Plant-inspired rearrangement of liquid in a porous structure for controlled swelling

Soft robots can adapt to dynamic environments without prior knowledge of their properties. Plants inspire mechanisms for counterbalancing dynamic loads by locally modulating compliance through anisotropic humidity-responsive materials and structures. In addition to well-known passive bilayers, plants may also actively control swelling. The combination of robust hygroscopic material-level response and simple electrical control makes active swelling particularly attractive for technological implementation. However, dynamic swelling demands the development and optimisation of congruent pumping solutions. This work suggests electrohydrodynamic pumping, enabled by highly reversible ion immobilisation at capacitive electrodes, as a particularly suitable low-pressure, high-area liquid displacement solution for active swelling. Local pore fill ratio (PFR) modulation is used as a measure for dynamic liquid displacement and swelling. A method for highly localised (10 μm membrane thickness) assessment of the dynamic variation of PFR in a 400 μm laminate undergoing cross-plane electrokinetic liquid displacement is developed. Two modes for transient PFR modulation were identified: electrokinetic ion transfer and diffusive solvent redistribution, pronounced at high and low voltage scan rates, respectively. The strategic combination of these modes enables various compliance-modulation scenarios. The system contains (within a cycle) a constant amount of liquid in an open network of liquid-filled pores. 30%–75% PFR yielded the highest dynamic PFR modulation: a high amount of empty pores is beneficial, yet a too-low PFR compromises the continuous liquid pathway necessary for electrokinetic pumping. The dynamic nature of internal liquid rearrangement was characterised by relatively fast electrokinetics-driven fluxes (6.3% PFR change in 80 s), followed by a slow equilibration of concentration and PFR. At high scan rates, PFR decreased at positive polarisation, while both positive and negative polarity yielded a similar decrease at low scan rates (5 mV s−1). Localised control over the swelling gradient enables the design of systems that morphologically adapt to complex dynamic loading conditions.


