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Poly(ethylene oxide)–poly(butadiene) interpenetrated networks as electroactive polymers for actuators: A molecular dynamics study
Electrochimica Acta 55 (2010) 1333–1337
Contents lists available at ScienceDirect
Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Poly(ethylene oxide)–poly(butadiene) interpenetrated networks as electroactive polymers for actuators: A molecular dynamics study Daniel Brandell a , Heiki Kasemägi b , Alvo Aabloo b,∗ a b
Department of Materials Chemistry, Uppsala University, Box 538, 751 21 Uppsala, Sweden Institute of Technology, University of Tartu, Nooruse 1, 50411 Tartu, Estonia
a r t i c l e
i n f o
Article history: Received 20 October 2008 Received in revised form 22 March 2009 Accepted 29 April 2009 Available online 6 May 2009 Keywords: Interpenetrating polymer network Molecular dynamics Poly(ethylene oxide) Lithium perchlorate Ion transport
a b s t r a c t Molecular dynamics (MD) techniques have been used to study ionic transport and coordination stability in an interpenetrating polymer (IPN) network used as electrolyte for actuator devices. The system consisted of poly(ethylene oxide) (PEO) and poly(butadiene) (PB) in a 80/20% weight ratio at a total polymer of 32%, immersed into propylene carbonate (PC) solutions of LiClO4 . The system has been studied for five different concentrations of LiClO4 in PC: 0.25, 0.5, 0.75, 1.0 and 1.25 M, and with applied external electric fields of 0, 1 and 5 MV/m. It is shown that the polymer matrix has little involvement in the movement of ions and solvent, but that the polymer arrangement is important for the solvent phase nano-structure, and thereby influences the mobility. The mobility of PC is higher than of the other species in the system, but the charged species display higher mobility under external field. The field threshold level for conductivity processes is between 1 and 5 MV/m. It is argued that ion pairing, phase separation and coordination stability are important for the overall dynamic properties. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Electroactive polymers (EAPs) are polymer materials that change their shape or size in response to electrical stimuli. This class of materials is therefore a good candidate for actuators in the field of medical devices, soft manipulators and biomimetics, since they mimic the behavior of biological muscles. EAPs which also inhibit properties similar to biological materials in terms of force, strain and speed are attractive for creating artificial muscles used in biologically inspired robots [1]. However, the most promising devices today in terms of operating voltage and high-strain output – the ionomeric polymer–metal composites (IPMCs) – are dependent on metallic surface layers, which are expensive, have low biocompatibility and have a tendency to crack upon actuator operation [2]. Recent years have shown some significant efforts to make an all-polymeric ionic EAP, by combining electronically (as electrodes) and ionically (as electrolyte) conductive polymer materials [3,4]. The architecture of such an all-polymeric EAP device can vary. The simplest mimics IPMCs, consisting of a solid polymer electrolyte (SPE) sandwiched between two layers of electronically conductive polymer (Fig. 1a). Unfortunately, these materials can undergo a delamination process, which limits the actuator’s life time severely
∗ Corresponding author. Tel.: +372 5078356. E-mail address: [email protected] (A. Aabloo). 0013-4686/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2009.04.070
[5]. However, this problem can be overcome [6,7] by designing the actuator as a three-component conducting interpenetrating polymer network (IPN), with the conducting polymer embedded in an elastic polymer electrolyte network (Fig. 1b). A promising all-polymeric IPN actuator combination studied in recent years has been using poly(3,4-ethylenedioxythiophene) (PEDOT) as the electronically conductive polymer, and a network of poly(ethylene oxide) (PEO) and polybutadiene (PB) as the SPE [8,9]. The simultaneous synthesis of PEO and PB ensures an IPN formation of good mechanical strength and relatively high ion conductivity. PEO act as a solvent for salts (in the present study LiClO4 dissolved in propylene carbonate (PC)), while PB is an elastomer. The actuation motion of the membrane is considered to be due to the ionic and solvent transport in the system. It is difficult to obtain detailed experimental information in such a complex material on all the molecular processes and interactions which are involved in the actuation motion. The studies have mostly been limited to morphological and mechanical investigations. Therefore, atomic level simulations can give valuable insights. For Nafion-based IPMCs for example, such studies have helped to gain insights on several scales for both size and time [10–13]. In an earlier study [14], we used molecular dynamics (MD) simulations to examine some basic structural and morphological properties of the SPE phase of the IPN material (i.e., with the PEDOT content omitted) – to our knowledge, the very first MD simulation of an IPN material for actuator applications. We were then able to reproduce the experimental picture of a phase-separated system between PEO
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Fig. 1. All-polymeric actuator designs. A three-layer device (a) and a “gradient” IPN actuator (b).
