Nafion-Pt IPMC electroactive behavior changes in response to environmental nonequilibrium conditions

Electroactive polymers (EAPs) continue to gain attention for their potential to offer unique and versatile solutions in the soft robotic and flexible electronic industries. Ionic polymer-metal composites (IPMCs) are a class of ionic-type EAPs which can be configured as capacitor actuators with very low voltage requirements (⩽5 V AC or DC). Their compact, portable, and lightweight properties, coupled with a biomimetic bending actuation response make them ideal for human-machine integrated technologies such as medical implants, active skins, and artificial muscles. This work tested the IPMC’s actuation and electrical response in varying saturation conditions (70% RH, 85% RH, 95% RH, and DI water liquid immersion) and voltage application schemes (direct current voltage (DCV) cycled, continuously applied, and relaxation responses upon voltage removal). This information was then used to establish actuation and back-relaxation response patterns through repetitive testing for statistical certainty. These demonstrated maximized actuation in water vapor conditions where the IPMC’s dielectric permittivity is maximized ( ε′≅1.37×106 ), and the dissipation factor is minimized ( tanδ=4.6 ). The response trends in vapor conditions are gradual but yield larger actuation ranges with increasing hydration. Liquid immersion restricts the IPMC’s range of motion but produces a sharper response pattern. These trends were validated against previously published IPMC actuator models. All of this creates a more pragmatic perspective on the potential of this technology which aids in the advancement of this material’s evolution towards viable real-world application configurations which capitalize on the material’s natural responses.


Introduction
The ionic polymer-metal composite (IPMC) is an electroactive material which can act as soft capacitive transducer. The material can convert electrical energy into mechanical displacement, as well as the reverse effect [1,2]. IPMCs are commonly comprised of a perfluorinated polymer ion exchange membrane composited by a conductive medium [3]. When configured as electroactive actuators, the material is most noted for large bending actuation ranges (termed 'deflections' or 'displacements') in response to low operating potentials (<5 V DC or AC), all while maintaining 'soft' actuator features which have modifiable geometry [1,3]. IPMC actuator applications include artificial muscles, mechanical grippers [4], biomimetic actuators with soft robotic solutions (ex. jellyfish or caterpillars), diaphragm and micro-pumps, molecular motors, micro-/nano-robots, and micro-manipulators [5][6][7]. The Nafion-based IPMC design scheme offers many outstanding qualities which make them ideal for soft and flexible actuator configurations. Unfortunately, the material's high sensitivity to changing hydration conditions has diminished its applicability in real-world scenarios [8][9][10][11][12][13]. The membrane's saturation quality and exposure affect the electroactive and physical properties of the IPMC and can produce significant performance variability when not controlled and/or maintained properly [8,9,[14][15][16]. Past research sought to minimize the material's sensitivity to solvent saturation gradients using methods such as: incorporation of alternative solvents (i.e. not water) [17,18], alternative electrode compositions and designs [19][20][21][22], modifications to the composite structure and/or alternative ionic polymer cores [23][24][25][26], as well as, coating solutions [27][28][29]. Unfortunately, many of these studies focus on singular conditions, and therefore, neglect to identify trends which emerge from testing IPMCs systematically in controlled hydration conditions. This is namely with respect to the material's electromechanical mechanism examination which can be executed via comparison of the material's electrical properties and actuation response.

Background
Past research initially focused on the influence of changing saturation on Nafion alone as the material is frequently used as an ion exchange membrane in fuel cells [8][9][10][11]13]. Still, the study and modeling of perfluorosulfonate ionomers towards IPMC actuators has continued to challenge researchers. This work will refer to the more universally accepted broader models for Nafion to support this work's conclusions [26]. A schematic of the Nafion structure was derived from literature featuring the three main regions of the Nafion core in correlation with the chemical structure [16,26,[30][31][32]. This same figure is provided in the supplementary section as figure S1 to represent the solvent-related structural features of the IPMC's Nafion core polymer. Literature's analysis of the IPMC's hydration mechanisms has predominantly focused on sensor configurations [9,33,34]. It was not until recent years that modeling began to include hydration property correlations with Nafion-IPMC actuator's response [35][36][37][38]. The most notable phenomenon is the 'back-relaxation' effects [39][40][41]. This effect can be defined as a visible return of the actuator towards the origin (during voltage application) in response to osmotic and other solvent diffusion mechanisms. The study of back-relaxation in IPMCs is overwhelmingly focused on theoretical modeling, with few including experimental validation [38][39][40]42]. Conversely, the back-relaxation effect, although can be identified in experimental studies of IPMCs, is commonly not the focus of those investigations. This is a significant oversight as understanding and quantifying the IPMC's back-relaxation behavior will be necessary for utilization of this material in real-world applications.

Research objectives and paper organization
This work focused on the evaluation of the Nafion-Pt IPMC's electromechanical response to various hydration conditions, with special attention on back-relaxation effects. Key parameters were derived based on the environmental exposure and IPMC's hydration quality and the configuration of applied external stimuli (i.e. DC voltage bias). Each of these significantly affect the electrical, hydration, and mechanical equilibrium of the IPMC. Therefore, this study first conducted electrical inspection of the IPMC's dielectric properties, as well as, quantified the membrane's water content properties in variable hydration conditions. This information was then used to classify the electrical-solvent correlations, with special attention on four selected conditions which yielded unique results. Actuation testing was conducted in those same conditions with emphasis on performance variation, actuation, and back-relaxation behavior. All work conducted in this publication was replicated for statistical certainty and quantitative deviation reporting. Lastly, experimental results were validated via fitting against an IPMC actuation model derived from literature, which included back-relaxation, electrical, mechanical, and hydration quality factors [43].

Results
This study's results are organized in consideration of the IPMC's three actuation stages: (I) neutral, which experimentally examines hydration-related properties prior to any voltage bias application; (II) voltage application (V on ), which measures the IPMC's electroactive response under an applied DC bias; and lastly, (III) voltage removal (V off ), which tracks the IPMC's actuation behavior when the voltage load is removed, as well as, post-actuation electrical measurements.

