# Autonomous oil flow generated by self-oscillating polymer gels

Jul 30, 2020

### Thermodynamic cycle of poly(NIPAAm-co-[Ru]-co-AMPS) gels

To discuss the fundamental physical mechanism, we formulate the thermodynamic relation in redox poly(NIPAAm-co-[Ru]-co-AMPS) gels. Let us begin with reversible changes in length (dl) generated by a redox reaction ([Ru]2+ ↔ [Ru]3+) in poly(NIPAAm-co-[Ru]-co-AMPS) gels. The work (S) performed in the redox process is ({-}fdl). Thermodynamic relation under isothermal and isobaric condition is described as follows (SI Appendix):

$$S = – oint {fdl} = oint {mathop sum limits_{i} mu_{i} dn_{i} } = int {mathop sum limits_{i} mu^{II}_{i} dn_{i} } – int {mathop sum limits_{j} mu^{I}_{j} dn_{j} } ,$$

(1)

where (mu_{i} ,) (dn_{i}) are the chemical potential of ith chemical and the change in the number of moles of the ith chemical, respectively. The term on the left-hand side denotes the maximum mechanical work that can be obtained in the redox reaction. Figure 2A shows schematics of the thermodynamic cycle of the poly(NIPAAm-co-[Ru]-co-AMPS) gel. To obtain the thermodynamic cycle, we first soak the gel into an acidic solution with NaBrO3 as an oxidizing agent, with a chemical potential (mu^{I}_{i}) from the reduced state of the gel and let the gel swell along path 1–2. The gel is then mechanically stretched (2–3) in its oxidized state. Similarly, we obtain path 3–4 and 4–1 containing chemical potential (mu^{II}_{i}). The area (S) encircled by the cycle 1–4 represents the work generated by the redox process. Thus, we can maximize the work in the redox process from the stress–strain curve of the redox poly(NIPAAm-co-[Ru]-co-AMPS) gels. To understand the system from the state equation of gel, we would mention the system at SI Appendix.

### Stress-extension ratio curves of redox poly(NIPAAm-co-[Ru]-co-AMPS) gels

We developed a custom testing machine to measure the mechanical properties of the redox poly(NIPAAm-co-[Ru]-co-AMPS) gels (Fig. S2). Let us define (sigma) and (varepsilon) as the stress and the strain of BZ gels, respectively. The strain ( varepsilon) is defined as (left( {l – l_{0} } right)/l_{0}), where (l) and (l_{0}) are the length of poly(NIPAAm-co-[Ru]-co-AMPS) gels at equilibrium state and gelation state, respectively. Figure 2B displays the stress–strain curves of BZ gels in both reduced ([Ru]2+) and oxidized ([Ru]3+) states. The elastic modulus (left( {partial sigma /partial varepsilon } right)_{T}) of the poly(NIPAAm-co-[Ru]-co-AMPS) gels in the oxidized ([Ru]3+) state is lower than in the reduced state. Also, as the strain of the gel increased, the stress difference between the reduced and oxidized states increased as well. As a consequence, pre-stretching the BZ gels leads to a larger work produced by the system at each cycle. It follows that also the force produced by a BZ gel would increase by using pre-stretch. The maximum work generated by a no pre-stretched BZ gel is represented by the area encircled by the ideal path 1–2–3–4 shown in Fig. 2B. We assessed the temperature dependency of the cycle and optimized the temperature (Fig. S3). In our system, the thermodynamic cycle is automatically driven by the oscillations of the BZ reaction. Figure 3 shows a schematic of the relation between the applied boundary conditions and swelling behavior of the BZ gels at thermodynamic equilibrium. BZ gels in free swelling generate limited displacement (Fig. 3A). Applying a constant load to the BZ gel leads to larger displacement (Fig. 3B) while constraining the length to a constant value results in large force-generation (Fig. 3C). We can use these findings to optimize the work that can be extracted from BZ gels.

