柔性棘轮在活性粒子浴内的自发定向转动

夏益祺; 谌庄琳; 郭永坤

doi:10.7498/aps.68.20190425

摘要

活性物质在自然界中广泛存在. 利用二维布朗动力学模拟方法, 设计了一种柔性边界棘轮, 并研究了其在活性粒子浴内的动力学行为. 发现棘轮在活性粒子浴内能够发生定向转动, 这是因为活性粒子在柔性边界周围的不均匀分布导致压力的不均匀分布, 进而对棘轮产生扭矩. 进一步研究了影响转动速率的因素, 发现平均转动角速度随活性粒子驱动力、活性粒子密度的增大而增大, 随粒子旋转扩散系数、支架数的增大而降低. 研究结果对于设计新的实验系统来研究此类非平衡物理现象具有一定的指导意义.

关键词:

Abstract

Self-propelling motionisubiquitous in the biological world, ranging from the molecular-level transportation of motor proteins along the microtubules, to the swimming of bacteria on a micrometer scale. An intriguing topic is to design microdevices or micromotors that can rectify the random motion and convert the energy into mechanical work. Here we design a soft microdevice, which may possess the advantages such as damage resistance, durability and adaptability, by utilizing two-dimensional Langevin dynamics simulation. We use a flexible chain to mimic the soft boundary of microdevice. We investigate the dynamical behaviors of microdevice when it is immersed in a thin film of active particle suspension. We find that the microdevicecan rotateunidirectionally and hence output the work. To uncover the physical mechanism of unidirectional rotation, we calculate the pressure distribution along the soft boundary. The spontaneous symmetry breaking of flexible boundary is the origin of the unidirectional rotation, which can lead to the inhomogeneous pressure distribution and hence torque on ratchet. It is because the persistent motion drives the particles to accumulate near the boundary and induce the soft boundary to deform. Further, we focus on the effect of active force and particle density on the angular velocity. With the increase of active force, the average angular velocity increases monotonically due to the increase of torque. With the increase of the number density of active particles, the average angular velocity increases. This is because the aggregation of a large number of particles is beneficial to the increase of ratchet torque. Additionally, we pay attention to the effect of rotational diffusion rate, D_r, of active particles and the number of ratchet wheels. We find the average angular velocity decreases with the increase of rotation diffusion D_r because ofthe ability of particles to weakly accumulate at high D_rs. The average angular velocity also decreases with the increase of the number of ratchet wheels. This is because a large number of ratchet wheels weaken the asymmetry of pressure distribution and hence reduce the torque on wheel. Our work provides a new insight into the design of soft microdevices for studying the non-equilibrium system.

Keywords:

作者及机构信息

苏州大学软凝聚态物理及交叉研究中心, 苏州大学物理科学与技术学院, 苏州　215006

通信作者: 谌庄琳, shenzl@suda.edu.cn

基金项目: 国家自然科学基金(批准号: 21674078)资助的课题.

Authors and contacts

Center for Soft Condensed Matter Physics and Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China

Corresponding author: Shen Zhuang-Lin, shenzl@suda.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 21674078).

文章全文 : translate this paragraph

参考文献

[1]	Marchetti M C, Joanny J F, Ramaswamy S, Liverpool T B, Prost J, Rao M D, AditiSimha R 2013 Rev. Mod. Phys. 85 1143 Google Scholar
[2]	Gao W, Sattayasamitsathit S, Manesh K M, Weihs D, Wang J 2010 J. Am. Chem. Soc. 132 14403 Google Scholar
[3]	Wang W, Castro L A, Hoyos M, Mallouk T E 2012 ACS Nano 6 6122 Google Scholar
[4]	Liu R, Sen A 2011 J. Am. Chem. Soc. 133 20064 Google Scholar
[5]	Deseigne J, Dauchot O, Chaté H 2010 Phys. Rev. Lett. 105 098001 Google Scholar
[6]	Shi X Q, Ma Y Q 2013 Nat. Commun. 4 3013 Google Scholar
[7]	Shi X Q, Ma Y Q 2010 Proc. Natl. Acad. Sci. USA 107 11709 Google Scholar
[8]	Cates M E, Marenduzzo D, Pagonabarraga I, Tailleur J 2010 Proc. Natl. Acad. Sci. USA 107 11715 Google Scholar
[9]	Lei Q L, Ni R, Ma Y Q 2018 ACS Nano 12 6860 Google Scholar
[10]	Nikola N, Solon A P, Kafri Y, Kardar M, Tailleur J, Voituriez R 2016 Phys. Rev. Lett. 117 098001 Google Scholar
[11]	Hiratsuka Y, Miyata M, Tada T, Uyeda T Q 2006 Proc. Natl. Acad. Sci. USA 103 13618 Google Scholar
[12]	Pelling A E, Sehati S, Gralla E B, Valentine J S, Gimzewski J K 2004 Science 305 1147 Google Scholar
[13]	Xia Y Q, Shen Z L, Tian W D, Chen K 2019 J. Chem. Phys. 150 154903 Google Scholar
[14]	Soong R K, Bachand G D, Neves H P, Olkhovets A G, Craighead H G, Montemagno C D 2000 Science 290 1555 Google Scholar
[15]	Sokolov A, Apodaca M M, Grzybowski B A, Aranson I S 2010 Proc. Natl. Acad. Sci. USA 107 969 Google Scholar
[16]	Di L R, Angelani L, Dell'arciprete D, Ruocco G, Iebba V, Schippa S, Conte M P, Mecarini F, De A F, Di F E 2010 Proc. Natl. Acad. Sci. USA 107 9541 Google Scholar
[17]	Angelani L, Di L R, Ruocco G 2009 Phys. Rev. Lett. 102 48104 Google Scholar
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[19]	Li H S, Zhang B K, Li J, Tian W D, Chen K 2015 J. Chem. Phys. 143 224903 Google Scholar
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施引文献