and PB, with the PC solvent forming a homogenous phase with PB and most of the ions, but also found that the degree of phase separation was dependent on the salt concentration. In the present study, we are making an in-depth analysis of the dynamical properties of the system. 2. The molecular dynamics simulations In an MD simulation, atomic motion in a chemical system is modelled in classical mechanics terms by solving Newton’s equations of motion simultaneously and repeatedly for all particles in an appropriately chosen periodic simulation box. This set of equations is solved by a computational algorithm and depends implicitly on the description of the forces acting between the particles, i.e., the force field. The result can be pictured as a “movie” of the material on the atomic scale; conventionally some nanoseconds long for some thousands of atoms. Simulation details such as force field, box generation, equilibration procedure, software, etc., have been given in [14]. Our 40 Å × 40 Å × 40 Å simulation box consisted of one single chain of a short chain methyl end-capped PEO homologue (260 monomers, i.e., CH3 –(OCH2 CH2 )259 –OCH3 , a poly(ethylene glycol)dimethyl ether); one 55 units long chain of PB 55 (CH3 –(CHCHCH2 CH2 )–CHCHCH3 ; all CH CH bonds initially in their trans configuration), 271 PC molecules and LiClO4 salt to the concentrations of 0.25, 0.5, 0.75, 1.0 or 1.25 M (corresponding to 6, 12, 17, 23 or 29 ion pairs). The systems thus contain 32 wt% polymer, of which 80% is PEO and 20% PB, and rest of the 68 wt% consist of LiClO4 and PC, in order to resemble the experimentally investigated systems [8]. The PEO chain has –CH3 instead of –OH terminal groups in order to prevent hydrogen-bonding interactions. The sampling period of the simulations was 2 ns at constant pressure (NPT simulation). Afterwards, external electric fields of size 1 × 106 V/m and 5 × 106 V/m were applied for another 2 ns for each field strength. The applied field is a non-equilibrium model, simulating the behavior under the potential drop close to the electrode surface upon actuation. A picture of the simulated system can be seen in Fig. 2, where the two polymer strands have been “unfolded” from the actual simulation box to better illustrate their size and shape.
Fig. 2. The MD simulation box for the 1.25 M concentration with PEO (grey and red spheres) and PB (blue) unfolded out of the box for clarity. Li+ are yellow spheres, ClO4 − green and gold, and PC molecules are depicted as grey wires.
or polydentate coordinations are not distinguished) and PC can be seen in Fig. 3. The most prevalent coordination of lithium is to the PC molecules, to which it has a CN of ∼3. There is a tendency to tendency to ion pairing and clustering (Fig. 3b), which naturally increases with increasing concentration, but also is prevalent at the very lowest concentration – around 20–25% of the ions are then in pairs. The only noticeable exception from the expected trends is that the 0.5 and 0.75 M systems come in opposite order to each other, which can be explained from the very profound phase separation at 0.5 M [14]. As the Li+ · · ·ClO4 − coordination increases with concentration, the Li–Ocarbonyl coordination decreases with the same amount.
3. Results and discussion It is useful to investigate the Radial distribution functions (RDF) and coordination number (CN) functions resulting from an MD simulation in order to study local structures of materials. The RDFs show that the species with the most stable and well-defined coordination spheres in the systems are the Li+ ions, which have a total coordination number of 4 with the nearest neighbors at 1.8 Å distance, and are coordinating to either the carbonyl oxygen atoms of the PC molecule, perchlorate oxygen atoms or – but to a much lesser extent, especially at higher concentrations – PEO ether oxygens. There is no coordination of Li+ to the other oxygens on PC. RDFs and CN functions for lithium towards ClO4 − (monodentate
Fig. 3. Li+ –Ocarbonyl (a) and Li+ –Cl (b) radial distribution functions and coordination numbers for different concentrations. External field applied: (a) 0 and (b) 5 MV/m, respectively.
D. Brandell et al. / Electrochimica Acta 55 (2010) 1333–1337
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Fig. 5. Mean square displacement functions for different species in the simulated system with 1.0 M concentration and no external field present.
Fig. 4. Distribution of coordination number for Li+ towards: (a) Ocarbonyl and (b) ClO4 − for different strength of applied electric field, summed over all simulated concentrations. The lines are only present to guide the eye, and indicate no intermediate values.