Stage I-neutral IPMC prior to actuation
When the IPMC is in its neutral state, water molecule mobility is dominated by solvent diffusion properties. These features can be analyzed via water content and electrical testing to interpret the solvent transport.  [9,13,46]. It should also be emphasized that these studies evaluate different composite designs than the one featured in this work, and therefore, these inferences are subjected to variability. As a result, we have made the generalized assumption that there is a degree of porosity, and thus, water permeability through the electrode with greater water exchange diffusion occurring along surfaces where the Nafion layer is directly exposed to the ambient conditions. In turn, hydration exchange is expected to vary across all surfaces of the IPMC exposed to its surroundings (i.e. both between the electrodes and where the Nafion core is directly exposed on the sides of the composite stack). To begin, immediately following IPMC fabrication, samples were separated into two groups with opposing conditions. 'Dry' IPMCs were first prepared via vacuum drying at room temperature, while 'wet' samples were submerged in DI water liquid for 24 h. Samples were then stored in four ambient conditions of interest (their selection is explained later in section 3.1.2). The test comprised of weighing the treated samples on an balance (sensitivity 0.01 mg) then calculating any weight change resulting from water uptake or loss. The results are tabulated in table 2. It should be noted that the saturation values reported in the table are the average of multiple sample replicas. Also, the wetted density was calculated for changing specifically the N117 polymer core.
'Dry IPMC (rehydrated)' and 'Wet IPMC (dehydrated)' % saturations are reported in the first columns of table 2. The 'rehydrated' samples denote IPMCs which gained water from the surroundings. In prior work, room temperature vacuum drying removed all solvent which could be lost via evaporation alone, and therefore, does not include water removed through physical manipulation of the IPMC (i.e. squeezing) [16]. Conversely, 'dehydrated' samples were IPMCs which began in a fully saturated 'wet' state, resulting in them losing moisture when exposed to less saturated conditions. Once these two sets of IPMCs were subjected to each condition, all wet samples produced a decrease in water content for all water vapor conditions. Similarly, dry prepared samples all gained water from the surroundings. Liquid DI water immersion allowed wet IPMCs to sustain full saturation, while exposure to water vapor resulted in only 97.6% saturation. This discrepancy aligns with previous findings which report that full saturation recovery in IPMCs is impossible in water vapor conditions alone [16]. This trend is further supported when we consider the The aim is to account for the Nafion core's variable absorption and desorption rates by examining the water uptake for samples prepared in two extreme states (i.e. wet, or dry). In doing so, one gains quantifiable perspective of how the Nafion-IPMC configuration responds to varying ambient conditions relative to its own hydration state. The IPMCs are unable to attain full saturation in vapor water conditions. DI water was the only condition to sustain saturation, while the water vapor conditions were unable to maintain the same moisture content. This was more evident in 'dry rehydrated' samples which were unable to attain the same moisture content as 'wet dehydrated' prepared samples for the same exposure timeframe. This further emphasized the need to fully saturate samples via liquid submersion prior to testing. Furthermore, the moisture loss witnessed in 'wet dehydrated' samples show that IPMCs must be allowed to attain equilibrium with the operation conditions prior to testing in order attain the IPMC's true response under that condition.
To further build upon this, water activity (a w ), which is defined as the amount of available unbound water in a system, was used to derive the water-sorption of the core polymer material (i.e. Nafion 117 alone) in table 2. Water activity can be used as an indicator of available water for the IPMC to absorb each environmental condition tested. It relates to the effective relative humidity (ERH) of an environment by: ERH = a w × 100%. This relation was rearranged for the three water vapor conditions detailed in table 2. The 96% RH, 85% RH, and 70% RH settings correlated with values of 0.96, 0.85, and 0.70, respectively. Similarly, liquid immersion a w is equivalent to 1.00. This information was then utilized in calculations for water-sorption (λ) of a Nafion 117 membrane which has been defined by Zawodzinski et al and Motupally et al for water content as follows [47]: This can then be used in combination with the mass ratio of water to Nafion ( f m = m H2O /m o ) and Nafion's equivalent weight equal to 1098 (∼1100), to establish the polymer's changing density with respect to hydration. Termed the 'wetted' density, it can be calculated as [9]: Interestingly, calculated f m values in water vapor conditions yield 0.025 at 70% RH, 0.059 at 85% RH and 0.064 at 96% RH, while liquid submersed sample produced ∼0.096. This provides an indication that IPMCs will respond differently with respect to vapor or liquid exposure. The resulting water-sorption factors, presented in table 2, increase as the saturation of the conditions increases. Inversely, density decreases with increasing saturation. To confirm these results, density calculations were compared against Morris and Sun work to produce an average difference of ∼6% [9]. As seen in literature, the IPMC's electroactive response is strongly influenced by electromechanical effects. These effects are largely influenced by the polymer core's degree of saturation, watersorption quality (influenced by the water activity of the surroundings), and the resulting changes to the mechanical properties (i.e. density). As can be seen here, as the water content (i.e. % saturation) increases, it will allow for increased free volume channels through which ion mobility is enhanced, producing increased actuation displacement potential. Therefore, by examining the water content and associated water properties, we gain perspective of how to better predict and/or control the IPMC actuation response.

