Abstract

Traditionally, the vertical convective self-assembly method (VCSA) uses time-invariant temperature conditions to obtain high-quality colloidal crystal (CC) films, leaving unexplored possible effects due to temperature variations during the elaboration process. Here, the quality of colloidal crystal films grown by the VCSA method when applying temperature ramps is investigated. This study is conducted by combining experimental measurements and simulations of concentration profile and meniscus displacement, using the temperature dependent Kynch’s theory. The quality of the elaborated CC films is evaluated by analyzing the resulting optical Bragg diffraction. Colloidal crystal films deposited under controlled parameters showed that high-quality films can be achieved by positioning the meniscus into the uniform zone under temperature ramping, as a definite relation between sedimentation velocity and evaporation rate, in agreement with modelling results.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Colloidal crystals (CC) are highly ordered three-dimensional periodic structures, typically conformed by SiO2 or polystyrene spheres, with diameters in the range of 100-1000 nm that exhibit a unique photonic band structure. Among their unique optical properties of CC, one of particular importance is the presence of a photonic bandgap, which prevents light propagation at specific wavelengths and directions. The CC’s bandgap has attracted attention of organic light-emitting diodes and solar cells industry, given their potential to promote either trapping or extraction of light inside the constitutive layers of these optical devices [15]. Incorporating CC’s bandgap in layered optical devices requires a fabrication method that provides not only a high control of the CC’s quality, but also compatibility with the fabrication parameters involved in the device layering process [6]. There are several reports concerning CC’s fabrication methods [710], from which the vertical convective self-assembly (VCSA) method stands out. This is probably due to extensive experimental studies correlating CC’s quality with a wide range of fabrication parameters [1120], such as humidity, pressure, temperature, colloidal suspension concentration, spheres size, and solvent volatility; among others, that allow to have a better control for improving the quality of CC films.

The VCSA method is a solvent evaporation-induced process that creates a convective fluid flow through closely packed spheres dragged into the top region of a meniscus, which is formed by vertically submerging a hydrophilic substrate into a colloidal suspension of microspheres (Fig. 1(a)). In this method, a crystallization process can occur, resulting in a thin film formed by an ordered stacking of spheres that predominantly exhibit a face-centered cubic (FCC) lattice [21,22]. Films with a high degree ordering of spheres are considered colloidal crystals and show at glance opalescence, angle-dependent bright, and intense colors due to Bragg’s law. In contrast, a low degree of ordering yields into white opaque films without remarkable optical properties. The degree of spheres ordering determines CC quality, which mainly depends on i) interactions between capillary forces responsible of the spheres close packing, and ii) balance between solvent evaporation and sphere sedimentation rates, which determines distribution of the spheres into the meniscus [2124]. Understanding the underlying mechanisms that govern these interactions is the key of the current crystal growth models [22,23,2527], which support the design of CC in terms of elaboration parameters in the VCSA method.

 figure: Fig. 1.

Fig. 1. (a) Vertical convective self-assembly diagram. (b) Concentration profiles of colloidal suspensions during sedimentation. (c) Experimental parameters applied for colloidal crystal growth.

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One of the fundamental VCSA fabrication parameters that plays a significant role in the crystallization process is temperature [15,19,20,28]. Rising temperature increases the evaporation rate [12,20], which affects the balance between evaporation and spheres sedimentation rate. Evaporation rate far above or below the sedimentation rate causes, respectively, excessive agglomeration [15] or absence of spheres in the meniscus, in detrimental of the crystallization process. Additionally, strong variations on spheres concentration in the meniscus during film growth can also promotes formation of crystal defects. Therefore, temperature must be kept in a suitable value such that evaporation and sedimentation rates are similar [28], and spheres concentration in the meniscus remains nearly constant. Estimating a suitable temperature value is usually experimentally achieved by evaluating the CC’s quality of diverse films grown at different temperature values (remaining constant during the process) [15,20]. Instead, here it is proposed an alternative way to estimate the proper temperature value, by modelling simultaneously sedimentation and evaporation rates as a function of temperature. However, this task represents a challenge due to the complex balance of the involved inter-particle hydrodynamic forces, as well as the interactions between medium and particles, during the sedimentation process of colloidal suspensions.

The sedimentation process in a colloidal suspension can be modeled by performing batch settling experiments in a vessel [29,30]. These experiments allow studying the suspension microstructure, i.e., the spatial and temporal distribution of particles. In general, five main forces are driving the suspension microstructure [31]: diffusion (Brownian), dispersion (Van der Waals), electrostatic, viscous, and inertial. Although dispersion and electrostatic forces affect suspension microstructure, they are usually balanced, considering that the colloidal suspension remains stable against spheres agglomeration and flocculation processes. This is experimentally achieved by varying the suspension pH level [32]. Balance between remaining forces depends on the characteristics of the colloidal suspension system, and is commonly described by Reynolds (${R_e}$) and Peclet numbers (${P_e}$) [31]. Viscous to inertial forces ratio is described by ${R_e}$, whereas ${P_e}$ correlates diffusion and viscous forces. At low ${R_e}$ values (${R_e} \ll 1$), viscous force is several orders of magnitude above inertial force. Therefore, the effect of the latter in the sedimentation process is negligible. At high ${P_e}$ values (${P_e} \gg 1$), viscous force overcomes diffusion force, counteracting the effect of Brownian motion that prevents spheres sedimentation. Stable colloidal suspension systems conformed by water-diluted suspensions (< 4 vol%) of small (< 1 µm in diameter) monodispersed (< 3%) rigid spheres, presents low ${R_e} \approx {10^{ - 4}}$ and high ${P_e} \approx {10^7}$ values [22], indicating that suspension microstructure is mainly driven by viscous force, which in turn depends on Stokes velocity.

Suspension microstructure presents gradients of concentration, known as concentration profiles. For the colloidal systems studied here, concentration profiles show three well-defined regions (Fig. 1(b)): i) absence of spheres (pristine fluid), ii) spheres settling at the initial concentration (uniform) and iii) close-packed sedimented spheres (sediment). Depending on ${R_e}$ and ${P_e}$ values, the profiles could present transition regions between pristine-uniform and uniform-sediment interfaces. For the case in which ${R_e} \ll 1$ and ${P_e} \gg 1$, concentration profiles exhibit strong transient regions (discontinuities) in both interfaces. At the pristine-uniform interface, particles settle at lower concentration than the initial. Conversely, particles settle in higher concentration than the initial at uniform-sediment interfaces. Here, in the VCSA method it is considered that the degree-of-sharpness of transients in concentration profiles plays a relevant role during growth of colloidal crystals. Thus, to ensure a constant concentration of particles in the meniscus, it should be located at the uniform zone, away of transient zones, consequently improving the quality of CC films.

Regarding the VCSA method, there are reports of high-quality CC films using only time-invariant temperatures during fabrication [15,19,20,28]. This indicates that there is a wide range of fabrication parameters available for successfully positioning the meniscus in the uniform zone and hence, to keep an adequate balance between evaporation and sedimentation rates. However, the effects on the quality of CCs grown by VCSA method, induced by applying time-dependent temperatures, remains unknown. They are explored in this work by applying temperature ramps during film growth, at different concentrations of the colloidal suspension (Fig. 1(c)). The CC quality is determined by contrasting angle-resolved transmittance spectroscopy (A-RTS) measurements with respect to the optical Bragg diffraction expected from a theoretical stacking of 230 nm spheres in an ideal FCC lattice. Furthermore, the impact of temperature ramps on the balance between evaporation and sedimentation rates is assessed here, by considering temperature as a time-dependent variable for modeling: i) Sedimentation concentration profiles of the colloidal suspension using Kynch’s theory, and ii) Meniscus displacement during film elaboration. The time-dependent temperature conditions implemented in this work represents an alternative control parameter for obtaining high-quality CC films. Moreover, the methodology for evaluating the balance between sedimentation and evaporation rates proposed here, constitutes a tool towards modelling the CC quality in the VCSA method for diverse sphere sizes, solvents, and applied temperatures.

2. Experimental section

2.1 Colloidal suspensions preparation

Colloidal suspensions are obtained by dispersing previously filtered SiO2 nanospheres (230 ± 13 nm diameter, ÅngströmSphere) into deionized water (Milli-Q water, 0.056 mS/cm). The dispersion is process is conducted by sonication for 2 h, using cycles of 15 min each, with switching off intervals of 5 min to avoid overheating. Spheres concentration levels used for the preparation of colloidal suspensions are set to CL1 = 0.05 vol%, CL2 = 0.1 vol%, CL3 = 0.26 vol%, and CL4 = 0.42 vol%. Suspensions are sonicated during 20 min prior to each experiment, to ensure a freshly dispersion. Finally, the colloidal suspensions are stabilized by setting the pH level to 8 in order to avoid precipitation of spheres caused by low pH levels [32]. The pH level of the colloidal suspension is tuned by adding hydrochloric acid (0.1N, HCl) and sodium hydroxide (0.1N, NaOH).

