Physics Department, Ural State Medical University, 3 Repin Str., Yekaterinburg 620028, Russian Federation. Tel.: +7 912 2885776. E-mail address: [email protected] (F.A. Blyakhman). http://dx.doi.org/10.1016/j.sna.2015.03.030 0924-4247/© 2015 Elsevier B.V. All rights reserved.
in case of the metal sandwiched polyanionic gel the shrinking of its anodal side makes the stripe bend to the anode. Meanwhile, the gel specimen placed in the solution apart from the electrodes responds to the electrical field differently. In a series of works made in 1990s [11,12] it was found that, if a polyanionic gel specimen was placed at a fixed position separated from the electrodes, the anodal side of the gel swelled. In some gels the swollen anodal part later began to shrink as the electric field was maintained. Shiga et al. [11] pointed out that these phenomena might be induced by a change in the ionic distribution in the applied electrical field. Theoretical consideration of the electromechanical response of a polyanionic gel to a DC field in a salt solution was given by Doi et al. [13]. To evaluate the ionic distribution in a gel under an electrical field they took into account (i) volume interactions between polymer network and the solvent; (ii) elastic entropic deformation of macromolecular subchains between cross-links; (iii) translational entropy of free counterions; Debye–Huckel electrostatic interactions; (iv) dissociation of ionic monomers in the network; (v) self-dissociation of water. However, as the mathematical difficulties for rigorous evaluation of the volume changes were insurmountable, the consideration was restricted solely to the osmotic pressure of mobile ions in the gel at a constant volume. Implicitly, increase or decrease in the osmotic pressure corresponded to swelling or to contraction of the gel. As a result, the theory successfully described both the trend to shrinkage of the
F.A. Blyakhman et al. / Sensors and Actuators A 229 (2015) 104–109
polyanionic gel in contact with the anode and the trend to swelling of its anodal side if separated from the anode. The theory as well predicted that swelling could switch to contraction if the field was kept for a longer time. Meanwhile, the actual electromechanical response of a polyelectrolyte gel to a DC field is more complex than it stems from the Doi, Matsumoto, and Hirose theory. Recently, we studied polyelectrolyte gels of acrylamide copolymers with acrylic and methacrylic acids and found out that a gel stripe placed in a DC electric field across its longer axis and affixed by one end produced at least three periodic inclinations of the free end in the opposite directions [14,15]. A similar effect was reported by Lim et al. [8] for stripes of polyelectrolyte gels with sulfonic acid ionic groups in the network. In this study two-way consequent bending in a DC field was observed for specimens with low cross-link density and only one bending for the specimens with high cross-link density. Lim et al. [8] had shown that periodic bending of a polyelectrolyte gel in a DC field could be understood on the basis of Doi, Matsumoto, and Hirose theory if volume changes at the anodal and cathodal interfaces of the stripe were taken into account. As the interface of the gel stripe swells or contracts, the concentration of ionic groups in the network consequently decreases or increases. It provides a negative feedback on the osmotic pressure. It was shown that the two-directional bending of the gel stripe in a DC field could be numerically modeled if a certain relation between the dynamics of the concentration changes for the mobile ions on one hand and for the ionic groups in the network on the other hand was maintained at the anodal and the cathodal interfaces. Thus, further insight on the mechanism of such unusual and counter-intuitive phenomena as electromechanical periodic bending should include the dynamics of the volume changes at the anodal and the cathodal sides of the gel stripe in a DC field. However, neither in our previous works [14,15], nor in the work by Lim et al. [8], the dynamics of volume changes at the interfaces was monitored. In the present study we intend to focus not only on the inclination of a gel stripe to cathode and anode in a DC field but more specifically on the time dependence of the geometrical dimensions of the gel stripe in the course of its periodic bending. 2. Experimental part 2.1. Preparation of gels Polyacrylic acid gels with sodium counterions (20% of ionization) were synthesized by free-radical polymerization in 2.7 M aqueous solution with N,N -methylene-diacrylamide as a crosslinker. In order to make gels with varying network density, cross-linker to monomer molar ratio was set at 1:25, 1:50, 1:100, and 1:200. All reagents were purchased from Merck (Schuchardt, Hohenbrunn). Polymerization was carried out in PE probe tubes, 10 mm in diameter, at 80 ◦ C for 2 h using ammonium persulfate as initiator. After the synthesis, cylindrical gel samples were extracted from the tubes and kept in an excess of distilled water, which was renewed every 2 days. The degree of gel swelling was monitored by weight until it reached equilibrium in ca 2 weeks at ambient conditions. Then, samples were cut by a razor blade to elongated rectangular stripes, 10 mm in length and approximately 2 mm × 2 mm in cross-section.
Fig. 1. Scheme of the experimental setup. 1 – experimental cell with gel specimen and Pt electrodes; 2 – DC power supply; 3 – digital video camera; 4 – computer.
oscillatory inclination of gel stripes in a DC electrical field. Samples were placed into an experimental cell made of a Teflon ring 5 mm in height and 30 mm in the inner diameter mounted upon a glass plaque. Two 5 mm × 5 mm platinum foil electrodes were placed at an opposite walls of the cell. Gel sample was positioned in center of the cell between electrodes with its longer axis across the electrical field lines. One end of sample was clamped mechanically in a gap of the cell’s wall, while the other end was left free to move in an applied field. During experiments, the cell was filled with 2.6 ml of 0.8 mM CaCl2 to cover on electrodes and gel sample. All experiments were performed at a room temperature and under constant voltage 27 V using “MATRIX” laboratory DC power supply MPS3002LK-1. The distance between electrodes was set at 27 mm so the electric-field intensity (E) was equal to 1.0 V/mm. There was a little evolution of gas bubbles at the electrodes during the experiment due to electrolysis. Meanwhile, as the electrical current was under 10 mA, electrolysis was not intense. The DC current was not reversed during the experiment. Computerized optical system of laboratory design was used for video recording of the gel sample bending during a DC field application. The digital video camera (“Panasonic” HX-WA2) was placed beneath of the cell’s transparent bottom, and video files were recorded. Contours of samples were outlined using the specially written software. Fig. 2 presents the layout of the geometrical parameters of the gel stripe planar projection, which were monitored during its bending. They were: the angle () of free end displacement (inclination) from the vertical (initial) position, the apparent area (S) and the lengths of cathodal (L1 ) and anodal (L2 ) borders of the gel stripe
2.2. Electromechanical testing The laboratory setup of the experiments on the periodical bending of gel sample in a DC electrical field is presented in Fig. 1. Basically, it was the same as in our recent study [14] reported the
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Fig. 2. Layout of the parameters monitored under the applied DC current.
