**3.3. Tubular gel motility driven by chemical reaction networks**

326 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

Period[s]

0 0

> 0 0

10

20

Gel length[ m]

30

10

Gel length[ m]

20

**Figure 12.** (a) Dependence of the self-oscillation period on the temperature. (●) plots and (○) plots show the linear relation and the saturated line vs temperature, respectively. (b) Self-oscillating profile of cubic poly(VP-*co*-Ru(bpy)3) gel at 50C (MA = 0.08M, NaBrO3 = 0.48M and HNO3 = 0.48M). (c) Self-oscillating profile of cubic poly(VP-*co*-Ru(bpy)3) gel at 20C (MA = 0.08M, NaBrO3 = 0.48M and HNO3 = 0.48M). Cubic gel (each side length is about 2mm and 20mm) was immersed in 8ml of the mixture solution of the BZ substrates. (Reprinted ref. 57, Copyright American Chemical Society. Reproduced with permission.)

(c)

25 50 75 100 125 150 175 200 Period[s]

(a)

Temperature[ C]

30 34 38 42 46 50

T=2.0

The point of saturation

(b)

12345678 Time[s]

In previous studies, De Kepper *et al*. showed a method to form the contraction waves by coupling the pH-responsive hydrogel and the acid autocatalytic chlorite tetrathionate (CT) reaction [42, 43]. They presented a system specially designed to show the chemomechanical instabilities, in other words, dynamical deformations of the functional gels, such as contraction waves and complex spatio-temporal volume oscillations. However, in this system, the pH responsive cylindrical gel is fixed to continuous stirred tank reactors (CSTR) because it must be permanently fed with constant flows of fresh CT reactants. Therefore, this system is unsuitable for the development of a locomotive gel robot. It is necessary to develop a novel concentration tuning mechanism without the stirred reactor for the coupled system of the functional gel and the CT reaction.

**Figure 13.** Schematic representation of the principles of the tubular gel feeding system (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)

In this chapter, we introduce a novel pH-responsive tubular gel and propose a new method of generating contraction waves on the functional gel. Figure 13 shows the schematic representation of the principle of the feeding system of the tubular gel. We controlled the reaction diffusion system by pouring the reactant solution into the hollow of the tubular gel, and attempted to achieve the peristaltic movement of the tubular gel by formulating contraction wave. This system enables us to feed with constant flow of fresh reactants, and also to be free from tank reactors.

The CT reaction is known as the acid autocatalytic reaction with the concentration changes of various sorts of reactive substrates, including the chlorite and tetrathionate ion, and this reaction exhibits a bi-stability of an acid steady state and an alkaline steady state. The CT reaction shows very complex kinetics which is still not completely understood [76]. However, it can be described by the following chemical reaction,

$$\text{7ClO}\_2^- + 2\text{S}\_4\text{O}\_6^{2-} + 6\text{H}\_2\text{O} \rightarrow \text{7Cl}^- + 8\text{SO}\_4^{2-} + 12\text{H}^+.$$

It runs in slight chlorite excess, and is associated with the following autocatalytic empirical rate law,

$$r = -\frac{1}{7} \frac{\text{d}[\text{ClO}\_2^-]}{\text{d}t} = k[\text{ClO}\_2^-][\text{S}\_4\text{O}\_6^-][\text{H}^+]^2 \dots$$

*r* indicates the concentration per unit mol of the reactive substrates, and k is a proportionally coefficient. The changes between the steady states of the CT reaction take place depending on the feeding condition of the proton. When an alkali is constantly supplied, the CT reaction solution can maintain an alkaline steady state. As an acid perturbation is added or an alkali supply decreases below a certain concentration, the acid autocatalytic reaction develops and acid region spreads by the reaction-diffusion process, finally the solution becomes acid steady state. When autocatalytic reactions are operated in a pH responsive spherical gel, the gel shrinks following the one-way reaction, regularly. However, in some conditions, the relatively faster diffusivity of the proton can lead to the oscillatory reaction diffusion instability [42,43,77,78]. The volume oscillation of spherical gel is generated by coupling the CT reaction with the volume phase transition of the pH-responsive gel, and we call the concatenation of the two phenomena "chemical reaction networks."