Introduction
Soft robotics improves machines to better adapt to complex and unstructured environments.These robotic systems often encounter dynamic, complex interactions with their surroundings, which require material-level negotiation strategies for successful operation.Many natural adaptive structures are modulated or mediated by liquids, inspiring robotics [1].In addition to using liquids for hydraulic pressurisation of deformable structures (mimicking turgor), reversible swelling of hygroscopic materials has gained attention in soft robotics due to its extreme robustness.Figure 1(A) recalls the mechanism for hygroscopic bilayer bending, responsible for opening the pine cone scales (composed of only dead tissues) in dry.Pine cone's ovuliferous scales are an example of a bilayered bio composite constituted of actuating (active, sclereid layer) and resistive (passive, sclerenchymatous layer).The sclereid layer comprises closely packed thin-walled cells expanding longitudinally when exposed to moisture [2,3] and acting as a natural response to the environment's relative humidity.Not surprisingly, the humidity content of the ambient air is the default control for hygromorphic robots [4].
We propose a two-stage system encompassing two semi-independent sequential mechanisms: pumping and swelling, each realized by dedicated components.Swellable materials respond to the amount of introduced liquid, either sorbed from the environment (as in hygromorphs) or displaced from other parts of the system (this work).By rearranging a swelling agent internally, robust hygromorphic actuators could operate without reliance on ambient air humidity.The pump used in this approach only needs to displace liquid to or from contact with the swellable material, which requires lower pressure-generating and volume-displacement performance than pumps for pressurising deformable-boundary fluidic actuators.This mechanism allows for a broader range of pumping strategies, including safer and multifunctional options such as electrohydrodynamics (EHDs) and electroosmosis.Low-pressure internal liquid rearrangement has been previously suggested in soft robotics for thermal management [5].
In living organisms, actively driven swelling gradients as a movement mechanism have received little research attention.The stems of trees are an interesting case study in this regard, as the xylem section that supports the plant's weight consists of metabolically inactive (i.e.'dead') cells.While xylem cells in a living tree are generally thought to be continuously fully hydrated [6] and thus (assumingly) not prone to transient swelling, the evidence does suggest that partially lignified xylem in Eucalyptus trees can shrink diurnally at reduced water potentials [7].In addition to water storage and maintenance of the functionality of the hydraulic apparatus [8], volumetric effects from swelling may have additional physiological significance.Trees effectively counterbalance asymmetric loads such as side winds [6] through movement that cannot be explained solely by (secondary) wood growth.Radial gradients of longitudinal stress are a mechanism for adjusting the tree toward vertical orientation [9].Cellulose fibrils embedded in a matrix of hemicelluloses and lignin in living spruce branches develop dynamic stress and strain [10], which allows the branch to effectively expose itself to sunlight and tune its compliance to mitigate heavy loads like snow while avoiding local stress concentrations [11], potentially involving active control of hygroscopic swelling.As the natural humidity-responsive structures are typically asymmetric (e.g.compression and tension wood in stems and sclereid and sclerenchymatous layer in cones), where a uniform control input (i.e.ambient humidity) already produces a mechanical response, there is little experimental evidence for active swelling gradients in the mechanical behaviour of plants.The potential significance of active swelling gradients in engineering has yet to be fully explored.However, biological cues suggest exciting possibilities for actively driven compliance in structures exposed to extreme stress levels (such as in tree stems) that may exceed the capable stress range of, e.g.osmotically driven mechanisms.
The active swelling gradient approach involves two sequential stages: (a) pumping and (b) swelling.This work focuses on stage (a), pumping, and characterises the liquid displacement kinetics experimentally.It also suggests key metrics for actively driven swelling and assesses the pumping performance as changes in pore fill ratio (PFR).The knowledge of step (a) is essential for follow-up work in stage (b), which involves optimising the interaction between the swelling agent and the porous polymer network.
Electroosmosis and EHD flow, based on the asymmetric interaction of cations and anions with the porous matrix, are the most promising candidates for miniaturised pumping [12] and actuation [13,14].Selection of the electrode materials for small-scale EHD flow is essential: the materials should be sustainable from an electrochemical point of view, assuming that no unsolicited redox reactions (leading to gas formation and dendritic growth) occur at the electrode.Indeed, electrolysis of the electrolytic solution [13,14] or electrooxidation of electrodes [12] are among the limitations of previously developed localised electroosmotic pumping systems.
This work uses the electrosorption of ions on capacitive high-specific-surface-area carbon electrodes for facilitating pumping.Ion electrosorption is a promising method for generating highly reversible and localised ion displacements.In case of asymmetric interaction of cations and anions with the matrix, can activate EHD pumping, as in figure 1(B).
A laminate of two carbon electrodes, separated by a membrane, is deployed for the cross-plane cyclic displacement of liquid.Figure 1(C) outlines the proposed active-compliance laminate.An open-porosity polymeric network (in brown) spans all system perimeter for hosting the mobile liquid.Poly(vinylidene fluoride-co-hexafluoropropylene) (PVdF-HFP) was chosen as the polymer.A mobile liquid, a solution of organic electrolyte (in blue), is contained within the pores.The electrolytic solution contains an organic electrolyte-1-ethyl-3-methylimidazolium trifluoromethanesulfonate ([EMIM][Otf]) in a mixture of organic solvents, facilitating asymmetric mobility while being electrochemically stable.Two layers rich in activated high-specific-surface-area carbon (in black) act as high-capacity electron-to-ion transducers, whereas the displaced electrolyte ions, in asymmetric interaction with the polymer matrix, cause displacement of electrolyte solution within the porous network via EHD pumping.
Mechanical compliance of electrodes is a common limitation of electroosmotic actuators: rigid constituents [15] effectively limit or obscure the resulting swelling magnitude.The selection of active materials for this work is inspired by electromechanically active actuators [16].Yet, strategic spatial separation of components responsible for pumping (more rigid) and swelling (softer) can be an effective technological solution.In existing electrosorptiondriven EHD actuators [17], the experimental systems have not allowed for the isolation of pumping action from the convoluted swelling of composite electrode materials containing the swellable material as the electrode-binder.A systematic investigation of liquid displacement in electrosorption-driven systems is needed to design controllable-swelling systems.In this work, the separation is attempted on a 100 µm scale, attractive for distributed action.
This paper isolates the kinetics and efficiency of cross-plane pumping in terms of transient PFR near the surface of the laminate under dynamic electrical input.For this, we incorporated an additional small metallic electrode to the laminate surface, separated from the electrode by a thin membrane, thus allowing for highly localised transient PFR monitoring where its variation is expected to be the highest.The impedance between the small electrode to the adjacent large carbon electrode is expected to correlate with PFR, as shown in figure 1(D): electric connection can occur only via the variable electrolytic resistance (noted as R ionic ) and a constant electrode resistance (R el ).The method assesses the conductance of the porous polymeric membrane, primarily affected by the incorporated volume of electrolyte solution.After the polarization of electrodes and redistribution of electrolytic solution within the laminate, the chemical gradient between the electrode and PFR assessment area of the membrane will drive electrolytic solution rearrangement.Due to the redistribution of the electrolytic solution, the electrolytic conductance becomes proportional to absolute PFR.This proportionality between electrolytic conductance and PFR value constitutes the fundamental principle of the kinetic studies performed in this work.The first experiment studies the PFR displacement kinetics as a function of electrode polarisation.The efficiency of electrolytic solution displacement is studied as a function of different absolute PFR values varied by the evaporation of volatile solvent from the electrolytic solution in the second experiment.

Membrane solution and electrode suspension
The membrane solution contained 2 g of poly(vinylidene fluoride-co-hexafluoropropylene) (PVdF-HFP, Sigma Aldrich, M w = 400 000), 2 g of [EMIM][Otf] (99.5%, Solvionic), 4 ml of propylene carbonate (PC, 99%, Sigma Aldrich) and 40 ml of 4-methyl-2-pentanone (MP, 99%, Alfa Aesar).The solutions were sealed with laboratory stretch film and mixed on a magnetic stirrer at 70 • C for 24 h.Electrode suspension.First, solutions A and B were prepared.Solution A contained 2 g of PVdF-HFP and 24 ml of MP.Solution B contained 1.75 g of amorphous carbon black (BP-2000), 2 g of [EMIM][Otf], and 10 ml of MP.The solutions were sealed with laboratory stretch film and put on a magnetic stirrer at 70 • C for 24 h of mixing.After 24 h, electrode solution A is added to solution B, and the flask is sealed and put on a magnetic stirrer for another 24 h.

