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WO2005047575A1 - Structure colloidale et procede de formation - Google Patents

Structure colloidale et procede de formation Download PDF

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Publication number
WO2005047575A1
WO2005047575A1 PCT/SG2004/000369 SG2004000369W WO2005047575A1 WO 2005047575 A1 WO2005047575 A1 WO 2005047575A1 SG 2004000369 W SG2004000369 W SG 2004000369W WO 2005047575 A1 WO2005047575 A1 WO 2005047575A1
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colloidal
phase
frequency
order
domain
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Keqin Zhang
Xiang Yang Liu
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National University of Singapore
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National University of Singapore
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    • C—CHEMISTRY; METALLURGY
    • C30—CRYSTAL GROWTH
    • C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
    • C30B5/00—Single-crystal growth from gels
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
    • B01J13/00—Colloid chemistry, e.g. the production of colloidal materials or their solutions, not otherwise provided for; Making microcapsules or microballoons
    • C—CHEMISTRY; METALLURGY
    • C30—CRYSTAL GROWTH
    • C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
    • C30B29/00—Single crystals or homogeneous polycrystalline material with defined structure characterised by the material or by their shape
    • C30B29/60—Single crystals or homogeneous polycrystalline material with defined structure characterised by the material or by their shape characterised by shape

Definitions

  • the present invention relates to 2D and 3D colloidal structures particularly though not solely to a method of forming colloidal crystals of large size, high stability and low defects.
  • colloidal crystals find application in for example the templating of photonic crystal, optical switching, drug delivery and biosensors.
  • the reversible aggregation of ordered 2D/3D colloidal particles into planar particles adjacent to an electrode surface may be induced by an electric field that is applied normal to the electrode surface. It has been demonstrated that the underlying attractive interaction between particles is mediated by electrokinetic flow (Yeh, Seul and Shraiman, "Assembly of ordered colloidal aggregates by electric field induced fluid flow", Nature 386,57-59, (1997) and US patent no. 6468811).
  • the present invention may be broadly said to consist in a method of identifying optimum electric field conditions for forming a colloidal structure of particles within a solution comprising the steps of: applying an AC electric field to the solution and varying the frequency, applying an AC electric field to the solution and varying the magnitude, identifying an optimum range of frequencies and magnitudes to form said colloidal particle structure.
  • said optimum range is at least partially bounded by at least one phase transition.
  • said optimum range of magnitude is bounded by an infinite order phase transition.
  • said optimum range of frequency is bounded by one or more second order phase transitions.
  • said optimum range is characterised by a particle spacing less than a predetermined threshold.
  • said optimum range is characterised by more than two particles spaced less than a predetermined threshold from one another.
  • said optimum range is further characterised by a particle to particle bond angle within a predetermined range.
  • said optimum range is characterised by said particles not being fluid or disordered.
  • said optimum range is characterised by said particles not being unstable or where the electric field is so high that chemical reaction occur.
  • said optimum range is further characterised by identifying the boundaries between ideally formed and non ideally formed structures.
  • said optimum range is further characterised by identifying the type or order of said phase transitions.
  • said optimum range is further comprised of a vortex ring phase.
  • said optimum range is further comprised of a 3D aggregation phase.
  • said optimum range is further comprised of a 2D hexagonal close packed phase, hi a second aspect the present invention may be broadly said to consist in a method or process of preparing a substantially crystalline colloidal structure (colloidal crystal) between electrodes comprising or including the steps of: selecting a colloid system from which the colloidal crystal will be formed, selecting a electrode AC voltage magnitude and frequency from a preferred domain of magnitude against frequency which gives rise to a substantially stable colloidal crystal, providing an electric field from said electrodes using said selection to prepare the colloidal crystal, which may be in substantially two dimensions or substantially in three dimensions, on or proximal to the surface of one electrode.
  • said preferred domain of electrode potential against frequency is compiled by- conducting at least three experiments/runs of measuring electrode potential against frequency herein there are at least two different potentials applied/used/measured and there are at least two different frequencies applied/used/measured.
