As the prerequisite of life evolution, survival and reproduction, autonomous locomotion is the most basic function of organisms. In recent years, many artificial systems have been developed to simulate the motion behavior and to study the locomotion mechanism of living organisms. Among many kinds of artificial bionics systems, self-oscillating gels have attracted much attention due to its performance of internal drive to generate kinetic energy, directionality, untethered ability and environmental self-adaptation. In this review, the origin of chemo-mechanical energy conversion and the bionic locomotion modes of self-oscillating gels observed until now are introduced and summarized. On the basis of this, the opportunities, challenges and future directions of this field are prospected.
Contents
1 Introduction
2 Chemomechanical origin of the locomotion of self-oscillating gels
Locomotion is an important function of life, including Locomotion and its emerging Collective behaviors: organelles, cells, organs, tissues and individuals in complex environments perceive the environment and absorb energy from it.Through material transport coupling, internal non-equilibrium and complex interaction processes (biochemical reactions, self-assembly and depolymerization of biological macromolecules, etc.), autonomous directional and adaptive movements (overcoming random resistance and thermal noise) are generated to achieve life functions such as nutrient transport, cell crawling, orientation, immunity and reproduction[1]. At the same time, many moving individuals communicate with each other to achieve collective behaviors such as injury healing, tissue growth, muscle contraction, fish school and bird flock at a higher level[1⇓⇓~4]. The non-equilibrium process of many structures in a living body feeds back and coordinates with each other at all levels and with the microenvironment. The theory of Active matter can not yet describe the extreme complexity of motion[2,5][1,6,7]. In recent years, the research of biomimetic motion in artificial chemical active substance system and the development of functional materials with application prospects are the emerging fields and frontiers of chemical research[8⇓⇓~11].
From the directional walking of DNA chains at nanoscale (molecular level), the crawling of single cells at microscale (cellular level), to the crawling, flying and swimming of multicellular organisms at macroscale, the directional movement behaviors of organisms at different scales are complex and different[12][13][14]. In recent years, much progress has been made in the study of the principles of biological motion and its application to the design of complex bionic artificial motion systems[8]. According to the driving mechanism of artificial systems, the work in this field can be divided into the following three types: first, soft matter systems driven by external fields or interface forces, such as functional polymer materials driven by microfluidic transport and liquid soft robots driven by surface tension[15,16][17,18]; Second, soft matter systems driven by biochemical reactions, such as ATP-driven tubulin movement and chemical fuel-driven soft robots[19][16]; Thirdly, soft matter systems driven by spatiotemporal signals (neural-like signals) of reaction networks, such as self-oscillating gel systems coupled with BZ reactions and synthetic molecular motor systems with chemotactic properties[20][21].
The core task of bionic motion research is to reveal the universal mechanism of biological motion and obtain the general design principles of bionic motion.The artificial system is required to have the following properties: (1) to realize the autonomous and continuous conversion from environmental energy to mechanical work at the molecular level (for example, the surge caused by the self-generated gradient physical field at the interface of Janus particles, the autonomous and continuous expansion-contraction of BZ reaction self-oscillating rubber, etc.);(2) coordinating local "molecular work processes" on a large spatial scale without counteracting each other to form macroscopic output (such as cell crawling modulated by cell membrane waves, motion modulated by peristaltic waves of liquid crystal polymer membranes, multi-mode peristalsis of time-sequential optical field modulated photoresponsive gels, etc.);(3) the global and continuous coordination (such as the reaction-microflow feedback loop controlling the rhythmic motion of the soft robot, and the sequential vector magnetic field controlling the multi-mode motion of the magnetic-adhesive composite medium); (4) the communication capability (such as sending and receiving signal molecules)[4,8,11][9,10][20,22][2][23][24][16][25].