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projective image. Additionally, the duration (t) of free end inclination from the beginning to the end of gel motion at any direction was calculated. The evolution of all parameters under applied DC field was analyzed at 10 s ramp. Each experiment included 5 gel specimens with the same network density. Software packages “Statistica 6.0” and “SigmaPlot” 12.0 were used for the statistical analysis. 3. Results and discussion The most obvious demonstration of mechanical oscillatory bending of the gel stripe in a DC field is changes in the angle of inclination to the vertical position, which can readily be observed by the naked eye. Fig. 3 presents a sequence of images taken from the video file recorded in a typical experiment and the corresponding time dependence of the angle of inclination. Gel with the network density of 1:25 was chosen for the snapshots. In the initial position (mark I in Fig. 3), the gel stripe was perpendicular to the force lines of a DC field. At the first step after a field was applied, the free end of stripe slightly moved to the cathode. This step was short and ended up in position II in Fig. 3. Cathodal inclination of 10–20 degrees, which corresponds to negative values of the angle in Fig. 3, was no depended on the cross-link density of samples within experimental error. The anodal bending followed this relatively short step, and it was substantially longer and more pronounced. In the second step the stripe reached position III in Fig. 3. The anodal bending was followed by the reversal cathodal displacement, which resulted in the straightening of the gel stripe (mark IV in Fig. 3). The third step of bending was much longer
Fig. 4. Time dependence of the relative area of the gel stripe in the planar projection. Network densities 1:25, 1:100. Curves fitted with the use of Eq. (1).
than the second (anodal) inclination. Final position of the gel stripe depended on its cross-link density. The gel with network density 1:25 stopped its movement slightly bent to the anode, while the less dense gel (1:50) was bent to the cathode (see plot in Fig. 3). Remarkably, the gel with the lowest network density of 1:100 demonstrated the fourth step of bending to the anode again as could be seen from the corresponding plot in Fig. 3. The snapshots shown in Fig. 3 also demonstrate that the gel periodic bending accompanies by noticeable contraction of the specimen (compare I and IV), which was more substantial in the case of less dense gels. Table 1 gives mean values of the step duration (t) and the maximal inclination () of three consequent steps for the gels with different network density. One can see a large deviation of presented data. Possibly, the reasons for that are ∼10% variations in width of used samples and/or the complexity of driving forces. Although the average values are dispersed, the general trend is clear: the decrease of gel network density makes the consequent steps of bending less durable and the maximal inclination in these steps more substantial. Thus, the weakness of macromolecular network of the gel stripe favors its bending in a DC electric field, and makes consequent steps faster and more pronounced. This result is consistent with the conclusions made by Lim et al. [8]. The area of gel stripe and the lengths of cathodal and anodal borders in the planar projection were disclosed using digital analysis of consequent snapshots of the gel stripe during periodic bending. Fig. 3 presents the trends of geometrical parameters in gel specimen. We will start with the apparent area of the stripe projection (S), which is related to the basic characteristics of gel – its degree of swelling (˛). Assuming that volume changes of the gel are locally isotropic, the relative degree of gel swelling is given by the equation: ˛ = ˛0
S 3/2 S0
.
Fig. 4 presents time plot of the gel stripe projection area for the gels with network density 1:25 and 1:100. Dynamics of the
Fig. 3. Sequential images of gel sample’s bending in DC electric field (see explanation in the text).
Table 1 Step duration and maximal inclination of the gel bending steps. Network density
1st step (cathodal)
1:25 1:50 1:100 1:200
28 28 16 7
max (deg)
t (s) ± ± ± ±
2nd step (anodal)
5 4 5 2
6 14 9 13
± ± ± ±
2 2 3 5
max (deg)
t (s) 390 228 198 99
3rd step (cathodal)
± ± ± ±
102 41 132 31
76 65 82 84
± ± ± ±
6 16 5 16
max (deg)
t (s) 1400 1360 1010 245
± ± ± ±
250 220 88 90
1 9 30 60
± ± ± ±
6 4 11 31
F.A. Blyakhman et al. / Sensors and Actuators A 229 (2015) 104–109 Table 2 Parameters of Eq. (1) for time evolution of the relative area of the gel stripe. Gel
y0
a
1
b
2
R2
1:25 1:50 1:100 1:200
0.36 0.24 0.16 0.08
0.63 0.47 0.47 0.45
373 305 187 57
0 0.31 0.40 0.46
0 592 453 463
0.996 0.997 0.995 0.991
gel contraction was well fitted by the combination of Gaussian and exponential decay functions. The fitting parameters for gel samples with different network density are listed in Table 2.
