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复杂受限环境中的扩散研究在凝聚态物理领域中备受关注. 胶体体系的出现, 为定量研究微观粒子的受限扩散提供了卓越的实验模型系统. 当胶体粒子的形状由球形变为椭球形时, 体系展现出各向异性的扩散动力学特性. 近年来, 研究者们发现粗糙表面能够诱发球形胶体体系异常的旋转动力学. 然而, 由于实验体系的局限性, 粗糙表面对椭球形胶体粒子的受限扩散的影响依然知之甚少. 本文建立了胶体受限扩散的模型体系, 由粗糙圆球胶体构成受限环境, 研究了粗糙和光滑椭球在其中的受限扩散. 当圆球的堆积分数较低时, 粗糙表面未发挥作用, 因此光滑和粗糙椭球的平动和转动扩散相近. 随着圆球堆积分数的增高, 粗糙表面之间发生互锁, 导致粗糙椭球的平动扩散明显慢于光滑椭球; 随着堆积分数的进一步增高, 由于粗糙表面产生的空间位阻效应, 粗糙椭球的转动扩散也显著慢于光滑椭球. 该工作表明粗糙表面会改变椭球的受限扩散, 为揭示复杂环境中具有粗糙表面物质的扩散规律提供了实验依据.The study of diffusion in complex confined environments has received great attention in the field of condensed matter physics. The emergence of colloidal systems provides an excellent experimental model system for quantitatively studying the confined diffusion of microscopic particles. When colloidal particles change from spherical to ellipsoidal shape, the system presents anisotropic diffusion dynamics. Recent studies have found that rough surfaces, another important physical parameter of colloids, can lead to unusual rotational dynamics in spherical colloidal systems. However, due to the lack of a suitable experimental system, little is known about the effect of rough surfaces on the confined diffusion of ellipsoidal colloidal particles. In this work, rough colloidal spheres, rough colloidal ellipsoids, and smooth colloidal ellipsoids are prepared, and then monolayer colloidal samples are prepared to study the confined diffusions of these two types of ellipsoids in dense packing of the rough sphere colloids. By calculating the mean square displacement, intermediate self-scattering function, and orientation correlation function of the ellipsoids, we quantitatively characterize the diffusion dynamics of rough and smooth ellipsoids in varying concentrations of rough spheres. The results indicate that the translational diffusion and rotational diffusion of rough ellipsoids and smooth ellipsoids slow down as the concentration of rough spheres increases. This is due to the confinement of the ellipsoid by the surrounding spheres. At low stacking fractions of spheres, smooth and rough ellipsoids show similar translational diffusion and rotational diffusion. However, as the stacking fraction of spheres increases, there is a significant difference in advection diffusion between rough ellipsoids and smooth ellipsoids. The advection diffusion of rough ellipsoids is significantly slower than that of smooth ellipsoids. This is because the rough surface strongly inhibits rotation, meaning that the rotational diffusion of the rough ellipsoids is significantly slower than that of the smooth ellipsoids. By extracting the diffusion coefficients for translation and rotation from the ellipsoid's long-time mean-square displacements, we find that at ϕ = 0.60 and 0.65, the diffusion coefficients of rough ellipsoids are smaller than those of smooth ellipsoids. The translational diffusion coefficient of the rough ellipsoids is notably smaller than that of the smooth ellipsoids. However, the rotation diffusion coefficient of the rough ellipsoids is not significantly different from that of the smooth ellipsoids. This suggests that the rough surface mainly affect translational diffusion, strongly suppressing the translational diffusion of the ellipsoids. By calculating the displacement probability distribution for ellipsoidal motion, we find that at ϕ = 0.65, the translational displacements of rough ellipsoids have a relatively narrow distribution. This suggests that the translational motion of particles is suppressed by the rough surface. However, the distributions of rotation displacement for smooth ellipsoids and rough ellipsoids are very similar, indicating that the rough surface has less influence on particle rotation. At ϕ = 0.74, the rough surface suppresses both the translation and the rotation of the ellipsoid, resulting in a narrower displacement distribution than in the case of smooth ellipsoid. These findings suggest that rough surfaces significantly impede ellipsoidal diffusion, leading the translational and rotational motions not to occur simultaneously. This study provides an in-depth understanding of the role of rough surfaces of colloidal particles in confined diffusion, as well as an experimental basis for explaining the diffusion laws of rough materials.
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Keywords:
- colloidal ellipsoids /
- rough particles /
- confined diffusion /
- dynamics
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图 1 制备的胶体粒子的扫描电镜图像 (a) 粗糙圆球; (b) 粗糙椭球; (c) 光滑椭球; (d) 单层样品的示意图; (e) 粗糙椭球在粗糙圆球体系(ϕ = 0.74)中的明场显微镜照片
Fig. 1. SEM images of the as-prepared colloidal particles: (a) Rough spheres; (b) rough ellipsoids; (c) smooth ellipsoids; (d) schematic diagram of a monolayer sample, rough and smooth ellipsoids in a dense packing of rough spheres; (e) bright-field micrographs of a rough ellipsoid among rough spheres (ϕ = 0.74).