Laminate assembly
Figures 2(A)-(E) covers the assembly steps of capacitive laminate.Initially, five membrane layers are deposited on a plain glass surface (figure 2(A)).Consequently, five layers of electrodes are deposited over previously deposited membrane layers (figure 2(B)).The electrode-membrane laminate is gently detached from the glass surface (figure 2(C)), cut into thin strips of 1 cm width, and attached again to the glass with sticky tape pointing the membrane layer upwards (figure 2(D)).Five electrode layers are deposited again on the membrane's surface.Both membrane and electrode are deposited by spraying coating with the airbrush (Iwata airbrush HP TR-2) to ensure porous structure and uniform thickness.Each layer (for both membrane and electrode) was sprayed at a 15 cm distance from the deposition surface for 10 s.After the deposition of each layer, it was left under direct infrared light for one minute to allow evaporation of the excess solvent and prevent the dissolution of beneath layers.Finally, the sample was removed from the glass surface (figure 2(E)), and a rectangular (1 cm 2 ) sample was cut out for analysis.

Set-up for PFR estimation
The system assembly for electrolytic solution displacement kinetics assessment is depicted in figures 2(F)-(K).The system comprises two glass plates: one with a plain gold working electrode for the excitation signal (figures 2(F)-(H)), another with a thin gold wire electrode covered with a membrane (PFR assessment volume) for the impedance excitation signal, and a plain gold electrode for both electrodes providing CV and impedance excitation signals (figures 2(I)-(K)).Assembly of the measurement system starts with the attachment of gold-plated tungsten 30 µm wire (Luma Metall) longitudinally to the surface of a glass plate with office stick tape (figure 2(F)).The wire electrode is covered with five layers of membrane solution by spraying the same way as the membrane was deposited to the glass surface for capacitive laminate assembly.When the glass surface is still moist, two rectangular shape gold current collectors (thickness ∼100 nm, Giusto Manetti Battiloro 24 K transfer leaves) are attached parallel to the wire electrode as depicted schematically in figure 2(G).The second glass surface was only covered with the plain rectangular golden current collector.
Finally, the capacitive laminate was fixed between two glass loading plates facing each electrode from each side, as shown in figure 2(L).A tiny constant pressure (approximately 1 N) is applied to the glass loading plates to ensure better contact between the gold current collectors and carbon electrodes.

Electrochemical measurements
PFR charge-dependence variation was assessed via a bipotentiostatic system (BioLogic BP-300 potentiostat) with a connection scheme in figure 2(M).The experimental setup for both the cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) investigations employ two independent two-electrode systems, one (i.e.channel 1) for PFR gradient formation and the second (i.e.channel 2) for PFR assessment.The designations 'counter electrode' and 'working electrode' denote voltage polarity: the sign of potential corresponds to the working electrode.The carbon electrode adjacent to the PFR assessment area (figure 2(H)) was used as a common counter electrode for both channels.Potentiostatic EIS (PEIS) analysis was performed with a sine amplitude of 10 mV within the frequency range from 200 kHz to 0.1 Hz.A representative Nyquist plot is in figure 2(N).The highest frequency, 200 kHz, was selected for in-situ conductance monitoring.
To access dynamic PFR variation kinetics as a function of different charging conditions in the first experiment, the PFR value was kept constant by preliminary evaporation of the volatile solvent (MP) and charging capacitive laminate with a variable set of scanning rates and potential ranges.Laminate's electrode potential was ramped linearly versus time in cyclical phases (CV) with different sets of scanning rates (from 5 to 50 mV s −1 ) and different voltage ranges (from ±1 to ±2 V).At the same time, the electrolytic conductance (G s ) of the membrane was monitored as described above.The properties of the triangular excitation signal were kept constant within the entire measurement.A quasistatic (subject to solvent evaporation) and dynamic (the result of active displacement) PFR components were separated using detrend function in MATLAB software (detrend removes linear trend).

Microscopy
Scanning electron microscopy (SEM) was performed on Hitachi TM3000 tabletop microscope at 15 kV acceleration voltage and a back-scatter electron detector.Samples investigated in this experiment, including the PFR assessment part of the membrane, were subjected to cryo-fracture for SEM observation.The membrane and the wire electrode from PFR assessment area were frozen and separated from the glass surface to avoid thin membrane film deformation before SEM observation.