  • said preferred domain of electrode potential against frequency is compiled according to any one of the preceding clauses.
  • the step of generally identifying the domain of electrode potential against frequency includes using the results of the at least three experiments/runs to prepare (whether very generally or in detail) a phase diagram showing (whether veiy generally or very accurately) regions of ordered and disordered colloidal behavior.
  • the step of preparing the phase diagram involves observing the pattern of the colloidal assembly with each experiment /ran.
  • the at least three experiments/runs are obtained by the acts of (in no particular, order) holding the AC voltage magnitude substantially constant, varying the frequency and observing the pattern of the colloidal assembly at least once, ' holding the AC voltage frequency substantially constant, varying the voltage and observing the pattern of the colloidal assembly at least once.
  • the step of generally identifying said domain of electrode potential against frequency includes using the results of the at least three experiments/runs to prepare (whether very generally or in detail) a phase diagram showing (whether very generally or very accurately) one or more of: a domain of oscillating chain like behavior of the colloid system a domain of vortex ring behavior of the colloid system a domain of three dimensional aggregation, between the electrodes, within the colloid system a domain of disordered behavior of the colloid system a domain of hexagonally close packed two dimensional formation of a colloidal crystal, between the electrodes, within the colloid system a domain of instability or of the solution chemically reacting.
  • the colloidal crystal may be substantially planar (in two dimensions).
  • the colloidal crystal may be in three dimensions.
  • the colloidal crystal may be a mixture of two and three dimension.
  • the step of selecting the colloid system includes selecting the solvent, concentration, pH, and diameter of colloidal spheres.
  • the step of preparing the phase diagram involves one or more of: knowledge of the distance of separation between the electrodes, knowledge of the volume fraction of the colloids, knowledge of the zeta potential of the colloids, knowledge of the size of the colloids.
  • the diameter of colloidal crystals is at least lOO ⁇ m.
  • Figure la is a block diagram of the experimental setup for assembling two-dimensional colloidal particles by controlling the alternating electric field.
  • Figure lb is a graph of the structure of the 2D colloidal crystal is quantified by the pair correlation function g(r). The position of the first peak of g(r) corresponds to a fixed centre to centre distance between neighbouring particles.
  • the effect on the colloidal crystal structure caused by varying the field strength from 0.9Vp-p to 2.8Vp-p, while keeping the frequency fixed at 600Hz, is illustrated by plotting the g(r) against r/a at 2.8Vp-p, 1.5 Vp-p, 0.9Vp-p.
  • Figure Id is a graph of the supersaturation is examined by the fraction of the area of the electrode occupied by colloidal particles versus the frequency while keeping the voltage fixed at 2.4Vp-p.
  • the nuclei indicated by the yellow circles will be disappearing or shrinking; the nuclei indicated by the red circles will grow and gradually increase in size.
  • the radius of red and yellow circles equals to the critical radius r c at the given supersaturation (2.4Vp-p, 600Hz).
  • t 34t 0 .
  • t 54t 0 .
  • Figure 3b is a graph of n*(t) versus time. After reaching the induction time ⁇ , n*(t) becomes stable, thus allowing the determination of the critical size.
  • Figure 3c is a graph of the number of nuclei having size larger than the critical size at different times. The nucleation rate per unit area can be obtained from the slope of a linear fit to the data points.
  • Figure 3d is a graph of the nucleation rate density versus supersaturation (driving force), hi the main text we show how the edge energy density (line tension) can be calculated from the linear fit to the data points.
  • Figure 4a is view from a microscope of the solution with DC electric field at 3.2V. The FFT in the inset on the upper right comer shows the ring of diffraction.
  • Figure 4b is view from a microscope of the solution with AC electric field at 2.4Vp-p, 600Hz. The FFT in the inset on the upper right comer shows the uninterrupted hexagonal symmetry of the crystal.
  • Figure 5 is a view from a microscope of colloidal particles at the isoelectric point.
  • Figure 6 is a phase diagram of AC electric field strength against frequency.
  • Figure 7 a is a plot of the translational correlational function as a function of strength O E .