2.2 Colloidal crystal film growth

Colloidal crystal films are deposited onto glass substrates using vertical convective self-assembly method [12] as shown in Fig. 1(a). In this method, a hydrophilic glass substrate is vertically positioned into a 30 ml volume vial, which contains a stable colloidal suspension of SiO2 spheres dispersed into deionized water (Milli-Q water) at a fixed concentration. The vial is then placed inside of a vibration-free furnace (Terrigeno furnace Mod L2) programmed with a time-dependent temperature condition (see Eq. (1)) using a PID controller. The applied temperature conditions are monitored using K-type thermocouples following the procedure described elsewhere [33]. The CC films are obtained using a 3 × 4 experimental design where the applied temperature conditions and the spheres’ concentration are varied using 3 and 4 levels, respectively, for a total of 12 combinations. For each combination, three sample replicas were prepared to obtain a complete set of 36 samples. The applied time-dependent temperature conditions (TLi(t)) follow the equation:

$${T_{Li}}(t )= \{ \begin{array}{cc} {\alpha t + {T_0},\,\quad t \le {t_{fi}}}\\ {{T_{fi}},\quad \quad t > {t_{fi}}} \end{array}, $$
where α = 0.5°C/h is the applied temperature ramp, T0= 25°C is the initial temperature of the ramp (room temperature), Tfi and tfi are the temperature and time in which the ramp ends, respectively. As shown in Fig. 1(c), each level of TLi(t) is denoted by the index $i$=1, 2, 3. Thus, for level $i$=1, it was applied TL1(t), with Tf1 = 40°C and tf1 = 30h; for level $i$=2, TL2(t) is set with Tf2 = 60°C and tf2 = 70h; and level $i$=3 corresponds to TL3(t), using Tf3 = 80°C and tf3 = 110h. All experiments started at a room temperature of 25°C and finished until full evaporation of the colloidal suspension was achieved, leaving a film coating on the substrate with an approximate length of 42.22 mm. The temperature ramp α = 0.5°C/h is selected to guarantee a smooth change on the temperature increment, thus avoiding undesired temperature variations that could affect negatively the crystallization process.

2.3 Colloidal crystal film characterization

The deposited CC films are optically characterized by angle-resolved transmission spectroscopy [34,35] (A-RTS) measurements. The beam-spot was located close to the middle of the sample substrate, i.e., nearly 20 mm from the bottom of the elaborated sample, as shown in Fig. 2(a). The A-RTS measurements are performed using a halogen lamp as light source. A sample holder mounted on a goniometer allows to set the incident angle for transmission measurements on CC films, and a computer controlled monochromator system equipped with a lock-in amplifier collects the transmitted beam signal from a photomultiplier tube [33].The A-RTS of a colloidal crystal exhibits an optical spectrum of the transmitted light beam, with an angular dependency described by the first-order Bragg’s law [33], which can be expressed in a linear form as:

$$\lambda _m^2 = 4{h^2}({n_e^2} )- 4{h^2}({{{\sin }^2}\theta } ), $$
where λm is the wavelength of the first-order diffraction peak, h is the distance between reflecting adjacent planes, θ is the angle between the incident light beam and the plane normal to the CC surface, and ne is the effective refractive index of the structure.

 figure: Fig. 2.

Fig. 2. (a) Optical characterization of CC films using A-RTS. (b) Typical A-RTS spectra of a CC film obtained at 0.5°C/h during 110 h with a volume fraction of 0.24 Vol% at incident angles of 0$^\circ $ (blue), 10$^\circ $ (red), 25$^\circ $ (yellow), and 40$^\circ $ (purple). (c) Bragg’s law dependency of A-RTS spectra (blue line) and RMSE estimation using an ideal FCC colloidal crystal as reference (black line).

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According to Eq. (2), a linear curve is obtained by plotting λ2m as a function of sin2θ. Here, this curve is calculated by extracting the λm values from the peaks of the A-RTS spectra, measured at incident angles of θ = $0^\circ $, $10^\circ $, $25^\circ $ and $40^\circ $ (Fig. 2(b)). The peaks are computationally extracted from the spectra by finding the local minima in the interval of 400 nm to 540 nm. The local minima are obtained by first calculating the points in which the slope of the spectra is equal to zero using the first derivate of the function. Then, the point corresponding to a local minimum is selected by applying the second derivate. The quality of the elaborated CC films is estimated by calculating the root mean square error (RMSE) between the experimental data (blue line on Fig. 2(c)) and the theoretical (black line on Fig. 2(c)) Bragg’s curves, as shown in the inset of Fig. 2(c). In particular, the ideal Bragg curve used here as reference, is obtained by considering a colloidal crystal of SiO2 spheres with a face-centered cubic (FCC) crystalline structure. The resulting effective refractive index ne is given by [33]:

$${n_e} = \sqrt {({1 - f} )n_{air}^2 + fn_{Si{O_2}}^2} , $$
where, nair = 1 is the refractive index of the air, nSiO2 = 1.45 is the bulk refractive index of silica [33], and f = 0.74 is the fill factor of a close-packed FCC crystal. For this stacking, the distance between reflecting adjacent planes is $h = d\sqrt {2/3} $, with a sphere diameter of d = 230 nm.

The RMSE is computationally obtained by calculating the square root of the average squared differences between the λm values of an ideal first-order diffraction peak and the squared λm values extracted from the measured A-RTS curves. The complete set of A-RTS measurements and their corresponding root mean squared error, for each combination of applied elaboration parameters, is presented in the Supplement 1. Curves for each set of replicas are presented consecutively: first set (RMSE#1) in Figure S1, second set (RMSE#2) in Figure S2, and third set (RMSE#3) in Figure S3.

2.4 Colloidal suspensions sedimentations

Kynch’s theory for sedimentation processes is used to obtain the time evolution of concentration profiles for the prepared colloidal suspensions. This theory is based on a continuity equation of solid flux in suspension. Assuming that the particles are homogeneously distributed, it follows:

$$\frac{{\partial \phi ({t,z} )}}{{\partial t}} = {K_D}\frac{{{\partial ^2}\phi ({t,z} )}}{{\partial {t^2}}} - \frac{{\partial {f_{bk}}(\phi )}}{{\partial t}}$$

There, ϕ(t,z) is the volume fraction as a function of height (z) and time (t), fbk(ϕ) is the Kynch’s batch flux density function, and KD is the diffusion coefficient, which is given by:

$${K_D} = \frac{{m{K_B}T}}{{3\pi \mu d}}, $$
where, KB is the Boltzmann constant, T is the temperature, d is the diameter of the SiO2 spheres (230 ± 13 nm), μ is the viscosity of water and m is an experimental fitting parameter introduced here to adjust the diffusion coefficient considering small variations on the spheres’ size and shape in the colloidal suspension.

Boundary conditions are defined as:

$$\phi ({t,z} )= \{ \begin{array}{lc} {0,\quad \quad z = L}\\ {{\phi _0},\quad 0 \le z \le L}\\ {{\phi _{\max }},\quad z = L} \end{array}$$

Here, L is the total height of the suspension (42.44 mm in the experimental procedures), ϕ0 is the initial volume fraction concentration (0.05, 0.1, 0.26, and 0.42 vol%), and ϕmax is the maximum volume fraction at the sediment zone, which is considered here to be equal to the FFC packing density (74 vol%).

Several equations that describe fbk have been proposed to calculate the local velocity of the particles in a sedimentation process. In the present work, the two-parameter equation [36,37] is used:

$${f_{bk}}(\phi )= {v_s}\phi ({t,z} ){({1 - \phi ({t,z} )} )^n};\quad for\quad n > 1, $$

There, n is the Richardson-Zaki index, and vs is the settling velocity of a particle in an infinite medium, i.e., the Stokes velocity of a single particle in a quiescent and unbounded fluid, defined as [31]:

$${v_s} = \frac{{{d^2}}}{{18\mu }}({{\rho_s} - {\rho_f}} )g, $$
being ρs the density of the spheres (1.8 g/cm3), ρf the solvent’s density (1.0 g/cm3), d the sphere’s diameter, and g the acceleration due to gravity (9.8 m/s2).

The Richardson-Zaki index mainly depends on the flow regime. For the viscous regime n takes values close to 4.8 and for the inertial regime it takes values near to 2.4 [38]. However small variations on the particle’s size and shape in the colloidal suspension can cause inaccuracy on the n-index calculations. For this reason, we have developed an experiment to model the concentration profiles (Fig. 3), thus determining experimentally the value of n and m, for the specific case of 230 ± 13 nm in diameter SiO2 spheres dispersed in deionized water.

 figure: Fig. 3.

Fig. 3. (a) Implemented experimental set-up for measuring concentration profiles of a colloidal suspension of SiO2 spheres in deionized water at 0.8vol%. (b) Concentration profiles of the colloidal suspension (asterisks) and fitting under Kynch’s sedimentation modelling (continuous lines) for 72 h (dark blue), 120 h (red), 168 h (yellow), 192 h (purple), 220 h (green), and 244 h (light blue), respectively.