y(t) = y0 + aexp
1 − 2
t 2 1
t
+ bexp −
2
(1)
The plots in Fig. 4 and data in Table 2 indicate that the degree of swelling of gel stripes does not remain constant in the applied experimental conditions. The gels substantially contract with time. With the decrease in the network density, the maximal contraction of the gel (y0 ) increases and the characteristic time of Gaussian decay ( 1 ) diminishes. Contraction of the gel samples is a result of the ionic exchange between gel interior and surrounding solution [16–18]. The gels under study contained Na counterions, which compensated negative electrical charge of the carboxylate residues attached to the subchains of network. Degree of swelling of the polyelectrolyte gel is affected by several factors, among which the osmotic pressure of counterions is one of the most strong. In the experimental setup, the gel stripes were placed in the 0.8 mM solution of CaCl2 , which contained divalent Ca2+ cations. Due to the diffusion Ca2+ cations enter the gel interior while Na+ ions leave it for the surrounding solution. According to the electroneutrality condition, the Ca2+ /Na+ ionic exchange should result in the two-fold diminishing of the counterions concentration in the gel network as Ca2+ is divalent, and it can compensate the charge of two carboxylate residues. Therefore, the osmotic pressure, which is proportional to the concentration of counterions inside the gel, will also decrease. One can see from Fig. 4 that the relative contraction of dense gel with the network density 1:25 was lower than that of the weak gel with 1:100 networking. These results are in a good agreement with the data for other polyelectrolyte gels available in literature [19]. However, the contraction of the NaPAA gel in CaCl2 solution cannot by itself provide the periodic bending of the gel stripe in a DC electrical field. Meanwhile, it forms the background for the analysis of local swelling in the gel stripe at the cathodal and anodal borders. From the general point of view, it is clear that the gel stripe bending is tightly linked with the local swelling of its opposed borders. If the cathodal side swells more than anodal side, the stripe bends to
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the anode, and vice versa. The same happens if the cathodal side contracts less than the anodal side. It will also provide the anodal inclination of stripe. In general, no matter if the gel swells or it contracts the higher relative degree of swelling at the cathodal border results in bending to the anode, while higher relative swelling of the anodal border provides the cathodal displacement. It makes the analysis of stripe local swelling crucially important for the understanding of underlying reasons for the periodic bending. In the layout of geometrical parameters monitored in the experiment (Fig. 1), the lengths of cathodal and the anodal borders of the stripe projection stand for the swelling of related sides. Fig. 5 presents the time dependence of relative lengths of cathodal and anodal borders for the gel stripe projection. It is obvious that the plots for cathodal and anodal sides of the stripe are the same in shape, which closely resemble a plot shape for the dynamics of stripe projection relative area (Fig. 4). It indicates that at both sides of gel stripe the same process of gel contraction takes place. Meanwhile, the curve, reflecting the cathodal border contraction, is clearly shifted to longer duration interval against the curve of anodal side. In other words, contraction at the anodal side happens earlier than contraction at the cathodal side. Principal reason for this time shift is certainly the ionic flux provided by a DC electric field. In general, anionic gels like NaPAA expel anions from the interior and absorb cations [20–22], which can act as the counterions for the network negative electrical charge. Therefore, the flux of cations is of the major importance for the gel contraction in a DC electrical field. As the cations move from the anode to the cathode, they enter the anodal side of gel stripe and leave the cathodal side. From this viewpoint is it reasonable that the cationic flux first influences the anodal side of gel and only after a certain time lag influences the cathodal side. Rough evaluation of time shift based on the plots in Fig. 5 gives the value of approximately 200 s for the cationic flux to cross the stripe from anodal to cathodal sides. Meanwhile, the time shift taken alone should only provide the steady contraction of anodal side over cathodal side and thus the steady inclination of gel stripe to the anode. The bending in the alternating directions stems from differences in the shapes of anodal and cathodal curves in Fig. 5. As one can clearly see from Fig. 5A in the beginning of a DC field exposure the anodal side a little bit swells while the cathodal side shrinks. The reason for it was clarified in Doi, Matsumoto, and Hirose theory [13]. Applied electrical field at the first step forms the gradient of counterion concentration inside the gel from anodal to cathodal side. Concentration of Na+ at the anodal side diminishes and it begins to swell. At the same time, Na+ concentration at the cathodal side increases and this side shrinks. The combination of these effects results in the first cathodal bending of gel specimen as shown in Fig. 3.
Fig. 5. Time dependence of the lengths of the cathodal and anodal borders of the gel stripe projection. A – network density 1:25. B – network density 1:100.
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After awhile a flux of Ca2+ cations from the outer solution to the anodal side is established, and it provides the contraction of this side. Most likely Ca2+ cations are reluctant to enter the cathodal side as electric field drives them in the opposite direction. Thus, the degree of swelling at the cathodal side is affected predominantly by the concentration of Na+ ions. In time, this concentration tends to decrease as Na+ ions leave gel moving to the cathode. It results in the limited swelling at the cathode side as seen from Fig. 5. At the same time, the flux of Ca2+ cations propagates across the gel stripe and finally reaches the cathodal side. The cathodal side begins to shrink. However, the concentration of Ca2+ remains lower at the cathodal side than at the anodal side and the gel stripe remains bent to the anode. These factors rule out the second (anodal) step of gel bending. Concentration of Ca2+ in the outer solution was relatively low – 0.8 mM. It was lower than the concentration of carboxylate anions in the gel (20–200 mM) depended on its network density. As Ca2+ ions were concentrated near the cathode, their concentration near the anode eventually diminished. Contraction of the stripe anodal side slowed down while the cathodal side was still under excess of Ca2+ cations. The contraction rate at the cathodal side exceeded the rate at the anodal side and the gel stripe began reversal displacement to the cathode. It was the third (cathodal) step of bending. At the end of this step, the relative degree of swelling at the anodal side became higher that at the cathodal side (see the interception of corresponding curves at ca 1000 s in Fig. 5A and B). As it was mentioned above, we have also observed the forth step of anodal movement in the case of weak gels with network density 1:100 and 1:200. At this step both the anodal and the cathodal sides of gel start to swell as it may be noticed from a location of the last points in Fig. 5B. In general, the swelling means that the ionic concentration inside of gel is decreased. As it was shown by Doi et al. [13], the dependence of gel swelling on the concentration of ions went through the maximum. It means that at a certain low level of ions concentration (0.01–0.1 mM) the further decrease of the ionic content will result not in the swelling but in the contraction of the gel. Most likely it is the reason why at the long stages of the DC treatment the cathodal side of the gel swells more than the anodal side, although the concentration of cations remains higher at the cathodal side. It provides the final inclination of gel stripe to the anode. The influence of network density on the duration of steps as given in Table 1 is consistent with the proposed mechanism. The main obstacle for the propagation of ionic flux inside the gel stripe is the macromolecular network, which is, in general, less polar than the water solution. Obviously, the weaker is the network the higher will be the speed of ionic flux. Therefore, the second step duration decreases with the network density (see Table 1).
