Ⅴ OLUME85. NUMBER25 PHYSICAL REVIEW LETTERS i 8 DECEMBER 2000 Planar Magnetic Colloidal Crystals Weijia Wen, Lingyun Zhang, and Ping Sheng Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China ( Received 14 June 2000) We report a novel form of planar magnetic colloidal crystals formed by coated magnetic microspheres floating on a liquid meniscus. Under an external magnetic field, the magnetic interaction and the"" interaction, due to the weight of rticles projected along the surface tangent, yields not only the triangular lattice with a variable lattice constant, but also all the other planar crystal symmetries such as the oblique, centered-rectangular, rectangular, and square lattices. By using two different sized magnetic particles, local formations of 2D quasicrystallites with fivefold symmetry are also observed. PACS numbers: 82.70. Kj, 64.70 Kb, 75.50. Mm, 83.80.Gv Since its discovery more than two decades ago, colloidal spheres [19]. The scanning electron microscope images crystals have blossomed into a fertile area of research indicate the Ni coating to be uniformly deposited, shown tion of three-dimensional mesocrystals, i.e., crystals with formed by dispersing 52-um-sized coated mi crystals were crons [1-11]. More recently, two-dimensional, or planar, diameter of I cm. The bottle ed in a glass bottle with a lattice constants ranging from submicrons to tens of mi- the surface of glycerin, contai placed in a rotatable colloidal crystals have been observed through a number aluminum stage located in the center region of a pair of of self-assembly techniques such as magnetic hole formed Holmholz coils, where the magnetic strength of coils was with nonmagnetic particles in a ferrofluid [12], field- adjusted by a computer-controlled current source. In order induced assembly of floating magnetic particles [13]. to change direction of magnetic field relative to the liquid electric-field-induced planar crystal [14], and surfactant- surface, the Helmholz coil can rotate freely along its di- mediated colloid 15]. In particular, two- ameter. Lattice formation and transitions were monitored dimensional magnetic colloidal crystals have afforded and recorded by a video system fundamental studies on 2D melting and crystallization, In the absence of a magnetic field, the coated micro- mediated with the hexatic phase [16] spheres aggregate in the center region of the slightly curved In this Letter, we report the unexpected discovery that liquid surface, visible in the upper inset in Fig. 1. Whe in a certain parameter range of monodispersed magnetic a perpendicular magnetic field was applied, the spheres particles, two-dimensional(2D)crystals can be formed move radially outward and form a stable hexagonal lattice on a fluid surface with not just the(hexagonal) triangular The entire process of hexagonal lattice formation is shown lattice, but also with all the other planar crystal symme- in the lower insets in Fig. 1, where the lattice constant is tries such as the oblique, centered-rectangular, rectangular, noted to increase monotonically as a function of the field and square lattices [17]. These lattice structures, some of strength. This behavior clearly indicates a competition be- which are metastable, can be reversibly tuned by adjusting tween the repulsive magnetic interaction and the"attrac the polar and azimuthal angles of the magnetic field rela- tive"interaction due to the weight of the particles projected ive to the surface normal and the symmetry direction of along the surface tangent. Such competition is possible the 2D lattices. Furthermore, by using two different sized because the attractive and repulsive interactions are on the magnetic particles, local formations of 2D quasicrystal- same order due to the fact that the magnetic interaction lites with fivefold symmetry were observed. Theoretical which depends on the coating thickness, and the weight of predictions based on energy considerations are shown to the sphere, which depends on the sphere di in good agreement with the experiments separately controlled in our system. Quantitative predic The spherical magnetic particles are fabricated by coat- tions based on this simple picture, given below, are shown ing 52(+2)-um and 26(+2)-um-sized glass spheres with to give excellent agreement with the experiment. 2-um and 1.5-um-thick nickel layers, respectively. In B the boundary condition and the Laplace order to obtain magnetic microspheres with controllable formula, the sha surface can be deduced as moments, we selected uniform glass microspheres with zoLlo(Ar)-1/o(Aro)-ll, where z denotes the sur- two different sizes as the initial cores and coated a thin face height, with z=0 at the center of the surface r =0, layer of nickel using the electroless plating technique [18]. Io(x)is the zeroth order modified Bessel function of the The nickel-coated microspheres were heated in a vacuum first kind, A=peg/o, where pe=1.26 x 10 kg/m3 chamber at 400C for 2 h and then annealed at 550C denotes the mass density of glycerin, g denotes the for 3 h. The annealed microspheres possess a small mag- gravitational acceleration, and o=63. 