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2.5 Concentration profiles modelling

Modelling of concentration profiles for prepared colloidal suspensions is performed through a sedimentation equation that includes temperature as a time-dependent parameter (Eq. (9)), which was deduced by combining Eqs. (4) to 8:

$$\frac{{\partial \phi ({t,z} )}}{{\partial t}} = \left( {\frac{{m{K_B}T(t )}}{{3\pi \mu (T )d}}} \right)\frac{{{\partial ^2}\phi ({t,z} )}}{{\partial {t^2}}} - \left( {\frac{{g{d^2}({{\rho_s} - {\rho_f}} )}}{{18\mu (T )}}} \right)\frac{{\partial \phi ({t,z} ){{({1 - \phi ({t,z} )} )}^n}}}{{\partial t}}$$

Thus, μ(T) represents the water viscosity as a function of temperature [39,40]

$$\mu (T )= A\ast {10^{\left( {\frac{B}{{T - C}}} \right)}}, $$
with A = 2.414 × 10−5 cP, B = 247.8 K, and C = 140 K. In Eq. (9), parameters n and m are experimentally determined by measuring concentration profiles as a function of time and height of the colloidal suspension system used in the present study (230 ± 13 nm in diameter SiO2 spheres in deionized water). Measurements were conducted on a set-up with a 30mm height glass column containing the SiO2 colloidal suspension, placed between a fixed laser-photodetector system, as illustrated in Fig. 3(a). The column is mounted on an automated motorized platform that moves the column from bottom to top, while the signal obtained from the photodetector is recorded and preprocessed in a computer. The recorded signal, corresponding to the transmitted light intensity, contains the information of spheres concentration at a specific height position. The highest intensity indicates pristine water (absence of spheres), and the lowest intensity (zero signal) corresponds to the sediment zone. Recorded signals are normalized using light intensity at 0 h as reference.

In Fig. 3(b), measured concentration profiles (marked with *) at different times (72 h, 120 h, 168 h, 192 h, 220 h, and 244 h) are compared to the calculated concentration profiles (continuous lines). These were obtained by solving Eq. (9) with the following parameters: initial concentration ϕ0 = 0.8 vol%, total height of the suspension L = 30 mm, sphere diameter d = 230 nm and room temperature of T = 25°C. Through an iterative process, the best fit between experimental data and model curves is found with n = 2, and m = 2.

2.6 Evaporation rate of the colloidal suspension

The evaporation rate mainly depends on the applied temperature conditions, the geometry of the vial containing the suspension, and the type of colloidal system (solvent and spheres). During the elaboration process of CC films performed here, the colloidal system and the vial containing the suspension remain constant for all the experiments. Therefore, the evaporation rate varies only due to the applied temperature. To estimate the evaporation rate as a function of temperature, using the elaboration conditions stablished here, a characterization process is implemented using the experimental set-up shown in Fig. 4(a).

 figure: Fig. 4.

Fig. 4. (a) Experimental set-up for estimating the evaporation rate of a colloidal suspension consisting of SiO2 spheres immersed in deionized water. (b) Evaporation rate measurements as a function of time (blue asterisks), experimental fitting curve (red line), confidence bounds (red dotted line), and log-log scale plot in the inset.

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For characterizing the evaporation rate, a fixed volume (VCS = 30 ml) of SiO2 colloidal suspension is fully evaporated using a furnace at different applied temperatures (from 60°C to 100°C in steps of 10°C). The elapsed time in which the suspension fully evaporates for a specific applied temperature (tevap(T)) is estimated here by measuring the time interval in which a thermocouple, located at the bottom of the suspension, detects the temperature jump between the liquid-vapor interface [41]. Considering that all evaporation processes were carried out using a cylindric glass vial of 30 mm diameter (dv), the height level that occupies the suspension volume in the vial can be estimated by:

$${h_{CS}} = \frac{{{V_{CS}}}}{{\pi {{({{d_v}/2} )}^2}}}$$

An expression for the evaporation rate (vevap(T)) in terms of height is obtained by calculating the ratio between the hCS and tevap(T), as follows:

$${v_{evap}}(T )= \frac{{{h_{CS}}}}{{{t_{evap}}(T )}}$$

Based on the experimental values of tevap(T) obtained in the characterization process and using Eq. (12), a plot of the vevap(T) as a function of temperature is presented in Fig. 4(b) (blue asterisks). The dataset in Fig. 4(b) is fitted (red line) by the non-linear least squared method using the fitting expression:

$${v_{evap}}(T )= \rho + \beta {e^{\frac{T}{\gamma }}}$$
where ρ = -0.350 ± 0.122 mm/h, β = 0.146 ± 0.036 mm/h, and γ = 29.820 ± 2.05°C. The coefficients variations were calculated by setting the confidence bounds of the fitting method to 95% (red dotted lines). The inset in Fig. 4(b) shows the vevap(T) fitting curve in a logarithmic scale to verify the suitability of the exponential fit.

2.7 Meniscus displacement modelling

To estimate the meniscus position in the formation process of CCs, an experimental model for the downward displacement of the meniscus is proposed here. First, it is deduced an expression for the solvent evaporation rate as function of time vevap(t). This is done by replacing the time-dependent temperature condition applied during film elaboration (Eq. (1)), into the experimental expression of the solvent evaporation rate as a function of temperature vevap(T) (Eq. (13)). The substitution yields:

$${v_{evap}}(t )= \{ \begin{array}{ll} {\rho + \beta {e^{\frac{{\alpha t + {T_0}}}{\gamma }}},\quad t \le {t_{fi}}}\\ {{v_{evap}}({{t_{fi}}} ),\quad \quad t > {t_{fi}}} \end{array}$$

The meniscus position for a specific time interval during film deposition can be calculated by integrating Eq. (14) over time. This results in a time-dependent expression for the meniscus displacement in the downward direction (zm(t)):

$${z_m}(t )= \{ \begin{array}{ll} { - \frac{{\beta \gamma }}{\alpha }{e^{\frac{{{T_0}}}{\gamma }}} + \rho t + \frac{{\beta \gamma }}{\alpha }{e^{\frac{{\alpha t + {T_0}}}{\gamma }}},\quad t \le {t_{fi}}}\\ {{z_m}({{t_{fi}}} )+ ({t - {t_{fi}}} ){v_{evap}}({{t_{fi}}} ),\quad t > {t_{fi}}} \end{array}$$

3. Results and discussion

A-RTS spectra were measured by triplicated on CC films elaborated from colloidal suspensions with four different concentrations, at three defined temperature conditions (3 × 4 experimental design). The corresponding squared wavelength values λ2m of A-RTS diffraction peaks as a function of the squared sine of the incident angle, measured for films obtained under the combination of parameters selected in the present study, are plotted in Fig. 5. In particular, the average λ2m values are shown (colored bars), including the standard deviation from three measured sample replicas (error bars) for each combination of parameters. For comparison purposes, it is also shown the expected behavior for an ideal CC according to Bragg’s law (gray bars). The columns display the chosen levels of time-dependent temperature: i) 0.5°C/h during 30 h followed by a constant temperature of 40°C (left column), ii) 0.5°C/h during 70 h followed by a constant temperature of 60°C (center column), and iii) 0.5°C/h during 110 h followed by a constant temperature of 80°C (right column). Rows in Fig. 5 denote spheres concentration level (volume fraction) ordered from top to down: 0.05, 0.1, 0.26, and 0.42 vol%, respectively.

 figure: Fig. 5.

Fig. 5. Bragg’s law dependency of three replicas from samples elaborated by a combination of parameters (volume fraction and Temperature ramp). RMSE estimation uses an ideal FCC-packed colloidal crystal (gray bars) as reference. Temperature conditions shown in the columns are: 0.5°C/h during 30 h, 70 h, and 110 h. Colloidal suspension concentrations shown in the rows are: 0.05, 0.1, 0.26, and 0.42 vol%.

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The experimental data follows an apparent trend according to Bragg’s law. Therefore, the CC quality is evaluated by implementing RMSE calculations for each film taking an ideal FCC-packed colloidal crystal (gray bars) as reference. Details of this calculations are given as Supplement 1 in Figures S1-S3. In addition, the average RMSE value of three replicas (RMSEavg) is computed per each combination of elaboration parameters (volume fraction and Temperature ramp). The lower the RMSEavg value, the better the quality of the CC. It should be pointed out that RMSEavg value near 484 indicates absence of Bragg’s peaks at all incident angles in A-RTS measurements. Similarly, values close to 222 correspond to absence of Bragg’s peak at an incident angle of 40° only.

The results in Fig. 5 show that samples obtained under the first temperature condition (left column) do not present a Bragg’s peak at any colloidal suspension concentration (RMSEavg${\approx} $484). In contrast, the second and third temperatures conditions generate CC films with a distinctive Bragg’s behavior and a clear RMSE dependency on the sphere’s concentration. For instance, high-quality colloidal crystal films with low RMSEavg values of 4.14 and 4.11 can be obtained using respectively, temperature ramps during 70 h at 0.1 vol%, and 110 h at 0.42 vol%. These results indicate two main correlations between the elaboration parameters and the CC quality: i) Only prolonged temperature ramps during 70 h and 110 h promotes the crystallization process, and ii) the CC quality improves with a specific volume fraction.

The observed correlation between temperature ramps and CC quality is analyzed here by simulating the time evolution of concentration profiles and the meniscus position during sample elaboration. Color maps on left column of Fig. 6 show time evolution of concentration profiles during 250 h for three different temperature ramps. The color code represents four main concentration zones, from top to down: clear (light blue), transition (dark blue), uniform (light yellow) and sediment (dark yellow). Using each color map as background, the time evolution of the meniscus position is also sketched (continuous black-red line with confidence boundaries shown as red dotted lines). Vertical dotted lines set the programmed time limit until the temperature for each ramp is increased and kept constant afterwards. These two temperature regimes are highlighted by two colors on the meniscus position line: black (ramp) and red (constant temperature), respectively.

 figure: Fig. 6.