At present, BZ self-oscillating gel in artificial chemical system can fully meet the above requirements[8,11]. In 1996, Yoshida et al. First coupled the nonlinear reaction (BZ reaction) with stimuli-responsive gel (the catalyst of BZ reaction was bound to the gel polymer chain NIPAAm-co-AMPS gel lattice spring model), and then Balazs et al. Proposed a reaction-diffusion-spring model to describe the self-oscillating gel[20][22,26]. The characteristics of BZ self-oscillating gel are as follows: (1) On the molecular level, the chemical positive and negative feedback loop produces BZ oscillating reaction (the periodic increase and decrease of the high valence concentration of ruthenium catalyst), which induces the spontaneous volume phase transformation of the gel (the recovery of the expansion and contraction of the gel), and the continuous transformation of chemical energy into mechanical energy[20][20,27]; (2) Chemical oscillation coupled with diffusion generates catalyst concentration space-time self-organized structure (chemical wave), which coordinates "molecular-level energy conversion" output into macroscopic net work and motion over a long distance and periodically. The basic effects include the wave front effect: the concentration of high-valence catalyst increases in the chemical wave front region, and the gel phase expands (gel-solution interdiffusion) and its center of mass moves along the wave propagation direction; Pull-back effect: the concentration of high-valence catalyst behind the wave decreases, the gel phase shrinks, and its center of mass moves in the opposite direction of wave propagation[27⇓~29]; (3) that reaction and transport parameter (reactant concentration, light intensity, temperature, etc.) Can control the positive and negative feedback loops of the BZ oscillation reaction, control the oscillation frequency of the change of the concentration of the high-valence catalyst and the push and pull effect of the related chemical waves to finally form directional motion, and also endow the gel with the ability to sense environmental parameters[30][29][27,30]; (4) Communication behavior, which refers to the coupling between different self-oscillating gel individuals through the diffusion and transport of positive and negative feedback intermediates (such as bromous acid and bromide ions), resulting in various group emergence behaviors such as chemical self-aggregation and coordinated movement[31].
Chemists have discovered the rich locomotor behavior of self-oscillating gels (large-scale periodic deformation, pressure-induced peristalsis, peristaltic waves, conveyor belts, inchworm walking, light-avoidance, and complex path motion), as well as the collective behavior of numerous individual communication (gel windmills)[27,28][32]. The chemical structural formula of the classical BZ self-oscillating gel is shown in Figure 1, and its expansion state and contraction state correspond to trivalent ruthenium and divalent ruthenium respectively. Experimental studies show that the expansion and contraction properties and oscillation period of the BZ self-oscillating gel can be adjusted by changing the monomer, catalyst and reaction temperature used in the synthesis of the gel[33,34][35⇓⇓⇓~39]. BZ self-oscillating gel has many advantages in the field of soft robot bionics, such as internal drive, cable-free, motion orientation and strong adaptability.In this paper, the chemical force origin of the directional motion of self-oscillating gel and its biomimetic motion mode are introduced, and the opportunities and challenges in this field in the future are put forward.
2 Chemo-mechanical origin of directed motion of self-oscillating gel
Biological systems belong to the category of active matter, and their directed motion is generally related to the spontaneous energy transformation of the system and the interaction between the system and the environment. For a long time, the asymmetric interaction between an individual and its environment has been generally considered to be a necessary condition for the directional movement of active substances, such as the asymmetric force produced by the interaction between a snail and the ground through the secretion of viscoelastic liquid, and the asymmetric friction between an earthworm's body surface bristles and the soil through the modulation of the process of peristalsis[40,41]. In artificial biomimetic systems, scientists generally use three methods to introduce asymmetry. The first is the inhomogeneity of the medium, such as the driving system of asymmetric particles in a uniform external field, such as diffusophoresis, electrophoresis, thermophoresis, acoustophoresis and osmotophoresis[9]. The second is the inhomogeneity of external fields, such as the directional motion of a homogeneous medium system in inhomogeneous external fields such as space potential, temperature, solute and sound pressure[24][42]. The third is the combination of the first two methods, that is, the inhomogeneous medium is coupled with the inhomogeneous external field, for example, the motor embedded with magnetic response particles is driven and controlled by the time-changing magnetic field to carry out complex and multi-mode movements, including swimming, crawling, rolling, walking, jumping and climbing[25]. However, the asymmetric interaction between the individual and its environment is not a necessary condition for directional movement. For example, the movement of amoeba is caused by the signal communication between cells in the body, and the group behavior of active liquid crystals in the liquid crystal-fluid coupling system can drive the autonomous movement of the whole system[43][44].