图 1 棘轮在活性粒子浴中(绿色部分)的初始示意结构虚线部分表示刚性支架, 红色表示柔性边界, 左上部分绿色粒子中的黑色箭头表示活性粒子的推进力方向, 右上部分为一段边界上的粒子排布, 粒子间间距为0.25σ

Fig. 1. The initial structure of flexible boundary (red) in the active particle bath (green). The dashed lines represent four rigid trestles. The black arrow in the green particle indicates the active force direction of the active particle in the upper left. The upper right part is the particle arrangement on a boundary. The spacing between the particles is 0.25σ.

下载: 全尺寸图片幻灯片

图 2 (a)四支架棘轮随时间转动的示意图, 图示中刚性支架被忽略, 左上图黑点代表棘轮质心, 其中黑色箭头表示从质心到一支点的方向以此表明棘轮发生转动, 右下图是该情况下的旋转角度与角速度随着时间的变化曲线图; (b)上图为棘轮柔性边界的曲率分布图, 下图为压力分布图, 其中棘轮支架数为N_s = 4, 活性粒子的数密度为φ = 0.025, 旋转扩散系数取D_r = 0.0001, 驱动力F = 40

Fig. 2. (a) Schematic diagram of the ratchet rotation with time for N_s = 4, φ = 0.025, D_r = 0.0001, F = 40. The black dot on the top left figure represents the center of mass of the ratchet; the black arrows denote the orientation from the center of mass of ratchet to the fixed point of boundary to indicate the rotation of the ratchet. The right-down figure shows the time evolution of angle and angular velocity of ratchet. (b) The curvature distribution (up) of boundary and the pressure distribution (down) around it

下载: 全尺寸图片幻灯片

图 3 支架数为4、不同活性力的作用下, 棘轮的旋转角速度 (a)平均角速度, (b)瞬时角速度, 误差棒表示平均角速度的标准方差

Fig. 3. (a) Average angular velocity and (b) instantaneous angular velocity for the four rigid trestles with various active forces. The error bars represent the standard the deviations of angular velocity of rigid trestles.

下载: 全尺寸图片幻灯片

图 4 棘轮的平均角速度与粒子数密度之间的关系, 内部两张插图分别对应活性粒子密度φ = 0.025和φ = 0.1, 误差棒表示平均角速度的标准方差

Fig. 4. Average angular velocity vs the number density of active particles. The insets are typical snapshots for φ = 0.025 and φ = 0.1. The error bars represent the standard the deviations of angular velocity.

下载: 全尺寸图片幻灯片

图 5 (a)不同旋转扩散系数D_r下棘轮的旋转角速度与时间的关系; (b)平均旋转角速度与D_r的关系, 内部两插图分别对应旋转扩散系数D_r = 0.0001和D_r = 0.01, 误差棒表示平均角速度的标准方差

Fig. 5. (a) The angular velocity as a function of time for various rotational diffusion coefficients, D_rs. (b) The average angular velocity as a function of D_r. The insets are typical snapshots for D_r = 0.0001和and D_r = 0.1. The error bars represent the standard the deviations of angular velocity.