  • Figure 7b is a plot of the bond-orientational correlation function as a function of strength O E -
  • Figures 8 a and 8b are In plots of the order parameters ⁇ y and ⁇ 6 against the critical field strength.
  • Figure 9 are In plots of the order parameters ⁇ ⁇ and ⁇ 6 against the critical field strength.
  • Figure 10 is a phase diagram of the order-disorder phase transitions in the space of strength and frequency of an alternating electric field.
  • Figure 11a is a plot of bond-orientational order against field strength at a fixed frequency of 800Hz.
  • Figure 1 lb is a plot of correlation length against field strength at a fixed frequency of 800Hz.
  • Figure l ie is a plot of bond-orientational order against frequency at a fixed field strength of 2.8xl0 4 V/m.
  • Figure l id is a plot of correlation length against frequency at a fixed field strength of 2.8x10 4 V/m.
  • Figure 12a is a log plot of the correlation length against the critical field strength at a fixed frequency of 800Hz
  • Figure 12b is a plot of ln( ⁇ / a) against ln(f-f c ) in the frequency-dependant phase transition at a fixed field strength of 2.8x10 4 V/m.
  • Figure 13 is a plot of the lattice spacing of the colloidal assembly against varying frequencies and varying field strengths.
  • Figure 14a is a view from a microscope of 2D colloidal crystals having a diameter of 5 ⁇ m.
  • Figure 14b is a view from a microscope of 2D colloidal crystals having a diameter of 200 mn.
  • Figure 15 a graph of the Zeta Potential against pH.
  • thermodynamic driving force ⁇ /k ⁇ T.
  • ⁇ is the difference of chemical potential between growth unit in the crystal and the liquid phases
  • k ⁇ denotes Boltzmann's constant
  • T is the absolute temperature
  • h the process of crystal growth this chemical potential difference is well defined, and hence it can be utilized to define the driving force in theoretical fonnations of crystal growth.
  • the present invention will present an in-situ real space microscopic imaging of the 2D nucleation process and the real time measurement of the kinetics for a colloidal system, h particular, the nucleation process will be observed under a well-defined supersaturation controlled by an AC electric field.
  • the growth of dislocation-free (or perfect) crystals is controlled by the 2D nucleation mechanism.
  • the growth of a new layer or the occurrence of steps on a perfect crystal surface will start via 2D nucleation.
  • We will measure the cluster distribution of colloidal spheres at the pre- and post nucleation stages. The transition from the non-steady to the steady state of nucleation can be observed for the first time.
  • Example experiment strategy h one example the present invention employs an alternating current to produce high quality two-dimensional structures.
  • High quality in this case means that the surface exhibits molecular arrangements of a high degree of regularity, and that the domains enclosing such regular an-angements are as large as possible with a minimum amount of defects or other irregularities.
  • end-products with large lattice spacing that is, large distances between the particles, are of relatively good quality.
  • the lattice spacing is small, the quality of the end-products of the prior art is poor, hi contrast, the high quality of the end- product of the present invention is not restricted to a large lattice spacing.
  • the invention provides not only for an improved end-product quality over a much broader range of lattice spacing than the prior art, it also provides for an optimal control of the obtained quality.
  • the present invention involves obtaining the ideal electric field in which the structure forms, h an example experimental strategy both the frequency and the magnitude of the applied voltage or electric field are varied, enabling the user of the invention to obtain an optimal quality under the given experimental conditions.
  • the prior art does not apply such variation.
  • the prior art utilizes low values of voltage magnitude and voltage frequency.
  • the invention provides for a method in which higher voltages and higher frequencies can be applied than is done in the prior art. High voltages are desirable because they allow the production of stractures with short lattice spacing.
  • the optimal quality of the end-product was obtained between 300Hz and 3 kHz, a value lying well above the maximum frequency applied in the prior art. We expect this to be true for the monodispersed system, but. for the binary we expect an ordered phase in the frequency range 20k-200kHz.
  • the prior art also fails at low concentrations, and hence it is limited to introducing high concentrations of particles are in the solution (usually water).
  • the method of the present invention succeeds in producing the desired product at low concentrations.