Electrical-solvent relations.
Electrical inspection was executed to quantify the correlating solvent and electroactive qualities of the IPMCs. Past studies have predominantly focused on vapor-only or liquid-only testing. This work considered both conditions, providing insight into how the state of the water affects the IPMC's response. Figure 1 shows two representations of the same test. IPMCs were subjected to varying hydration conditions while the electrical properties were actively tracked in real-time via an LCR-meter set to 100 Hz and a 0.25 V source for 2 h or more. Figure 1(a) plots the dielectric constant (ε ′ ), calculated from parallel capacitance measurements (C p ) and equation (3) for IPMCs in all conditions: The permittivity of free space (ε 0 = 8.85 × 10 −15 F mm −1 ), area (A = 121 mm 2 ) and total thickness (h = 0.2 mm) of the IPMC actuator strip were all maintained constant. The results are plotted versus the 'environment setting' which indicates the relative humidity, water vapor setting for each measurement in figure 1(a). Liquid immersion results are denoted by the DI water constant line with ∇ markers. The plotted trend depicts an initial exponential increase from 55% to 85% RH, after which the dielectric qualities reach an inflection point at 95% RH, before decreasing until 100% RH.
Similarly, figure 1(b) shows the same test arrangement but instead compares the capacitance (C p ) and dissipation factor (D, or tangent loss, tan δ) measurements against time. Each test began with samples hydrated to 100% saturation as indicated by the 'DI Water' label at 0 ⩽ t ⩽ 2 h. From here, the ambient conditions were modified in increments of 5% RH every 2 h until conditions reached 60% RH. The condition settings are labeled accordingly along the capacitance curve, while dissipation was aligned via the time axis. Overall, as the environmental conditions decrease in hydration quality, we see an initial increase (0 ⩽ t ⩽ 4 h) when the IPMC transitions from DI liquid to water vapor. This is followed by a decrease in capacitance for all settings at t > 4 h. The steepest decrease in capacitance is within the 65%-80% RH region, at 8 ⩽ t ⩽ 12 h. This correlates with a gradual exponential increase in the IPMC's dissipation factor with the sharpest increase around t = 16 h in the 60%-65% RH conditions.
The ionic domain of the Nafion core structure dominates the electroactive potential of the IPMC actuator. Factors influencing the ion-ion interactions, electrostatic bonding, and ion transport can be inspected via electrical-solvent relations. In both arrangements, we see that the IPMC's dielectric potential is maximized in the 95%-100% RH setting, while dissipation is minimized from 85% to 100% RH. As the ionic domain of the IPMC is synonymous with the hydrophilic region of Nafion, it suggests that there will be a strong correlation between the dielectric and hydration quality of an IPMC. This approach has been used in IPMC relative humidity sensor configurations [9,33,34,48]. This suggests that an IPMC will produce the largest electromechanical potential and least electrical losses in the 95%-100% RH range. The distinct drop visible between 85% and 75% RH is likely indicative of a change in the IPMC's hydration and electrical interactions within the IPMC's polymer network structure. These regions of significant change have been supported by water content studies depicting distinct changes ⩾ 80% RH [9]. Throughout electrical and actuation testing it was apparent that the IPMC struggled to stabilize and maintain water vapor conditions in the 80%-90% RH range, indicated by visibly larger error bars in figure 1(a). Figure 1(b) provides insight into the timeresponse at each stage. For each step (every 2 h), we see an initial rapid response by the IPMC where capacitance sharply changes. After this, the material finds quasi-equilibrium as the trend begins to plateau towards its final true equilibrium (note the linear to constant plateaus). Liquid submerged IPMCs produces a more gradual, exponential equilibration response. Water vapor samples from 80% to 100% RH showed similar linear responses. Settings at conditions ⩽75% RH show similar steady trends which resemble inverted versions of the high saturation (>80% RH) trends. The region spanning these two (i.e. 75%-80% RH) showed exponential changes unlike all other vapor zones. All samples fully equilibrated within a 1 h exposure window.
To determine if maximized ion transport properties correlate with increased bending displacement range, the dielectric and dissipation measurements were used to understand the effective potential of the IPMC's ionic domains to generate actuation. Therefore, based on the study featured in figure 1, four environmental conditions of interest were selected for more in-depth testing. The test environments are designated as: DI water (liquid state of the solvent), 96% RH (control sample, measured 95%-100% RH), 85% RH (measured 85%-90% RH), and 70% RH (measured 70%-75% RH). The collected data agrees with prior examinations and this perspective was included in the identification and justification of these regions for further analysis [16].
DI water liquid immersion was selected to provide insight as to the influence of the various states of water (i.e. liquid versus vapor). DI water conditions produced dielectric values of ε ′ = 1.21 × 10 6 ± 25%, with dissipation of tan δ = 6.5 ± 33%. The 96% RH setting was chosen as the 'ideal operating environment' in a prior study and therefore was used for comparison and validation in this work [16,45]. The ideal (or maximized displacement) operating environment is classified in this work as being any ambient conditions which produce optimized IPMC performance. This is defined as maximizing deflection, uniform and repeatable actuation response behavior, and minimization of electrical and solvent degradation. In the 95%-100% RH region, the dielectric constant (ε ′ = 1.37 × 10 6 ± 5%) was maximized, while dissipation factor (tan δ = 5.4 ± 4%) was minimized in this humidity range, quantitatively substantiating this designation. The 85% RH condition was chosen as the last point before a significant drop off in dielectric and dissipation quality (see setting 0.85 in figure 1(a), ε ′ = 1.32 × 10 6 ± 2% and also note t = 8 h in figure 1(b) where tan δ = 8.6 ± 11%). This also correlated with regions of interest in reported hydration studies [9,16,45]. Lastly, 70% RH was chosen as it was located after the dielectric properties diminished significantly (see environment setting 0.7 in figure 1(a) yielding ε ′ = 1.42 × 10 5 ± 44%) and t = 10 h in figure 1(b) where tan δ = 24.6 ± 15%). This setting was expected to yield the smallest displacement and largest variability as indicative by the large deviation in the electric measurements and smallest dielectric constant with largest dissipation factor. The dielectric measurements reported in this work were validated against similar IPMC designs conducted by Nemat-Nasser et al who published Nafion-Pt IPMC dielectric values calculated as 3.0 × 10 8 and Barramba et al who published dielectric qualities around 2.8 × 10 9 (when converted to comparable units and parameters) [27,49]. Figure 2 shows the equilibration time-related response for: (a) capacitance and (b) dissipation factor. Samples were prepared via liquid DI water submersion., then loaded into the test rig at pre-set conditions. The test began at time t = 0 min once samples were loaded and the chamber was sealed. The plotted trends show the IPMC's electrical-solvent equilibration relative to time as the samples respond to the hydration conditions of the operating environment immediately prior to testing.

Electrical equilibration.
The DI water condition caused the largest change in capacitance (C p, t=0 = 0.6 µF to C p, t=60 = 7.3 µF) and dissipation factor (D t=0 = 18-D t=60 = 4.2). The second largest change was witnessed in the 70% setting where the sample nearlinearly equilibrates until ∼40 min after which it plateaus to C p = 1.8 µF and D = 14. Similarly, we see a slight downward trend for the 85% RH and 96% RH settings. The 85% RH setting stabilized to C p = 7 µF and D = 8.1. The 96% RH setting stabilized to C p = 7.8 µF and D = 4.3. All samples required 60 min to reach equilibrium in the test chamber, as evident by the constant plateau of each trend.
In addition to figure 2, DC resistance measurements were acquired using the LCR-meter and a 1 DCV source. This data was used with equation (4) and the IPMC's dimensions to calculate the specific conductivity (σ sp ) of the actuator: where h is the IPMC thickness, DCR is the DC resistance measured, and A is the area of the IPMC film (0.25 in × 0.75 in) [50]. These results are plotted in figure 3 with respect to time for each environment. Measurements were taken every 5 min. For all conditions, initial values begin sporadic and then settle to constant trends by t = 60 min. These results show that the final equilibrium conductivity of the IPMCs yields the following relations between hydration conditions: Correlating with values of 2.8 × 10 −4 , 7.5 × 10 −4 , 9.5 × 10 −4 , and 9.8 × 10 −4 S/m, respectively. As was seen in prior work, the conductivity is maximized in the 85%-100% RH range, while it is minimized in the driest condition (i.e. 70% RH). This shows that as the IPMC becomes more hydrated, the bulk conductivity increases through the thickness of the membrane. This also indicates that ion transport mobility is improving as the IPMC becomes more hydrated. Interestingly, again we see that the liquid immersion condition produced poorer mobility conditions when compared against 95%-100% RH; although it was larger than all other relative humidity conditions. The amount of change experienced for each condition while equilibrating was shown to be consistent. The 96% RH condition stays consistent with minor fluctuations within the initial 15 min (where it was a shorter interval of <10 min for capacitance in dissipation). Conversely, the 85% and 70% RH conditions produced the largest changes, albeit all within that same initial 15 min window. Beyond this first 15 min, IPMCs in all environments reached equilibrium, telling us that the feasibly for the pre-operation equilibration window could be refined to shorter timeframes with further experimental investigation and validation.

Stage II-bending actuation response to applied voltage bias
IPMC actuation performance (i.e. bending displacement, mm), voltage bias, and hydration correlations were tested in a vertical cantilever arrangement. While the input bias was maintained for each test scenario, environmental conditions were varied. Replica tests were conducted to reveal the average and standard deviation of the actuators for a more practical perspective. The direction of the IPMC's response will be classified in one of two ways. 'Actuation' indicates movement towards the positive electrode (+y axis), and 'back-relaxation' defines the opposite direction (−y axis).