Localisation of PFR observation
In a two-electrode laminate, charge-driven PFR gradients are anticipated to occur in the cross-plane (thickness) direction.In the first approximation, when the electrolyte solution is exchanged between the two electrodes, it results in excess electrolyte solution near the negatively polarised electrode and a deficiency near the positively polarised electrode, as illustrated in figure 1(C).Direct observation of the actual PFR gradient is experimentally challenging; thus, this work experimentally assesses PFR locally in one spatially confined location at the outer surface of one electrode.Although the electrical current loop for impedance assessment crosses a membrane section (characterised by R ionic ) and a part of one carbon composite electrode (described by R el ) in series, as in figure 1(D), the contribution by R el is expected to be minor: electronically conductive carbon is not expected to undergo a significant PFR-dependent impedance variation (at least not comparable in magnitude to the polymer network that develops conductance solely by the presence of the mobile conductive liquid).Consequently, the signal representing dynamic PFR was localised to a thin micro-and mesoporous polymeric membrane in press contact with the surface of one (allowing for polarity discrimination) electrosorptive electrode.The membrane quality was confirmed by impedance measurement (see figure 2(L)).The high slope angle observed at the low-frequency end of the spectrum is a characteristic feature of a capacitive system, indicating the absence of carbon bridging.
Figure 3(A) shows the arrangement of current collectors with respect to sensing electrodes on the bottom glass plate (the thin transparent membrane was not visible in the optical image).To further characterise this critical element, the system was disassembled destructively by removing the metal wire (as shown in figure 3(B)), resulting in an empty cavity corresponding to the negative impression of the wire electrode.SEM micrographs in figure 3(C) confirm the continuity and homogeneity of the membrane: the membrane with a 20 µm thick lamina section fully wrapped around the 29 µm diameter metal wire.The thickness of the membrane at the critical spot, dividing the metal wire and the composite electrode, was further reduced to 11 µm (figure 3(C)).Thus, the PFR measurements were localised to the 11 µm thick membrane separating the metal wire and the carbon composite electrode, as the lateral distance from the wire electrode to the current collectors was much larger (closest distance approximately 120 µm, figure 3(A)).The sensitive region was as much as 36× thinner than the 400 µm laminate, guaranteeing highly localised measurement.The SEM observation (figure 3(C)) did not reveal any discernible structure at the observed resolution (i.e. the membrane's porosity was beyond the resolution of the apparatus).

Sample morphology
The carbon-polymer composite electrodes were characterised by hierarchical porosity, with the largest pores measuring up to 50 µm (as depicted in figure 3(D)), which accounted for a substantial proportion (a quarter) of the composite electrode's overall thickness of the composite electrode (ca 200 µm).The membrane separating two carbon composite electrodes was much thinner than the electrodes-approx.15 µm (figure 3(E)).The SEM observation (figure 3(F)) revealed a smooth and continuous membrane identical to that in the PFR assessment area (figure 3(C)).This is as expected, as the two membranes are identical in composition and preparation.The macropore-free membrane area (figure 3(G)) was likely functional to the pumping behaviour: if the structure of both the electrode and the membrane contained macropores, no pressure gradient could be formed across the laminate, and no swelling gradient could be observed.Vice versa, if both the electrode and the membrane contained only micro-and mesopores, the highest magnitude for the swelling gradient would be expected at the cost of decreased speed of EHD medium displacement.Electrodes with hierarchical porosity are the compromise between swelling magnitude and the rate of EHD medium displacement.

Composition of the mobile liquid
The liquid medium contains both volatile and nonvolatile solvents and an electrolyte.The organic salt chosen as the electrolyte, [EMIM][Otf], is ionic liquid at room temperature, enabling 100% electrolyte concentration and implying that it can also act as its own solvent.Yet, in a system exposed to an ambient environment, the hygroscopic ionic liquid absorbs a significant amount of water, which effectively increases their conductivity and decreases viscosity (both effects are favourable in this work) but also limits the operating voltage window (see CV below).Plasticisers (low-volatility solvents such as PC) are often added to ionic-liquid-containing systems at significant proportions (2:1) [18], rendering the electrolytic medium even more mobile.Additionally, the highly volatile solvents used in the manufacturing process (such as MP) are still slow to be removed from the composite, with residues influencing the performance.As preparation of samples with a constant electrolyte solution amount and composition is experimentally challenging on a small scale (due to absorption and evaporation), this work uses natural evaporation of volatile solvents as the means to tune the amount of electrolyte solution in the system, in line with the bioinspired motive (humidity sorption as a control for processes).Consequently, the system effectively contains three solvents: non-volatile ([EMIM][Otf]), low-volatility (PC), and high-volatility (MP).All pores of asproduced samples are filled with electrolytic solution completely (defining the 100% PFR operating point, used below).In ambient conditions, the volatile solvents evaporate, leaving an increasing amount of partially empty pores and thus decreasing the conductance of the system.

Liquid rearrangement in a porous matrix
The evolution of conductance through a liquid partially occupying a porous matrix is a complex process that depends on polymer-liquid interaction and anisotropy of the porous matrix (valid for both synthetic and natural systems); however, this work assumes proportionality that suffices for trend observation.Consequently, the variation of the electrolytic conductance of the membrane is taken as the measure for transient PFR level, fully aware of the concurrent contribution of electrolyte concentration variation on the membrane conductance.
Previous theoretical investigations on ionic liquid solutions have suggested that ions develop a solvation shell and display asymmetrical mobility [19].Since the cation mobility is typically higher, the rate of solution transfer in the direction of negative polarisation is more pronounced than in the positive polarisation direction.In addition, solvent redistributes diffusively towards uniform ion concentration.
EHD pumping is driven by capacitively charging the two-electrode laminate: current applied between the electrodes causes ions to migrate toward the capacitive electrodes to compensate for the electronic charge.CV data on the charging signal depicted in figures 4(A) and (B) confirmed high electrochemical stability and high reversibility of the system.No significant faradaic currents can be denoted from cyclic voltammograms and, thus, no unsolicited redox reactions, except for a tiny contribution from the electrolysis of water absorbed by hygroscopic constituents.