### Measurements of force-generation of BZ gels

We investigated the relationship between the generated force and the length of BZ gels in redox states. The experimental setup is shown in Fig. S2. The apparatus consists of an automatic stage, a load cell, a thermo bath, and a manual stage. The load cell has a capacity of 50 mN (LVS-5GA, KYOWA Electronic Instruments Co., Ltd.). The BZ gel in our experiments has an initial diameter of 1.0 mm and an initial length of 12.0 mm. Figure 4 presents the oscillating profiles of the generated force of BZ gels. These results have been used in the design of the self-actuating pumps. We found that the generated force of BZ gels could be controlled through the pre-stretch ratio (Fig. 4A). As shown in Fig. 4B, the generated force of the BZ gel increases as the pre-stretched ratio (lambda) increases, until (lambda) = 1.5. The observed generated force of the pre-stretched BZ gel during the reaction was around 0.9 mN. The generated force of the pre-stretched BZ gel is 1.6 times higher than that of unstretched BZ gel. The generated pressure of the pre-stretched BZ gel is around 1.15 kPa. As shown in Fig. 4C, the generated force of the pre-stretched BZ gel has the saturation point at the following initial concentration.

We connected up to three pre-stretched BZ gels in parallel to obtain a greater force. Figure 5 shows an increasing force with the number of gels connected in parallel. We fitted the curve using the linear function, which is a line with a slope of 0.75 and y-intercept of 0.05 (Fig. 5B). The coefficient of determination is 0.9586. Three pre-stretched BZ gels produced around 2.4 mN. BZ reaction features several unique dynamics17,18,19,20,21, including a macroscopic synchronization between adjacent gels. We exploited such synchronization between our gels connected in parallel by leaving a small gap between them.

### Self-actuating pump

Few efforts report the generation of the self-motion with chemical systems. Examples include self-motion of droplets22, self-motion of hydrogels23, and catalytic motors24 driven by chemical energy. All these self-moving systems share the common limitation of having being demonstrated only submerged in chemical baths. Recently, researchers have demonstrated the autonomous motion of soft robots based on the integration of fluidic logic gates and simple, monotonical chemical reactions25. While these systems produced autonomous motion driven by chemical reaction, they are still complex and comprising many components (e.g., reaction chamber, pinch-valves, exhaust valves). On the contrary, our self-actuating pumps rely on intrinsic chemical oscillations, removing the need for any valve and microfluidic circuit and opening to unconventional computation through chemo-mechanical networks. We experimentally demonstrated a self-actuating pump that is powered by BZ gels as shown in Fig. 6A. We physically separated the BZ gel system and a working oil using a thin stretchable PDMS membrane (thickness: 100 µm). We computed the expected fluidic flow of the working oil in our machine through FEM simulation (Fig. S4). The FEM simulations predicted a fluid flow of a few millimeters.

We tested the pumps by attaching one end of the pre-stretched BZ gels to the jig connected to the PDMS membrane. The BZ gels push and pull the PDMS membrane while it swells and shrinks, displacing the working oil back and forth. The actuator works under the condition with a constant pre-strained length (pre-stretched ratio λ = 1.5). During the oscillation process, the length changed with the redox reaction. The working mechanism of our pump is shown in Fig. S5. The observed pumping displacement during the BZ reaction was over 1.0 mm in a cylindrical tube (inner diameter: 1.0 mm). The average flow rate produced by our pump is 0.16 mm3/min. The experimental value of the fluidic flow is in good agreement with the FEM simulation (Fig. S4). We monitored the color change of three BZ gels and evaluated the hue value of it. The fluidic flow of the working oil synchronizes with the pre-stretched BZ gels as shown in Fig. 6B. Furthermore, we applied our self-actuating pump to the microfluidic device as shown in Fig. 6C. The width, height, and length in the microchannel are 800 µm, 70 µm, and 20 mm, respectively. We developed a microfluidic device including a straight micro-channel using PDMS (Polydimethylsiloxane). The micro-channel is connected to the self-actuating pump so that the oil can move back and forth through it following the periodic swelling and shrinking of the BZ reaction (Fig. 6C,D).

The oil position is primarily decided by the oscillation states of the BZ gels, membrane deflection, and damping of the oil fluid. In this case, the oil position keeps increasing is due to the membrane moves down further than that retracts back under the actuation of the three gels. In a period, the deflected membrane causes the oil to level up. The generated power of our actuator is estimated to 5.76 × 10−2 nW. Our future work will focus on the optimization of the system. There are two methods to optimize the system: physical and chemical methods. For the chemical method, the oscillated amplitude of the BZ gels increases with the growth of the period and amplitude of the redox changes. We can control the amplitude by changing the initial concentration of Malonic acid. For the physical method, we can change the beating rhythm of the gel by changing the solution temperature, changing the diameter of the gel, using different sequences to form the BZ reaction, the parallelized and seriated patterns of the gels, etc. Finally, we also consider optimizing the structures of the actuators.