  • the present method leads to end-products of a quality that is higher than the quality obtained by the prior art at similar concentrations.
  • the prior art teaches application of a single non ideal wave form as the electric field.
  • the voltage wave form may be varied to provide a means of quality control.
  • the parameters which affect the formation of 2D and 3D crystals in a given application are: The size of colloidal spheres The density of colloidal spheres The zeta potentials of colloidal spheres The volume fraction of colloidal spheres in the solutions The type of solvent - ' The pH of the solutions The type and the concentration of electrolytes. Therefore changing any of these will result in different ideal conditions.
  • One strategy is to vary the field strength E and frequency f of the applied electric field, and observe the results using optical microscopy.
  • the applicant has identified that the ideal conditions for a given application may be obtained by applying a customised electric field.
  • This involves identifying at least an optimal voltage magnitude and frequency for a given type of resulting structure. Also throughout the formation these in turn may be varied and/or different wave form shapes applied depending on the desired result.
  • the variable power supply 108 may be manually or automatically varied according to AC voltage magnitude, frequency and / or waveform type, h a further example the supply may be computer of microprocessor controlled to vary the voltage according to a stored program.
  • Supply 108 is connected to parallel plate electrodes 104.
  • the electrodes are ITO glass which allows observation of the solution form the exterior.
  • the electrodes are spaded by spacers 106 to give a uniform electrode gap of desired dimension.
  • the microscope or other optical recorder 102 is situation perpendicular to the electrode to observe formation on the electrode surfaces. For example with ideal AC field one might expect to view hexagonally close packed crystals, and without a disordered pattern 100.
  • a domain may be identified which defines the boundaries of electric field conditions which will allow optimum structure formation 606 as seen in Figure 6. i order to obtain the high quality order colloidal crystals, the chosen electric field 600 should not be to close to the domain boundary 602, or the density of defects will be too high.
  • the field should not be too far from the phase boundary, otherwise the nucleation rate of colloidal crystals will be too high, which will lead to a multi-domain assembly (polycrystalline). Other domains could result in different stractures forming, hi general the liquid state 604 is undesirable. Also by applying too high a voltage an unstable state 608 occurs where the electrodes chemically react with the solution. As well this state is transient or meta-stable and is not desirable for continued use of the cell. Within the desirable state various types of structures may be accommodated by selecting an appropriate magnitude and frequency combination. For example an ordered 3D crystal region 610 can be used as the template for 3D photonic crystals. The chain like phase 612 can be used to fabricate nanowire.
  • the vortex ring 614 and chainlike 612 phases may be applied to electro-rheological fluids.
  • the growth of 3D colloidal crystals may be achieved in one example by growing 2D colloidal crystals in a layer-by-layer manner.
  • V-F phase diagram a) Repeat the step 2 to identify the different phases and phase boundaries. b) Cover the whole E-f (or V-f) regime by changing the voltage and frequency.
  • Nucleation is a dynamic process associated with overcoming a nucleation barrier. It occurs when small crystalline clusters fo ⁇ n from structural when the liquid is in a state of supersaturation. The growth of these clusters depends on the competition between a decrease in bulk energy, which favours growth, and an increase in surface energy (line energy in 2D nucleation), which favours slninlcage. The smallest crystals are continually fo ⁇ ned by fluctuations but then typically shrink away because of the high surface energy. Growth becomes energetically favourable only when the crystallites reach a critical size. According to the 2D nucleation theory,8-10 the nucleation barrier that is the cost of the total (Gibbs) free-energy Gent to fo ⁇ n a critical circular nucleus with radius r c in a supersaturated solution, is
  • the zeta potential of the surface charge of the PS spheres is -26mV.
  • the suspended PS spheres are uniformly dispersed in the water when the electric field is turned off. Once the alternating electric field is applied, the particles are transported to the surface of the electrode by the electric-field-induced fluid flow. Colloidal spheres were assembled in a 2D hexagonal close packing (hep) fo ⁇ ned at the bottom of the cell (see the inset of Fig. la).