Kinetics of internal liquid rearrangement
The kinetics of PFR variation was analysed in a (nearly) constant total amount of working fluid (i.e. the electrolyte solution) at different ranges of applied voltages and scanning rates.To achieve a stable PFR value, the volatile part of the electrolytic solution was evaporated (reaching approximately 20% PFR, estimated in the experiment below).A representative snapshot of the experiment, corresponding to 20 mV s −1 scanning rate and ±2 V voltage range, is depicted in figure 4(C).Re(Z s ) is a real part of impedance at the PFR observation point, referred to as the PFR assessment area.A small (approximately 4.5% h −1 ) linear trend Z 0 (Z s ) was separated for analysis (figure 4(D)).Indeed, after compensation for the slight evaporation-driven drift of Z 0 (Z s ), a periodic input waveform resulted in a highly repeatable cyclic pattern for Re(Z s ).The cyclic variation of the membrane's electrolytic resistance (∆Re(Z s )-Z 0 (Z s )) versus applied charge is given in figures 4(E) and (F) for different scan rates and voltage ranges, respectively.According to our interpretation of bulk electrolytic solution displacement, the pores within the membrane are not emptied or filled uniformly but filled in the direction of liquid displacement (and emptied behind), forming a PFR gradient across the membrane, as depicted in figure 1(D).At high scanning rates (50 mV s −1 , figure 4(E)), the membrane's electrolytic conductance variation is pronouncedly asymmetric: conductance increased at negative polarisation (PFR is increased by bulk electrolytic solution influx) and decreased at positive polarization, confirming the membrane as cation-active transporter.The asymmetric mobility phenomenon is also evident from the width of the hysteresis loop of electrolytic conductance variation.By charging the laminate at a low scanning rate (5 mV s −1 ), the shape of the charge-discharge curve had an almost equal slope in positive and negative polarisation and showed a very narrow (approximately 10-20 ohm, figure 4(E)) hysteresis loop, indicating that solvent redistribution kinetics prevailed over bulk electrolytic solution displacement at this scan rate.Thus, the absolute electrolytic conductance variation measured at different scanning rates (with respect to charge in figure 4(E)), the variation of the electrolytic conductance is due to the combination of two interdependent mechanisms, electrokinetic transfer and diffusive solvent redistribution, in different proportions.This is an intriguing insight into the hypothetical solvent redistribution mechanism in tree stems.
The ion-and solvent-permeable membrane in this work equalises the electrolytic concentration and PFR by diffusion, given sufficient time.At the same time, after a fast displacement of the electrolytic solution, a gradient of PFR is formed, and solvent redistribution kinetics is not fast enough to equalise PFR and concentration.This behaviour assumes that, at high scan rates, the high cross-membrane ionic current results in a pronounced PFR gradient and solvent redistribution is hindered by the intense field-driven forward flux of electrolytic solution.This observation characterises pumping as a dynamic process, much more efficient at a high scan rate.Nevertheless, a symmetric (polarity-independent) PFR observed at lower scanning rates may also find practical use.
Capacitive electrodes can facilitate ionic current (and the resulting electrodynamic flow) only up to compensation of charges at the given operating point (i.e. the open-circuit potential of the electrode), limited by the electrochemical stability of the compounds forming the electrical double-layer.Consequently, capacitive electrodes could not work in a continuous pumping regime, restricting their use in several microfluidic pumping solutions.Notably, only cyclic operation is not an issue for internal fluid rearrangement because the total amount of working liquid in a system is finite (and relatively small).In the not-fullyoptimized system of this work, the amount of mobile liquid was still limited by the sorption capacity of the electrodes, evidenced by a comparably small (6.3%) span of ∆Re(Z s ) compared to Z 0 (Z s ) in figure 4(E).
Figure 4(F) depicts electrolytic conductance variation at different voltage ranges (from 1 to 2 V) at a constant (20 mV s −1 ) scan rate, where both pumping (bulk displacement of electrolytic solution) and redistribution of solvent occur.We have selected an intermediate scanning rate of 20 mV s −1 at which both mechanisms are taking place in different proportions (without excessive dominance of one of them) to investigate the effect of the voltage range.By increasing the voltage range (figure 4(B)), the amount of charge immobilised at electrodes and the volume of the displaced electrolytic solution is expected to increase proportionally (figure 4(F)).
Characteristic points 'a'-'e' in figure 4(F), corresponding to the 2 V range, revealed a polaritydependent trend: a cycle at positive polarity yielded a 30 Ω higher impedance value (i.e. a lower PFR) vs the negative ('a' vs 'd' in figure 4(F)), evidencing the bulk transfer of electrolytic solution by filling and emptying pores at negative and positive polarisation, respectively.Characteristic points 'c' and 'e' (figure 4(F)), corresponding to the maximum applied charge at negative and positive polarisation, respectively, were also polarity-dependent: the impedance was 38 Ω higher at a maximum positive charge.The dynamic impedance range was still moderate at the chosen scan rate of 20 mV s −1 : 2.1% of Z 0 (Z s ) for 'a'-'d' and 2.5% of Z 0 (Z s ) for 'c'-'e' .
The effect of partial solvent redistribution can be observed from differences in absolute values of electrolytic conductance and the charge applied to laminate at points 'b' and 'c' (figure 4(F)).The amount of charge in the laminate increased from point 'b' to point 'c'; however, the resistance of the membrane from PFR assessment area decreased.Since the variation of electrolytic conductance in the membrane is due to the variation of both PFR and ionic concentration of electrolytic solution values, the increase of electrolytic conductance can be attributed to the rise of PFR value or ionic concentration.In the segment 'a'-'b' , liquid redistribution due to asymmetric mobility (active pumping) dominated, whereas in section 'b'-'c' , the kinetics of diffusive solvent redistribution to equalise the concentration became more dominant.As a result, the conductance likely increased from 'b' to 'c' due to concentration-driven liquid influx (as the formation of an EDL decreases the ionic concentration in bulk at the vicinity of the electrode), increasing the PFR value at the point of observation.