The above points lead to the basic question: in biological and artificial systems, besides introducing asymmetric factors from the outside, can directional movement and its mode transformation be regulated only from the internal dynamics of the system[45]? In order to answer this question, the artificial system, photosensitive BZ self-oscillating gel system, which is simpler than the biological system, was studied.The system is formed by coupling a polymer hydrogel grafted with a ruthenium catalyst with a Belousov-Zhabotinsky reaction system (BZR). The redox state of the catalyst changes periodically with the BZR, resulting in the corresponding expansion and contraction of the gel[20]. By coupling the Yashin-Balazs model (gLSM) and the Amemiya photosensitive BZ reaction model in two-variable form, Gao et al. Obtained the partial differential equations (equations 1 ~ 3) of photosensitive BZ self-oscillating gel:[26,46,47][48,49][50]
Where Vp=∇σ/ζ’(ϕ)
∇σ=∇(ϕ+l n(1-ϕ)+χ(ϕ)ϕ2-χ*ϕv+c 0 v 0[(ϕ/ϕ0)-1λ⊥-4-ϕ(2ϕ0)-1])F(u,v,ϕ,I)=(1-ϕ)2 u-u 2-(f v+I P 1)(1-ϕ)[u-q(1-ϕ)2][u+q(1-ϕ)2]-1+I P 2 G(u,v,ϕ,I)=ε[(1-ϕ)2 u-(1-ϕ)v+I(0.5 P 1+P 2)]
In the equation, the u and V variables are the dimensionless quantities of HBrO2 and Ru(bpy)33+ concentration in the Oregonator model, respectively, ϕ is the volume fraction of gel, Vp represents the local point velocity vector of gel, σ is the stress gradient, ζ’(ϕ) is the apparent friction coefficient (which is a monotonic function of ϕ), and J is the diffusion flow of u variable. c0 is the crosslinking density, v0 the volume of gel chain monomer, ϕ0 is the volume fraction of undeformed gel, χ* is the coupling coefficient of chemical reaction coupling gel dynamics, which represents the strength of mechanical-chemical effect of the system.Equations F and G describe the photosensitized BZ reaction kinetics (modified Oregonator model), where ε, f, and Q are Oregonator parameters, I represents the dimensionless uniform light intensity, and P1 and P2 are proportional coefficients characterizing the two core photoreaction steps.
As shown in Fig. 2, in order to reveal the root cause of the directional motion of active substances, Gao et al. Studied the directional motion of self-oscillating glue driven by pulse waves in one-dimensional periodic space[50]. Under initial conditions in space, a simple pulse wave propagates and drives the self-oscillating gel in a reverse wave motion (the direction of gel motion is opposite to the direction of pulse wave propagation, Fig. 2a and B). The inset diagram in Fig. 2b shows that the net displacement of a local point in the gel driven by the push effect of the wave front is less than the pull effect of the wave back during a pulse wave driving period. With the increase of the spatially uniform light intensity, the simple pulse wave is gradually twisted with the bifurcation of the local point dynamics of the light-induced system to produce a complex pulse wave with a tempering structure (as shown in Fig. 2C, e, and G).Causes its driven gel motion pattern to change from antiwave motion (Fig. 2b and d), with zero net displacement (Fig. 2 f), to synwave motion (gel motion in the same direction as the pulse wave propagation, Fig. 2 H). The space-time distortion of the pulse wave structure leads to the change of the driving effect, so it is necessary to divide the chemical wave region by the total differential of the catalyst variable V in time and space, so as to identify the chemical wave region governing the transition of the gel motion mode. The total differential expression is as follows:
Where vx and vt represent the spatial gradient and the rate of change with time of the V variable, respectively. According to the values of these two dynamic quantities in space, the criteria for dividing the chemical wave region can be given (as shown in Table 1).