Fig. 6. Simulations of the sedimentation concentration profiles (color maps on left column), meniscus position (blue-red line in the left column), concentration profile on the substrate (color map on middle column), and A-RTS spectra of a representative elaborated film (right column) for 0.5°C/h temperature ramps applied during 30 h, 70 h and 110 h, respectively.

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According to Kynch’s theory, concentration profiles are not influenced by the initial volume fraction. Therefore, the profiles are identical for all values applied in the present study (0.05, 0.1, 0.26, and 0.42 vol%). For this reason, only the results for an initial volume fraction of 0.5 vol% are presented here. The results show: i) an increase in the clear and transition zones, ii) a decrease in the uniform zone, and iii) no significant variation on the sediment zone when duration of temperature ramp is increased. In addition, it can be appreciated that meniscus position evolves across different concentration zones (black-red line in Figs. 6(a), 6(d), 6(g)), allowing to estimate the concentration profile (volume fraction) that remains on the sample substrate during film elaboration (Figs. 6(b), 6(e), 6(h)).

The presence of different concentration zones in Fig. 6 points to a colloidal suspension in the low Reynolds regime (Re << 1), which agrees within the range of Reynolds number (0.13*10−7 to 0.86*10−7) estimated for a temperature range between 25°C and 80°C. Interestingly, there is a long and smoothed transition zone in the clear-uniform interface, which is attributed to low Peclet numbers of all colloidal suspensions used here (Pe values between 514.93 and 434.74 for the applied temperature range). This behavior is attributed to an increase in the sphere’s diffusion effect due to the acidity level (pH=8) used in all colloidal suspensions. This pH level might lead to an enhancement of dispersive forces that opposes to the sedimentation process, resulting in an increased transition zone.

For films obtained under temperature ramp applied for 30h (Fig. 6(a)), the meniscus position is predominantly located in the transition zone. Therefore, the contact line of the meniscus is located into a non-stable zone (transition zone), yielding low sphere ordering, as corroborated by the absence of Bragg’s peaks in the A-RTS measurements (Fig. 6(c)) performed onto the sample substrate (red dotted circle). Conversely, in Figs. 6(d) and 6(g) the contact line of the meniscus is located into a stable zone (uniform zone), which promotes the crystallization process. They are assigned to films elaborated at temperature ramps of 0.5°C/h applied for longer time (70 h and 110 h, respectively). Their film quality can be assessed by the presence of Bragg’s peaks in the corresponding A-RTS measurements shown in Figs. 6(f) and 6(i).

The CC film quality increases (lower RMSEavg values) with the concentration of colloidal suspensions, when temperature ramps are applied during time periods longer than 70 h, as observed in Fig. 7(a) (yellow curve). In particular, the samples obtained with temperature ramps applied during 110 h at 0.42 vol% exhibit the highest CC film quality as corroborated by SEM images in Figs. 7(b)–7(c). Interestingly, results obtained at 70 h and 110 h follow a slightly different trend although in both cases the meniscus remains into the uniform zone during film deposition. This effect is attributed to the evaporation rate given at the height in which the A-RTS measurements were conducted on the samples (20 mm from the bottom). At this height, the evaporation rate has already reached a constant value for the shorter ramp, while it is still linearly increasing for the longer. Given that the evaporation rate controls the flux of particles through the contact line and thus the crystallization process, a constant or linearly increasing rate explains the difference in the CC quality observed for the films. In this aspect, we observed a marked reduction in the measurement dispersions for the samples obtained with a constant increasing rate, as shown in Fig. 7(a) (red curve).

 figure: Fig. 7.

Fig. 7. (a) RMSE average values as a function of volume fraction for samples fabricated under applied temperature ramps of 0.5°C/h during 30 h (in blue), 70 h (in red), and 110 h (in yellow). (b) and (c) SEM images of samples obtained with ramps of 0.5°C/h during 110 h at 0.42vol%.

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4. Conclusions

In this work, an alternative method for obtaining high-quality colloidal crystal films using the VCSA deposition technique has been presented. The method applies temperature ramps to aqueous colloidal suspensions of silica at a fixed rate during a selected time interval. These results were analyzed by modeling the time evolution of the meniscus position and the concentration profile during CC film elaboration. Modeling reveals that high-quality films could be obtained when the meniscus mainly remains into the uniform zone of sedimentation, which exhibits a constant sphere concentration, promoting sphere ordering in the meniscus and subsequent crystal formation. Conversely, when the meniscus stays into the transition zone, where a wide variation on sphere concentration is presented, spheres’ ordering is prevented, which is detrimental of CC films quality. Colloidal crystal films deposited under controlled parameters showed that high-quality films can be achieved by positioning the meniscus into the uniform zone using temperature ramps, as a definite relation between sedimentation velocity and evaporation rate, in agreement with modelling results. Moreover, experimental results indicates that quality of colloidal crystal films can be further improved by tuning the colloidal suspension concentration and the stability of the evaporation rate. The presented elaboration and analysis methodology for obtaining high-quality CC films represents an alternative route for designing CC films using time-dependent temperatures.

Funding

Ministerio de Ciencia, Tecnología e Innovación (MINCIENCIAS) (Postdoctoral program # 848 of 2019).

Acknowledgments

The authors greatly acknowledge the support from Minciencias/Colciencias with the 2019 postdoctoral program#848, the department of Physics of Pontificia Universidad Javeriana, and the research facilities of the Thin Films & Nanophotonics Group.

Disclosures

The authors declare no conflicts of interest.

Data Availability

No data were generated or analyzed in the presented research.

Supplemental document

See Supplement 1 for supporting content.

References

1. J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019). [CrossRef]  

2. J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019). [CrossRef]  

3. F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007). [CrossRef]  

4. A. Mihi, F. J. López-Alcaraz, and H. Míguez, “Full spectrum enhancement of the light harvesting efficiency of dye sensitized solar cells by including colloidal photonic crystal multilayers,” Appl. Phys. Lett. 88(19), 193110 (2006). [CrossRef]  

5. A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008). [CrossRef]  

6. J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and L. C. Jiménez-Borrego, “Method for manufacturing a thin film consisting of a colloidal crystal infiltrated with the luminescent MDMO-PPV polymer made of silica (SiO2) spheres, having a face-centered cubic system (FCC),” U.S. patent US Patent 9,859,497, 2018 (2018).

7. N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015). [CrossRef]  

8. R. van Dommelen, P. Fanzio, and L. Sasso, “Surface self-assembly of colloidal crystals for micro- and nano-patterning,” Adv. Colloid Interface Sci. 251, 97–114 (2018). [CrossRef]  

9. B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1(2), 15011 (2016). [CrossRef]  

10. I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018). [CrossRef]  

11. A. S. Dimitrov and K. Nagayama, “Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces,” Langmuir 12(5), 1303–1311 (1996). [CrossRef]  

12. P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999). [CrossRef]  

13. Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000). [CrossRef]  

14. Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001). [CrossRef]  

15. Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001). [CrossRef]  

16. S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125(50), 15589–15598 (2003). [CrossRef]  

17. S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004). [CrossRef]  

18. G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008). [CrossRef]  

19. J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008). [CrossRef]  

20. G. Q. Liu, Z. S. Wang, and Y. H. Ji, “Influence of growth parameters on the fabrication of high-quality colloidal crystals via a controlled evaporation self-assembly method,” Thin Solid Films 518(18), 5083–5090 (2010). [CrossRef]  

21. D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004). [CrossRef]  

22. D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008). [CrossRef]  

23. G. Lozano and H. Míguez, “Growth dynamics of self-assembled colloidal crystal thin films,” Langmuir 23(20), 9933–9938 (2007). [CrossRef]  

24. L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006). [CrossRef]  

25. S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009). [CrossRef]  

26. Y. Mino, S. Watanabe, and M. T. Miyahara, “In Situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly,” Langmuir 31(14), 4121–4128 (2015). [CrossRef]  

27. Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019). [CrossRef]  

28. Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001). [CrossRef]  

29. L. Hernando, A. Omari, and D. Reungoat, “Experimental study of sedimentation of concentrated mono-disperse suspensions: determination of sedimentation modes,” Powder Technol. 258, 265–271 (2014). [CrossRef]  

30. S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008). [CrossRef]  

31. W. B. Russel, D. A. Saville, and W. R. Schowalter, “Sedimentation,” in Colloidal Dispersions (Cambridge University Press, 1989), pp. 394–428. [CrossRef]  

32. R. D. Harding, “Stability of silica dispersions,” J. Colloid Interface Sci. 35(1), 172–174 (1971). [CrossRef]  

33. O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010). [CrossRef]  

34. K. Liu, T. A. Schmedake, and R. Tsu, “A comparative study of colloidal silica spheres: photonic crystals versus Bragg’s law,” Phys. Lett. A 372(24), 4517–4520 (2008). [CrossRef]  