Short single voltage interval: experimental bending
response. The first actuation configuration tested examined how the IPMC responds to a 1 DCV applied and then remove at 30 s intervals (f = 0.03Hz). The average actuation response (separated by hydration condition) is plotted in figure 4 with respect to time and includes standard deviation bars. The four environmental conditions (i.e. liquid DI water, called 'DI liq.' or 'DI Water', 96% RH, 85% RH, and 70% RH) are designated in the plot's legend. An additional rendition of this data is provided in supplementary data, figure S3. Furthermore, four actuation-relaxation phases were identified and indicated on this plot. These phases are used to identify and define the IPMC bending response [16]. First is (i) the initial response of the IPMC to the applied bias; it is the fastest, with an increasing exponential trend that heads towards an inflection point at the displacement maximum. Next (ii) defines the inflection point of the maximum deflection curve. Following this, (iii) depicts the V on backrelaxation where the IPMC begins a gradual downward parabolic slope towards its original position (i.e. origin at y = 0). Finally, when voltage is removed (iv), the V off relaxation produces an exponential decay towards a plateau in the region of the origin. Although all four conditions produced these same general responses, they varied considerably in their trend's shape. Therefore, to differentiate the results for each condition, experimental results were analyzed for (a) the response speed of the actuator when voltage is applied, (b) the displacement range potential and variability (i.e. standard deviation), (c) the response rate when voltage is removed, and (d) the actuator's ability to maintain positions at each juncture.
First, region (i) in figure 4, defines the IPMC's response speed and trend towards the maximum actuation displacement. As the 1 DCV bias is applied, the free moving cations are quick to respond and produce actuation. To determine the initial actuation rate (i.e. actuation speed, v in mm s −1 ), the slope of the actuation curve in figure 4 was examined for the timeframe of 0 ⩽ t ⩽ 3 s. The correlations between these conditions are as follows and show how the IPMC's response is highly dependent on external conditions: These correspond with values of 0.028, 0.029, 0.045, and 0.052 mm s −1 , respectively. Water vapor conditions ⩾ 85 % RH allow the IPMC to respond more quickly. If the IPMC is submerged in liquid or is surrounded by a drier environment, the IPMC's response rate is slowed. As the IPMC approaches its maximum displacement (i.e. region ii), this initial rate is slowed as the IPMC curves towards the inflection point. The most significant change is in the liquid water condition, while vapor conditions maintain similar response. The DI water required the least time to reach its maximum, while the driest condition (70% RH) took the longest. The 85 and 96% RH conditions produced similar response rates, with IPMCs in 85% RH reaching their maximums 3.7 s sooner than 96% RH. The maximum actuation displacement (δ max ), indicated as (ii) in figure 4 produced the following correlation: δ max, DI liq < δ max, 70% RH < δ max, 85% RH < δ max, 96% RH with equivalent values of 0.11, 0.14, 0.22, and 0.28 mm, respectively. Although the maximum displacement defines the actuation potential of the IPMC, this study identified additional significance in the analysis of how long this is maintained. This lead us to contemplate the immediacy and distance the IPMC back-relaxes away from this maximum while voltage is still applied (region iii). After δ max is reached, the solvent-controlled forces begin to dominate producing V on back relaxation [41,43,51,52]. The V on relaxation displacement witnessed was as follows: δ relax, 70% RH < δ relax, 85% RH < δ relax, DI liq < δ relax, 96% RH with the correlating values are 0.002, 0.041, 0.058, and 0.069 mm, respectively. When we combine the information learned from regions (ii) and (iii), we see that DI submerged samples were the least capable of maintaining maximum deflection, only holding for <50% of the time that the other well hydrated samples measured. Conversely, the drier environment (70% RH), although took longer to reach δ max , showed a delay in the induced V on back relaxation response, extending the hold time by more than double. Meaning that, as the environment became drier, the back relaxation quality lessened.
Finally, phase (iv) showed how well the IPMC could return to its original position. Any deviation from y = 0 was classified as 'drift' and described uncontrollable deviation from intended motion. In this work, the drift can be likened to a form of creep or permanent gradual degradation of the material's electromechanical response with respect to operation and/or exposure to varying hydration conditions. At the test's conclusion, the DI liquid submerged sample was closest to regaining its original position deviating by ∼0.11 mm. Water vapor conditions showed a trend of increasing drift with increasing saturation: 0.14 mm (70% RH), 0.22 mm (85% RH), and 0.28 mm (96% RH).
Nemat-Nasser and Li also described a similar initial fast actuation response of the IPMCs (within the first 6 s). This validates the data shown in actuation phase (i) in figure 4 where the electrostatic effects induced by the 1 DCV load produced the fastest responses in highly saturated water vapor conditions (i.e. 96% RH and 85% RH) [51]. Previous authors have also identified discrepancies in IPMC back-relaxation under varying conditions. Zhu et al studied the deformation of IPMCs with specific emphasis on forces which correlate with the IPMC's hydration [53]. Their results confirm the trends shown in figure 4 of this work which depict considerable changes to the back relaxation distance, rate, and duration based on the hydration of the IPMC. This is attributed to the intra-and intersolvent-diffusion forces driven by the contained water concentration gradient which increases with the degree of hydration. Once the voltage is removed completely, the IPMC can seek a new point of hydration equilibrium, as evident by the plateau trends at t = 60 s which may not align with the origin. This new equilibrium is affected by the IPMC's contained solvent, its continuous diffusion exchange with the ambient conditions, electrical modifications due to the capacitor's ion exchange with the DC source, as well as mechanical influence from any developed structural changes induced through operation and changing saturation states (i.e. shrink and swelling). The result is the IPMC will be unable to return to its original configuration, which can be seen in all conditions, with the least deviation generated by the liquid DI water submerged samples.