  • the driving force for the assembly of 2D crystals is determined by the interaction between the colloidal spheres and the local volume/area fraction of the colloidal spheres, hi order to obtain a well defined supersaturation based on Eq.(3) in describing the nucleation kinetics, we examine the impact of Voltage Magnitude (V) and Voltage Frequency (f) of the applied AC field on the interparticle interaction and on the area fraction, that is the fraction of area covered by the colloidal particles on the surface of the electrode.
  • the interparticle interaction is characterized by the position of the fist peak of the 2D pair correlation function (PCF) g(r).
  • Fig.lb shows the variation of the position of the first peak of g(r) with increasing Voltage Magnitude.
  • V P-P 2.4V
  • E 0.02V/m
  • f 600Hz
  • the critical size of nuclei is the size of the crystalline cluster which allows the crystalline clusters to grow continuously at n>n c (r>r c ).
  • Z*(t) we define Z*(t) to be the number of the largest crystalline cluster at a given time t, which should reach a constant value at n>n c (r>r c ) as shown in Fig.3a.
  • the intercept between Z(t) and Z*(t) gives rise to a critical cluster size n*(f) (see the inset in Fig. 3a).
  • Fig. 3b shows that n*(t) increases with time and reaches a constant value at t> ⁇ .
  • ⁇ is the induction time for the transition from the non-steady state to the steady state
  • n c is the critical nucleation size of a 2D nucleus at the steady nucleation state.
  • D s is the diffusion coefficient
  • nj is the number of single particles (monomers)
  • C is the kinetic coefficient
  • a is the diameter of the colloidal particles.
  • the Image recording setup is shown as Fig. la.
  • the in-situ continuous images are recorded by the digital imaging camera (Photometries, CoolSNAP cf) which is mounted on an Olympus BX51 microscope.
  • the digital imaging camera Photometries, CoolSNAP cf
  • the sequence of images is saved on a hard disc having large volume (120GB) by the image processing software. Based on these real-space images, we can identify the individual colloidal spheres and analyze the continuous process of pre- and post- nucleation.
  • the external fields such as electric and magnetic fields, gravity, structured or confining walls and shear, can guide and manipulate the self-organization of the colloidal particles in desired directions.
  • the controls of the colloidal systems involving electric fields are especially popular topics of research.
  • the response of charged particles dispersed in water to the influence of electric fields remains a mystery and is opposite to what is expected from electrostatic considerations, especially in cases when the particles also interact strongly with each other.
  • alternating electric fields have been found to organize colloidal dispersions into such complex configurations as circulating chevron bands oblique to the field, vortex rings perpendicular to the field, super lattice stractures in the binary system, and even colloidal crystals, hi particular, particles driven by electric fields onto the surface of an electrode develop long-range in-plane attractions strong enough to induce two-dimensional (2D) crystallization. It was suggested by Trau et al. (Trau,
  • the present invention allows the first measurement of the phase diagram of colloidal patterns obtained by varying the field strength ⁇ E and frequency/ of a vertical AEF.
  • a wide range of patterns such as oscillatory interlinked chains, oscillatory vortex ring, three-dimensional (3D) aggregation and crystalline monolayer are generated by an alternating electric field.
  • 3D three-dimensional
  • PS monodisperse colloidal polystyrene
  • both the lower and the upper glass coverslips are coated with a thin layer of fridium Titanium Oxide (ITO, ⁇ 100nm), while they are still optically thin and allows for the application of uniform vertical electric fields to the confined suspension.
  • ITO fridium Titanium Oxide
  • This simple setup gives rise to a complicated coupling among hydrodynamic flows and reaction-diffusion of ions and colloidal particles in the electric field.
  • the sample cell is mounted on an optical microscope (Olympus BX51) so that the motions of colloidal particles can be recorded with a digital CCD camera connected to a computer.
  • AEF is applied.
  • a detailed ⁇ E ⁇ / phase diagram of colloidal suspensions from a 2D crystal, a 3D aggregation, oscillating vortex rings and chains is given in Figure 6 and its insets.
  • ⁇ E ⁇ 0.9x 10 4 V / m the response of the colloidal spheres is quite slow, and insensitive to the field (not shown in the figure).