35. M. Muldarisnur, I. Popa, and F. Marlow, “Angle-resolved transmission spectroscopy of opal films,” Phys. Rev. B 86(2), 024105 (2012). [CrossRef]  

36. F. Concha and R. Bürger, “A century of research in sedimentation and thickening,” KONA Powder Part. J. 20(0), 38–70 (2002). [CrossRef]  

37. J. F. Richardson and W. N. Zaki, “Sedimentation and fluidisation: Part I,” Chem. Eng. Res. Des. 75, S82–S100 (1997). [CrossRef]  

38. O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019). [CrossRef]  

39. F. Zonta, M. Onorato, and A. Soldati, “Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties,” J. Fluid Mech. 697, 175–203 (2012). [CrossRef]  

40. F. Zonta, C. Marchioli, and A. Soldati, “Modulation of turbulence in forced convection by temperature-dependent viscosity,” J. Fluid Mech. 697, 150–174 (2012). [CrossRef]  

41. V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007). [CrossRef]  

References

  • View by:

  1. J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
    [Crossref]
  2. J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
    [Crossref]
  3. F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007).
    [Crossref]
  4. A. Mihi, F. J. López-Alcaraz, and H. Míguez, “Full spectrum enhancement of the light harvesting efficiency of dye sensitized solar cells by including colloidal photonic crystal multilayers,” Appl. Phys. Lett. 88(19), 193110 (2006).
    [Crossref]
  5. A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008).
    [Crossref]
  6. J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and L. C. Jiménez-Borrego, “Method for manufacturing a thin film consisting of a colloidal crystal infiltrated with the luminescent MDMO-PPV polymer made of silica (SiO2) spheres, having a face-centered cubic system (FCC),” U.S. patent US Patent 9,859,497, 2018 (2018).
  7. N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
    [Crossref]
  8. R. van Dommelen, P. Fanzio, and L. Sasso, “Surface self-assembly of colloidal crystals for micro- and nano-patterning,” Adv. Colloid Interface Sci. 251, 97–114 (2018).
    [Crossref]
  9. B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1(2), 15011 (2016).
    [Crossref]
  10. I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018).
    [Crossref]
  11. A. S. Dimitrov and K. Nagayama, “Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces,” Langmuir 12(5), 1303–1311 (1996).
    [Crossref]
  12. P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999).
    [Crossref]
  13. Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000).
    [Crossref]
  14. Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
    [Crossref]
  15. Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001).
    [Crossref]
  16. S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125(50), 15589–15598 (2003).
    [Crossref]
  17. S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004).
    [Crossref]
  18. G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008).
    [Crossref]
  19. J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008).
    [Crossref]
  20. G. Q. Liu, Z. S. Wang, and Y. H. Ji, “Influence of growth parameters on the fabrication of high-quality colloidal crystals via a controlled evaporation self-assembly method,” Thin Solid Films 518(18), 5083–5090 (2010).
    [Crossref]
  21. D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
    [Crossref]
  22. D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
    [Crossref]
  23. G. Lozano and H. Míguez, “Growth dynamics of self-assembled colloidal crystal thin films,” Langmuir 23(20), 9933–9938 (2007).
    [Crossref]
  24. L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
    [Crossref]
  25. S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009).
    [Crossref]
  26. Y. Mino, S. Watanabe, and M. T. Miyahara, “In Situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly,” Langmuir 31(14), 4121–4128 (2015).
    [Crossref]
  27. Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019).
    [Crossref]
  28. Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001).
    [Crossref]
  29. L. Hernando, A. Omari, and D. Reungoat, “Experimental study of sedimentation of concentrated mono-disperse suspensions: determination of sedimentation modes,” Powder Technol. 258, 265–271 (2014).
    [Crossref]
  30. S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
    [Crossref]
  31. W. B. Russel, D. A. Saville, and W. R. Schowalter, “Sedimentation,” in Colloidal Dispersions (Cambridge University Press, 1989), pp. 394–428.
    [Crossref]
  32. R. D. Harding, “Stability of silica dispersions,” J. Colloid Interface Sci. 35(1), 172–174 (1971).
    [Crossref]
  33. O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010).
    [Crossref]
  34. K. Liu, T. A. Schmedake, and R. Tsu, “A comparative study of colloidal silica spheres: photonic crystals versus Bragg’s law,” Phys. Lett. A 372(24), 4517–4520 (2008).
    [Crossref]
  35. M. Muldarisnur, I. Popa, and F. Marlow, “Angle-resolved transmission spectroscopy of opal films,” Phys. Rev. B 86(2), 024105 (2012).
    [Crossref]
  36. F. Concha and R. Bürger, “A century of research in sedimentation and thickening,” KONA Powder Part. J. 20(0), 38–70 (2002).
    [Crossref]
  37. J. F. Richardson and W. N. Zaki, “Sedimentation and fluidisation: Part I,” Chem. Eng. Res. Des. 75, S82–S100 (1997).
    [Crossref]
  38. O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
    [Crossref]
  39. F. Zonta, M. Onorato, and A. Soldati, “Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties,” J. Fluid Mech. 697, 175–203 (2012).
    [Crossref]
  40. F. Zonta, C. Marchioli, and A. Soldati, “Modulation of turbulence in forced convection by temperature-dependent viscosity,” J. Fluid Mech. 697, 150–174 (2012).
    [Crossref]
  41. V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007).
    [Crossref]

2019 (4)

J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
[Crossref]

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
[Crossref]

Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019).
[Crossref]

O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
[Crossref]

2018 (2)

R. van Dommelen, P. Fanzio, and L. Sasso, “Surface self-assembly of colloidal crystals for micro- and nano-patterning,” Adv. Colloid Interface Sci. 251, 97–114 (2018).
[Crossref]

I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018).
[Crossref]

2016 (1)

B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1(2), 15011 (2016).
[Crossref]

2015 (2)

N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
[Crossref]

Y. Mino, S. Watanabe, and M. T. Miyahara, “In Situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly,” Langmuir 31(14), 4121–4128 (2015).
[Crossref]

2014 (1)

L. Hernando, A. Omari, and D. Reungoat, “Experimental study of sedimentation of concentrated mono-disperse suspensions: determination of sedimentation modes,” Powder Technol. 258, 265–271 (2014).
[Crossref]

2012 (3)

M. Muldarisnur, I. Popa, and F. Marlow, “Angle-resolved transmission spectroscopy of opal films,” Phys. Rev. B 86(2), 024105 (2012).
[Crossref]

F. Zonta, M. Onorato, and A. Soldati, “Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties,” J. Fluid Mech. 697, 175–203 (2012).
[Crossref]

F. Zonta, C. Marchioli, and A. Soldati, “Modulation of turbulence in forced convection by temperature-dependent viscosity,” J. Fluid Mech. 697, 150–174 (2012).
[Crossref]

2010 (2)

O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010).
[Crossref]

G. Q. Liu, Z. S. Wang, and Y. H. Ji, “Influence of growth parameters on the fabrication of high-quality colloidal crystals via a controlled evaporation self-assembly method,” Thin Solid Films 518(18), 5083–5090 (2010).
[Crossref]

2009 (1)

S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009).
[Crossref]

2008 (6)

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008).
[Crossref]

J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008).
[Crossref]

K. Liu, T. A. Schmedake, and R. Tsu, “A comparative study of colloidal silica spheres: photonic crystals versus Bragg’s law,” Phys. Lett. A 372(24), 4517–4520 (2008).
[Crossref]

S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
[Crossref]

A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008).
[Crossref]

2007 (3)

F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007).
[Crossref]

G. Lozano and H. Míguez, “Growth dynamics of self-assembled colloidal crystal thin films,” Langmuir 23(20), 9933–9938 (2007).
[Crossref]

V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007).
[Crossref]

2006 (2)

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

A. Mihi, F. J. López-Alcaraz, and H. Míguez, “Full spectrum enhancement of the light harvesting efficiency of dye sensitized solar cells by including colloidal photonic crystal multilayers,” Appl. Phys. Lett. 88(19), 193110 (2006).
[Crossref]

2004 (2)

S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004).
[Crossref]

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
[Crossref]

2003 (1)

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125(50), 15589–15598 (2003).
[Crossref]

2002 (1)

F. Concha and R. Bürger, “A century of research in sedimentation and thickening,” KONA Powder Part. J. 20(0), 38–70 (2002).
[Crossref]

2001 (3)

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001).
[Crossref]

Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
[Crossref]

Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001).
[Crossref]

2000 (1)

Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000).
[Crossref]

1999 (1)

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999).
[Crossref]

1997 (1)

J. F. Richardson and W. N. Zaki, “Sedimentation and fluidisation: Part I,” Chem. Eng. Res. Des. 75, S82–S100 (1997).
[Crossref]

1996 (1)

A. S. Dimitrov and K. Nagayama, “Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces,” Langmuir 12(5), 1303–1311 (1996).
[Crossref]

1971 (1)

R. D. Harding, “Stability of silica dispersions,” J. Colloid Interface Sci. 35(1), 172–174 (1971).
[Crossref]

Allen, J.

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

Anta, J. A.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008).
[Crossref]

Arlinghaus, E. G.

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
[Crossref]

Baars, E. T.

O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
[Crossref]

Badam, V. K.

V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007).
[Crossref]

Badilescu, S.

Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
[Crossref]

Bertone, J. F.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999).
[Crossref]

Bo, X. Z.

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001).
[Crossref]

Brewer, D. D.

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

Bürger, R.

F. Concha and R. Bürger, “A century of research in sedimentation and thickening,” KONA Powder Part. J. 20(0), 38–70 (2002).
[Crossref]

Buzzaccaro, S.

S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
[Crossref]

Calvo, M. E.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008).
[Crossref]

Castañeda-Uribe, O. A.

J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
[Crossref]

O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010).
[Crossref]

Chen, Y.

G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008).
[Crossref]

Chen, Y. K.

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
[Crossref]

Colvin, V. L.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999).
[Crossref]

Concha, F.

F. Concha and R. Bürger, “A century of research in sedimentation and thickening,” KONA Powder Part. J. 20(0), 38–70 (2002).
[Crossref]

Danov, K.

V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007).
[Crossref]

de Moel, P. J.

O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
[Crossref]

Del Campo, A.

N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
[Crossref]

Dimitrov, A. S.

A. S. Dimitrov and K. Nagayama, “Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces,” Langmuir 12(5), 1303–1311 (1996).
[Crossref]

Dumitrache, F.

I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018).
[Crossref]

Dumitru, M.

I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018).
[Crossref]

Durst, F.

V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007).
[Crossref]

Fanzio, P.

R. van Dommelen, P. Fanzio, and L. Sasso, “Surface self-assembly of colloidal crystals for micro- and nano-patterning,” Adv. Colloid Interface Sci. 251, 97–114 (2018).
[Crossref]

Fleaca, C. T.

I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018).
[Crossref]

Fujishima, A.

Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000).
[Crossref]

Fung, M. K.

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
[Crossref]

Fustin, C. A.

N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
[Crossref]

Gu, Z. Z.

Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000).
[Crossref]

Haché, A.

S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004).
[Crossref]

Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001).
[Crossref]

Han, Y.

B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1(2), 15011 (2016).
[Crossref]

Harding, R. D.

R. D. Harding, “Stability of silica dispersions,” J. Colloid Interface Sci. 35(1), 172–174 (1971).
[Crossref]

Heiny, R.

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
[Crossref]

Hernando, L.

L. Hernando, A. Omari, and D. Reungoat, “Experimental study of sedimentation of concentrated mono-disperse suspensions: determination of sedimentation modes,” Powder Technol. 258, 265–271 (2014).
[Crossref]

Hu, X. F.

S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004).
[Crossref]

Hua, X. C.

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
[Crossref]

Huang, C. C.

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
[Crossref]

Hwang, K. S.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999).
[Crossref]

Inukai, K.

S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009).
[Crossref]

Ji, Y. H.

G. Q. Liu, Z. S. Wang, and Y. H. Ji, “Influence of growth parameters on the fabrication of high-quality colloidal crystals via a controlled evaporation self-assembly method,” Thin Solid Films 518(18), 5083–5090 (2010).
[Crossref]

Jiang, P.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999).
[Crossref]

Jiménez-Borrego, L. C.

J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
[Crossref]

J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and L. C. Jiménez-Borrego, “Method for manufacturing a thin film consisting of a colloidal crystal infiltrated with the luminescent MDMO-PPV polymer made of silica (SiO2) spheres, having a face-centered cubic system (FCC),” U.S. patent US Patent 9,859,497, 2018 (2018).

Jonas, U.

N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
[Crossref]

Kitaev, V.

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125(50), 15589–15598 (2003).
[Crossref]

Kramer, O. J. I.

O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
[Crossref]

Kuai, S. L.

S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004).
[Crossref]

Kumar, S.

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

Kumar, V.

V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007).
[Crossref]

LeBlanc, F.

Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001).
[Crossref]

Li, B.

B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1(2), 15011 (2016).
[Crossref]

Li, F.

F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007).
[Crossref]

Li, X.

F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007).
[Crossref]

Liao, Y. B.

G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008).
[Crossref]

Liu, G. Q.

G. Q. Liu, Z. S. Wang, and Y. H. Ji, “Influence of growth parameters on the fabrication of high-quality colloidal crystals via a controlled evaporation self-assembly method,” Thin Solid Films 518(18), 5083–5090 (2010).
[Crossref]

G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008).
[Crossref]

Liu, H.

J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008).
[Crossref]

Liu, K.

K. Liu, T. A. Schmedake, and R. Tsu, “A comparative study of colloidal silica spheres: photonic crystals versus Bragg’s law,” Phys. Lett. A 372(24), 4517–4520 (2008).
[Crossref]

Liu, Z. M.

G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008).
[Crossref]

López-Alcaraz, F. J.

A. Mihi, F. J. López-Alcaraz, and H. Míguez, “Full spectrum enhancement of the light harvesting efficiency of dye sensitized solar cells by including colloidal photonic crystal multilayers,” Appl. Phys. Lett. 88(19), 193110 (2006).
[Crossref]

Lozano, G.

G. Lozano and H. Míguez, “Growth dynamics of self-assembled colloidal crystal thin films,” Langmuir 23(20), 9933–9938 (2007).
[Crossref]

Ma, Y. Y.

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
[Crossref]

Marchioli, C.

F. Zonta, C. Marchioli, and A. Soldati, “Modulation of turbulence in forced convection by temperature-dependent viscosity,” J. Fluid Mech. 697, 150–174 (2012).
[Crossref]

Marlow, F.

M. Muldarisnur, I. Popa, and F. Marlow, “Angle-resolved transmission spectroscopy of opal films,” Phys. Rev. B 86(2), 024105 (2012).
[Crossref]

Méndez-Pinzón, H. A.

J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
[Crossref]

O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010).
[Crossref]

J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and L. C. Jiménez-Borrego, “Method for manufacturing a thin film consisting of a colloidal crystal infiltrated with the luminescent MDMO-PPV polymer made of silica (SiO2) spheres, having a face-centered cubic system (FCC),” U.S. patent US Patent 9,859,497, 2018 (2018).

Meng, L.

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
[Crossref]

Meng, Q. B.

Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000).
[Crossref]

Míguez, H.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008).
[Crossref]

G. Lozano and H. Míguez, “Growth dynamics of self-assembled colloidal crystal thin films,” Langmuir 23(20), 9933–9938 (2007).
[Crossref]

A. Mihi, F. J. López-Alcaraz, and H. Míguez, “Full spectrum enhancement of the light harvesting efficiency of dye sensitized solar cells by including colloidal photonic crystal multilayers,” Appl. Phys. Lett. 88(19), 193110 (2006).
[Crossref]

Mihi, A.

A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008).
[Crossref]

A. Mihi, F. J. López-Alcaraz, and H. Míguez, “Full spectrum enhancement of the light harvesting efficiency of dye sensitized solar cells by including colloidal photonic crystal multilayers,” Appl. Phys. Lett. 88(19), 193110 (2006).
[Crossref]

Miller, M. R.

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

Ming, N.

J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008).
[Crossref]

Mino, Y.

Y. Mino, S. Watanabe, and M. T. Miyahara, “In Situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly,” Langmuir 31(14), 4121–4128 (2015).
[Crossref]

Miyahara, M. T.

Y. Mino, S. Watanabe, and M. T. Miyahara, “In Situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly,” Langmuir 31(14), 4121–4128 (2015).
[Crossref]

S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009).
[Crossref]

Mizuta, S.

S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009).
[Crossref]

Muldarisnur, M.

M. Muldarisnur, I. Popa, and F. Marlow, “Angle-resolved transmission spectroscopy of opal films,” Phys. Rev. B 86(2), 024105 (2012).
[Crossref]

Nagayama, K.

A. S. Dimitrov and K. Nagayama, “Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces,” Langmuir 12(5), 1303–1311 (1996).
[Crossref]

Nagel, A.

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

Natansohn, A.

Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
[Crossref]

Norris, D. J.

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
[Crossref]

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001).
[Crossref]

Omari, A.

L. Hernando, A. Omari, and D. Reungoat, “Experimental study of sedimentation of concentrated mono-disperse suspensions: determination of sedimentation modes,” Powder Technol. 258, 265–271 (2014).
[Crossref]

Onorato, M.

F. Zonta, M. Onorato, and A. Soldati, “Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties,” J. Fluid Mech. 697, 175–203 (2012).
[Crossref]

Ozin, G. A.

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125(50), 15589–15598 (2003).
[Crossref]

Padding, J. T.

O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
[Crossref]

Pedroza-Rodríguez, A. M.

O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010).
[Crossref]

Pham, Q.

Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019).
[Crossref]

Piazza, R.

S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
[Crossref]

Popa, I.

M. Muldarisnur, I. Popa, and F. Marlow, “Angle-resolved transmission spectroscopy of opal films,” Phys. Rev. B 86(2), 024105 (2012).
[Crossref]

Retsch, M.

N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
[Crossref]

Reungoat, D.

L. Hernando, A. Omari, and D. Reungoat, “Experimental study of sedimentation of concentrated mono-disperse suspensions: determination of sedimentation modes,” Powder Technol. 258, 265–271 (2014).
[Crossref]

Richardson, J. F.

J. F. Richardson and W. N. Zaki, “Sedimentation and fluidisation: Part I,” Chem. Eng. Res. Des. 75, S82–S100 (1997).
[Crossref]

Rochon, P.

Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
[Crossref]

Rusconi, R.

S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
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W. B. Russel, D. A. Saville, and W. R. Schowalter, “Sedimentation,” in Colloidal Dispersions (Cambridge University Press, 1989), pp. 394–428.
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Salcedo-Reyes, J. C.

J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
[Crossref]

O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010).
[Crossref]

J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and L. C. Jiménez-Borrego, “Method for manufacturing a thin film consisting of a colloidal crystal infiltrated with the luminescent MDMO-PPV polymer made of silica (SiO2) spheres, having a face-centered cubic system (FCC),” U.S. patent US Patent 9,859,497, 2018 (2018).

Sandu, I.

I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018).
[Crossref]

Santos, J. M. D.

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

Sasso, L.

R. van Dommelen, P. Fanzio, and L. Sasso, “Surface self-assembly of colloidal crystals for micro- and nano-patterning,” Adv. Colloid Interface Sci. 251, 97–114 (2018).
[Crossref]

Sato, O.

Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000).
[Crossref]

Saville, D. A.

W. B. Russel, D. A. Saville, and W. R. Schowalter, “Sedimentation,” in Colloidal Dispersions (Cambridge University Press, 1989), pp. 394–428.
[Crossref]

Schmedake, T. A.

K. Liu, T. A. Schmedake, and R. Tsu, “A comparative study of colloidal silica spheres: photonic crystals versus Bragg’s law,” Phys. Lett. A 372(24), 4517–4520 (2008).
[Crossref]

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W. B. Russel, D. A. Saville, and W. R. Schowalter, “Sedimentation,” in Colloidal Dispersions (Cambridge University Press, 1989), pp. 394–428.
[Crossref]

Scriven, L. E.

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
[Crossref]

Shao, B.

Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019).
[Crossref]

Soldati, A.

F. Zonta, M. Onorato, and A. Soldati, “Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties,” J. Fluid Mech. 697, 175–203 (2012).
[Crossref]

F. Zonta, C. Marchioli, and A. Soldati, “Modulation of turbulence in forced convection by temperature-dependent viscosity,” J. Fluid Mech. 697, 150–174 (2012).
[Crossref]

Sturm, J. C.

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001).
[Crossref]

Suh, Y.

Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019).
[Crossref]

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S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
[Crossref]

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D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
[Crossref]

Tsu, R.

K. Liu, T. A. Schmedake, and R. Tsu, “A comparative study of colloidal silica spheres: photonic crystals versus Bragg’s law,” Phys. Lett. A 372(24), 4517–4520 (2008).
[Crossref]

van der Hoek, J. P.

O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
[Crossref]

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R. van Dommelen, P. Fanzio, and L. Sasso, “Surface self-assembly of colloidal crystals for micro- and nano-patterning,” Adv. Colloid Interface Sci. 251, 97–114 (2018).
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Van Truong, V.

S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004).
[Crossref]

Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001).
[Crossref]

Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
[Crossref]

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O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
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J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
[Crossref]

Vigolo, D.

S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
[Crossref]

Vlasov, Y. A.

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001).
[Crossref]

Vogel, N.

N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
[Crossref]

Wang, Y. D.

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
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Wang, Z.

J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008).
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G. Q. Liu, Z. S. Wang, and Y. H. Ji, “Influence of growth parameters on the fabrication of high-quality colloidal crystals via a controlled evaporation self-assembly method,” Thin Solid Films 518(18), 5083–5090 (2010).
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Y. Mino, S. Watanabe, and M. T. Miyahara, “In Situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly,” Langmuir 31(14), 4121–4128 (2015).
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S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009).
[Crossref]

Wei, H.

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

Wiley, B. J.

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

Won, Y.

Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019).
[Crossref]

Wong, S.

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125(50), 15589–15598 (2003).
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Yang, B.

F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007).
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Ye, Y. H.

Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001).
[Crossref]

Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
[Crossref]

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J. F. Richardson and W. N. Zaki, “Sedimentation and fluidisation: Part I,” Chem. Eng. Res. Des. 75, S82–S100 (1997).
[Crossref]

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J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008).
[Crossref]

F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007).
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Zhou, D.

B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1(2), 15011 (2016).
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Zhou, J. G.

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
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Zonta, F.

F. Zonta, M. Onorato, and A. Soldati, “Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties,” J. Fluid Mech. 697, 175–203 (2012).
[Crossref]

F. Zonta, C. Marchioli, and A. Soldati, “Modulation of turbulence in forced convection by temperature-dependent viscosity,” J. Fluid Mech. 697, 150–174 (2012).
[Crossref]

Adv. Colloid Interface Sci. (1)

R. van Dommelen, P. Fanzio, and L. Sasso, “Surface self-assembly of colloidal crystals for micro- and nano-patterning,” Adv. Colloid Interface Sci. 251, 97–114 (2018).
[Crossref]

Adv. Mater. (1)

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline photonic crystals: How does self-assembly work?” Adv. Mater. 16(16), 1393–1399 (2004).
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Appl. Phys. Lett. (4)

A. Mihi, F. J. López-Alcaraz, and H. Míguez, “Full spectrum enhancement of the light harvesting efficiency of dye sensitized solar cells by including colloidal photonic crystal multilayers,” Appl. Phys. Lett. 88(19), 193110 (2006).
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Q. B. Meng, Z. Z. Gu, O. Sato, and A. Fujishima, “Fabrication of highly ordered porous structures,” Appl. Phys. Lett. 77(26), 4313–4315 (2000).
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Y. H. Ye, S. Badilescu, V. Van Truong, P. Rochon, and A. Natansohn, “Self-assembly of colloidal spheres on patterned substrates,” Appl. Phys. Lett. 79(6), 872–874 (2001).
[Crossref]

Y. H. Ye, F. LeBlanc, A. Haché, and V. Van Truong, “Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality,” Appl. Phys. Lett. 78(1), 52–54 (2001).
[Crossref]

Chem. Eng. Res. Des. (1)

J. F. Richardson and W. N. Zaki, “Sedimentation and fluidisation: Part I,” Chem. Eng. Res. Des. 75, S82–S100 (1997).
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Chem. Mater. (1)

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-crystal colloidal multilayers of controlled thickness,” Chem. Mater. 11(8), 2132–2140 (1999).
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Chem. Rev. (1)

N. Vogel, M. Retsch, C. A. Fustin, A. Del Campo, and U. Jonas, “Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions,” Chem. Rev. 115(13), 6265–6311 (2015).
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Exp. Therm. Fluid Sci. (1)

V. K. Badam, V. Kumar, F. Durst, and K. Danov, “Experimental and theoretical investigations on interfacial temperature jumps during evaporation,” Exp. Therm. Fluid Sci. 32(1), 276–292 (2007).
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J. Am. Chem. Soc. (1)

S. Wong, V. Kitaev, and G. A. Ozin, “Colloidal crystal films: advances in universality and perfection,” J. Am. Chem. Soc. 125(50), 15589–15598 (2003).
[Crossref]

J. Appl. Phys. (1)

J. Zhang, H. Liu, Z. Wang, and N. Ming, “Assembly of high-quality colloidal crystals under negative pressure,” J. Appl. Phys. 103(1), 013517 (2008).
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J. Colloid Interface Sci. (1)

R. D. Harding, “Stability of silica dispersions,” J. Colloid Interface Sci. 35(1), 172–174 (1971).
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J. Cryst. Growth (1)

S. L. Kuai, X. F. Hu, A. Haché, and V. Van Truong, “High-quality colloidal photonic crystals obtained by optimizing growth parameters in a vertical deposition technique,” J. Cryst. Growth 267(1-2), 317–324 (2004).
[Crossref]

J. Fluid Mech. (2)

F. Zonta, M. Onorato, and A. Soldati, “Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties,” J. Fluid Mech. 697, 175–203 (2012).
[Crossref]

F. Zonta, C. Marchioli, and A. Soldati, “Modulation of turbulence in forced convection by temperature-dependent viscosity,” J. Fluid Mech. 697, 150–174 (2012).
[Crossref]

J. Mater. Chem. C (1)

J. G. Zhou, X. C. Hua, Y. K. Chen, Y. Y. Ma, C. C. Huang, Y. D. Wang, and M. K. Fung, “Nano-modified indium tin oxide incorporated with ideal microlens array for light extraction of OLED,” J. Mater. Chem. C 7(13), 3958–3964 (2019).
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J. Opt. A: Pure Appl. Opt. (1)

G. Q. Liu, Y. B. Liao, Z. M. Liu, and Y. Chen, “Characteristic investigation of high quality three-dimensional photonic crystals fabricated by self-assembly: theory analysis, simulation and measurement,” J. Opt. A: Pure Appl. Opt. 10(11), 115202 (2008).
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J. Phys. Chem. C (1)

A. Mihi, M. E. Calvo, J. A. Anta, and H. Míguez, “Spectral response of opal-based dye-sensitized solar cells,” J. Phys. Chem. C 112(1), 13–17 (2008).
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J. Phys.: Condens. Matter (1)

S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, “Kinetics of sedimentation in colloidal suspensions,” J. Phys.: Condens. Matter 20(49), 494219 (2008).
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F. Concha and R. Bürger, “A century of research in sedimentation and thickening,” KONA Powder Part. J. 20(0), 38–70 (2002).
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Langmuir (5)