4. Conclusions If the elongated stripe or filament of sodium polyacrylate gel is placed in a DC electrical field across the field lines with one end affixed, it undergoes several periodic inclinations in the opposite directions starting with bending to cathode. Up to four consequent sways can be observed. This phenomenon is not readily understood as it takes place in the constant electric field with the constant polarity. In order to disclose the underlying mechanism of periodic bending, we have monitored the angle of inclination of gel stripe from the vertical and three parameters of the planar projection of stripe – its area and the lengths of both side borders, which were recorded digitally at a 10 s ramp. The time dependences analysis revealed the essential feature of process, which was the monotonous contraction of gel stripe in the course of experiment. The contraction dynamics can be
well fitted by the linear combination of Gaussian and exponential decay functions. As neither of them are periodical, the gel contraction in the isotropic conditions can never be performed in a periodic manner. However, applied electrical field by the oriented ionic flux introduces an anisotropy in the system. As anionic gels absorb cations and expel anions from the outer solution, the flux of cations plays dominant role. It makes the boundary conditions at the cathodal and the anodal sides of gel stripe different. Therefore, the same curve of contraction dynamics on the cathodal side of gel stripe is substantially shifted against the same curve at the anodal side. It means that at the same moment of time the swelling degree at the cathodal and anodal sides can be different, and it makes the gel stripe bent to one of the electrodes. Importantly, the inclination of gel stripe does not demand net swelling of the side opposed to the direction of movement. It is not the absolute but the relative value of swelling at both the cathodal and the anodal sides that governs the bending. A certain value of the local degree of gel swelling is subjected both to the total ionic concentration and to the balance between mono and divalent ions. The ionic flux provided by a DC field across the gel stripe changes both of these factors at the cathodal and the anodal sides independently. It makes the curves of cathodal and anodal local contraction dynamics intercept at least twice. The result of misbalance between the cathodal and the anodal contraction of gel stripe is its periodic bending. Although the presented results were restricted to the mechanism of the periodic bending of the gel in a DC electrical field, we believe that the same phenomenon can take place in any conditions, which provide the ionic flux vector across the gel filament or membrane. According to the proposed mechanism, it will provide the periodic bending of gel in the opposite directions along the flux.
Acknowledgments The study was supported by the Russian Foundation for Basic Research (Grants 13-08-01050a and 13-03-96068r-a).
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F.A. Blyakhman et al. / Sensors and Actuators A 229 (2015) 104–109 [14] A. Safronov, M. Shakhnovich, A. Kalganov, T.F. Shklyar, F.A. Blyakhman, G.H. Pollack, Periodic bending of polyelectrolyte gels in dc electric field, Polymer 52 (2011) 2430–2436. [15] M.A. Filipovich, T.F. Shklyar, A.P. Safronov, S.Yu. Sokolov, F.A. Blyakhman, Effect of the polyelectrolyte hydrogel actuator network density on its mechanical behavior in the DC electric field, IFMBE Proc. 43 (2014) 247– 250. [16] O.E. Philippova, Responsive polymer gels, Polym. Sci. Ser. C 42 (2) (2000) 208–228. [17] E. Kokufuta, in: T. Radeva (Ed.), Physical Chemistry of Polyelectrolytes, Marcel Dekker, New York, Basel, 2001, p. 591. [18] M. Quesada-Perez, J.A. Maroto-Centeno, J. Forcada, R. Hidalgo-Alvarez, Gel swelling theories: the classical formalism and recent approaches, Soft Matter 7 (2011) 10536–10547. [19] D. Kaneko, J.P. Gong, Y. Osada, J. Mater. Chem. 12 (2002) 2169–2177. [20] A. Katchalsky, I. Michaeli, Polyelectrolyte gels in salt solutions, J. Polym. Sci. A 15 (79) (1955) 69–85. [21] H.J. Kwon, Y. Osada, J.P. Gong, Polyelectrolyte gels – fundamentals and applications, Polymer 38 (12) (2006) 1211–1219. [22] M. Rubinstein, R.H. Colby, Polymer Physics, Oxford University Press, 2003.
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Prof. Alexander P. Safronov graduated Ural State University (Yekaterinburg, Russia) in 1982 (Chemistry), got Ph.D. in 1989 (Physical Chemistry) and D.Sc. in 2000 (Thermodynamics and Molecular Physics) at Ural State Technical University (Yekaterinburg, Russia). Present employment: Prof. of Chemistry Dept., Ural Federal University (Yekaterinburg). Current field of interest: polymer physical chemistry, thermodynamics, blends and composites, aqueous polymer solutions and gels, biomimetics.
Dr. Tatyana F. Shklyar graduated Ural State University (Yekaterinburg, Russia) in 1979 (Biology), got Ph.D. in 1988 (Pharmacology) and D.Sc. in 2012 (Physiology) at South Urals Pedagogical University (Chelyabinsk). Present employment: Leading Researcher of Biomedical physics and engineering Dept., Ural State Medical University (Yekaterinburg); Prof. of Physics Dept., Ural Federal University (Yekaterinburg). Current field of interest: muscle physiology, polyelectrolyte gel properties, biomimetics.
Biographies
Prof. Felix A. Blyakhman graduated Ural State University (Yekaterinburg, Russia) in 1979 (Biology), got Ph.D. in 1986 (Physiology) and D.Sc. in 1996 (Transplantology and artificial organs) at Moscow’s Institute of Transplantology and Artificial Organs. Present employment: Head of Biomedical physics and Engineering Dept., Ural State Medical University (Yekaterinburg); Prof. of Physics Dept., Ural Federal University (Yekaterinburg). Current field of interest: muscle physiology, biological motility, biomedical physics and engineering, biomimetics.
Michael A. Filipovich graduated Ural Federal University (Yekaterinburg, Russia) in 2013 (Physics) and got M.S. (Medical Physics). Present employment – Ph.D. student of Ural Federal University. Current field of interest: polyelectrolyte gel properties.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
To the mechanism of polyelectrolyte gel periodic acting in the constant DC electric field F.A. Blyakhman a,b,∗ , A.P. Safronov c , T.F. Shklyar a,b , M.A. Filipovich b a b c
Biomedical Physics Department, Ural State Medical University, Yekaterinburg 620028, Russian Federation Physics Department, Ural Federal University Named After the First President of Russia B.N. Yeltsyn, Yekaterinburg 620083, Russian Federation Chemical Department, Ural Federal University Named After the First President of Russia B.N. Yeltsyn, Yekaterinburg 620083, Russian Federation
a r t i c l e
i n f o
Article history: Received 30 January 2015 Received in revised form 23 March 2015 Accepted 25 March 2015 Available online 3 April 2015 Keywords: Polyelectrolyte gels DC electric field Mechanical behavior
a b s t r a c t If the elongated filament of sodium polyacrylate gel immersed in 0.8 mM CaCl2 solution is placed in a DC electrical field across the field lines with one end affixed, up to four consequent sways of strip’s free end can be observed. This phenomenon is still not clear as it takes place in the constant electric field with the constant polarity. To disclose underlying mechanism of the periodic bending, angle of the gel free end displacement (inclination) from the vertical (initial) position, the apparent area and the lengths of the cathodal and anodal borders of the projective image of the gel stripe were monitored. It was found, both the cathodal and the anodal sides of the stripe followed the trend of the gel shrinkage, but with a substantial time lag between them. The misbalance between the cathodal and the anodal contraction of the gel resulted in the strip periodic acting. The underlying mechanism of this phenomenon based on ionic diffusion and ionic exchange due to oriented ionic flux in a DC electric field is proposed. © 2015 Elsevier B.V. All rights reserved.