Through this criterion, it is found that the simple pulse wave has only two chemical wave regions of 1 and 2, and with the distortion of the pulse wave, the chemical wave region increases to 4 regions. The values of the driving effect of each chemical wave region in a pulse wave propagation period in the above process were measured by numerical analysis. The measurement shows that the transition of the gel from the reverse wave motion to the forward wave motion is mainly determined by the chemical wave region 2, and the driving effect does not change significantly with the increase of light intensity.This is due to the coexistence of push and pull effects within wave region 2 as the light intensity increases (as shown by 2b and 2C in Figure 3A), and the new push effect counteracts the pull effect, which eventually leads to a shift in the motion pattern. The dynamic equation of the stress gradient is given as follows:
Where B(ϕ,v)=1-1/(1-ϕ)+2χ0ϕ+3χ1ϕ2-χ*v+c0(λ⊥ϕ0/ϕ2-1/(2ϕ0))
χ0 and χ1 are the Flory-Huggins interaction coefficients, ϕx is the spatial gradient of the ϕ variable, and λ⊥ is the expansion rate of the gel in the constrained direction. The right-hand side of equation (5) contains two terms, B(ϕ,v)ϕx and ϕvx(χ* identically equal to 1.0). The numerical analysis of the variables V, ϕ, vx, ϕx, and B according to equation (5) shows that the negative value of the kinetic term of ϕx in the chemical wave region 2 is the reason for the appearance of the positive σx. The chemical wave driving mechanism determines that there is an anti-phase trend between the variable ϕx and the variable vx at the local point of the gel medium (as shown in Fig. 3B, the positive value of vx drives the local gel phase deformation corresponding to the negative value of ϕx). Therefore, the evolution processes of the variables of gel kinetics, ϕ, ϕx, V and vx, are coupled by diffusion-stress interaction, resulting in synergistic changes. As shown in Fig. 3C, the local point oscillation dynamics of the gel undergoes a bifurcation with the increase of light intensity, resulting in the transformation of simple oscillation into complex oscillation, which is manifested by the divergence of the limit cycle of the local point oscillation on the u-v plane.It causes a large change of the variable V in space (vx) and time (vt), and at the same time, it causes a corresponding change of the space-time structure of the variable ϕ (ϕx) and produces a negative value of the dynamic quantity ϕx in the region of chemical wave 2. In essence, the dynamical destabilization of the light-intensity parameter-induced simple local oscillation is the dynamical origin of the emergence of the tempering wave, which is the fundamental reason for the transition of gel motion from retrograde to prograde motion in the absence of external asymmetry.
In a word, the polymer hydrogel coupled with the oxidized and reduced catalysts in the self-oscillating gel expands and contracts alternately, a pulse wave is generated in space during reaction-diffusion coupling, the oxidized and reduced catalysts in the front and back of the wave respectively generate a pushing force and a pulling force, and the gel is driven to move directionally under the condition that the net acting force is not zero.That is to say, the asymmetry of the internal push-pull force of the chemical wave is the source of the directional motion of the self-oscillating gel. In the absence of external effects (such as zero light intensity), the gel also moves directionally, while the change of external environmental conditions only changes the direction of the structural modulation motion of the chemical wave[50].
3 Biomimetic motion of self-oscillating gels.
3.1 Peristaltic motion and self-walking
In living systems, cells and unicellular organisms in organisms generally produce peristaltic behavior through volume deformation, and the modified BZ self-oscillating gel can achieve this kind of biomimetic behavior. Yoshida et al. Found that the addition of hydrophilic group AMPS in the process of synthesizing BZ self-oscillating gel by thermal polymerization can greatly improve the hydrophilicity of the gel, which shows that in the process of BZ self-oscillating reaction,The expansion-contraction ratio of the gel coupled by the reduced ruthenium and the oxidized ruthenium is greatly increased, and the volume of the gel part corresponding to the chemical wave is obviously expanded (Fig. 4A). The propagation of the chemical wave in the gel is synchronized with the periodic expansion and contraction of the gel itself, which eventually leads to the peristalsis of the gels[51].