  • the phase is in the liquid state as shown at 604.
  • the transition to dynamical patterns occurs at a field strength ⁇ E exceedinglxl0 4 K /m , thus the regions involving chains, oscillating vortex rings, three- dimensional aggregation and the ordered colloidal monolayer occur subsequently within different frequency domains.
  • the spheres will nucleate and grow to two- dimensional highly-ordered colloidal crystals when the appropriate AEF is applied; while in reference 616, the disordered 3D aggregation of particles is formed under an electric field of lower frequency ( ⁇ E - 2.4y. ⁇ 0 ⁇ V I niif - 100Hz) .
  • the interior of the aggregation region is invisible under the optical microscope.
  • the patterns shown in references 606 and 616 are stationary unlike references 612 and 614.
  • a strength-dependent phase transition from the liquid state to the crystalline monolayer occurs at a constant frequency/ as the strength ⁇ E increases (the cross dot in Figure 6).
  • the translational con-elation function g(r) and bond- orientational con-elation function g 6 (r) were computed from the data of the central-mass positions of the particles, as dete ⁇ nined by the digitized and processed images.
  • Figures 7 A and B show the plots of g(r) and g 6 (r) as functions of strength ⁇ E .
  • a dramatic change of the translational order and angular order is observed as the strength ⁇ E decreases gradually.
  • the peaks of g(r) become discrete and smoothened off, converging to 1.
  • the curve of g 6 (r) decays rapidly from 1 to 0.
  • the g(r) and g 6 (r) functions of computer-generated hexagonal lattices are displayed in Figure 7
  • g(r) is composed of the discrete delta peaks at certain distances r and approaches 1 at the infinite distance.
  • g 6 (r) comprises discrete constants (equal to 1) at certain distances.
  • FIG. 8b As shown in the phase diagram ( Figure 6), the disorder-order phase transition occurs on the phase boundary of the 2D colloidal crystals.
  • the experimental data of the order parameters can be fit very well by the above exponential function with the given fitting parameters.
  • Such an infinite-order type or Kosterlitz-Thouless type of order-disorder phase transition has never been observed in real systems before.
  • the richness of the phases and phase behaviours of colloidal assembly controlled by an AEF has given rise to interesting fundamental questions of condensed matter.
  • the remarkable and unexpected results of the investigation of the field-strength-dependent phase transition in the colloidal system presents a real model system for the infinite-order phase transition, which is only predicted by the theoretical models or simulations.
  • the present system significantly extends the use of colloids as condensed matter model systems.
  • the different colloidal phases with the control of external fields are being used in the realization of new materials.
  • the rich colloidal patterns that can be produced by achieving an increased manipulation by the external field will lead to important extensions of model systems for condensed matter and creation of new functional materials.
  • phase Transitions The solid-liquid phase transition is one of the fundamental topics in condensed matter physics. Its study has received new impulses since phase transitions can be observed on a microscopic level by accompanying the development of direct imaging in model system of colloids. Unlike the atoms in conventional materials, the individual spheres can be imaged with a conventional light microscope on time scales compatible with standard video equipment and microscopic structure and dynamics of colloidal suspensions can be studied with "atomic" resolution. The frontiers investigated the phase transitions of 2D colloidal system and found qualitative consistency with a two-step melting transition through a hexatic phase, which still exhibits quasi-long-range orientational order but only short-range translational order.
  • G denotes a reciprocal-lattice vector of the solid, and ⁇ (r y ) is the angle between the bond connecting particles i and j and an arbitrary fixed reference axis.
  • ⁇ ⁇ is the con-elation length which are defined the exponentially-decayed exponents of g(r) : e ⁇ rl ⁇ r
  • ⁇ 6 is the characteristic exponents of power-law-decayed g 6 (r) : r ⁇ 6 .
  • the translational conelation length ⁇ ⁇ of g(r) is quite large ( ⁇ 40 ⁇ ) and bond-orientational order ⁇ 6 is a near-zero value; for the isotropic liquid, ⁇ ⁇ is close to a and ⁇ 6 is larger than 0.25.