1. Introduction One of the interesting features of polyelectrolyte gels is their sensitivity to external electrical fields [1]. In this respect they might be undoubtedly referred to as electroactive smart materials, the most promising application of which relates to the biocompatible electromechanical actuators, sensors, and transducers [2–4]. Furthermore, the use of gels as a smart polymeric scaffold to optimize the cells’ growth and differentiation demonstrates prospects of success in the field of tissue engineering [5–8]. The main underlying principle of gel-based devices functioning is to obtain the mechanical response of the gel due to its volume changes under an applied electrical field. The essential part of the known prototypes [9] is the sandwich metal-plated gel stripe, which bends as a voltage is applied to the metal films on its sides. This effect is based on early results of Tanaka et al. [10], who found that if a partly hydrolyzed polyacrylamide gel specimen was placed between electrodes in close contact with them, the anodal side of the gel shrank proportionally to the voltage applied. Consequently,
∗ Corresponding author at: Biomedical Physics Department, Ural State Medical University, 3 Repin Str., Yekaterinburg 620028, Russian Federation. Tel.: +7 912 2885776. E-mail address: [email protected] (F.A. Blyakhman). http://dx.doi.org/10.1016/j.sna.2015.03.030 0924-4247/© 2015 Elsevier B.V. All rights reserved.
in case of the metal sandwiched polyanionic gel the shrinking of its anodal side makes the stripe bend to the anode. Meanwhile, the gel specimen placed in the solution apart from the electrodes responds to the electrical field differently. In a series of works made in 1990s [11,12] it was found that, if a polyanionic gel specimen was placed at a fixed position separated from the electrodes, the anodal side of the gel swelled. In some gels the swollen anodal part later began to shrink as the electric field was maintained. Shiga et al. [11] pointed out that these phenomena might be induced by a change in the ionic distribution in the applied electrical field. Theoretical consideration of the electromechanical response of a polyanionic gel to a DC field in a salt solution was given by Doi et al. [13]. To evaluate the ionic distribution in a gel under an electrical field they took into account (i) volume interactions between polymer network and the solvent; (ii) elastic entropic deformation of macromolecular subchains between cross-links; (iii) translational entropy of free counterions; Debye–Huckel electrostatic interactions; (iv) dissociation of ionic monomers in the network; (v) self-dissociation of water. However, as the mathematical difficulties for rigorous evaluation of the volume changes were insurmountable, the consideration was restricted solely to the osmotic pressure of mobile ions in the gel at a constant volume. Implicitly, increase or decrease in the osmotic pressure corresponded to swelling or to contraction of the gel. As a result, the theory successfully described both the trend to shrinkage of the
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polyanionic gel in contact with the anode and the trend to swelling of its anodal side if separated from the anode. The theory as well predicted that swelling could switch to contraction if the field was kept for a longer time. Meanwhile, the actual electromechanical response of a polyelectrolyte gel to a DC field is more complex than it stems from the Doi, Matsumoto, and Hirose theory. Recently, we studied polyelectrolyte gels of acrylamide copolymers with acrylic and methacrylic acids and found out that a gel stripe placed in a DC electric field across its longer axis and affixed by one end produced at least three periodic inclinations of the free end in the opposite directions [14,15]. A similar effect was reported by Lim et al. [8] for stripes of polyelectrolyte gels with sulfonic acid ionic groups in the network. In this study two-way consequent bending in a DC field was observed for specimens with low cross-link density and only one bending for the specimens with high cross-link density. Lim et al. [8] had shown that periodic bending of a polyelectrolyte gel in a DC field could be understood on the basis of Doi, Matsumoto, and Hirose theory if volume changes at the anodal and cathodal interfaces of the stripe were taken into account. As the interface of the gel stripe swells or contracts, the concentration of ionic groups in the network consequently decreases or increases. It provides a negative feedback on the osmotic pressure. It was shown that the two-directional bending of the gel stripe in a DC field could be numerically modeled if a certain relation between the dynamics of the concentration changes for the mobile ions on one hand and for the ionic groups in the network on the other hand was maintained at the anodal and the cathodal interfaces. Thus, further insight on the mechanism of such unusual and counter-intuitive phenomena as electromechanical periodic bending should include the dynamics of the volume changes at the anodal and the cathodal sides of the gel stripe in a DC field. However, neither in our previous works [14,15], nor in the work by Lim et al. [8], the dynamics of volume changes at the interfaces was monitored. In the present study we intend to focus not only on the inclination of a gel stripe to cathode and anode in a DC field but more specifically on the time dependence of the geometrical dimensions of the gel stripe in the course of its periodic bending. 2. Experimental part 2.1. Preparation of gels Polyacrylic acid gels with sodium counterions (20% of ionization) were synthesized by free-radical polymerization in 2.7 M aqueous solution with N,N -methylene-diacrylamide as a crosslinker. In order to make gels with varying network density, cross-linker to monomer molar ratio was set at 1:25, 1:50, 1:100, and 1:200. All reagents were purchased from Merck (Schuchardt, Hohenbrunn). Polymerization was carried out in PE probe tubes, 10 mm in diameter, at 80 ◦ C for 2 h using ammonium persulfate as initiator. After the synthesis, cylindrical gel samples were extracted from the tubes and kept in an excess of distilled water, which was renewed every 2 days. The degree of gel swelling was monitored by weight until it reached equilibrium in ca 2 weeks at ambient conditions. Then, samples were cut by a razor blade to elongated rectangular stripes, 10 mm in length and approximately 2 mm × 2 mm in cross-section.