**Figure 14.** Flowchart of the chemical reaction networks. Each disk shows the condition of a spherical gel. The red arrows indicate changes of the interior CT solution and the green arrows indicate volume phase transition of the pH-responsive gel, that is, the gel causes shrinking or swelling. (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)

Figure 14 shows the flowchart of the chemical reaction networks. The red areas indicate the acid steady state and the yellow areas indicate the alkaline steady state. There are four steps in the networks:


As described above, the stabilities of such steady states depend on the gel radius. It is shown theoretically and experimentally that the switching between the chemical reaction networks occurs with hysteresis as a function of such geometric parameters. In this case, the reaction diffuses symmetrically from the center of the gel. When the reaction is applied to the cylindrical gels or tubular gels, it diffuses symmetrically to the diameter direction and also diffuses to the length direction. The disks shown in Figure 14 indicate the changes of the cross-section surface at one location of the cylindrical gel.

328 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

*r k t* −

call the concatenation of the two phenomena "chemical reaction networks."

58, Copyright *IEEE*. Reproduced with permission.)

rises in the core of the gel.

inflowing of alkali solution.

1. The spherical gel is in the uniform alkaline steady state.

3. The acid region fills the gel entirely, and the gel shrinks.

in the networks:

**Figure 14.** Flowchart of the chemical reaction networks. Each disk shows the condition of a spherical gel. The red arrows indicate changes of the interior CT solution and the green arrows indicate volume phase transition of the pH-responsive gel, that is, the gel causes shrinking or swelling. (Reprinted ref.

Figure 14 shows the flowchart of the chemical reaction networks. The red areas indicate the acid steady state and the yellow areas indicate the alkaline steady state. There are four steps

2. When the gel radius grows and exceeds a certain threshold value, an acid perturbation

4. When the gel radius shrinks below a certain threshold value, it swells again by

As described above, the stabilities of such steady states depend on the gel radius. It is shown theoretically and experimentally that the switching between the chemical reaction networks

rate law,

It runs in slight chlorite excess, and is associated with the following autocatalytic empirical

− −+ =− =

*r* indicates the concentration per unit mol of the reactive substrates, and k is a proportionally coefficient. The changes between the steady states of the CT reaction take place depending on the feeding condition of the proton. When an alkali is constantly supplied, the CT reaction solution can maintain an alkaline steady state. As an acid perturbation is added or an alkali supply decreases below a certain concentration, the acid autocatalytic reaction develops and acid region spreads by the reaction-diffusion process, finally the solution becomes acid steady state. When autocatalytic reactions are operated in a pH responsive spherical gel, the gel shrinks following the one-way reaction, regularly. However, in some conditions, the relatively faster diffusivity of the proton can lead to the oscillatory reaction diffusion instability [42,43,77,78]. The volume oscillation of spherical gel is generated by coupling the CT reaction with the volume phase transition of the pH-responsive gel, and we