  • a is the lattice spacing.
  • the linear fitting parameter ⁇ is exactly equal to 2.09 + 0.03 indicating that the appropriate asymptotic fonn for ⁇ ⁇ is ⁇ ⁇ la : (f - f c ) 2 .
  • the first order derivative of the function of the conelation length ⁇ r (f) is still continuous. That means the frequency- dependent phase transition is a second-order phase transition.
  • the strength and frequency of an alternating electric field can induce two different phase behaviours which have the different characters. The essential physics in these phase behaviours is a subtle difference of interaction between the colloidal particles. When decreasing the strength with a fixed frequency, the crystalline monolayer starts to expand and simultaneously the coordinates of particles are distorted compared to the highly- ordered lattice.
  • the lattice spacing of the 2D crystallites increases and expands to 25% than the most compact lattice before transferring to the isotropic liquid.
  • the 2D crystallites keep their lattice until the frequency anive a critical value. After that, the lattice will dismiss and return to disorder state quickly.
  • the lattice spacing remains constant throughout the range of frequency.
  • a(f) is the polarizability of the sphere and can be expressed as: ⁇ 0 and / 0 are the static polarizability and eigenfrequency respectively.
  • the dipole-dipole interaction between the pair of particles can be given by P. -P. ⁇ - r -. (5)
  • the eigenfrequency of the spheres should have a range of distribution ⁇ / 0 .
  • the polarizability is a nonmonotonic function of frequency.
  • the dipole moment P has the same sign. According to Eqs. (3)-(5),. the interaction is repulsive (U t . > 0).
  • phase transitions Described above are two scenarios of colloidal phase transitions induced by the field strength and frequency of an alternating electric field respectively. It is surprising that the strength-dependent phase transition is an infinite-order phase transition, whereas the frequency-dependent phase transition is a second-order phase transition. This very interesting fact may be induced by the subtle competition of two parameters of external electric field. This experimental accessibility coupled with their rich and varied phase behaviour set colloidal suspensions apart as an unusually powerful class of model systems for studying the microscopic processes underlying structural phase transitions.
  • the methods of the present can produce particle sizes from 200nm to 5 ⁇ m .
  • the 2D colloidal crystals can be obtained with the particles of 200nm and 5 ⁇ m . While this is the range produced experimentally, it is not to limit the range of particle sizes produced by the method of the invention. It is envisioned that the present invention may be employed for the nano scale assembly of colloidal particles. hi Figure 5 we see that at the isoelectric point (where the colloidal particles are nearly neutral), the particles only form the short chains under an alternating electric field.
  • the value of zeta potential represents the density of the surface charge of the particles (the sign of zeta potential corresponds to the sign of charge of particles).
  • the zeta potential can be changed by altering the pH or the ionic strength of the suspension.
  • the titration curve and the pattern of neutral particles are presented in Figure 15. It appears that lower zeta potentials can not facilitate the assembly of 2D colloidal crystals, and the sign of the zeta potential has no. affect on the experimental results.
  • the value of zeta potential equals to zero at certain pH value. From the curve in Figure 15, we can see the zeta potential can change from the positive to negative.
  • the prior art is restricted to monodisperse and binary mixtures, whereas the present method is applicable to mondisperse mixtures of particles. It is also possible to extend the present invention to binary as well as polydisperse mixtures.
  • the prior art utilizes flat surfaces that are parallel or inclined at an angle, i.e. the flat surfaces need not be parallel, whereas the present invention provides for an improved method of preparing an improved end-product on flat surfaces. It is possible to extend the present invention to non-parallel flat surfaces. It is additionally possible to control the shape of the surface by extending the present invention to curved surfaces, that may be concave or convex. Nowhere in the prior art are curved surfaces introduced, whereas, the present invention is applicable for curved surfaces applications for which flat surfaces are inappropriate.
  • the present invention provides a way of controlling the symmetry properties of the two-dimensional stracture.

