自振荡凝胶的动力学模型及可控性分析  

DYNAMIC MODEL OF SELF-OSCILLATING GELS AND THE CONTROLLABILITY ANALYSIS

作　　者：王鹏飞[1,2] 刘少宝[1,2] 周进雄[1,2] 卢天健[1,2] 徐峰[2,3] 

机构地区：[1]西安交通大学航天航空学院机械结构强度与振动国家重点实验室,西安710049 [2]西安交通大学仿生工程与生物力学中心,西安710049 [3]西安交通大学生命科学与技术学院生物医学信息工程教育部重点实验室,西安710049

出　　处：《力学学报》2013年第6期888-896,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(11072185;11372243);高等学校学科创新"111"引智计划项目(B06024);新世纪人才计划;中国南方智谷引进创新团队资助项目~~

摘　　要：自振荡凝胶是一类在Belousov--Zhabotinsky化学反应(BZ反应)驱动下能够产生周期性收缩和膨胀大变形的智能软材料,简称为BZ凝胶,在微型激励器、传感器、药物释放、仿生材料等领域有着广泛的应用前景.基于BZ化学反应的Oregonator模型以及凝胶变形的力平衡方程,建立了由二阶微分方程表示的BZ凝胶的简化动力学模型,并通过对BZ凝胶的振荡动力学模型的分析,发现其在动力学相轨迹空间内呈现出稳定的周期性极限环振荡,进而利用改进的打靶法求得了BZ凝胶的振荡周期解,系统研究了反应物浓度、催化剂效率和链状高分子的亲水性等可控系统参数对其振荡形式、周期和幅值的影响.结果表明,只有在特定的系统参数取值下,BZ凝胶才能发生持续的周期性振荡;随着这些参数的改变,BZ凝胶的振荡形式、周期和幅值均产生规律性变化.证明了对自振荡凝胶实施周期性调控在理论上是可行的.Self-oscillating gels, i.e., BZ gels, are a typical branch of soft smart materials with a large periodic deformation of shrinking and swelling driven by the Belousov-Zhabotinsky chemical reaction （BZ reaction）. BZ gels could be widely applied in the fields of actuators, sensors, drug release and bionic system. Based on the Oregonator model of the BZ reaction and the mechanical equilibrium of the gel deformation a simplified dynamic model, only consisting of a second order differential equation, is given to reformulate the complicated process of the oscillatory deformation. It is demon- strated that the phase space trajectory of BZ gels presents a limit-cycle oscillation （i.e., steady-state periodic oscillation）. Subsequently, the periodic solution of oscillation is obtained by adopting an improved shooting method and the influence of some adjustable system parameters on the mechanical characters of the oscillatory deformation（i.e., pattern, period, amplitude） is systematically investigated, where the system parameters are dependent on the concentration of reactants, catalyst efficiency and hydrophobicity of polymers. The Conclusion demonstrates that the system maintains a limit-cycle oscillation in the case of certain selected values of the system parameters and the mechanical characters of the system appear predictable changes while the parameters are changed. This study theoretically supports the controllability of self-oscillating gels and their potential applications.

关 键 词：智能凝胶 BZ反应 非线性振荡 周期性调控 

分 类 号：O648.17[理学—物理化学]