4 mJ/m2 denotes netic moment, on the order of 10 emu for the larger the surface tension. Here the maximum depth of liquid 0031-9007/00/85(25)/5464(4)$15.00 O 2000 The American Physical SocietyVOLUME 85, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 18 DECEMBER 2000 Planar Magnetic Colloidal Crystals Weijia Wen, Lingyun Zhang, and Ping Sheng Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China (Received 14 June 2000) We report a novel form of planar magnetic colloidal crystals formed by coated magnetic microspheres floating on a liquid meniscus. Under an external magnetic field, the balance between the repulsive magnetic interaction and the “attractive” interaction, due to the weight of the particles projected along the surface tangent, yields not only the triangular lattice with a variable lattice constant, but also all the other planar crystal symmetries such as the oblique, centered-rectangular, rectangular, and square lattices. By using two different sized magnetic particles, local formations of 2D quasicrystallites with fivefold symmetry are also observed. PACS numbers: 82.70.Kj, 64.70.Kb, 75.50.Mm, 83.80.Gv Since its discovery more than two decades ago, colloidal crystals have blossomed into a fertile area of research encompassing diverse approaches for controlled fabrica￾tion of three-dimensional mesocrystals, i.e., crystals with lattice constants ranging from submicrons to tens of mi￾crons [1–11]. More recently, two-dimensional, or planar, colloidal crystals have been observed through a number of self-assembly techniques such as magnetic hole formed with nonmagnetic particles in a ferrofluid [12], field￾induced assembly of floating magnetic particles [13], electric-field-induced planar crystal [14], and surfactant￾mediated colloid crystals [15]. In particular, two￾dimensional magnetic colloidal crystals have afforded fundamental studies on 2D melting and crystallization, mediated with the hexatic phase [16]. In this Letter, we report the unexpected discovery that in a certain parameter range of monodispersed magnetic particles, two-dimensional (2D) crystals can be formed on a fluid surface with not just the (hexagonal) triangular lattice, but also with all the other planar crystal symme￾tries such as the oblique, centered-rectangular, rectangular, and square lattices [17]. These lattice structures, some of which are metastable, can be reversibly tuned by adjusting the polar and azimuthal angles of the magnetic field rela￾tive to the surface normal and the symmetry direction of the 2D lattices. Furthermore, by using two different sized magnetic particles, local formations of 2D quasicrystal￾lites with fivefold symmetry were observed. Theoretical predictions based on energy considerations are shown to be in good agreement with the experiments. The spherical magnetic particles are fabricated by coat￾ing 52
62-mm and 26
62-mm-sized glass spheres with 2-mm and 1.5-mm-thick nickel layers, respectively. In order to obtain magnetic microspheres with controllable moments, we selected uniform glass microspheres with two different sizes as the initial cores and coated a thin layer of nickel using the electroless plating technique [18]. The nickel-coated microspheres were heated in a vacuum chamber at 400 ±C for 2 h and then annealed at 550 ±C for 3 h. The annealed microspheres possess a small mag￾netic moment, on the order of 1026 emu for the larger spheres [19]. The scanning electron microscope images indicate the Ni coating to be uniformly deposited, shown in the lower inset in Fig. 1. Planar colloidal crystals were formed by dispersing 52-mm-sized coated microspheres on the surface of glycerin, contained in a glass bottle with a diameter of 1 cm. The bottle was placed in a rotatable aluminum stage located in the center region of a pair of Holmholz coils, where the magnetic strength of coils was adjusted by a computer-controlled current source. In order to change direction of magnetic field relative to the liquid surface, the Helmholz coil can rotate freely along its di￾ameter. Lattice formation and transitions were monitored and recorded by a video system. In the absence of a magnetic field, the coated micro￾spheres aggregate in the center region of the slightly curved liquid surface, visible in the upper inset in Fig. 1. When a perpendicular magnetic field was applied, the spheres move radially outward and form a stable hexagonal lattice. The entire process of hexagonal lattice formation is shown in the lower insets in Fig. 1, where the lattice constant is noted to increase monotonically as a function of the field strength. This behavior clearly indicates a competition be￾tween the repulsive magnetic interaction and the “attrac￾tive” interaction due to the weight of the particles projected along the surface tangent. Such competition is possible because the attractive and repulsive interactions are on the same order due to the fact that the magnetic interaction, which depends on the coating thickness, and the weight of the sphere, which depends on the sphere diameter, can be separately controlled in our system. Quantitative predic￾tions based on this simple picture, given below, are shown to give excellent agreement with the experiment. By using the boundary condition and the Laplace formula, the shape of surface can be deduced as z
z0I0
lr 2 1I0
lr0 2 1, where z denotes the sur￾face height, with z
0 at the center of the surface r
0, I0
x is the zeroth order modified Bessel function of the first kind, l
p r
gs, where r

1.26 3 103 kgm3 denotes the mass density of glycerin, g denotes the gravitational acceleration, and s
63.4 mJm2 denotes the surface tension. Here the maximum depth of liquid 5464 0031-90070085(25)5464(4)$15.00 © 2000 The American Physical Society