图 2 在不同圆球浓度(ϕ)下, 粗糙椭球和光滑椭球的平动均方位移(a)和转动均方位移(b). 实心符号表示光滑椭球, 空心符号表示粗糙椭球
Fig. 2. Translational (a) and rotational (b) MSDs for rough (hollow symbols) and smooth (solid symbols) ellipsoids at different concentrations (ϕ) of microspheres.
图 3 粗糙椭球和光滑椭球的扩散系数 (a) 平动扩散系数; (b) 转动扩散系数. DTS和DRS表示光滑椭球的扩散系数, DTR和DRR表示粗糙椭球的扩散系数. 误差是通过测量不同粒子的扩散系数得到的
Fig. 3. The diffusion coefficients of the rough ellipsoid (DTR and DRR) and smooth ellipsoid (DTS and DRS): (a) Translational diffusion coefficient; (b) rotational diffusion coefficient. Error bars are obtained by measuring the diffusion coefficients of different particles.
图 4 椭球运动10 s的位移概率分布 (a) 平动位移; (b) 转动位移. 实心符号表示光滑椭球, 空心表示粗糙椭球
Fig. 4. The probability distributions of the displacements of the smooth ellipsoid (solid symbol) and rough ellipsoid (hollow symbol) for lag time of 10 s: (a) Translational displacement; (b) rotational displacement.
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[1] Weeks E R, Crocker J C, Levitt A C, Schofield A, Weitz D A 2000 Science 287 627
Google Scholar
[2] Mitragotri S, Lahann J 2009 Nat. Mater. 8 15
Google Scholar
[3] Anderson V J, Lekkerkerker H N W 2002 Nature 416 811
Google Scholar
[4] Carrasco-Fadanelli V, Mao Y S, Nakakomi T, Xu H A, Yamamoto J, Yanagishima T, Buttinoni I 2024 Soft Matter 20 2024
Google Scholar
[5] Doan D, Kulikowski J, Gu X W 2024 Nat. Commun. 15 1954
Google Scholar
[6] Han Y, Alsayed A M, Nobili M, Zhang J, Lubensky T C, Yodh A G 2006 Science 314 626
Google Scholar
[7] Chakrabarty A, Konya A, Wang F, Selinger J V, Sun K, Wei Q H 2013 Phys. Rev. Lett. 111 160603
Google Scholar
[8] Zhou F, Wang H G, Zhang Z X 2020 Langmuir 36 11866
Google Scholar
[9] Zhou H X, Rivas G N, Minton A P 2008 Annu. Rev. Biophys. 37 375
Google Scholar
[10] 刘心卓, 王华光 2020 物理学报 69 238201
Google Scholar
Liu X Z, Wang H G 2020 Acta Phys. Sin. 69 238201
Google Scholar
[11] Carbajal-Tinoco M D, Lopez-Fernandez R, Arauz-Lara J L 2007 Phys. Rev. Lett. 99 138303
Google Scholar
[12] Boniello G, Blanc C, Fedorenko D, Medfai M, Ben Mbarek N, In M, Gross M, Stocco A, Nobili M 2015 Nat. Mater. 14 908
Google Scholar
[13] Edmond K V, Elsesser M T, Hunter G L, Pine D J, Weeks E R 2012 Proc. Natl. Acad. Sci. U. S. A. 109 17891
Google Scholar
[14] Peng Y, Lai L, Tai Y S, Zhang K, Xu X, Cheng X 2016 Phys. Rev. Lett. 116 068303
Google Scholar
[15] Kim J, Sung B J 2015 Phys. Rev. Lett. 115 158302
Google Scholar
[16] Cervantes-Martínez A E, Ramírez-Saito A, Armenta-Calderón R, Ojeda-López M A, Arauz-Lara J L 2011 Phys. Rev. E 83 030402
Google Scholar
[17] He K, Khorasani F B, Retterer S T, Thomas D K, Conrad J C, Krishnamoorti R 2013 ACS Nano 7 5122
Google Scholar
[18] Hsu C P, Mandal J, Ramakrishna S N, Spencer N D, Isa L 2021 Nat. Commun. 12 1477
Google Scholar
[19] Moinuddin M, Biswas P, Tripathy M 2020 J. Chem. Phys. 152 044902
Google Scholar
[20] Ilhan B, Mugele F, Duits M H G 2022 J. Colloid Interface Sci. 607 1709
Google Scholar
[21] Zhang H, Pham P, Metzger B, Kopelevich D I, Butler J E 2023 Phys. Rev. Fluids 8 064303
Google Scholar
[22] Zhang Z X, Yunker P J, Habdas P, Yodh A G 2011 Phys. Rev. Lett. 107 208303
Google Scholar
[23] 王华光, 张泽新 2016 物理学报 65 178705
Google Scholar
Wang H G, Zhang Z X 2016 Acta Phys. Sin. 65 178705
Google Scholar
[24] Xu Z Y, Gao L J, Chen P Y, Yan L T 2020 Soft Matter 16 3869
Google Scholar
[25] Mishra C K, Rangarajan A, Ganapathy R 2013 Phys. Rev. Lett. 110 188301
Google Scholar
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