Optimal PFR range
The second experiment investigated the efficiency of the electrolyte solution displacement (i.e. the pumping performance) at different estimated PFR absolute values.A time-varying total amount of EHD medium in the system was established by evaporation of a volatile solvent, MP, enabling to study of EHD medium displacement at various PFR absolute values.Due to its high vapour pressure (2.1 kPa), MP evaporates rapidly when exposed to the ambient atmosphere.In our experimental set-up, the laminate was exposed to the environment only via the edges of the laminate, while the glass plates prevented evaporation from both sides.Consequently, the evaporation of MP was slow enough to facilitate the continuous assessment of dynamic PFR at a variable (decreasing due to evaporation of MP) of the total amount of mobile liquid.The PFR value of just-produced samples is maximum (100%) by definition.It can only decrease by volatile solvent evaporation to its minimum value (i.e.only non-volatile components, the solvents, and the electrolytes remain).
For an estimated value of PFR, this work assumed proportionality between PFR and the electrolytic conductance of the membrane.The minimum PFR value is calculated by interpolating between the initial electrolytic conductance (100% PFR) and zero electrolytic conductance (0% PFR; an empty porous membrane without electrolytic solution).To confirm the possibility of 0% PFR, a separate piece of the membrane was depleted from the electrolyte by leaching out using pure MP.Indeed, the resulting membrane displayed a resistance value of more than 50 kΩ, much larger than in dynamic PFR experiments (figure 4(C)), confirming the mobility of the working fluid and little attachment of ions to the polymer matrix.When the porous structure is initially wholly filled with electrolytic solution (PFR = 100%), the displacement of electrolyte is the most efficient; however, this displacement does not effectively translate into a swelling gradient: while the PFR at the source (i.e.positively polarised) electrode may decrease, there are no empty pores at the target (i.e.negatively polarised) electrode to be filled.Vice versa, when the porous structure is excessively empty, electrolytic solution displacement becomes hindered by an increased electrolytic resistance (causing energetic inefficiency and decreasing transfer rate).We expect an optimal absolute amount of mobile liquid in the porous system to yield the highest pumping effect (i.e.dynamic PFR variation).
Figure 5(A) shows the dynamic variation of electrolytic conductance G s (i.e. the real part of susceptance) and electrolytic resistance Re(Z s ) (i.e. the real part of impedance) in the sensing area, evidencing displacement of EHD medium across the laminate in response to periodic excitation at 2.5 mHz triangular voltage (±2 V at 20 mV s −1 scan rate) during a long (65 h) experiment.The max, min and mean curves correspond to maximum, minimum and mean values within each cycle.Figure 5(B) zooms into the first hour of the experiment.Two very first cycles (800 s) showed an almost stable offset value of G s 0 , as the effect of MP evaporation at the surface (i.e. the four side faces of the laminate) has not reached the PFR assessment area, or there was initially an excess of solvent at the surface due to the applied slight pressure (figure 2(K)).This starting level, G s 0 = 3.0 mS, was taken as the reading for PFR = 100%.The experiment proceeded until complete evaporation of the volatile solvents, reaching the asymptotic value G s final of 0.6 mS (corresponding to an estimated PFR of 20%), as shown in figure 5(A).open-porosity system is a probabilistic processanother common characteristic of analogous processes in natural systems that may deliberately deploy probabilistic fluid rearrangement to negotiate the unknown and dynamic environments.
Figure 5(D) shows the course of dynamic PFR during the experiment, estimated by normalising G s p-p to G s (explained below).Finally, the pumping efficiency was estimated in figure 5(E) by plotting dynamic PFR to PFR (considered static within each cycle) to express the amount of displaced liquid for the total liquid in the system.Indeed, as predicted above, the mostly full as well as mostly empty pore conditions were inefficient, and there is an optimal PFR range.Figure 5(E) suggests a wide range of optimum PFR values: approximately 30%-75%, corresponding to PFR values that yielded the most pronounced dynamic swelling performance.
Figure 5(D) also shows the electronic charge injected into the system (proportional to ionic charge displaced) in each cycle (calculated as the integral of charging current in time).A drift in charge-percycle parameter was well expected, as a potentiostatic waveform was applied on a variable-impedance system.The variable impedance, in turn, contributes not only from electrolytic conductivity variation but also from the accessibility of the electrode surface and PFR in the membrane separating the electrodes.Normalising the dynamics PFR to charge-per-cycle parameter, figure 5(E) showed a shift of efficiency towards lower PFR values, revealing a maximum at around 32% PFR.The reader's attention is brought to the indicative characteristic of the PFR absolute value, as concentration variation could not be accounted for in the used experimental setup.
To better capture the processes determining the dynamic PFR, the course of the experiment was divided into four consecutive segments (a)-(d) in figures 5(D) and (E) as follows.
• Segment (a), PFR 100%-70%: the amount of charge per cycle introduced to the system increased by 28%, from 0.36 to 0.46 C, indicating an increase in G s due to solvent evaporation.The dynamic PFR (initial value: 7%) also reached its maximum value (11%) at the end of the segment (a).However, the PFR variation per charge, as well as per PFR absolute value, showed a medium value-because the pores that are already close to full could not be filled further, as explained above.• Segment (b), PFR 70%-32%: the dynamic PFR variation attained its maximum value and remained almost stable (9.5% ± 0.5%), indicating an effective filling and emptying of the pores, depending on the polarity.The decrease in the charge-per-cycle parameter by 41% (from 0.46 C to 0.27 C) is likely due to the decreasing amount of filled pores between the electrodes caused by solvent evaporation.
• Segment (c), PFR 32%-21%: the dynamic PFR variation as well as the charge-per-cycle parameter decreased rapidly (47% and 37%, respectively).The decrease in dynamic PFR can be attributed to continuity breaks between the sensing membrane and the driver electrodes, not being able to deliver the displaced liquid volume to distal parts of the system.The charge per cycle decreased, likely because of a decrease in accessible electrode surface for ion immobilisation.