Living things in nature have a variety of movement patterns. In many cases, the movement of living things is spontaneous without any external stimulation, just like the heart will beat spontaneously and periodically[3]. Walking is the most common mode of locomotion among all modes of locomotion in organisms. On the basis of the BZ self-oscillating gel which can spontaneously convert chemical energy into mechanical energy first synthesized by Yoshida et al. In 1996, the bent BZ self-oscillating gel designed by Maeda et al. Accompanied by the BZ oscillating reaction, the self-oscillating gel can realize the spontaneous conversion of chemical energy into mechanical work in the BZ reaction.In the process of chemical wave propagation, with the periodic change of the curvature radius of the colloid itself, both ends of the gel are in contact with the sawtooth surface of the inert substrate, resulting in asymmetric friction, and the curved gel is similar to the two feet of an animal, realizing the self-walking of the gel (Fig. 4B)[20][51]. A template polymerization method is adopted when the long flaky BZ self-oscillation gel is synthesized, an upper template and a lower template respectively adopt a hydrophilic glass plate and a hydrophobic polytetrafluoroethylene plate, a pre-polymerized polymer solution is injected in the middle, the hydrophilicity and the hydrophobicity of the upper surface and the lower surface of the flaky BZ self-oscillation gel formed after heating polymerization are obviously different,After contacting the BZ solution on the inert serrated substrate, the gel will automatically bend to form "two feet" due to the hydrophilicity difference between the two sides. The serrated substrate enables the "two feet" of the gel to stand and "walk" forward driven by the chemical wave (Fig. 4B).
3.2 Photophobic movement and phototropic movement
Phototaxis is a common biological movement behavior in nature, such as the phototropic movement of chloroplasts and the photophobic movement of cyanobacteria, which is of great significance to the survival of organisms[3]. To study and design the phototactic movement through the self-oscillating colloidal system, the first step is to explore the light-controlled dynamics of the system. In the homogeneous BZ reaction, Gao et al. Found that the relationship between the oscillation frequency and the light intensity was non-monotonic, which showed that the oscillation frequency increased rapidly with the increase of the light intensity at low light intensity, as shown in the positive slope region of the curve in Fig. 5A, corresponding to the light-induced kinetic region of the system oscillation frequency[53]; When the peak value is reached, the oscillation frequency slowly decreases with the increase of light intensity until the oscillation stops, as shown in the negative slope region of the oscillation frequency curve in fig. 5A, which corresponds to the photoinhibition kinetic region of the system oscillation frequency.
According to the relationship between the homogeneous oscillation frequency and the light intensity of the self-oscillating gel, Gao et al. Set up a spatial step light intensity environment (consisting of two sections of light intensity), and placed the self-oscillating gel in the capillary reactor in the middle of the differential light environment, as shown in Figure 5B. If the two light intensity values are selected in the light-induced region of the oscillation-frequency curve, according to the principle of high frequency domination of chemical waves, the pulse wave propagates from the high frequency region (high light intensity) to the low frequency region (low light intensity) of the medium, thus driving the gel to spontaneously reverse motion (reverse wave mode), that is, positive phototactic motion (Fig. 5B left)[54⇓~56]. If the differential light intensity is selected in the photoinhibitory region, the pulse wave will propagate from the high frequency region (low light intensity) to the low frequency region (high light intensity) of the medium, driving the gel to move spontaneously in the opposite direction, that is, negative phototaxis (right in Figure 5B). This study not only observed the negative phototactic behavior predicted by Dayal et al in their model simulation, but also systematically designed the positive phototactic motion of self-oscillating glue[57]. The results show that the non-monotonic relationship of chemical kinetics in active gel dominates its motion mode and its transition, which mimics the general process of biological phototaxis driven by biochemical reaction network.
3.3 Wave motion against and along
There are two basic movement modes in nature and artificial systems, wave movement (muscle peristaltic wave and movement in the same direction, such as snail crawling) and wave movement (muscle peristaltic wave and movement in the opposite direction, such as earthworm movement). On the basis of basic movement patterns, organisms can realize various complex movement patterns by coupling appendages such as cilia, limbs and wings and modulating a variety of motor nervous systems. Gao et al. Studied the general process of muscle peristalsis driven by nerve signal transduction in bionic animals, and studied the control law of gel reverse wave and forward wave motion and their transformation through the photosensitive BZ gel model (see the description of the model in the second part)[29]. As shown in fig. 6, a step light intensity environment is set in space (fixed low light intensity at the left end and variable high light intensity at the right end), and the one-dimensional self-oscillating glue is placed in the middle (corresponding to the self-oscillating glue in the capillary reactor). It is found that the propagation direction of the pulse wave does not change with the gradual increase of the light intensity on the right side (as shown in Fig. 6 d, e and f, respectively, the pulse wave propagates from the high light intensity area on the right side to the low light intensity area on the left side).However, the direction of gel motion changes from the original rightward motion (Fig. 6G, opposite to the direction of wave propagation) to zero net displacement (Fig. 6h), and finally to the leftward motion (Fig. 6i, in the same direction as wave propagation). This shows that with the increase of the step difference of spatial light intensity, the motion mode of the gel changes from the original anti-wave motion to the zero net displacement, and finally to the co-wave motion.