Short single voltage interval: validation via model fitting.
Although many authors have attempted to theoretically define IPMC's bending deformation, it was not until recently where models have attained a degree of complexity which can more accurately align with experimental IPMCs actuation results. Maximum actuation displacement and bending actuation fitting derived by Al-Allaq et al are used to compare against the experimental findings of this work. This analytical model was selected based on its use of measurable and geometric parameters, with the inclusion of an IPMC's hydration properties, which make it so that experimental data can be directly implemented and compared [43]. The model fitting results are summarized in tables 3 and table 4. Denisty values reported in tables 3 were interpreted from Morris and Sun [9], while the Youngs modulus values were interpreted from Bauer et al [8].
It is important to note several discrepancies between the original findings of the model (i.e. labeled 'model,' and the calculations utilizing the experimental data in this work (labeled 'exp.'). Firstly, the capacitance, resistance, and young's modulus values were held constant in the Al-Allaq, mode. Alternatively, in this work we have shown that they vary with hydration quality and thus these values were adjusted in accordance with each environment condition tested and the corresponding experimental data obtained. Secondly, this model does not specify the state of the water contained in the IPMC, and will be modeled using a 'hydration parameter' which, when adapted in this work, is representative of the amount and form of water. Lastly, Al-Allaq et al did not report the dimensions of their IPMC and ionic polymer core [43]. The Al-Allaq et al model includes consideration of electro-osmosis, electrophoresis, and ionic diffusion of various species within an IPMC system and is derived from earlier work by Shahinpoor and Kim [54]. Their approach first defined the curvature of the initial bending actuation towards the anode. They then used this relation to determine maximum displacement (δ max ) of the actuator [43]: This relation was utilized in combination with model parameters specific to this experimental work. These parameters and their identification are summarized in the supplementary materials section S6, table S1, while the established values are summarized in table 3. Equation (5) defines the maximum tip displacement (δ max ), relative to time (t), with consideration of several design parameters and hydration-dependent properties. The calculation also includes constants such as Avogadro's number (A v ), elemental charge (e), and the universal gas constant (R). The design parameters include dimensions of the IPMC strip polymer core (length (l p ), width (w p ), and thickness (h p )), influence of the chose lithium cations (number of electrons in the valence shell (n * = 1)), the applied electric field ( − → E ), and the chosen constant absolute temperature (T =303.2 K). The hydration-dependent properties include capacitance (C p ) and resistance (DCR) measurements, density (ρ) and Young's modulus (Y) of the Nafion polymer core, and the hydration/osmotic (o w ) and water content (λ w ) parameters which were defined by Al-Allaq et al. The supplied 1 DCV is converted into a field input via the relation: The field is a non-linear function of the capacitance (C p ) and cross-resistance (DCR) and is inversely proportional to the strip volume (V p ). The 'hydration parameter' was adapted for this work from the model's osmotic parameter (o w ) which defines the pressure generated by migrating water: This is used to represent the influence of the contained water in the IPMC, although some discrepancies are expected as this model does not specify the form of the water contained in the Nafion-IPMC system [43]. The hydration parameter was calculated using the hydration-dependent properties noted in table 3. This included the IPMC's water content (λ w ), the water contribution to the stretch generated on the cathode side), displaced volume of water (V w ), and the IPMC's dimensions (i.e., height h p , width w p , and length l p ): It should be noted that the hydration/osmotic parameter featured in equation (6) will typically produce a negative value as the water content (λ w ) is a fraction and this will net a negative differential with the calculation of this term in the parenthesis of equation (6). This can then be used to calculate the 'volume of migrated hydrated water' (V w ) with mass (M w ), and water density (ρ w ). The mass of the water absorbed by the IPMC, relative to the respective environments, was collected experimentally and used to calculate in the relation for M w (recall table 2). The volume of the strip was defined by its dimensions (V p = h p w p l p ). It should also be noted that, like how the density of Nafion changes with respect to hydration, so does the modulus of elasticity of the material. As a result, the Young's modulus (Y) was also considered a hydration-dependent quality of the IPMC. The density is reported based on experimental findings by Morris and Sun [9], while the modulus was derived from relations reported by Bauer et al [8]. Bauer et al plotted the modulus of Nafion 117 H as a function of temperature and ambient conditions (0%-100% RH as well as liquid water, and 25 • C). Note that the value for 70% RH was not reported, and thus was estimated based on the trends of the other conditions when re-plotted. Although other authors were considered [14,15] Bauer et al values were chosen as it agreed with those reported by Al-Allaq [43].
It is very apparent in table 3 on how the mechanical qualities of the IPMC change with respect to the Nafion's hydration state. The Nafion core decreases in stiffness and density at a larger interval of change when transitioning from water to maximum vapor saturation (ρ ∼ 2.9%, and Y ∼ 32%) when compared against the transitions within vapor only conditions (ρ ∼ 2.5%, Y ∼ 5.9%). Meaning that as conditions become more hydrated, the density and Young's modulus both decrease with increasing saturation. This also provides perspective of the impact of how the state of the water affects the IPMC's properties. Recalling modeling by Nemat-Nasser et al, we know that the total stress influencing the IPMC is a combination of stresses produced by forces resulting from osmotic stress. Likewise, when voltage is applied to the IPMC, it induces charge imbalances which will also contribute [51,53]. Regardless, whatever state the water surrounding and within the IPMC takes will determine what types of solvent pressures will develop, affecting actuation. Although one would expect the most saturated IPMC to optimize these forces, instead we see this occur in water vapor conditions. Furthermore, we know from past studies that the IPMC's absorptions capabilities change based on the form of water. This translates into similar changes by the hydration parameter, validating the importance of how the change in state of water affects IPMC actuation. All of this ties back into the aforementioned discrepancies between the electrical data expectations and the actuation results surrounding the DI water condition. To note, based on the capacitance, dissipation factor, and conductivity measurements conducted in section 3.1.3, it was expected that the DI water condition would be comparable to 85% RH and 96% RH conditions, but both in the experimental data and in the model analysis, DI water conditions produced smaller maximum displacements than the 70% RH condition. As this work does not quantitatively identify the state of the water within the IPMC structure during operation, it leaves much room for interpretation as to how the form of the water impacts the mobility of the counterions when the voltage bias is applied. Therefore, although this study does provide perspective, we acknowledge that any inference regarding what mechanism is dominating in each of these hydration regions would be based on speculation and assumptions.
The maximum displacement model estimations compiled in table 4 were compared with data retrieved from figure 4 via equation (5) and the established values in table S1 and  table 3. The model results tabulated in table 4 validate the experimental data presented in this work. It is important to note that the maximum displacement calculated using the model's data are considerably larger than the values calculated from the experimental data. This was expected due to several differences in the studies performed. Firstly, Al-Allaq's model is unclear regarding the sample's hydration, defining it as 'assumed to be sufficiently wet.' As has been experimentally quantified throughout this work, knowing the precise hydration quality is necessary for a reliable comparison of data. Secondly, the reported testing schematics depict ambient air testing, but they neglect to specify the degree of saturation of the environment. Referring back to figure 1, we know that the dielectric constant continues to decrease with decreasing water vapor content of the ambient conditions. Assuming the ambient air condition would produce a relative humidity much lower than the 70% RH condition analyzed, it is reasonable to speculate that the values could potentially correlate more with the experimental data. Finally, it is expected that there is a large degree of variability resulting from the differences in IPMC design (i.e. Al-Allaq examined IPMCs plated with platinum and silver and protonated with sodium cations). Literature has shown that an IPMC actuator's properties vary considerably with minor modifications to the composites design and fabrication methodology.
Al-Allaq's model does validate the trends witnessed between the various ambient conditions. Noting the ranking columns for experimental and modeling data, we can see that each follows the same trend: δ max, 70% RH < δ max, DI < δ max, 85% RH < δ max, 96% RH where the smallest maximum displacement was produced in the 70% RH condition (below DI water immersion), while maximum displacement was achieved by samples tested in 96% RH water vapor conditions.
To address the calculation discrepancies in table 4, the parameters were considered individually for their respective influence on the maximum displacement. Specifically, Young's modulus (Y) and the water content (λ w ) were noted as most impactful. The Young's modulus of an IPMC will change with the hydration state of the core Nafion polymer becoming smaller as hydration increases. It also impacts δ max twofold as it is both incorporated in the bulk equation (5), as well as, in the calculation of the hydration parameter (o w ) defined by equation (6). The values used in this work were reported in table 3 based on findings by Bauer et al and are for the Nafion core polymer alone, and therefore do not account for the influence of the modified composite structure (namely the influence of the embedded platinum) [8]. Therefore, it was expected that the modulus values utilized in the model calculations were smaller than what the true modulus of the IPMC would yield. Still, to achieve the model estimated values in table 4 required increasing the Young's modulus values by an order of magnitude. When we consider the Young's modulus of Teflon (which has the same backbone polymer structure) is 575 MPa, it makes this modification unreasonable. Furthermore, with this modification, δ max still exhibited large error when compared against experimental values (exceeding 70%). Alternatively, when the water content (λ w ) is modified, more reasonable estimations are generated. To note, nearly doubling the water contents of IPMCs produced δ max values with less than 20% error deviation. This implies that, although there are some errors when comparing this model to experimental findings, there is potential to fine-tune this analysis for more accurate results. It also emphasizes the model's mistreatment of how the water content affects the IPMC's actuation performance. One final consideration is the range reported in Al-Allaq's experimental findings compared against this work. Al-Allaq showed maximum displacement values around ∼3.75 mm. When this is compared against the calculations from the parameters of this study (in table 4), we see a comparable magnitude in the 96% RH (optimized) condition estimated to δ max = 3.6 mm (∼4% error).