2 2 2 46

<sup>1</sup> d[ClO ] [ClO ][S O ][H ] , 7 d

For coupling pH-responsive gels and the CT reaction, it is quite important to achieve large volume changes of the gels, because the stabilities of the steady states depend on the gel sizes. Also, the speed of volume change has a high correlation with the contraction wave shape. However, in general, the reactivities of hydrogels composed of chemically crosslinked polymer networks are low because the polymer chains are molecularly restricted by a large number of cross-links. An *N*-isopropylacrylamide (NIPAAm) gel with a microscale phase separation that underwent a quick response has previously been reported [79]. By preparing a NIPAAm gel above the LCST, the NIPAAm gel forms a porous structure with polymer-rich domains and aggregations in the matrix of loosely bound network structures [80]. Consequently, polymer-rich domains inside the gel aggregate or disperse rapidly through the porous structure within the gel by an effluent pathway of the solvent. Therefore, in this investigation, we prepared the microphase-separated AAm-based gels. The microphase-separation in the gel depends strongly on the methods of gel preparation. Meanwhile, a method for preparing the microphase-separated gels by altering the composition of the solvent has been reported [55]. Therefore, we synthesized the poly (AAm-*co*-AAc) gels in water/acetone solvents. Also, we investigated the gels kinetics at the different mixture proportions of the solvents.

**Figure 15.** SEM images of the interior morphologies of poly (AAm-*co*-AAc) microphase-separated gel with the mixing ratio of water/acetone solvents at 50/50 ((a) swelling state and (b) shrinking state at equal magnification). (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)

First, we observed the structures of the gels. Figure 15 shows the SEM images of the interior morphologies of the poly(AAm-*co*-AAc) microphase-separated gels with the mixing ratio of water/acetone solvents at 50/50. There are polymer rich domains inside the both gels (swelling state and shrinking state) and their sizes change in proportion as the volume phase transitions of the gels. This microscale structures are quite different from those of ordinary poly(AAm-*co*-AAc) gels with water solvents.

Next, we investigated the phase transition kinetics of the poly(AAm-*co*-AAc) cylindrical gels. When the external pH was rapidly changed, the gel diameters gradually changed to approach the equilibrium state. Figure 16 shows the plots of the gel diameters as a function of time on the shrinking process. Here, let us define *Lf, L*(*t*) and *Li*, as the final gel diameter*,*  the gel diameter at t = *t* and the initial gel diameter (*t* = 0), respectively. The time evolution was found to be well described by a single exponential:

$$L(t) = L\_i - \Delta L(1 - e^{-(t/\tau)}) \tag{1}$$

where Δ*L* and *τ* represents the total gel length change (=*Li* – *Lf*) and the characteristic time of shrinking. When *τ* and *Lf* are determined, we can estimate the diffusion constant *D* by using the following relation for cylindrical gels [81]:

$$D = \frac{{L\_f}^2}{24\pi} \tag{2}$$

From the results, the corrective diffusion constant of the poly(AAm-*co*-AAc) cylindrical gels can be estimated as follows; (A) 4.39 × 10<sup>−</sup>5 mm2/s, (B) 5.38 × 10<sup>−</sup>5 mm2/s, (C) 1.75 × 10<sup>−</sup><sup>3</sup> mm2/s, (D) 1.99 × 10<sup>−</sup>3 mm2/s, (E) 2.07 × 10<sup>−</sup>3 mm2/s. In the case of sample (A) and (B), the corrective diffusion constants are almost the same as those of the normal type hydrogels. On the other hand, in the case of sample (C), (D) and (E), they are two orders of magnitudes larger than those of sample (A) and (B). These results indicate that the mixture fractions of acetone to the solvents have the threshold values for the microphase-separation. Also, these results confirm that the microphase-separation plays an important role for increasing speed of the volume phase transition.

We also investigated the detailed pH-responsiveness of the gels. Figure 17 shows the equilibrium swelling of the poly (AAm-*co*-AAc) cylindrical gels at various pH values. From this results, all samples caused volume phase transition between the pH variation range of the CT reaction (from pH = 2 to pH = 11). Also, the diameter change rates of sample (A) and (C) are larger than that of sample (E). It is notable that the stiffness of the gels depends on the mixture proportions of water/acetone solvents. The stiffness of the gels tends to get lower as the mixture fractions of acetone increase. In this experiment, sample (D) and (E) do not stand up under their own weight and became easily deformed in air. Therefore, for this reason, we chose sample (C) as the material of the tubular gel because of its stiffness and phase transition kinetics.