Fig. 1. Scheme of the experimental setup. 1 – experimental cell with gel specimen and Pt electrodes; 2 – DC power supply; 3 – digital video camera; 4 – computer.
oscillatory inclination of gel stripes in a DC electrical field. Samples were placed into an experimental cell made of a Teflon ring 5 mm in height and 30 mm in the inner diameter mounted upon a glass plaque. Two 5 mm × 5 mm platinum foil electrodes were placed at an opposite walls of the cell. Gel sample was positioned in center of the cell between electrodes with its longer axis across the electrical field lines. One end of sample was clamped mechanically in a gap of the cell’s wall, while the other end was left free to move in an applied field. During experiments, the cell was filled with 2.6 ml of 0.8 mM CaCl2 to cover on electrodes and gel sample. All experiments were performed at a room temperature and under constant voltage 27 V using “MATRIX” laboratory DC power supply MPS3002LK-1. The distance between electrodes was set at 27 mm so the electric-field intensity (E) was equal to 1.0 V/mm. There was a little evolution of gas bubbles at the electrodes during the experiment due to electrolysis. Meanwhile, as the electrical current was under 10 mA, electrolysis was not intense. The DC current was not reversed during the experiment. Computerized optical system of laboratory design was used for video recording of the gel sample bending during a DC field application. The digital video camera (“Panasonic” HX-WA2) was placed beneath of the cell’s transparent bottom, and video files were recorded. Contours of samples were outlined using the specially written software. Fig. 2 presents the layout of the geometrical parameters of the gel stripe planar projection, which were monitored during its bending. They were: the angle () of free end displacement (inclination) from the vertical (initial) position, the apparent area (S) and the lengths of cathodal (L1 ) and anodal (L2 ) borders of the gel stripe
2.2. Electromechanical testing The laboratory setup of the experiments on the periodical bending of gel sample in a DC electrical field is presented in Fig. 1. Basically, it was the same as in our recent study [14] reported the
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Fig. 2. Layout of the parameters monitored under the applied DC current.
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projective image. Additionally, the duration (t) of free end inclination from the beginning to the end of gel motion at any direction was calculated. The evolution of all parameters under applied DC field was analyzed at 10 s ramp. Each experiment included 5 gel specimens with the same network density. Software packages “Statistica 6.0” and “SigmaPlot” 12.0 were used for the statistical analysis. 3. Results and discussion The most obvious demonstration of mechanical oscillatory bending of the gel stripe in a DC field is changes in the angle of inclination to the vertical position, which can readily be observed by the naked eye. Fig. 3 presents a sequence of images taken from the video file recorded in a typical experiment and the corresponding time dependence of the angle of inclination. Gel with the network density of 1:25 was chosen for the snapshots. In the initial position (mark I in Fig. 3), the gel stripe was perpendicular to the force lines of a DC field. At the first step after a field was applied, the free end of stripe slightly moved to the cathode. This step was short and ended up in position II in Fig. 3. Cathodal inclination of 10–20 degrees, which corresponds to negative values of the angle in Fig. 3, was no depended on the cross-link density of samples within experimental error. The anodal bending followed this relatively short step, and it was substantially longer and more pronounced. In the second step the stripe reached position III in Fig. 3. The anodal bending was followed by the reversal cathodal displacement, which resulted in the straightening of the gel stripe (mark IV in Fig. 3). The third step of bending was much longer
Fig. 4. Time dependence of the relative area of the gel stripe in the planar projection. Network densities 1:25, 1:100. Curves fitted with the use of Eq. (1).
than the second (anodal) inclination. Final position of the gel stripe depended on its cross-link density. The gel with network density 1:25 stopped its movement slightly bent to the anode, while the less dense gel (1:50) was bent to the cathode (see plot in Fig. 3). Remarkably, the gel with the lowest network density of 1:100 demonstrated the fourth step of bending to the anode again as could be seen from the corresponding plot in Fig. 3. The snapshots shown in Fig. 3 also demonstrate that the gel periodic bending accompanies by noticeable contraction of the specimen (compare I and IV), which was more substantial in the case of less dense gels. Table 1 gives mean values of the step duration (t) and the maximal inclination () of three consequent steps for the gels with different network density. One can see a large deviation of presented data. Possibly, the reasons for that are ∼10% variations in width of used samples and/or the complexity of driving forces. Although the average values are dispersed, the general trend is clear: the decrease of gel network density makes the consequent steps of bending less durable and the maximal inclination in these steps more substantial. Thus, the weakness of macromolecular network of the gel stripe favors its bending in a DC electric field, and makes consequent steps faster and more pronounced. This result is consistent with the conclusions made by Lim et al. [8]. The area of gel stripe and the lengths of cathodal and anodal borders in the planar projection were disclosed using digital analysis of consequent snapshots of the gel stripe during periodic bending. Fig. 3 presents the trends of geometrical parameters in gel specimen. We will start with the apparent area of the stripe projection (S), which is related to the basic characteristics of gel – its degree of swelling (˛). Assuming that volume changes of the gel are locally isotropic, the relative degree of gel swelling is given by the equation: ˛ = ˛0
S 3/2 S0
.
Fig. 4 presents time plot of the gel stripe projection area for the gels with network density 1:25 and 1:100. Dynamics of the
Fig. 3. Sequential images of gel sample’s bending in DC electric field (see explanation in the text).
Table 1 Step duration and maximal inclination of the gel bending steps. Network density
1st step (cathodal)
1:25 1:50 1:100 1:200
28 28 16 7
max (deg)
t (s) ± ± ± ±
2nd step (anodal)
5 4 5 2
6 14 9 13
± ± ± ±
2 2 3 5
max (deg)
t (s) 390 228 198 99
3rd step (cathodal)
± ± ± ±
102 41 132 31
76 65 82 84
± ± ± ±
6 16 5 16
max (deg)
t (s) 1400 1360 1010 245
± ± ± ±
250 220 88 90
1 9 30 60
± ± ± ±
6 4 11 31
F.A. Blyakhman et al. / Sensors and Actuators A 229 (2015) 104–109 Table 2 Parameters of Eq. (1) for time evolution of the relative area of the gel stripe. Gel
y0
a
1
b
2
R2
1:25 1:50 1:100 1:200
0.36 0.24 0.16 0.08
0.63 0.47 0.47 0.45
373 305 187 57
0 0.31 0.40 0.46
0 592 453 463
0.996 0.997 0.995 0.991
gel contraction was well fitted by the combination of Gaussian and exponential decay functions. The fitting parameters for gel samples with different network density are listed in Table 2.