Long single voltage interval: experimental bending response.
A 1 DCV bias was maintained for 400 s for samples exposed to the same four conditions. The resulting IPMC tip displacement responses were plotted against time in figure 5. An alternative representation of figure 5 can be found in supplementary section S7, figure S4, which plots each condition separately. The aim of this test was to get a better perspective on how much the V on back-relaxation property dominated the IPMC's actuation behavior. Again, the influence of the external hydration conditions was significant.
As with the arrangement discussed in section 3.2.1, the smallest deflection peak (δ max ) was produced in DI water (0.086 ± 0.06 mm at t = 10 s) and 70% RH (0.084 ± 0.06 mm at t = 29 s). Interestingly, the maximum distance was achieved by the actuators tested in 85% RH (0.32 ± 0.09 mm at t = 38 s), outperforming samples in 96% RH (0.29 ± 0.04 mm at t = 15 s). Still, one should note the considerable overlap between the deviation bars for the 96% RH and 85% RH settings. Furthermore, 85% RH testing yielded the largest deviation (±0.09 mm) resulting from several challenges in sustaining the hydration quality without significant condensation residue on samples.
In this test arrangement, because the voltage is never removed, we omit actuation phase (iv) from consideration. Furthermore, we increase the time duration of region (iii) resulting in an extension of the V on back-relaxation trend. In all cases, the relaxation is so significant that the IPMC nearly returns to its position of origin. Total back-relaxation displacement was ordered (smallest to largest) as follows: DI water liquid relaxed 0.024 mm (28% of δ max, DIliq ) to a plateau point of 0.06 mm; 70% RH relaxed 0.041 mm (49% of δ max, 70% RH ) back to sustain a level at 0.04 mm; 85% RH relaxed 0.22 mm (68% of δ max, 85% RH ) to 0.1 mm; and the 96% RH condition IPMCs relaxed 0.25 mm (86% of δ max, 96% RH ) to a plateau point of 0.05 mm. So, although the 96% RH and 85% RH conditions produced much larger actuation displacements when compared to the DI water and 70% RH settings, they also produce the steepest deflection drop off, with the drier condition showing a more gradual trend. This is also reflected when we compare DI water and 70% RH where the liquid submerged samples yielded a sharper response.
In summary, the outstanding qualities for each condition are as follows. DI water was the fastest to actuate to maximum displacement, but it was unable to maintain this position, exhibiting near immediate V on relaxation. This makes it the poorest at minimizing the effects of back-relaxation. Still, it yielded the smallest back relaxation range, and again, remained relatively consistent in its behavior through all replicated tests. Alternatively, although the 96% RH condition was the most consistent trend, yielding the smallest deviation and aligning with previous 1 DCV studies and still producing large actuation displacements, it also produced the largest back relaxation of any condition. This implies that while the improved hydration allows the +y motion to be increased, it also conversely increases the negative effects of −y motion (i.e.,V on back-relaxation). Similarly, the 85% RH environment took the longest to achieve δ max and produced comparable V on relaxation with the largest deviation. Lastly, the 70% RH condition took the longest to reach maximum displacement, produced minimal deviation, and yielded the smallest V on relaxation in the region t ⩽ 100 s. Therefore, these results highlight how V on relaxation (i.e. −y motion) is dramatically reduced by one of two methods. (a) Operating the IPMC submerged in DI water liquid or (b) minimizing the water content in water vapor conditions between 70% and 100% RH. This conclusion was further validated by Shoji and Hirayama who reported similar findings for samples tested in 90% RH but neglected to include liquid immersion conditions [41]. Therefore, this study showed that, when operating IPMCs, one must decide what motion qualities are desirable to determine the proper operation conditions. Overall, higher water vapor saturation regions will yield increased bending actuation, and with that increased V on back-relaxation, while drier vapor conditions and liquid immersion diminish actuation range but retain their actuation max position more successfully by minimizing V on back-relaxation.

Stage III-'back-relaxation' in response to voltage removal
The V off back-relaxation phase (iv) defines the IPMC's reaction to DCV removal. The aim of this test is to characterize the relaxation trend in the −y direction towards the origin (y = 0). A 1 DCV bias was applied for 30 s, then removed and continuous tracking of the free-end tip displacement with respect to time was executed for 330 s, see figure 6. An alternative illustration of figure 6 can be found in the supplementary section S7, figure S5, which plots each condition separately. Environmental testing was continued with samples contained within the same four atmospheric conditions.
Each trend plotted shows the same fast initial actuation (i), inflection at maximum displacement (ii), V on back-relaxation (iii), and V off relaxation (iv). The DI water condition produced fast actuation response (0.044 mm s −1 ), reached δ max = 0.15 ± 0.13 mm, and then began to V on relax by t = 4 s. The V off back relaxation trend showed a fast initial drop (nearly a perfect vertical) to a dip below the origin before rebounding back up towards the origin, settling at 0.002 mm above y = 0. Water vapor conditions showed increasing response range with increasing hydration. As with the liquid condition, all samples produced a dip shortly after voltage was removed before rebounding upward in a positive linear trend until the test ended at t = 360 s. The 96% RH condition produced the slowest actuation rate (0.027 mm s −1 ), achieving the largest δ max = 0.33 ± 0.13 mm, and V on relax initiated at t = 18 s and relaxed a total of 0.076 mm before voltage was removed at t = 30 s. The V off relaxation displacement was the most controlled (smallest deviation error bars) and produced the smallest drift from the origin (0.008 mm below y = 0). The 85% RH condition was much faster than 96% RH, at 0.075 mm s −1 , reaching δ max = 0.27 ± 0. 05 mm by t = 10 s, after which V on relax initiated with a similar decreasing linear slope as the 96% RH condition, relaxing the same total amount of 0.076 mm. The V off relaxation displacement yielded significant drift (0.062 mm above y = 0) with a 'bouncy' trend from 60 ⩽ t ⩽ 360 s. Lastly, the 70% RH condition required 26 s to reach δ max = 0.18 ± 0. 08 mm. This meant that it was by far the slowest to attain maximum displacement, but in turn, produced much less V on back-relaxation (0.014 mm). The V off relaxation produced significant drift, 0.19 mm, which was larger than the intended actuation.
Overall, the data reflected the initial presumption that the 96% RH (95%-100% RH vapor condition) would yield the largest actuation with most controlled and sustained performance. This was validated again through this test configuration. Overall, this test highlighted that the more saturated conditions produced the least drift during the V off back relaxation phase, with trends moving from linear towards a constant plateau. Interestingly, the liquid condition produced the second fastest response, behind 85% RH, while the 96% RH and 70% RH were much slower. It should be noted that in section 3.2.1 the 96% RH condition produced the fastest response, being nearly identical to 85% RH. These discrepancies between figures 4-6 regarding the IPMC's initial actuation speed is attributed to the larger data pool in the test portrayed in figure 4. To note, figure 4 utilized data from the first 60 s from all tests conducted between sections 3.1 and 3.3, while sections 3.2-3.4 portray smaller sample data pools. Therefore, when analyzing the first 60 s of actuation data one should employ figure 4 as the most reliable reporting. The discrepancies noted in figures 5 and 6 further emphasize how the complex and ambiguous regions of water distribution within the IPMC and exchanging with its surroundings produce large variability in the IPMC's actuation response behavior. All samples yielded the largest deviation in their maximum displacement peaks. The DI water and 70% RH environments yielded the poorest results. These environments exhibited the largest deviation in sample responses and back relaxation drift away from the origin (nearly the amount of displacement achieved by the actuator). It is believed the visible drift resulting from DCV removal is indicative of the IPMC finding a new equilibrium arrangement. This new equilibrium is determined by the material's changing electromechanical properties with operation and hydration conditions. This is identified as one primary driving factor for the IPMC's unique varying behavior. Although the voltage is removed, the IPMC must now cope with the residual effects of the applied field and modified solvent gradient. The electrical input has charged the system, resulting in modifications to the contained solvent's form and electrical bonds, ion-ion interactions, and mechanical stresses/strains which are now elastically springing back towards the origin. Where the IPMC settles is at a new point of equilibrium, where all features have found a new low energy state. This new equilibrium is identified by the constant plateau trends seen around t = 360 s. It is also theorized that several actions could be taken to allow the IPMC to regain its original orientation and configuration. The first suggestion is incorporation of a 'discharge' step. This implies connecting the capacitor to a ground source which would allow the rapid release of stored charge from the system, and, in theory, allow the stored mobile ions to migrate back toward their original structural configuration, in turn, allowing the actuator to return to its original position. Another solution is flipping the DC bias (or use an AC input) which reverses the anode and cathode to control the rate and direction of diffusion within the IPMC.