We succeeded in coupling the pH-responsive hydrogel and the CT reaction. Figure 18 shows the propagation of the acid region in the swollen part of the tubular gel. The mixture proportion of the solvent of the tubular gel was same as sample (C). As shown in Figure 18, the CT solution was colored with methyl red. The yellow area corresponds to alkaline composition and the red area corresponds to acid composition. The red allows indicate the forefront of the acid region and the green allows indicate the forefront of the gel contraction. When the acid perturbation was applied to the left part of the tubular gel, the red area propagated to the right, and finally covered the entire gel. Also, the gel diameter shrank following the propagation of the acid region, as shown in Figure 18. These results suggest that the poly(AAm-*co*-AAc) tubular gel can be coupled with the CT solution, in terms of the acid propagation and the volume change of the gel.

330 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

ordinary poly(AAm-*co*-AAc) gels with water solvents.

was found to be well described by a single exponential:

the following relation for cylindrical gels [81]:

of the volume phase transition.

phase transition kinetics.

phase transitions of the gels. This microscale structures are quite different from those of

Next, we investigated the phase transition kinetics of the poly(AAm-*co*-AAc) cylindrical gels. When the external pH was rapidly changed, the gel diameters gradually changed to approach the equilibrium state. Figure 16 shows the plots of the gel diameters as a function of time on the shrinking process. Here, let us define *Lf, L*(*t*) and *Li*, as the final gel diameter*,*  the gel diameter at t = *t* and the initial gel diameter (*t* = 0), respectively. The time evolution

> (/ ) ( ) (1 ) *<sup>t</sup> <sup>i</sup> Lt L L e*<sup>−</sup>

where Δ*L* and *τ* represents the total gel length change (=*Li* – *Lf*) and the characteristic time of shrinking. When *τ* and *Lf* are determined, we can estimate the diffusion constant *D* by using

2

τ

24 *f L*

From the results, the corrective diffusion constant of the poly(AAm-*co*-AAc) cylindrical gels can be estimated as follows; (A) 4.39 × 10<sup>−</sup>5 mm2/s, (B) 5.38 × 10<sup>−</sup>5 mm2/s, (C) 1.75 × 10<sup>−</sup><sup>3</sup> mm2/s, (D) 1.99 × 10<sup>−</sup>3 mm2/s, (E) 2.07 × 10<sup>−</sup>3 mm2/s. In the case of sample (A) and (B), the corrective diffusion constants are almost the same as those of the normal type hydrogels. On the other hand, in the case of sample (C), (D) and (E), they are two orders of magnitudes larger than those of sample (A) and (B). These results indicate that the mixture fractions of acetone to the solvents have the threshold values for the microphase-separation. Also, these results confirm that the microphase-separation plays an important role for increasing speed

We also investigated the detailed pH-responsiveness of the gels. Figure 17 shows the equilibrium swelling of the poly (AAm-*co*-AAc) cylindrical gels at various pH values. From this results, all samples caused volume phase transition between the pH variation range of the CT reaction (from pH = 2 to pH = 11). Also, the diameter change rates of sample (A) and (C) are larger than that of sample (E). It is notable that the stiffness of the gels depends on the mixture proportions of water/acetone solvents. The stiffness of the gels tends to get lower as the mixture fractions of acetone increase. In this experiment, sample (D) and (E) do not stand up under their own weight and became easily deformed in air. Therefore, for this reason, we chose sample (C) as the material of the tubular gel because of its stiffness and

We succeeded in coupling the pH-responsive hydrogel and the CT reaction. Figure 18 shows the propagation of the acid region in the swollen part of the tubular gel. The mixture proportion of the solvent of the tubular gel was same as sample (C). As shown in Figure 18, the CT solution was colored with methyl red. The yellow area corresponds to alkaline composition and the red area corresponds to acid composition. The red allows indicate the

*D*

τ

= −Δ − (1)

<sup>=</sup> (2)