Conclusions
Hygromorphs inspired by, e.g.pine cone opening, are already well-known engineering solutions, backed by an abundance of swellable (bio)materials, yet passive control, i.e. by changing the ambient humidity level, has strictly bounded their robotic applications.In this paper, we report on a synthetic system that can produce dynamic swelling gradients also internally, inspired by an intriguing natural process of swelling gradient formation in tree stems.We suggest a modular design, consisting of a pump and swellable components.Two systems operate independently: the pump is to displace a finite volume of liquid between different areas of a structure that also contain swellable materials responding to the local amount of liquid.
For internal liquid rearrangement, we chose electroosmosis combined with electrosorption as the most compliant and reversible integrated mechanism, consisting merely of two flow-through electrodes separated by a porous membrane.Our experimental setup, based on electrolytic conductance variation monitoring, enabled the evaluation of dynamic liquid displacement within solid porous structures.Moreover, the experimental arrangement can detect the type of electrolyte redistribution mechanism and assess the impact of the empty-to-filled pores ratio on the efficiency of electrolytic solution displacement.We also introduced a custom technique for localised assessment of the kinetics of displacement of the electrolytic solution in porous structures.
Based on experimental results, we identified two concurrent mechanisms: (a) electrokinetic transfer due to ionic asymmetric mobility and (b) diffusive solvent redistribution, dividing the dynamic swelling process into components of faster and slower time constant, respectively.At high scan rates, the experimental results showed that the high cross-membrane ionic current induces an intense field-driven flux of electrolytic solution, resulting in higher swelling performance and characterising pumping as an efficient dynamic process for localised modification of the system's mechanical properties due to swelling.However, observing a symmetric PFR at lower scanning rates indicates that electrolytic solution displacement, i.e. the mechanism (a), is compensated by the backflow of liquid and diffusive equilibration.The slow charging process accumulates electrolyte to the electrode surface, potentially enabling amplification of unidirectional electrolytic solution displacement (enhanced swelling performance).Either of the two mechanisms can be activated by changing the excitation signal parameters, allowing the selection between bi-and unidirectional localised swelling for even more complicated bioinspired stiffness variation scenarios.
The macropore-free membrane was functional for the pumping process, as macropores in both the electrode and membrane prevented a pressure gradient from forming across the laminate and inhibited swelling gradient observation.Electrodes with a hierarchical pore structure were necessary for balancing the magnitude of swelling with the rate of EHD medium displacement.
The stringent compromise between the porosity distribution and response speed determines the engineering applicability of diffusion-based movement mechanisms.Although swelling occurs relatively rapidly, recovery in a reasonable timeframe needs special attention (phenomenological analogy to the cooling bottleneck in thermal actuation).Consequently, the interaction between the mobile liquid to the polymer matrix needs to be strong enough for pronounced swelling yet weak enough for reversibility.A combination of the relatively hydrophobic PVdF(HFP) copolymer and the hydrophilic electrolyte provided a compromise in this work.
The charge-controlled material level stiffness variation has excellent potential for use in various robotic applications due to its simplicity and high reliability.Our experimental findings suggest that these mechanisms can be used in bioinspired, actively controlled hygromorphs and micro-pumping systems.This study opens perspectives for developing morphologically computative charge-controlled soft robotic systems, allowing dynamic variation of its mechanical compliance locally and reversibly.Localised swelling can be treated as a mechanism for expressing embodied intelligence, i.e. assignment of interaction management to the robot's internal body structures.
Additionally, the designed synthetic structure may aid in understanding the potential role of active swelling mechanisms in plants.This could also help confirm hypotheses on compliance regulation for structures exposed to challenging dynamic environments and subjected to extreme loading densities, such as the tension wood in trees.