Fig. 4 shows how the CN varies with the strength of the applied field. The Li–PC CN is still ∼3–4, but is decreasing at the highest field strength. At the same time, the ion pairing and clustering – i.e., larger aggregations of ions (CN > 1) – is increasing with increased field strength. The coordination of Li to PEO also decreases with increasing field strength, but it is – as stated above – very small to begin with (>95% uncoordinated to PEO). The anion coordination sphere, on the other hand, is not as well-defined and consists almost exclusively of different carbon atoms within the PC molecules. Dynamic properties of the different components have been extracted from the mean square displacement (MSD) functions. Diffusion coefficients (D) for the different atom types can in theory be calculated from the slope of the MSD plots of systems in equilibrium, and direct qualitative insight can be seen directly from the plots: the steeper slope in the MSD graph, the higher the molecular diffusion is. Fig. 5 shows the mobility of different molecular species at 1.0 M concentration without external electric field. The main trends are nevertheless the same independent of concentration: the PC molecules are the most mobile, while the ionic species are the least mobile, with the cations exhibiting the lowest mobility. The differences between the two polymer types are negligible. Since the Li+ ions are strongly coordinated to PC molecules, it can be concluded that the mobile PC molecules are uncoordinated. Fig. 6 provides a comparison between the MSD functions of Ocarbonyl in PC for all different concentrations simulated at the lower electric field value (1 MV/m). The trends among the different concentrated systems are the same also at zero field, or for Li+ and ClO4 − as well as PC. The 0.5 M system apparently is the most mobile, while
the 0.25 M system mobility is significantly below the rest of the concentrations. This is unexpected, considering that the ion pairing is higher at higher concentrations, and generally decreases the ion mobility. The mobility differences are more correlated to the degree of phase separation, which was shown to be high at 0.5 M and low at 0.25 M concentrations [14]. When the phase separation is low, PEO might complex some Li ions and immobilize them. According to the RDFs, the 0.25 M system also has a higher degree of its cations coordinated by PEO. The relative mobilities changes when the electric field values become high (5 MV/m), which can be seen from the MSD functions in Fig. 7. The 0.75 M system apparently has much more of mobility increase when the field strength increases. The 0.25 M system also increases its conductivity more than the other concentrations. This is most likely due to structural changes at the higher field strengths, such as more phase separation, which benefits ion conductivity. For the two higher concentrations, ion pairing is getting more severe at 5 MV/m field strength, which certainly decreases the ion mobility. The mobility of Li+ and ClO4 − generally also increases more than other species with higher field strength, which is natural considering that they have a coulombic charge. To understand the conduction mechanisms in the system, it is vital to achieve a picture of the time-scale involved in ionic interaction with the solvents. If the coordination sphere is very persistent, it means that there is a significant solvent drag when the ions
Fig. 6. Mean square displacement functions for Ocarbonyl in PC for different concentrations under an external electric field of 1 MV/m.
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Fig. 7. Mean square displacement functions for ClO4 − for different concentrations under an external electric field of 5 MV/m.
move towards the electrodes upon actuation, which will have a clear effect on the actuators response time. Following the methodology from Lee and Rasaiah [15], we have calculated the mean residence time ( mrt ) for ClO4 − and Ocarbonyl around Li+ , i.e., the time during it takes for a fixed proportion (here 1 − 1/e1 = 0.63) of the solvent molecules to be exchanged around the coordinating Li+ ion. In other words, mrt represents the time it takes for ca. 63% of a particular coordinating specie to be exchanged. By dividing the individual ions into four subcategories depending on mrt (<1 ns, 1–5 ns, 5–50 ns and >50 ns; representing “unstable”, “rather unstable”, “rather stable” and “very stable”, respectively) and summing the ions over different concentrations, the results given in Table 1 are achieved. Since the results are given in percentage, the sum is 100% in each column, which means that every Li+ ion belongs to one of the four subcategories (unless they are uncoordinated of Ocarbonyl or ClO4 − , respectively, in which case they have been discarded). Table 1 shows that coordination stability decreases significantly for the higher field value. This is not unexpected, considering that the high field strength represents a rather strong perturbation on the system. This tendency is strongest for Li+ –ClO4 − , since the field pushes the particles in different directions. Nevertheless, the results show that the high field strength of 5 MV/m is not abnormal: more than 26% of the ion pairs are still in very stable confirmation, and are not torn apart. Even a substantial portion (9%) of the Li+ ions is in stable coordination with the solvent molecules, which means that there is a portion of the PC molecules which travel together with the cations through the matrix. The lower field value (1 MV/m), however, gives rise to an unexpected increase in stability as compared to the simulations without field. The difference is small, though, suggesting that this field value might be under the threshold limit for Li+ ion hopping mechanisms – between anions and/or PEO ether oxygens – to start.