**Figure 16.** Shrinking behaviors of poly(AAm-*co*-AAc) cylindrical gels at the different mixture proportions of water/acetone solvents ((a): (A) 100/0, (B) 80/20, (b): (C) 70/30, (D) 60/40, and (E) 50/50 wt %). (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)

**Figure 17.** Equilibrium swelling of poly(AAm-*co*-AAc) cylindrical gels at various pH values adjusted using HCl and NaOH solutions, at the different mixture proportions of water/acetone solvents ((A) 100/0, (C) 70/30, and (E) 50/50 wt %). (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)

Fig. 19 shows the spatiotemporal diagram constructed from sequential images of the acid propagation. The extractive line is the black bar in Figure 18 (a). As shown in Figure 19, the acid region propagates at the constant speed, and the velocity of the acid propagation was 16 μm/s. It is 10 times faster than that of the previous research [42]. We also measured the velocity of the acid propagation in the mixed CT solution in the glass tube, and it was 200 μm/s. This is much larger value than that in the case of Figure 18. This result indicates that the propagation occurred inside the gel. These results confirm that a part of the chemical reaction networks, from step (1) to step (3) in Figure 14, was realized experimentally. In order to achieve autonomous swelling of the gel, from step (3) to step (4) in Figure 14, the gel diameter needs to shrink below a certain threshold value. It means that the minimum and maximum sizes of the tubular gels should be regulated for realizing oscillatory volume changes by inflowing of alkali in the CT solutions. The concentrations or mixing ratios of the CT solutions also affect the forming of the chemical reaction networks. The regulation of the gel sizes and the CT solutions will take an important role in the generation of the contraction waves in the tubular gels. This research will be the first step for realizing the biomimetic chemical robot which causes peristaltic locomotion.

**Figure 17.** Equilibrium swelling of poly(AAm-*co*-AAc) cylindrical gels at various pH values adjusted using HCl and NaOH solutions, at the different mixture proportions of water/acetone solvents ((A) 100/0, (C) 70/30, and (E) 50/50 wt %). (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)

Fig. 19 shows the spatiotemporal diagram constructed from sequential images of the acid propagation. The extractive line is the black bar in Figure 18 (a). As shown in Figure 19, the acid region propagates at the constant speed, and the velocity of the acid propagation was 16 μm/s. It is 10 times faster than that of the previous research [42]. We also measured the velocity of the acid propagation in the mixed CT solution in the glass tube, and it was 200 μm/s. This is much larger value than that in the case of Figure 18. This result indicates that the propagation occurred inside the gel. These results confirm that a part of the chemical reaction networks, from step (1) to step (3) in Figure 14, was realized experimentally. In order to achieve autonomous swelling of the gel, from step (3) to step (4) in Figure 14, the gel diameter needs to shrink below a certain threshold value. It means that the minimum and maximum sizes of the tubular gels should be regulated for realizing oscillatory volume changes by inflowing of alkali in the CT solutions. The concentrations or mixing ratios of the CT solutions also affect the forming of the chemical reaction networks. The regulation of the gel sizes and the CT solutions will take an important role in the generation of the contraction waves in the tubular gels. This research will be the first step for realizing the biomimetic

chemical robot which causes peristaltic locomotion.

**Figure 18.** Propagation of the acid front in the swollen part of the tubular gel. An acid perturbation was applied to the left part of the gel. The yellow area corresponds to alkaline composition and the red area corresponds to acid composition. The red allows indicate the forefronts of the acid regions and the green allows indicate the forefronts of the gel contraction, which are the rightmost points obtained locally minimum diameters. (a) t = 0 indicates the criterion time after applying the acid perturbation. (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)

**Figure 19.** Spatiotemporal diagram constructed from sequential images of the acid propagation. The extracted horizontal lines correspond to the black bar in Fig. 18 (a). (Reprinted ref. 58, Copyright *IEEE*. Reproduced with permission.)