In order to analyze the evolution process of the pulse wave driving effect with the light intensity difference, the change of the local stress gradient ▽ σ of the gel with the light intensity difference in a pulse wave driving period is calculated, as shown in Fig. 7, with the increase of the step light intensity difference, the stress gradient value corresponding to the pulse wave pushing effect in the driving period continues to increase.At the same time, the pulling effect changes slowly, which directly leads to the change of the net displacement direction of the gel driven by the chemical wave from the initial pulling effect (anti-wave motion) to the pushing effect (co-wave motion), resulting in the change of the gel motion mode.
The subsequent analysis shows that the step difference of light intensity can enhance the intensity of pulse wave pushing, which is rooted in the "dynamic relationship between light intensity and the maximum of oscillation V variable", that is, in the range of parameters used, it is found that the maximum of local oscillation V variable increases linearly with light intensity. Therefore, on the difference boundary, the light intensity acts on the system dynamics to produce a drop of the V variable (Δv), which directly enhances the pushing intensity of the nearby pulse wave, so it can be used to modulate the transition of the system's motion mode from the reverse wave to the forward wave[50]. This mechanism, which modulates the net displacement of system movement by light differences, is completely consistent with the "anchoring mechanism" of animal movement, which is called chemical anchoring mechanism[3].
3.4 Spontaneous round-trip migration
Many organisms, such as birds and fish, show periodic migration between two habitats, and migration can occur with seasonal or geographical changes in the environment or resources[58]. The periodic round-trip migration of animals is a kind of complex movement behavior, and its mechanism is still a mystery. Gao et al. studied the periodic migration motion (Fig. 8B) of one-dimensional self-oscillating glue in a spatially slowly varying gradient field (Fig. 8A) through model simulation, and discussed the general mechanism of periodic round-trip migration[59]. The gel is initially placed in the center of the light intensity gradient environment, and by adjusting the system parameters, it can be observed that the gel is driven by the pulse wave to spontaneously reverse its motion direction on the left and right sides of the space, so that it is limited to a certain range of the light intensity gradient space for spontaneous periodic reciprocating motion. As shown in Figure 8B and Figure 9, the pulse wave driving the motion of the gel always propagates from the right side to the left side (because the oscillation frequency corresponding to the light intensity on the right side is larger than that on the left side), and the gel turns due to the periodic transition of its motion pattern between the retrograde and prograde motion.
Fig. 9 demonstrates the kinematic details of the periodic migration process of the gel. The trajectories of the left boundary, the center point, and the right boundary of the gel over time indicate that the gel as a whole continues to migrate periodically (fig. 9a). Zoom in on the motion trajectory of the gel center point during one cycle of migration, as shown in Figure 9b. The four inset figures are the details of several phase points of the motion trajectory. Fig. 1 (simple trajectory) and Fig. 3 (complex periodic trajectory) are inserted to correspond to the reverse phase and the forward phase of the periodic migration, respectively, and the corresponding driving pulse waves are shown in Fig. 9 e (simple pulse wave) and f (tempering pulse wave), respectively. Through kinematic analysis, it can be found that the reverse and forward phases of period migration are driven by two kinds of pulse waves (simple pulse wave and tempering pulse wave). Similar to the periodic migration behavior of salmon, the juvenile and adult fish are in two different physiological States, moving seaward and landward respectively, which is consistent with the periodic migration of self-oscillating glue at the dynamic level. The mechanical analysis shows that the pushing effect of the simple pulse wave is less than the pulling effect, while the driving effect of the tempering pulse wave is just the opposite, so the two waves drive the gel to move against the wave and along the wave, respectively. Dynamic analysis reveals that the origin of the spontaneous transition of the two pulse waves lies in the homoclinic bifurcation of the local dynamics of the system accompanied by the motion of the gel to achieve the repeated reorientation of the motion direction, which is the ultimate origin of the periodic migration of the gel. The results of this study provide new ideas for the development of smart materials for drug delivery or self-cleaning systems[59].