Figure 1 .
Figure 1.Electrokinetic internal liquid rearrangement as a bioinspired method for active swelling.(A) Hygroscopic swelling of layered structures as a natural actuation mechanism, illustrated by the opening mechanism of pine cone scales.(B) Electrokinetic displacement of electrolytic solution (in blue) between polarisable (capacitive) electrodes (in black) induced by asymmetric mobility of cations and anions (only cations as more mobile species shown).The electrode surface area correlates with displacement d and more mobile ion determines the flow direction.(C) Actively controlled swelling of the porous polymeric matrix during displacement of electrolytic solution.The influx of electrolytic solution to partially empty porous polymeric matrix increases the local pore fill ratio (PFR).As the total volume of electrolytic solution in the system is fixed, the PFR decreases due to outflux in other part of the system.The formed PFR gradient induces swelling gradient.(D) A readout of local PFR value by proportionality to electrolytic conductance (1/R ionic ).

Figure 2 .
Figure 2. Capacitive laminate assembly: (A) deposition of membrane layer by spraying on a plain glass surface (repeated four times); (B) deposition of the electrode layers (repeated four times); (C) flipping over the electrode-membrane laminate; (D) deposition of the electrode layers on the opposite side (repeated 4 times); (E) The resulting free-standing electrode-membrane-electrode laminate.Assembly of the bottom plate: (F) a gold-plated tungsten wire attached to a glass surface and covered with a membrane layer by spraying with membrane solution (spraying repeated 4 times); (G) transfer of gold foil current collectors onto the membrane, except 100-300 µm margin around the wire; (H) cross-section of a completed bottom plate assembly.Assembly of the top plate: (I) plain glass surface sprayed with membrane solution; (J) transfer of a gold current collector; (K) cross-section of a completed top plate assembly.(L) Assembly of the complete measurement system by stacking laminate (E) between the top (H) and bottom (K) plates.(M) Bipotentiostatic measurement system for simultaneous internal liquid rearrangement (by triangular input voltage) and in-situ electrolytic conductance measurement (by impedance monitoring).(N) A typical spectrum of impedance (channel 2) for electrolytic conductance measurement.

Figure 3 .
Figure 3. (A) Optical photographs of the gold-plated tungsten wire embedded into the membrane and SEM micrograph of the free-standing gold-plated tungsten wire.(B) Scheme of post-experiment destructive disassembly of the system for micrographing.SEM micrographs of (C) the PFR assessment membrane cross-section with a negative impression of the wire electrode, (D) composite electrode; (E) cross-section of the laminate; (F) zoom-in to the membrane cross-section.An arrow pointing to the red cross indicates that the observation was conducted following the removal of this component.

Figure 4 .
Figure 4. (A) Cross-laminate cyclic voltammetry of the capacitive laminate at scan rates from 5 mV s −1 to 50 mV s −1 .(B) Cross-laminate cyclic voltammetry of capacitive laminate at voltage ranges from ±1 V to ±2 V. (C) A representative snapshot of the real part of impedance measurement: cross-laminate input voltage (in orange) and a representative snapshot of the resulting transient impedance variation (in blue); the quasistatic component is given as Z0(Zs).(D) Dynamic variation of Re(Zs) after subtraction of Z0(Zs).Dynamic variation of Re(Zs) with respect to cross-laminate charge (E) at 5 mV s −1 -50 mV s −1 scan rate and (F) ±1 V to ±2 V voltage range.

Figure 5 .
Figure 5. (A) Maximum, minimum and mean values of electrolytic conductance Gs (and resistance Re(Zs)) in consecutive cycles during natural evaporation of the volatile solvent.(B) Transient course of Gs during the first hour of the experiment, showing initial plateau of Gs 0 , corresponding to 100% PFR.(C) Transient cycle-averaged PFR estimation and dynamic peak-to-peak conductance Gs p-p variation.(D) Transient dynamic PFR variation and variation of the charge introduced to capacitive laminate per cycle.(E) Dynamic PFR variation (in blue) in respect to absolute PFR estimate.Charge-normalized dynamic PFR variation (in orange).

Figure 5 (
C) shows the transient cycle-averaged PFR level during the entire experiment.PFR was estimated for each consecutive cycle by dividing the mean G s value of the corresponding cycle by G s 0 , multiplied by 100%.Figure 5(C) compares the PFR value to the dynamic conductance amplitude, G s p-p , revealing a similar trend: cycles with smaller PFR value corresponded to a lower G s p-p .A nonsmooth dynamic conductance curve indicates a high level of sensitivity to even minor variations in electrolytic conductance during measurement.Indeed, the dynamic rearrangement of mobile fluid in an