Stage II and III interactions: cycled actuation
These series of tests examined the IPMCs performance resulting from a DCV load being applied and removed (i.e. cycled) for 15 repetitions utilizing the same 30 s intervals (i.e. 0.03 Hz). Plots are separated by their respective test environment (see figure 7 through figure 10). Figure 7 shows a set of plots representing (a) the cycle displacement response with respect to time, including the standard deviation (error bars), and (b) the maximum and minimum trends of part (a) plotted with respect to time, with the fitted trend (dashed lines). For figure 8 through figure 10, only the (b) plot is shown of the maximum and minimum trends. The tip displacement with respect to time plot is included in the supplementary section S7 figures S6, S7, and S8 for additional reference. In the previous sections, the maximum displacement varied in correlation with the respective environment. That same trend was continued when the IPMCs were subjected to cycle voltage schemes. First looking at figure 7(a), all subsequent voltage applications beyond the first voltage application cycle produce smaller bending actuation displacements. To get a clearer perspective of this the maximums (actuation peaks) and minimums (relaxation valleys) were plotted as trends in figure 7(b). With this perspective we see downward sloping trends which become closer together with increasing actuation cycle. This implies that not only is the IPMC drifting away from its original orientation, but it is also diminishing in actuation range. This trend can also be seen in figures [8][9][10]. To expand upon this information, fittings were applied (see dashed lines along the maximum and minimum trends). These helped to classify the 'drift' of the IPMCs. Drift increases as the IPMC's V off relaxation point migrates away from its original position (y = 0) at time t = 0 s. Increasing drift also correlates with larger deviation and/or degradation by the actuator. Interestingly, curve fittings showed the water vapor conditions produced Boltzmann trends in both actuation and back relaxation, while liquid submerged IPMCs produced an exponential decay fit. The Boltzmann relation is defined as: where, A 1 is the initial value, A 2 is the final value, x 0 is the center, and d x is a time constant. The liquid immersed samples produced smoother trends when compared against the bumpier trends seen in the RH conditions. Both plots in figure 7 depict the 'optimized' IPMC cycled tip displacement response with respect to time in the 96% RH water vapor environment. These results confirmed previous findings where the actuator produced the largest values (average δ max = 0.26 mm in this case). The IPMC's actuation decreases with the number of voltage cycles, plateauing ∼0.2 mm below δ max . Interestingly, the IPMCs appear to diminish in deviation with subsequent DCV cycle application. This presents the possibility that an IPMC could be pre-operated to remove any initial excessive deviation and achieve a more predictable and reliable performance when usage is needed. In figure 7(b) the dashed line represents the Boltzmann fit (R 2 actuation = 0.96 and R 2 relax = 0.99), with correlating maximum and minimum trendlines. Distinct variation is visible around cycles 4-12. Overall, the 96% RH hydrated IPMC drifted ∼0.2 mm below y = 0 by the end of the test.
In figure 8, we see the lowest saturation exposure condition, 70% RH, produced δ max = 0.11 mm, the second smallest range. The actuation potential shows an overall decrease with voltage cycle by 0.075 mm, below maximum displacement. There is no clear trend defining the variability of the error bars, with the deviation initially very large, diminishing significantly in cycles 3-9, then only to increase again beyond cycle 10. The Boltzmann fit resembles the 96% RH trend, with poorer fitting values of R 2 actuation = 0.95 and R 2 relax = 0.91, for the actuation and relaxation trends respectively. The net drift of the IPMC is ∼0.013 mm above the origin.
The 85% RH condition (see figure 9) produced a maximum displacement (δ max ) of 0.18 mm in the first peak, doing slightly better than the 70% RH condition, but not as well as the 96% RH condition. This environment produced the smoothest cycle trend but with the largest deviation, which increases as the number of voltage applications increases. As was noted in previous tests, this operation condition was the most challenging to work with, producing the largest variability in all cycle tests conducted. This condition produced two different trends in the respective actuation (Boltzmann, R 2 actuation = 0.87) and back relaxation curves (Gauss, R 2 relax = 0.90). Seemingly, the two trends appear to be heading towards a convergence point, and overall maintained a constant range. This implies significant losses for actuation displacement range. Furthermore, the significant deviation away from y = 0 suggests that the IPMC is unable to relax quickly enough before actuation pushes the sample more in the +y direction. The actuation trends appear to be reaching a new plateau region that has drifted above the origin by ∼0.12 mm (or 0.056 mm below its maximum displacement peak value at 0.175 mm). This new sustained range is attained by the 15th voltage cycle.
Lastly, DI water submerged samples, featured in figure 10, produced the weakest maximum deflection (δ max ) around 0.1 mm. In all plots, the first actuation peak is the maximum displacement range attained. These samples showed actuation potential decreasing to ∼0.05 mm below the maximum displacement in the first cycle. Contrary to the RH conditions, liquid submersion testing produced more rectangularshaped peaks (note supplementary figure S8). This is the result of the max displacement being attained rapidly followed by immediate back-relaxation. This suggests that designing an IPMC for quick-response applications would best be  executed in liquid submerged conditions. Overall, deviation of performance is larger than the water vapor conditions. It is consistent throughout liquid testing, with a slight increase in variability as the IPMC is cycled. In DI water, we can see the most uniform correlation between actuation and backrelaxation response trends, where the two curve fittings are similar in their trends matching an exponential decay fit with R 2 = 0.97 (actuation) and 0.94 (back relaxation). Interestingly, DI water submerged was the only condition to produce the decay-like trend.
Interestingly, although the electrical estimations made in section 3.1.2 figure 1 were largely able to predict the overall performance trends (recall previous findings in sections 3.2.1, 3.2.3, and 3.3), some inaccuracies became identifiable when IPMCs were subjected to cycle loading. Based on the capacitance and tangent loss measurements, the liquid submersion condition was expected to produce comparable results to the 85% RH environment. This was not the result. When directly compared against the 85% RH condition, we see that the vapor condition produced an 80% higher maximum displacement than DI water. Although the trends were consistent, we see deviations in performance comparable to the displacement attained by each actuator (e.g. in DI water, using one of the deviation bounds, actuation varies by ±43%). Focusing on the DI water environment further, we see regular spiking of the deviation trends during voltage application and removal which increases with subsequent voltage applications. Meaning, as the IPMC is actuated, the performance certainty gradually degrades. In the DI water condition, the deviation trends were the most uniform. Furthermore, although this work was able to provide preliminary quantitative inspection into overall trends in the IPMC's actuation drift via the 15 voltage cycles tested, future evaluations of these actuators should increase the number of cycles evaluated to determine if the plateaus witnessed here are sustained. This would further validate the 85%-90% RH as the most favorable condition to provide sustained cycled motion of IPMC actuators.
When we look at the water vapor conditions, all scenarios produced significantly variable performance deviation. Interestingly, although the 96% RH condition produces the smallest error bars, the overall drift is much more erratic than its 85% RH counterpart. Also, interesting to note was that the 70% RH condition had the smallest error bar deviation, but again, was highly unpredictable in its net actuation behavior. All of this alludes to the conclusion that IPMCs subjected to water vapor conditions produce very different response when compared against liquid submersion. A specific example is in the shape of the tip displacement trends. All three water vapor conditions produced softened peaks, resembling the single cycle tests where the approach to the maximum displacement was more gradual (softening more at lower hydration conditions).