y(t) = y0 + aexp
1 − 2
t 2 1
t
+ bexp −
2
(1)
The plots in Fig. 4 and data in Table 2 indicate that the degree of swelling of gel stripes does not remain constant in the applied experimental conditions. The gels substantially contract with time. With the decrease in the network density, the maximal contraction of the gel (y0 ) increases and the characteristic time of Gaussian decay ( 1 ) diminishes. Contraction of the gel samples is a result of the ionic exchange between gel interior and surrounding solution [16–18]. The gels under study contained Na counterions, which compensated negative electrical charge of the carboxylate residues attached to the subchains of network. Degree of swelling of the polyelectrolyte gel is affected by several factors, among which the osmotic pressure of counterions is one of the most strong. In the experimental setup, the gel stripes were placed in the 0.8 mM solution of CaCl2 , which contained divalent Ca2+ cations. Due to the diffusion Ca2+ cations enter the gel interior while Na+ ions leave it for the surrounding solution. According to the electroneutrality condition, the Ca2+ /Na+ ionic exchange should result in the two-fold diminishing of the counterions concentration in the gel network as Ca2+ is divalent, and it can compensate the charge of two carboxylate residues. Therefore, the osmotic pressure, which is proportional to the concentration of counterions inside the gel, will also decrease. One can see from Fig. 4 that the relative contraction of dense gel with the network density 1:25 was lower than that of the weak gel with 1:100 networking. These results are in a good agreement with the data for other polyelectrolyte gels available in literature [19]. However, the contraction of the NaPAA gel in CaCl2 solution cannot by itself provide the periodic bending of the gel stripe in a DC electrical field. Meanwhile, it forms the background for the analysis of local swelling in the gel stripe at the cathodal and anodal borders. From the general point of view, it is clear that the gel stripe bending is tightly linked with the local swelling of its opposed borders. If the cathodal side swells more than anodal side, the stripe bends to
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the anode, and vice versa. The same happens if the cathodal side contracts less than the anodal side. It will also provide the anodal inclination of stripe. In general, no matter if the gel swells or it contracts the higher relative degree of swelling at the cathodal border results in bending to the anode, while higher relative swelling of the anodal border provides the cathodal displacement. It makes the analysis of stripe local swelling crucially important for the understanding of underlying reasons for the periodic bending. In the layout of geometrical parameters monitored in the experiment (Fig. 1), the lengths of cathodal and the anodal borders of the stripe projection stand for the swelling of related sides. Fig. 5 presents the time dependence of relative lengths of cathodal and anodal borders for the gel stripe projection. It is obvious that the plots for cathodal and anodal sides of the stripe are the same in shape, which closely resemble a plot shape for the dynamics of stripe projection relative area (Fig. 4). It indicates that at both sides of gel stripe the same process of gel contraction takes place. Meanwhile, the curve, reflecting the cathodal border contraction, is clearly shifted to longer duration interval against the curve of anodal side. In other words, contraction at the anodal side happens earlier than contraction at the cathodal side. Principal reason for this time shift is certainly the ionic flux provided by a DC electric field. In general, anionic gels like NaPAA expel anions from the interior and absorb cations [20–22], which can act as the counterions for the network negative electrical charge. Therefore, the flux of cations is of the major importance for the gel contraction in a DC electrical field. As the cations move from the anode to the cathode, they enter the anodal side of gel stripe and leave the cathodal side. From this viewpoint is it reasonable that the cationic flux first influences the anodal side of gel and only after a certain time lag influences the cathodal side. Rough evaluation of time shift based on the plots in Fig. 5 gives the value of approximately 200 s for the cationic flux to cross the stripe from anodal to cathodal sides. Meanwhile, the time shift taken alone should only provide the steady contraction of anodal side over cathodal side and thus the steady inclination of gel stripe to the anode. The bending in the alternating directions stems from differences in the shapes of anodal and cathodal curves in Fig. 5. As one can clearly see from Fig. 5A in the beginning of a DC field exposure the anodal side a little bit swells while the cathodal side shrinks. The reason for it was clarified in Doi, Matsumoto, and Hirose theory [13]. Applied electrical field at the first step forms the gradient of counterion concentration inside the gel from anodal to cathodal side. Concentration of Na+ at the anodal side diminishes and it begins to swell. At the same time, Na+ concentration at the cathodal side increases and this side shrinks. The combination of these effects results in the first cathodal bending of gel specimen as shown in Fig. 3.
Fig. 5. Time dependence of the lengths of the cathodal and anodal borders of the gel stripe projection. A – network density 1:25. B – network density 1:100.
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After awhile a flux of Ca2+ cations from the outer solution to the anodal side is established, and it provides the contraction of this side. Most likely Ca2+ cations are reluctant to enter the cathodal side as electric field drives them in the opposite direction. Thus, the degree of swelling at the cathodal side is affected predominantly by the concentration of Na+ ions. In time, this concentration tends to decrease as Na+ ions leave gel moving to the cathode. It results in the limited swelling at the cathode side as seen from Fig. 5. At the same time, the flux of Ca2+ cations propagates across the gel stripe and finally reaches the cathodal side. The cathodal side begins to shrink. However, the concentration of Ca2+ remains lower at the cathodal side than at the anodal side and the gel stripe remains bent to the anode. These factors rule out the second (anodal) step of gel bending. Concentration of Ca2+ in the outer solution was relatively low – 0.8 mM. It was lower than the concentration of carboxylate anions in the gel (20–200 mM) depended on its network density. As Ca2+ ions were concentrated near the cathode, their concentration near the anode eventually diminished. Contraction of the stripe anodal side slowed down while the cathodal side was still under excess of Ca2+ cations. The contraction rate at the cathodal side exceeded the rate at the anodal side and the gel stripe began reversal displacement to the cathode. It was the third (cathodal) step of bending. At the end of this step, the relative degree of swelling at the anodal side became higher that at the cathodal side (see the interception of corresponding curves at ca 1000 s in Fig. 5A and B). As it was mentioned above, we have also observed the forth step of anodal movement in the case of weak gels with network density 1:100 and 1:200. At this step both the anodal and the cathodal sides of gel start to swell as it may be noticed from a location of the last points in Fig. 5B. In general, the swelling means that the ionic concentration inside of gel is decreased. As it was shown by Doi et al. [13], the dependence of gel swelling on the concentration of ions went through the maximum. It means that at a certain low level of ions concentration (0.01–0.1 mM) the further decrease of the ionic content will result not in the swelling but in the contraction of the gel. Most likely it is the reason why at the long stages of the DC treatment the cathodal side of the gel swells more than the anodal side, although the concentration of cations remains higher at the cathodal side. It provides the final inclination of gel stripe to the anode. The influence of network density on the duration of steps as given in Table 1 is consistent with the proposed mechanism. The main obstacle for the propagation of ionic flux inside the gel stripe is the macromolecular network, which is, in general, less polar than the water solution. Obviously, the weaker is the network the higher will be the speed of ionic flux. Therefore, the second step duration decreases with the network density (see Table 1).