Table 1 Distribution (in percentage) of the stability of different coordination spheres around Li+ based on the mean residence time ( mrt ) values for the coordinating species. mrt < 1 ns are considered “unstable”, mrt = 1–5 ns are “rather unstable”, mrt = 5–50 ns are “rather stable”, and mrt > 50 ns are very stable. E=0
Unstable Rather unstable Rather stable Very stable
E = 1 MV/m
E = 5 MV/m
Li–PC
Li–ClO4
Li–PC
Li–ClO4
Li–PC
Li–ClO4
3 42 17 37
16 18 7 60
2 37 24 36
10 10 7 72
16 53 21 9
30 23 21 26
Furthermore, it is clear from Table 1 that the Li+ –ClO4 − coordination has a higher population of very stable and unstable coordination spheres, while the Li+ –PC show more intermediate stability. This is somewhat surprising considering the strong electrostatic interaction between the two ionic species, and apparently there are two distinct forms of ionic interactions in the systems: one stable (pairing or clustering), and one very fast where the ions suddenly approach each other’s coordination spheres. The latter case could well be between ions which already have full coordination spheres – and might be already paired – and thus achieve a more unstable configuration when the counterion is approaching. If the stability distribution is plotted for each concentration, it is seen that the coordination stability is rather independent of concentration. The 0.25 M system is an exception, with a higher degree of stability, but the statistics for this particular system is poor. At 0.25 M, however, the ionic mobility is less than for the other concentration, which suggests a positive correlation between the ionic conductivity and the destabilization of the coordination sphere around Li+ . 4. Conclusions MD simulations of SPEs containing PEO, PB and PC solutions of LiClO4 have been presented in this paper. A general trend is that the polymer matrix is very little involved in the movement of the ions and solvent. Neither PEO nor PB, which themselves are phase separated for all systems but the very lowest concentration, are any part of the coordination sphere of either Li+ or ClO4 − , and therefore do not influence their mobility. The general polymer arrangement is however important for the nano-structure of the solvent, which can well influence the mobility indirectly. It is shown that at equilibrium, the mobility of PC is higher than of the other species in the system, but that the charged species naturally has a higher mobility when an external field is applied. The field threshold level for conductivity processes to start seems to lie between the two investigated strengths – 1 and 5 MV/m – since the lower field value display structural and dynamical properties close to the systems without external field. Applying a field apparently also changes the order in mobility between the different concentrated systems; although the lower concentrated systems in general display a higher mobility. However, the numbers of charge carriers are higher at higher concentration, making the total ion conductivity more independent of concentration. Acknowledgements Estonian Science foundation grant #ETF6763 is acknowledged for their effort to support current research. DB wishes to thank the Sweden–America Foundation for financial support. References [1] Y. Bar-Cohen, Biomimetics, Biologically Inspired Technologies, CRC, 2005. [2] Y. Bar-Cohen, Electroactive Polymer (EAP) Actuators as Artificial Muscles – Reality, Potential and Challenges, SPIE Press, 2001. ˜ [3] J.-M. Sansinena, V. Olazàbal, in: Y. Bar-Cohen (Ed.), Electroactive Polymer (EAP) Actuators as Artificial Muscles – Reality, Potential and Challenges, SPIE Press, 2001, p. p. 193. [4] S.S. Jang, V. Molinero, T. C¸a˘gin, W.A. Goddard III, J. Phys. Chem. B, 108 (in press) 3149. [5] F. Vidal, C. Plesse, D. Teyssié, C. Chevrot, Synth. Met. 142 (2004) 287. [6] F. Vidal, J.-F. Popp, C. Chevrot, D. Teyssié, Proc. SPIE Int. Soc. Opt. Eng 4695 (2002) 95. [7] F. Vidal, J.-F. Popp, C. Plesse, C. Chevrot, D. Teyssié, J. Appl. Polym. Sci. 90 (2003) 3569. [8] C. Plesse, F. Vidal, H. Randriamahazaka, D. Teyssié, C. Chevrot, Polymer 46 (2005) 7771.
D. Brandell et al. / Electrochimica Acta 55 (2010) 1333–1337 [9] C. Plesse, F. Vidal, C. Gauthier, J.-M. Pelletier, C. Chevrot, D. Teyssié, Polymer 48 (2007) 696. [10] S. Nemat-Nasser, J. Appl. Phys. 92 (2002) 2899. [11] Z. Chen, X. Tan, A. Will, C. Ziel, Smart Mater. Struct. 16 (2007) 1477. [12] D. Brandell, A. Ainla, A. Liivat, A. Aabloo, Proc. SPIE Int. Soc. Opt. Eng. 6168 (2006) 61680G-9.