Pre-and post-actuation electrical testing
Dielectric properties were measured pre-and post-actuation and are summarized in the figure 11 bar chart. These plots show the dielectric constant for the three stages surrounding IPMC operation. Each section of the bar chart represents the environment condition sustained for the 1 DCV cycle deflection test executed. Each group is divided into the three testing stages: (a) sample preparation via 24 h DI water equilibration (i.e. 'DI Equil'), (b) immediately prior to actuation testing but after being allowed to equilibrate for 1 h (i.e. 'pre-δ'), and (iii) after 1 DCV constant deflection was executed (i.e. 'post-δ'). As all samples were prepared in the same way, the 'DI Equil' quality was averaged amongst all samples tested and is shown as a constant comparison value for all conditions. The DI water condition showed a decrease in the dielectric constant of the sample once loaded into the chamber with fresh DI water. This is likely due to the DI water's resistivity decreasing with time exposure to the IPMCs and open air. Post actuation testing showed dielectric values of 1.39 × 10 6 ± 5.7 × 10 3 , a 2.3% increase from the preactuation value. The 96% RH condition improved the preδ dielectric quality by nearly 15%, and the post-δ value (2.28 × 10 6 ± 9.2 × 10 4 ) was an additional 11% increase. The 85% RH and 70% RH conditions both showed decreased preδ dielectric values from DI Equil., as well as, in post-δ. The post-δ dielectric measurements for 85% RH is 1.12 × 10 6 ± 1.7 × 10 5 while, 70% RH is 5.46 × 10 5 ± 3.5 × 10 4 . The largest decrease and deviation were witnessed in the 70% RH condition, which was anticipated as the decreased hydration will negatively impact the dielectric constant of the IPMC. Interestingly though, similar deviation was seen in the 96% RH condition, which produced the largest dielectric constant values both prior to and following actuation testing. It is also interesting to note that the DI water conditions sustained electrical properties, when operated cyclically, more successfully than the 70% RH and 85% RH conditions. This suggests that, although the mobility and behavior of the cation migration within the liquid submerged samples may differ greatly from water vapor, the quality of the dielectric material is still on par with the maximum water vapor conditions. Therefore, it is concluded that the response discrepancies between liquid and vapor are the result of how the ions migrate within the hydrophilic ionic domain of the IPMC.

Conclusions
Electrical measurements were used successfully to identify changes to an IPMC's dielectric constant and tangent loss properties with respect to varying hydration conditions. This information was used to successfully predict how the IPMC's maximum displacement would change with varying water vapor exposures. The identified maximum in 95%-100% RH conditions was found to correlate with a maximized dielectric constant, minimized dissipation factor minimized, and optimized actuation performance. Actuation testing exposed correlations between the ambient hydration conditions and the membrane's actuation rate, variability, inability to maintain actuation positions (i.e. V on back-relaxation), as well as, how the material would behave when a DCV load was removed (i.e. V off back-relaxation). It was found that water vapor conditions produced more gradual actuation response trends when compared against the sharper liquid results. Vapor conditions depicted larger actuation and greater V on backrelaxation movement with increasing saturation. As hydration decreased, IPMCs were able to maintain longer δ max hold durations. Conversely, samples immersed in liquid exhibited faster responses and larger back-relaxation. This is most evident in the cycle actuation testing where vapor actuation trends resembled softened shark fins, while actuation in liquid was squarer in shape. In all, this further emphasized how the form of water interacts with the IPMC's electroactive properties and suggests that more focused investigation of the mechanisms causing this change would greatly advance understanding of IPMC's structural, solvent, and electrical interactions.
The results of this work were validated via fitting against a model published by Al-Allaq et al which produced the same correlations between δ max and hydration conditions. Using their approach, an IPMC 'hydration parameter' was identified to represent the effects of the solvent conditions on the IPMC's electroactive response. The discrepancies between this work's results and the estimations by the Al-Allaq et al model suggest current models have a more successful representation of IPMCs in water vapor conditions but are less accurate when applied to liquid-immersed actuator operation [43]. Furthermore, they neglect to consider the state of the water (i.e. liquid, vapor, or a mixture of the two).
Using the results of this work as a roadmap, one can determine what movement response they desire and then modify the IPMC's saturation quality and the input scheme accordingly. To achieve this, real-world solutions will require that the solvent sensitivity of the material is controlled and/or isolated to reduce performance deviation. Potential solutions include (a) application of IPMC actuator designs in conditions which naturally maintain the desired hydration conditions; (b) additional modification to the IPMC actuator composite design to isolate the IPMC's saturation quality prior to operation; or (c) programming of a controller system that is designed to modify and/or optimize the IPMC's performance based on its natural behavior. Some researchers have initiated investigations into encapsulation of the IPMC to prohibit the membranes exchange with external conditions. This is likely the right approach as it would ensure the IPMC's hydration conditions are sustained, although their work leaves questions regarding the robustness of the final product, as well as, how this coating will affect the resulting bending response behavior. Ultimately, a similar approach as that used in this work could provide this perspective allowing the IPMC the opportunity to be adapted for a wider array of applications.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).