4. Conclusions If the elongated stripe or filament of sodium polyacrylate gel is placed in a DC electrical field across the field lines with one end affixed, it undergoes several periodic inclinations in the opposite directions starting with bending to cathode. Up to four consequent sways can be observed. This phenomenon is not readily understood as it takes place in the constant electric field with the constant polarity. In order to disclose the underlying mechanism of periodic bending, we have monitored the angle of inclination of gel stripe from the vertical and three parameters of the planar projection of stripe – its area and the lengths of both side borders, which were recorded digitally at a 10 s ramp. The time dependences analysis revealed the essential feature of process, which was the monotonous contraction of gel stripe in the course of experiment. The contraction dynamics can be
well fitted by the linear combination of Gaussian and exponential decay functions. As neither of them are periodical, the gel contraction in the isotropic conditions can never be performed in a periodic manner. However, applied electrical field by the oriented ionic flux introduces an anisotropy in the system. As anionic gels absorb cations and expel anions from the outer solution, the flux of cations plays dominant role. It makes the boundary conditions at the cathodal and the anodal sides of gel stripe different. Therefore, the same curve of contraction dynamics on the cathodal side of gel stripe is substantially shifted against the same curve at the anodal side. It means that at the same moment of time the swelling degree at the cathodal and anodal sides can be different, and it makes the gel stripe bent to one of the electrodes. Importantly, the inclination of gel stripe does not demand net swelling of the side opposed to the direction of movement. It is not the absolute but the relative value of swelling at both the cathodal and the anodal sides that governs the bending. A certain value of the local degree of gel swelling is subjected both to the total ionic concentration and to the balance between mono and divalent ions. The ionic flux provided by a DC field across the gel stripe changes both of these factors at the cathodal and the anodal sides independently. It makes the curves of cathodal and anodal local contraction dynamics intercept at least twice. The result of misbalance between the cathodal and the anodal contraction of gel stripe is its periodic bending. Although the presented results were restricted to the mechanism of the periodic bending of the gel in a DC electrical field, we believe that the same phenomenon can take place in any conditions, which provide the ionic flux vector across the gel filament or membrane. According to the proposed mechanism, it will provide the periodic bending of gel in the opposite directions along the flux.
Acknowledgments The study was supported by the Russian Foundation for Basic Research (Grants 13-08-01050a and 13-03-96068r-a).
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F.A. Blyakhman et al. / Sensors and Actuators A 229 (2015) 104–109 [14] A. Safronov, M. Shakhnovich, A. Kalganov, T.F. Shklyar, F.A. Blyakhman, G.H. Pollack, Periodic bending of polyelectrolyte gels in dc electric field, Polymer 52 (2011) 2430–2436. [15] M.A. Filipovich, T.F. Shklyar, A.P. Safronov, S.Yu. Sokolov, F.A. Blyakhman, Effect of the polyelectrolyte hydrogel actuator network density on its mechanical behavior in the DC electric field, IFMBE Proc. 43 (2014) 247– 250. [16] O.E. Philippova, Responsive polymer gels, Polym. Sci. Ser. C 42 (2) (2000) 208–228. [17] E. Kokufuta, in: T. Radeva (Ed.), Physical Chemistry of Polyelectrolytes, Marcel Dekker, New York, Basel, 2001, p. 591. [18] M. Quesada-Perez, J.A. Maroto-Centeno, J. Forcada, R. Hidalgo-Alvarez, Gel swelling theories: the classical formalism and recent approaches, Soft Matter 7 (2011) 10536–10547. [19] D. Kaneko, J.P. Gong, Y. Osada, J. Mater. Chem. 12 (2002) 2169–2177. [20] A. Katchalsky, I. Michaeli, Polyelectrolyte gels in salt solutions, J. Polym. Sci. A 15 (79) (1955) 69–85. [21] H.J. Kwon, Y. Osada, J.P. Gong, Polyelectrolyte gels – fundamentals and applications, Polymer 38 (12) (2006) 1211–1219. [22] M. Rubinstein, R.H. Colby, Polymer Physics, Oxford University Press, 2003.
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Prof. Alexander P. Safronov graduated Ural State University (Yekaterinburg, Russia) in 1982 (Chemistry), got Ph.D. in 1989 (Physical Chemistry) and D.Sc. in 2000 (Thermodynamics and Molecular Physics) at Ural State Technical University (Yekaterinburg, Russia). Present employment: Prof. of Chemistry Dept., Ural Federal University (Yekaterinburg). Current field of interest: polymer physical chemistry, thermodynamics, blends and composites, aqueous polymer solutions and gels, biomimetics.
Dr. Tatyana F. Shklyar graduated Ural State University (Yekaterinburg, Russia) in 1979 (Biology), got Ph.D. in 1988 (Pharmacology) and D.Sc. in 2012 (Physiology) at South Urals Pedagogical University (Chelyabinsk). Present employment: Leading Researcher of Biomedical physics and engineering Dept., Ural State Medical University (Yekaterinburg); Prof. of Physics Dept., Ural Federal University (Yekaterinburg). Current field of interest: muscle physiology, polyelectrolyte gel properties, biomimetics.
Biographies
Prof. Felix A. Blyakhman graduated Ural State University (Yekaterinburg, Russia) in 1979 (Biology), got Ph.D. in 1986 (Physiology) and D.Sc. in 1996 (Transplantology and artificial organs) at Moscow’s Institute of Transplantology and Artificial Organs. Present employment: Head of Biomedical physics and Engineering Dept., Ural State Medical University (Yekaterinburg); Prof. of Physics Dept., Ural Federal University (Yekaterinburg). Current field of interest: muscle physiology, biological motility, biomedical physics and engineering, biomimetics.
Michael A. Filipovich graduated Ural Federal University (Yekaterinburg, Russia) in 2013 (Physics) and got M.S. (Medical Physics). Present employment – Ph.D. student of Ural Federal University. Current field of interest: polyelectrolyte gel properties.