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[13] E. Soolo, A. Liivat, H. Kasemägi, T. Tamm, D. Brandell, A. Aabloo, Proc. SPIE Int. Soc. Opt. Eng. 6927 (2008) 6927–7013. [14] D. Brandell, H. Kasemägi, J. Citérin, F. Vidal, C. Chevrot, A. Aabloo, Proc. SPIE Int. Soc. Opt. Eng. 6927 (2008) 6927–6969. [15] S.H. Lee, J.C. Rasaiah, J. Phys. Chem. 100 (1996) 1420.
Contents lists available at ScienceDirect
Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Poly(ethylene oxide)–poly(butadiene) interpenetrated networks as electroactive polymers for actuators: A molecular dynamics study Daniel Brandell a , Heiki Kasemägi b , Alvo Aabloo b,∗ a b
Department of Materials Chemistry, Uppsala University, Box 538, 751 21 Uppsala, Sweden Institute of Technology, University of Tartu, Nooruse 1, 50411 Tartu, Estonia
a r t i c l e
i n f o
Article history: Received 20 October 2008 Received in revised form 22 March 2009 Accepted 29 April 2009 Available online 6 May 2009 Keywords: Interpenetrating polymer network Molecular dynamics Poly(ethylene oxide) Lithium perchlorate Ion transport
a b s t r a c t Molecular dynamics (MD) techniques have been used to study ionic transport and coordination stability in an interpenetrating polymer (IPN) network used as electrolyte for actuator devices. The system consisted of poly(ethylene oxide) (PEO) and poly(butadiene) (PB) in a 80/20% weight ratio at a total polymer of 32%, immersed into propylene carbonate (PC) solutions of LiClO4 . The system has been studied for five different concentrations of LiClO4 in PC: 0.25, 0.5, 0.75, 1.0 and 1.25 M, and with applied external electric fields of 0, 1 and 5 MV/m. It is shown that the polymer matrix has little involvement in the movement of ions and solvent, but that the polymer arrangement is important for the solvent phase nano-structure, and thereby influences the mobility. The mobility of PC is higher than of the other species in the system, but the charged species display higher mobility under external field. The field threshold level for conductivity processes is between 1 and 5 MV/m. It is argued that ion pairing, phase separation and coordination stability are important for the overall dynamic properties. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Electroactive polymers (EAPs) are polymer materials that change their shape or size in response to electrical stimuli. This class of materials is therefore a good candidate for actuators in the field of medical devices, soft manipulators and biomimetics, since they mimic the behavior of biological muscles. EAPs which also inhibit properties similar to biological materials in terms of force, strain and speed are attractive for creating artificial muscles used in biologically inspired robots [1]. However, the most promising devices today in terms of operating voltage and high-strain output – the ionomeric polymer–metal composites (IPMCs) – are dependent on metallic surface layers, which are expensive, have low biocompatibility and have a tendency to crack upon actuator operation [2]. Recent years have shown some significant efforts to make an all-polymeric ionic EAP, by combining electronically (as electrodes) and ionically (as electrolyte) conductive polymer materials [3,4]. The architecture of such an all-polymeric EAP device can vary. The simplest mimics IPMCs, consisting of a solid polymer electrolyte (SPE) sandwiched between two layers of electronically conductive polymer (Fig. 1a). Unfortunately, these materials can undergo a delamination process, which limits the actuator’s life time severely
∗ Corresponding author. Tel.: +372 5078356. E-mail address: [email protected] (A. Aabloo). 0013-4686/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2009.04.070
[5]. However, this problem can be overcome [6,7] by designing the actuator as a three-component conducting interpenetrating polymer network (IPN), with the conducting polymer embedded in an elastic polymer electrolyte network (Fig. 1b). A promising all-polymeric IPN actuator combination studied in recent years has been using poly(3,4-ethylenedioxythiophene) (PEDOT) as the electronically conductive polymer, and a network of poly(ethylene oxide) (PEO) and polybutadiene (PB) as the SPE [8,9]. The simultaneous synthesis of PEO and PB ensures an IPN formation of good mechanical strength and relatively high ion conductivity. PEO act as a solvent for salts (in the present study LiClO4 dissolved in propylene carbonate (PC)), while PB is an elastomer. The actuation motion of the membrane is considered to be due to the ionic and solvent transport in the system. It is difficult to obtain detailed experimental information in such a complex material on all the molecular processes and interactions which are involved in the actuation motion. The studies have mostly been limited to morphological and mechanical investigations. Therefore, atomic level simulations can give valuable insights. For Nafion-based IPMCs for example, such studies have helped to gain insights on several scales for both size and time [10–13]. In an earlier study [14], we used molecular dynamics (MD) simulations to examine some basic structural and morphological properties of the SPE phase of the IPN material (i.e., with the PEDOT content omitted) – to our knowledge, the very first MD simulation of an IPN material for actuator applications. We were then able to reproduce the experimental picture of a phase-separated system between PEO
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Fig. 1. All-polymeric actuator designs. A three-layer device (a) and a “gradient” IPN actuator (b).