3.5 Circular and angular motion
Compared with one-dimensional systems, there are more complex forms of chemical waves in high-dimensional space (two-dimensional or three-dimensional), and spiral waves are its representatives. Spiral wave structures arise from the coupling of nonlinear physical or chemical interactions with material transport processes and are ubiquitous in nature as well as in physical and chemical artificial systems. According to the principle of self-oscillating internal driving and recent research results, three characteristics of self-oscillating gel motion driven by spiral waves can be judged: first, the self-persistence of spiral waves can ensure the continuous conversion of chemical energy from BZ reaction to gel peristalsis[50][29,59]; Secondly, the force asymmetry between the push-pull before and after the spiral wave produces the basal motion pattern of the gel. Thirdly, by adjusting the system parameters, the simple spiral wave dynamic instability can produce a new asymmetric driving effect, which corresponds to a more complex gel motion mode.
Through model simulation, it is found that with the increase of light intensity in uniform light intensity environment, the spiral wave changes from simple spiral wave to wave tip roaming spiral wave, accompanied by the change of gel motion mode from circular motion to toroidal motion trajectory, as shown in Figure 10[60]. The above two motion modes are compound motion modes, which are compound trajectories of gel translational motion and rotational motion. The local dynamics analysis of the system shows that the transition of the above two motion modes of the gel is rooted in the second Hopf bifurcation of the spiral wave tip dynamics with the increase of light intensity. This dynamical instability of the system introduces a second small-scale circular motion inside the gel caused by the wandering of the spiral wave tip.
Considering that the circular motion and the turning motion of the gel can be respectively analogized to two alternate sub-processes of "running" and "turning" in the broken-line motion mode commonly adopted by insect larvae, a light intensity square wave time series can be set through formula (6) to control the alternate process of "running and turning" of the gel motor.
Where ΩS and ΩT are the transport velocities of the gel undergoing closed circular motion (shown in Fig. 10 a for the large black circle) and toroidal motion (shown in Fig. 10 B for the small blue circle), respectively. Δβ is the phase angle (integer multiple of π/2) experienced by the spiral wave tip during wandering, and γ is the sum of the rotation angles during a "running" process and a "turning" process. The different polyline motion trajectories depend on the selected value of γ (for example, the triangular trajectory in Figure 11c corresponds to γ = 2π/3), so that the corresponding Δβ (the turning angle of the gel motion direction in a polyline motion cycle is mainly contributed by the phase angle experienced by the wave tip) and the related turning time Tturn (shown in Figure 11A) can be determined, and finally the Trun can be calculated according to Equation (6). After obtaining the Trun and Tturn values, the spatial uniform light intensity time series square wave can be designed, as shown in Fig. 11 B, where Trun and Tturn are the duration of uniform light intensity corresponding to circular motion and turning motion, respectively. Therefore, the gel broken line motion corresponding to different broken line rotation angles γ can be designed, such as the geometric trajectories of triangle, petal, Pentagon and circle (Fig. 11c ~ f).
The programmed motion of the gel is not limited to being controlled by a uniform light intensity time series, but can also be modulated by encoding of the spatial light intensity (spatial differential light intensity). By applying the reversible change of the motion mode of the light-induced gel from circular motion to turning motion, the gel can be designed to spontaneously carry out "run-turn-run" light-avoiding motion in the environment with different light intensities, just like the negative phototaxis motion behavior of organisms[61].
3.6 Group movement
Biomimetic functional surfaces have attracted much attention because of their unique functions and potential applications. The most typical biomimetic functional surfaces are superhydrophobic surfaces imitating the structure of lotus leaves and smooth surfaces imitating pitcher plants.Yoshida et al. Reported a biomimetic self-cleaning surface based on the population behavior of BZ self-oscillating gel, which is composed of columnar BZ self-oscillating gel densely grafted on an inert substrate.When the BZ oscillation reaction occurs, with the propagation of chemical waves in the polymer "bristles", the columnar self-oscillating gel grafted with oxidized ruthenium will absorb water and expand, while the columnar self-oscillating gel grafted with reduced ruthenium will shrink Hydrophobically, causing spontaneous periodic changes in the shape of the "bristles" and having a self-cleaning function (Fig. 12)[62][63][64].