D. D. Brewer, J. Allen, M. R. Miller, J. M. D. Santos, S. Kumar, D. J. Norris, M. Tsapatsis, and L. E. Scriven, “Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering,” Langmuir 24(23), 13683–13693 (2008).
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G. Lozano and H. Míguez, “Growth dynamics of self-assembled colloidal crystal thin films,” Langmuir 23(20), 9933–9938 (2007).
[Crossref]

S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25(13), 7287–7295 (2009).
[Crossref]

Y. Mino, S. Watanabe, and M. T. Miyahara, “In Situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly,” Langmuir 31(14), 4121–4128 (2015).
[Crossref]

A. S. Dimitrov and K. Nagayama, “Continuous convective assembling of fine particles into two-dimensional arrays on solid surfaces,” Langmuir 12(5), 1303–1311 (1996).
[Crossref]

Nano Lett. (1)

L. Meng, H. Wei, A. Nagel, B. J. Wiley, L. E. Scriven, and D. J. Norris, “The role of thickness transitions in convective assembly,” Nano Lett. 6(10), 2249–2253 (2006).
[Crossref]

Nat. Rev. Mater. (1)

B. Li, D. Zhou, and Y. Han, “Assembly and phase transitions of colloidal crystals,” Nat. Rev. Mater. 1(2), 15011 (2016).
[Crossref]

Nature (1)

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001).
[Crossref]

Org. Electron. (1)

F. Li, X. Li, J. Zhang, and B. Yang, “Enhanced light extraction from organic light-emitting devices by using microcontact printed silica colloidal crystals,” Org. Electron. 8(5), 635–639 (2007).
[Crossref]

Photonics Nanostructures - Fundam. Appl. (1)

I. Sandu, M. Dumitru, C. T. Fleaca, and F. Dumitrache, “Hanging colloidal drop: a new photonic crystal synthesis route,” Photonics Nanostructures - Fundam. Appl. 29, 42–48 (2018).
[Crossref]

Phys. Lett. A (1)

K. Liu, T. A. Schmedake, and R. Tsu, “A comparative study of colloidal silica spheres: photonic crystals versus Bragg’s law,” Phys. Lett. A 372(24), 4517–4520 (2008).
[Crossref]

Phys. Rev. B (1)

M. Muldarisnur, I. Popa, and F. Marlow, “Angle-resolved transmission spectroscopy of opal films,” Phys. Rev. B 86(2), 024105 (2012).
[Crossref]

Powder Technol. (2)

O. J. I. Kramer, P. J. de Moel, E. T. Baars, W. H. van Vugt, J. T. Padding, and J. P. van der Hoek, “Improvement of the Richardson-Zaki liquid-solid fluidisation model on the basis of hydraulics,” Powder Technol. 343, 465–478 (2019).
[Crossref]

L. Hernando, A. Omari, and D. Reungoat, “Experimental study of sedimentation of concentrated mono-disperse suspensions: determination of sedimentation modes,” Powder Technol. 258, 265–271 (2014).
[Crossref]

Semicond. Sci. Technol. (1)

J. C. Salcedo-Reyes, J. R. Vásquez-Rojas, L. C. Jiménez-Borrego, O. A. Castañeda-Uribe, and H. A. Méndez-Pinzón, “Improving extraction efficiency of OLEDs by a luminescent polymer embedded in a colloidal crystal matrix,” Semicond. Sci. Technol. 34(11), 115016 (2019).
[Crossref]

Small (1)

Y. Suh, Q. Pham, B. Shao, and Y. Won, “The control of colloidal grain boundaries through evaporative vertical self-assembly,” Small 15(12), 1804523 (2019).
[Crossref]

Thin Solid Films (1)

G. Q. Liu, Z. S. Wang, and Y. H. Ji, “Influence of growth parameters on the fabrication of high-quality colloidal crystals via a controlled evaporation self-assembly method,” Thin Solid Films 518(18), 5083–5090 (2010).
[Crossref]

Univ. Sci. (1)

O. A. Castañeda-Uribe, J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and A. M. Pedroza-Rodríguez, “Fabrication and optical characterization of high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method,” Univ. Sci. 15(2), 150 (2010).
[Crossref]

Other (2)

W. B. Russel, D. A. Saville, and W. R. Schowalter, “Sedimentation,” in Colloidal Dispersions (Cambridge University Press, 1989), pp. 394–428.
[Crossref]

J. C. Salcedo-Reyes, H. A. Méndez-Pinzón, and L. C. Jiménez-Borrego, “Method for manufacturing a thin film consisting of a colloidal crystal infiltrated with the luminescent MDMO-PPV polymer made of silica (SiO2) spheres, having a face-centered cubic system (FCC),” U.S. patent US Patent 9,859,497, 2018 (2018).

Supplementary Material (1)

NameDescription
Supplement 1       A-RTS spectra of fabricated CC films

Data Availability

No data were generated or analyzed in the presented research.

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Figures (7)

Fig. 1.
Fig. 1. (a) Vertical convective self-assembly diagram. (b) Concentration profiles of colloidal suspensions during sedimentation. (c) Experimental parameters applied for colloidal crystal growth.
Fig. 2.
Fig. 2. (a) Optical characterization of CC films using A-RTS. (b) Typical A-RTS spectra of a CC film obtained at 0.5°C/h during 110 h with a volume fraction of 0.24 Vol% at incident angles of 0 $^\circ $ (blue), 10 $^\circ $ (red), 25 $^\circ $ (yellow), and 40 $^\circ $ (purple). (c) Bragg’s law dependency of A-RTS spectra (blue line) and RMSE estimation using an ideal FCC colloidal crystal as reference (black line).
Fig. 3.
Fig. 3. (a) Implemented experimental set-up for measuring concentration profiles of a colloidal suspension of SiO2 spheres in deionized water at 0.8vol%. (b) Concentration profiles of the colloidal suspension (asterisks) and fitting under Kynch’s sedimentation modelling (continuous lines) for 72 h (dark blue), 120 h (red), 168 h (yellow), 192 h (purple), 220 h (green), and 244 h (light blue), respectively.
Fig. 4.
Fig. 4. (a) Experimental set-up for estimating the evaporation rate of a colloidal suspension consisting of SiO2 spheres immersed in deionized water. (b) Evaporation rate measurements as a function of time (blue asterisks), experimental fitting curve (red line), confidence bounds (red dotted line), and log-log scale plot in the inset.
Fig. 5.
Fig. 5. Bragg’s law dependency of three replicas from samples elaborated by a combination of parameters (volume fraction and Temperature ramp). RMSE estimation uses an ideal FCC-packed colloidal crystal (gray bars) as reference. Temperature conditions shown in the columns are: 0.5°C/h during 30 h, 70 h, and 110 h. Colloidal suspension concentrations shown in the rows are: 0.05, 0.1, 0.26, and 0.42 vol%.
Fig. 6.
Fig. 6. Simulations of the sedimentation concentration profiles (color maps on left column), meniscus position (blue-red line in the left column), concentration profile on the substrate (color map on middle column), and A-RTS spectra of a representative elaborated film (right column) for 0.5°C/h temperature ramps applied during 30 h, 70 h and 110 h, respectively.
Fig. 7.
Fig. 7. (a) RMSE average values as a function of volume fraction for samples fabricated under applied temperature ramps of 0.5°C/h during 30 h (in blue), 70 h (in red), and 110 h (in yellow). (b) and (c) SEM images of samples obtained with ramps of 0.5°C/h during 110 h at 0.42vol%.

Equations (15)

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T L i ( t ) = { α t + T 0 , t t f i T f i , t > t f i ,
λ m 2 = 4 h 2 ( n e 2 ) 4 h 2 ( sin 2 θ ) ,
n e = ( 1 f ) n a i r 2 + f n S i O 2 2 ,
ϕ ( t , z ) t = K D 2 ϕ ( t , z ) t 2 f b k ( ϕ ) t
K D = m K B T 3 π μ d ,
ϕ ( t , z ) = { 0 , z = L ϕ 0 , 0 z L ϕ max , z = L
f b k ( ϕ ) = v s ϕ ( t , z ) ( 1 ϕ ( t , z ) ) n ; f o r n > 1 ,
v s = d 2 18 μ ( ρ s ρ f ) g ,
ϕ ( t , z ) t = ( m K B T ( t ) 3 π μ ( T ) d ) 2 ϕ ( t , z ) t 2 ( g d 2 ( ρ s ρ f ) 18 μ ( T ) ) ϕ ( t , z ) ( 1 ϕ ( t , z ) ) n t
μ ( T ) = A 10 ( B T C ) ,
h C S = V C S π ( d v / 2 ) 2
v e v a p ( T ) = h C S t e v a p ( T )
v e v a p ( T ) = ρ + β e T γ
v e v a p ( t ) = { ρ + β e α t + T 0 γ , t t f i v e v a p ( t f i ) , t > t f i
z m ( t ) = { β γ α e T 0 γ + ρ t + β γ α e α t + T 0 γ , t t f i z m ( t f i ) + ( t t f i ) v e v a p ( t f i ) , t > t f i

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