and PB, with the PC solvent forming a homogenous phase with PB and most of the ions, but also found that the degree of phase separation was dependent on the salt concentration. In the present study, we are making an in-depth analysis of the dynamical properties of the system. 2. The molecular dynamics simulations In an MD simulation, atomic motion in a chemical system is modelled in classical mechanics terms by solving Newton’s equations of motion simultaneously and repeatedly for all particles in an appropriately chosen periodic simulation box. This set of equations is solved by a computational algorithm and depends implicitly on the description of the forces acting between the particles, i.e., the force field. The result can be pictured as a “movie” of the material on the atomic scale; conventionally some nanoseconds long for some thousands of atoms. Simulation details such as force field, box generation, equilibration procedure, software, etc., have been given in [14]. Our 40 Å × 40 Å × 40 Å simulation box consisted of one single chain of a short chain methyl end-capped PEO homologue (260 monomers, i.e., CH3 –(OCH2 CH2 )259 –OCH3 , a poly(ethylene glycol)dimethyl ether); one 55 units long chain of PB 55 (CH3 –(CHCHCH2 CH2 )–CHCHCH3 ; all CH CH bonds initially in their trans configuration), 271 PC molecules and LiClO4 salt to the concentrations of 0.25, 0.5, 0.75, 1.0 or 1.25 M (corresponding to 6, 12, 17, 23 or 29 ion pairs). The systems thus contain 32 wt% polymer, of which 80% is PEO and 20% PB, and rest of the 68 wt% consist of LiClO4 and PC, in order to resemble the experimentally investigated systems [8]. The PEO chain has –CH3 instead of –OH terminal groups in order to prevent hydrogen-bonding interactions. The sampling period of the simulations was 2 ns at constant pressure (NPT simulation). Afterwards, external electric fields of size 1 × 106 V/m and 5 × 106 V/m were applied for another 2 ns for each field strength. The applied field is a non-equilibrium model, simulating the behavior under the potential drop close to the electrode surface upon actuation. A picture of the simulated system can be seen in Fig. 2, where the two polymer strands have been “unfolded” from the actual simulation box to better illustrate their size and shape.
Fig. 2. The MD simulation box for the 1.25 M concentration with PEO (grey and red spheres) and PB (blue) unfolded out of the box for clarity. Li+ are yellow spheres, ClO4 − green and gold, and PC molecules are depicted as grey wires.
or polydentate coordinations are not distinguished) and PC can be seen in Fig. 3. The most prevalent coordination of lithium is to the PC molecules, to which it has a CN of ∼3. There is a tendency to tendency to ion pairing and clustering (Fig. 3b), which naturally increases with increasing concentration, but also is prevalent at the very lowest concentration – around 20–25% of the ions are then in pairs. The only noticeable exception from the expected trends is that the 0.5 and 0.75 M systems come in opposite order to each other, which can be explained from the very profound phase separation at 0.5 M [14]. As the Li+ · · ·ClO4 − coordination increases with concentration, the Li–Ocarbonyl coordination decreases with the same amount.
3. Results and discussion It is useful to investigate the Radial distribution functions (RDF) and coordination number (CN) functions resulting from an MD simulation in order to study local structures of materials. The RDFs show that the species with the most stable and well-defined coordination spheres in the systems are the Li+ ions, which have a total coordination number of 4 with the nearest neighbors at 1.8 Å distance, and are coordinating to either the carbonyl oxygen atoms of the PC molecule, perchlorate oxygen atoms or – but to a much lesser extent, especially at higher concentrations – PEO ether oxygens. There is no coordination of Li+ to the other oxygens on PC. RDFs and CN functions for lithium towards ClO4 − (monodentate
Fig. 3. Li+ –Ocarbonyl (a) and Li+ –Cl (b) radial distribution functions and coordination numbers for different concentrations. External field applied: (a) 0 and (b) 5 MV/m, respectively.