Balazs et al. Simulated the communication and interaction between cylindrical BZ self-oscillating gels through a model, and found that the communication behavior between cylindrical BZ self-oscillating gels could be controlled by modulating the concentration of BZ substrate[65]. In addition, Balazs et al. And Yoshida et al. Cooperated to study the chemical wave propagation path between heterogeneous BZ self-oscillating gels, studied the communication behavior between BZ self-oscillating gels through experiments and model analysis, and found the synergistic effect of chemical oscillation between multiple gels, that is, the oscillation frequency and phase of adjacent self-oscillating gels gradually reached a consensus[66]. The synergy accompanied by oscillatory dynamics is the synergistic directional motion of the gel population. Deb et al. Used the Balazs-Yashin model to simulate the group motion of multiple BZ self-oscillating gel squares and found that the gel driven by chemical waves would produce collective motion behavior (Fig. 13).Finally, they rotate and gather together like windmills, that is, four uniform BZ self-oscillating gel blocks are initially arranged regularly at equal intervals, and the internal dynamics of multiple gels first cooperate to generate chemical waves propagating clockwise across the gel, and drive the gel group to move against the waves, forming a "gel windmill" rotating counterclockwise[22][67].
4 Conclusion and prospect
Self-oscillating gel system is an artificial biomimetic system driven by an internal reaction network, so it has the ability of self-drive, motion orientation, adaptability and the ability to achieve complex motion. The bionic motion design of self-oscillating gel system follows the following principles: first, the propagation of chemical waves always follows the principle of high frequency control, that is, the highest frequency chemical wave in the system determines the final propagation direction of chemical waves[54⇓~56]; Secondly, with the increase of light intensity, the homoclinic bifurcation of the light-frequency relationship will occur in the photosensitive self-oscillating gel system, resulting in the backfire wave, which leads to the transition of the gel motion mode from the inverse wave motion to the forward wave motion. Double phototactic movement (reciprocating migration) can be designed by combining the above two points; Thirdly, for the gel system driven by high-dimensional chemical waves, for example, the Hopf bifurcation of the simple spiral wave tip is transformed into the wandering spiral wave tip, which can be used to design the polygonal turning motion of the light-stressed gel, and the gel can obtain positive and negative phototactic motion when it is driven by two-dimensional spiral waves through the light intensity or light weakness region.
Based on the summary of previous studies on the biomimetic motion behavior of self-oscillating gels, we propose the future development direction of this field as follows:
(1) how to achieve more complex motion? The previous work basically focused on the motion of BZ self-oscillating gel driven by pulse wave and spiral wave. The motion is limited to one-dimensional and two-dimensional space, and the motion mode is limited. If the motion of BZ self-oscillating gel can be extended to three-dimensional space, the vector superposition of simple motion patterns and the occurrence of helical motion behavior can be predicted[68⇓⇓⇓~72].
(2) How to realize the small-scale of self-oscillating gel? Previous work has found that the existing self-oscillating gels have problems such as insufficient toughness and too long wavelength. In the future, the technology should focus on enhancing the gel toughness and shortening the chemical wave wavelength, so that smaller scale self-oscillating gels can be obtained[73,74].
(3) How to control the self-oscillating gel motion? The motion modes of self-oscillating gel are relatively complex and diverse, and the criterion of motion mode conversion is very important, which determines whether the motion behavior can be controlled by artificially modulating the reaction parameters.
(4) How to realize the group motion of the complex structure of multi-driven self-oscillating gel? Both the internal chemical wave and the external accessory brake or environment (light, mechanical force) can produce forces on the self-oscillating gel system, and the coupling of the two can produce more complex forms of motion, such as variable speed, adaptability, and automatic conversion of multi-mode motion[32].
(5) How to develop self-oscillating gel system with biocompatibility and realize the application of soft gel robot? Although potential applications of self-oscillating gels have been reported, such as self-oscillating gel brushes and cargo transportation, the currently developed self-oscillating gel systems involve strong acids and strong oxidizing media, limiting their wide application, especially in clinical medicine[64][51,75]. Only by finding suitable biocompatible or near-neutral weak redox oscillation reactions and bending deformation oscillations can they be widely used in biomanufacturing, drug delivery, medical surgery and so on[76][77⇓~79].
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