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  • Engineering & Computer Science (AREA)
  • Crystallography & Structural Chemistry (AREA)
  • Materials Engineering (AREA)
  • Metallurgy (AREA)
  • Chemical Kinetics & Catalysis (AREA)
  • Crystals, And After-Treatments Of Crystals (AREA)

Abstract

L'invention concerne un procédé d'assemblage de particules colloïdales chargées entraînées par un champ électrique alternatif (AEF). Ce système permet l'imagerie directe et l'observation in situ du processus de nucléation et, en particulier, du processus de prénucléation, qui sont explorés en espace réel par un microscope à lumière. En suivant leur évolution, un ensemble de paramètres de nucléation importants peuvent être mesurés sous différentes forces motrices. Les avantages de ce système sont la visualisation directe du processus de nucléation pour l'assemblage de particules colloïdales et un meilleur contrôle du niveau de perfection des cristaux sur la base d'une force motrice bien définie.
PCT/SG2004/000369 2003-11-12 2004-11-12 Structure colloidale et procede de formation Ceased WO2005047575A1 (fr)

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US8263129B2 (en) 2003-12-19 2012-09-11 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro-and nano-structures using soft or imprint lithography
US9040090B2 (en) 2003-12-19 2015-05-26 The University Of North Carolina At Chapel Hill Isolated and fixed micro and nano structures and methods thereof
JP2016147348A (ja) * 2015-02-12 2016-08-18 秋田県 ゼータ電位制御法を用いた処理方法
US9849464B2 (en) 2014-04-18 2017-12-26 The Regents Of The University Of Michigan Devices and methods for spatially and temporally reconfigurable assembly of colloidal crystals
US10465091B2 (en) 2015-04-27 2019-11-05 The Regents Of The University Of Michigan Durable icephobic surfaces
CN114637196A (zh) * 2020-12-15 2022-06-17 帕洛阿尔托研究中心公司 用于借助于数字计算机进行的机器学习实现的微对象密度分布控制的系统和方法
US11965112B2 (en) 2018-03-05 2024-04-23 The Regents Of The University Of Michigan Anti-icing surfaces exhibiting low interfacial toughness with ice

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Publication number Priority date Publication date Assignee Title
US9877920B2 (en) 2003-12-19 2018-01-30 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro- or nano-structures using soft or imprint lithography
US10842748B2 (en) 2003-12-19 2020-11-24 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro- or nano-structures using soft or imprint lithography
US8992992B2 (en) 2003-12-19 2015-03-31 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro- or nano-structures using soft or imprint lithography
US9040090B2 (en) 2003-12-19 2015-05-26 The University Of North Carolina At Chapel Hill Isolated and fixed micro and nano structures and methods thereof
US9902818B2 (en) 2003-12-19 2018-02-27 The University Of North Carolina At Chapel Hill Isolated and fixed micro and nano structures and methods thereof
US8263129B2 (en) 2003-12-19 2012-09-11 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro-and nano-structures using soft or imprint lithography
US10517824B2 (en) 2003-12-19 2019-12-31 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro- or nano-structures using soft or imprint lithography
US11642313B2 (en) 2003-12-19 2023-05-09 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro- or nano-structures using soft or imprint lithography
US8420124B2 (en) 2003-12-19 2013-04-16 The University Of North Carolina At Chapel Hill Methods for fabricating isolated micro- and nano-structures using soft or imprint lithography
US9849464B2 (en) 2014-04-18 2017-12-26 The Regents Of The University Of Michigan Devices and methods for spatially and temporally reconfigurable assembly of colloidal crystals
JP2016147348A (ja) * 2015-02-12 2016-08-18 秋田県 ゼータ電位制御法を用いた処理方法
US10465091B2 (en) 2015-04-27 2019-11-05 The Regents Of The University Of Michigan Durable icephobic surfaces
US11965112B2 (en) 2018-03-05 2024-04-23 The Regents Of The University Of Michigan Anti-icing surfaces exhibiting low interfacial toughness with ice
CN114637196A (zh) * 2020-12-15 2022-06-17 帕洛阿尔托研究中心公司 用于借助于数字计算机进行的机器学习实现的微对象密度分布控制的系统和方法

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