D. Brandell et al. / Electrochimica Acta 55 (2010) 1333–1337
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Fig. 5. Mean square displacement functions for different species in the simulated system with 1.0 M concentration and no external field present.
Fig. 4. Distribution of coordination number for Li+ towards: (a) Ocarbonyl and (b) ClO4 − for different strength of applied electric field, summed over all simulated concentrations. The lines are only present to guide the eye, and indicate no intermediate values.
Fig. 4 shows how the CN varies with the strength of the applied field. The Li–PC CN is still ∼3–4, but is decreasing at the highest field strength. At the same time, the ion pairing and clustering – i.e., larger aggregations of ions (CN > 1) – is increasing with increased field strength. The coordination of Li to PEO also decreases with increasing field strength, but it is – as stated above – very small to begin with (>95% uncoordinated to PEO). The anion coordination sphere, on the other hand, is not as well-defined and consists almost exclusively of different carbon atoms within the PC molecules. Dynamic properties of the different components have been extracted from the mean square displacement (MSD) functions. Diffusion coefficients (D) for the different atom types can in theory be calculated from the slope of the MSD plots of systems in equilibrium, and direct qualitative insight can be seen directly from the plots: the steeper slope in the MSD graph, the higher the molecular diffusion is. Fig. 5 shows the mobility of different molecular species at 1.0 M concentration without external electric field. The main trends are nevertheless the same independent of concentration: the PC molecules are the most mobile, while the ionic species are the least mobile, with the cations exhibiting the lowest mobility. The differences between the two polymer types are negligible. Since the Li+ ions are strongly coordinated to PC molecules, it can be concluded that the mobile PC molecules are uncoordinated. Fig. 6 provides a comparison between the MSD functions of Ocarbonyl in PC for all different concentrations simulated at the lower electric field value (1 MV/m). The trends among the different concentrated systems are the same also at zero field, or for Li+ and ClO4 − as well as PC. The 0.5 M system apparently is the most mobile, while
the 0.25 M system mobility is significantly below the rest of the concentrations. This is unexpected, considering that the ion pairing is higher at higher concentrations, and generally decreases the ion mobility. The mobility differences are more correlated to the degree of phase separation, which was shown to be high at 0.5 M and low at 0.25 M concentrations [14]. When the phase separation is low, PEO might complex some Li ions and immobilize them. According to the RDFs, the 0.25 M system also has a higher degree of its cations coordinated by PEO. The relative mobilities changes when the electric field values become high (5 MV/m), which can be seen from the MSD functions in Fig. 7. The 0.75 M system apparently has much more of mobility increase when the field strength increases. The 0.25 M system also increases its conductivity more than the other concentrations. This is most likely due to structural changes at the higher field strengths, such as more phase separation, which benefits ion conductivity. For the two higher concentrations, ion pairing is getting more severe at 5 MV/m field strength, which certainly decreases the ion mobility. The mobility of Li+ and ClO4 − generally also increases more than other species with higher field strength, which is natural considering that they have a coulombic charge. To understand the conduction mechanisms in the system, it is vital to achieve a picture of the time-scale involved in ionic interaction with the solvents. If the coordination sphere is very persistent, it means that there is a significant solvent drag when the ions
Fig. 6. Mean square displacement functions for Ocarbonyl in PC for different concentrations under an external electric field of 1 MV/m.
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Fig. 7. Mean square displacement functions for ClO4 − for different concentrations under an external electric field of 5 MV/m.
move towards the electrodes upon actuation, which will have a clear effect on the actuators response time. Following the methodology from Lee and Rasaiah [15], we have calculated the mean residence time ( mrt ) for ClO4 − and Ocarbonyl around Li+ , i.e., the time during it takes for a fixed proportion (here 1 − 1/e1 = 0.63) of the solvent molecules to be exchanged around the coordinating Li+ ion. In other words, mrt represents the time it takes for ca. 63% of a particular coordinating specie to be exchanged. By dividing the individual ions into four subcategories depending on mrt (<1 ns, 1–5 ns, 5–50 ns and >50 ns; representing “unstable”, “rather unstable”, “rather stable” and “very stable”, respectively) and summing the ions over different concentrations, the results given in Table 1 are achieved. Since the results are given in percentage, the sum is 100% in each column, which means that every Li+ ion belongs to one of the four subcategories (unless they are uncoordinated of Ocarbonyl or ClO4 − , respectively, in which case they have been discarded). Table 1 shows that coordination stability decreases significantly for the higher field value. This is not unexpected, considering that the high field strength represents a rather strong perturbation on the system. This tendency is strongest for Li+ –ClO4 − , since the field pushes the particles in different directions. Nevertheless, the results show that the high field strength of 5 MV/m is not abnormal: more than 26% of the ion pairs are still in very stable confirmation, and are not torn apart. Even a substantial portion (9%) of the Li+ ions is in stable coordination with the solvent molecules, which means that there is a portion of the PC molecules which travel together with the cations through the matrix. The lower field value (1 MV/m), however, gives rise to an unexpected increase in stability as compared to the simulations without field. The difference is small, though, suggesting that this field value might be under the threshold limit for Li+ ion hopping mechanisms – between anions and/or PEO ether oxygens – to start.