下载: 全尺寸图片幻灯片

图 6 棘轮的平均角速度与支架数之间的关系, 内部两插图分别对应支架数为4和6, 误差棒表示平均角速度的标准方差

Fig. 6. The average angular velocity of ratchet vs the number of rigid trestle. The insets are typical snapshots for the number of ratchet wheel. The error bars represent the standard the deviations of angular velocity.

下载: 全尺寸图片幻灯片

[1]	Marchetti M C, Joanny J F, Ramaswamy S, Liverpool T B, Prost J, Rao M D, AditiSimha R 2013 Rev. Mod. Phys. 85 1143 Google Scholar
[2]	Gao W, Sattayasamitsathit S, Manesh K M, Weihs D, Wang J 2010 J. Am. Chem. Soc. 132 14403 Google Scholar
[3]	Wang W, Castro L A, Hoyos M, Mallouk T E 2012 ACS Nano 6 6122 Google Scholar
[4]	Liu R, Sen A 2011 J. Am. Chem. Soc. 133 20064 Google Scholar
[5]	Deseigne J, Dauchot O, Chaté H 2010 Phys. Rev. Lett. 105 098001 Google Scholar
[6]	Shi X Q, Ma Y Q 2013 Nat. Commun. 4 3013 Google Scholar
[7]	Shi X Q, Ma Y Q 2010 Proc. Natl. Acad. Sci. USA 107 11709 Google Scholar
[8]	Cates M E, Marenduzzo D, Pagonabarraga I, Tailleur J 2010 Proc. Natl. Acad. Sci. USA 107 11715 Google Scholar
[9]	Lei Q L, Ni R, Ma Y Q 2018 ACS Nano 12 6860 Google Scholar
[10]	Nikola N, Solon A P, Kafri Y, Kardar M, Tailleur J, Voituriez R 2016 Phys. Rev. Lett. 117 098001 Google Scholar
[11]	Hiratsuka Y, Miyata M, Tada T, Uyeda T Q 2006 Proc. Natl. Acad. Sci. USA 103 13618 Google Scholar
[12]	Pelling A E, Sehati S, Gralla E B, Valentine J S, Gimzewski J K 2004 Science 305 1147 Google Scholar
[13]	Xia Y Q, Shen Z L, Tian W D, Chen K 2019 J. Chem. Phys. 150 154903 Google Scholar
[14]	Soong R K, Bachand G D, Neves H P, Olkhovets A G, Craighead H G, Montemagno C D 2000 Science 290 1555 Google Scholar
[15]	Sokolov A, Apodaca M M, Grzybowski B A, Aranson I S 2010 Proc. Natl. Acad. Sci. USA 107 969 Google Scholar
[16]	Di L R, Angelani L, Dell'arciprete D, Ruocco G, Iebba V, Schippa S, Conte M P, Mecarini F, De A F, Di F E 2010 Proc. Natl. Acad. Sci. USA 107 9541 Google Scholar
[17]	Angelani L, Di L R, Ruocco G 2009 Phys. Rev. Lett. 102 48104 Google Scholar
[18]	Kaiser A, Löwen H 2014 J. Chem. Phys. 141 158102
[19]	Li H S, Zhang B K, Li J, Tian W D, Chen K 2015 J. Chem. Phys. 143 224903 Google Scholar
[20]	Tian W D, Gu Y, Guo Y K, Chen K 2017 Chin. Phys. B 26 100502 Google Scholar
[21]	Li H S, Wang C, Tian W D, Ma Y Q, Xu C, Zheng N, Chen K 2017 Soft Matter 13 8031 Google Scholar
[22]	Wang C, Ma Y Q, Tian W D, Chen K 2018 J. Chem. Phys. 149 164902 Google Scholar
[23]	Xia Y Q, Tian W D, Chen K, Ma Y Q 2019 Phys. Chem. Chem. Phys. 21 4487 Google Scholar
[24]	Plimpton S, Crozier P, Thompson A 2015 J. Appl. Phys. 2 4740
[25]	Humphrey W, Dalke A, Schulten K 1996 J. Molec. Graphics. 14 33 Google Scholar
[26]	Eisenstecken T, Gompper G, Winkler R G 2017 J. Chem. Phys. 146 154903 Google Scholar
[27]	Bechinger C, Leonardo R D, Löwen H, Reichhardt C, Volpe G, Volpe G 2016 Rev. Mod. Phys. 88 045006 Google Scholar
[28]	Redner G S, Hagan M F, Baskaran A 2013 Phys. Rev. Lett. 110 055701 Google Scholar
[29]	Fily Y, Baskaran A, Hagan M F 2014 Soft Matter 10 5609 Google Scholar

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柔性棘轮在活性粒子浴内的自发定向转动