Table 1 Distribution (in percentage) of the stability of different coordination spheres around Li+ based on the mean residence time ( mrt ) values for the coordinating species. mrt < 1 ns are considered “unstable”, mrt = 1–5 ns are “rather unstable”, mrt = 5–50 ns are “rather stable”, and mrt > 50 ns are very stable. E=0
Unstable Rather unstable Rather stable Very stable
E = 1 MV/m
E = 5 MV/m
Li–PC
Li–ClO4
Li–PC
Li–ClO4
Li–PC
Li–ClO4
3 42 17 37
16 18 7 60
2 37 24 36
10 10 7 72
16 53 21 9
30 23 21 26
Furthermore, it is clear from Table 1 that the Li+ –ClO4 − coordination has a higher population of very stable and unstable coordination spheres, while the Li+ –PC show more intermediate stability. This is somewhat surprising considering the strong electrostatic interaction between the two ionic species, and apparently there are two distinct forms of ionic interactions in the systems: one stable (pairing or clustering), and one very fast where the ions suddenly approach each other’s coordination spheres. The latter case could well be between ions which already have full coordination spheres – and might be already paired – and thus achieve a more unstable configuration when the counterion is approaching. If the stability distribution is plotted for each concentration, it is seen that the coordination stability is rather independent of concentration. The 0.25 M system is an exception, with a higher degree of stability, but the statistics for this particular system is poor. At 0.25 M, however, the ionic mobility is less than for the other concentration, which suggests a positive correlation between the ionic conductivity and the destabilization of the coordination sphere around Li+ . 4. Conclusions MD simulations of SPEs containing PEO, PB and PC solutions of LiClO4 have been presented in this paper. A general trend is that the polymer matrix is very little involved in the movement of the ions and solvent. Neither PEO nor PB, which themselves are phase separated for all systems but the very lowest concentration, are any part of the coordination sphere of either Li+ or ClO4 − , and therefore do not influence their mobility. The general polymer arrangement is however important for the nano-structure of the solvent, which can well influence the mobility indirectly. It is shown that at equilibrium, the mobility of PC is higher than of the other species in the system, but that the charged species naturally has a higher mobility when an external field is applied. The field threshold level for conductivity processes to start seems to lie between the two investigated strengths – 1 and 5 MV/m – since the lower field value display structural and dynamical properties close to the systems without external field. Applying a field apparently also changes the order in mobility between the different concentrated systems; although the lower concentrated systems in general display a higher mobility. However, the numbers of charge carriers are higher at higher concentration, making the total ion conductivity more independent of concentration. Acknowledgements Estonian Science foundation grant #ETF6763 is acknowledged for their effort to support current research. DB wishes to thank the Sweden–America Foundation for financial support. References [1] Y. Bar-Cohen, Biomimetics, Biologically Inspired Technologies, CRC, 2005. [2] Y. Bar-Cohen, Electroactive Polymer (EAP) Actuators as Artificial Muscles – Reality, Potential and Challenges, SPIE Press, 2001. ˜ [3] J.-M. Sansinena, V. Olazàbal, in: Y. Bar-Cohen (Ed.), Electroactive Polymer (EAP) Actuators as Artificial Muscles – Reality, Potential and Challenges, SPIE Press, 2001, p. p. 193. [4] S.S. Jang, V. Molinero, T. C¸a˘gin, W.A. Goddard III, J. Phys. Chem. B, 108 (in press) 3149. [5] F. Vidal, C. Plesse, D. Teyssié, C. Chevrot, Synth. Met. 142 (2004) 287. [6] F. Vidal, J.-F. Popp, C. Chevrot, D. Teyssié, Proc. SPIE Int. Soc. Opt. Eng 4695 (2002) 95. [7] F. Vidal, J.-F. Popp, C. Plesse, C. Chevrot, D. Teyssié, J. Appl. Polym. Sci. 90 (2003) 3569. [8] C. Plesse, F. Vidal, H. Randriamahazaka, D. Teyssié, C. Chevrot, Polymer 46 (2005) 7771.
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