Effect of Substrate on Nucleation Rate of Two-Dimensional Colloidal

Apr 25, 2019 - Graduate School of Pharmaceutical Sciences, Nagoya City University , 3-1 Tanabe, Mizuho, Nagoya , Aichi 467-8603 , Japan. Cryst. Growth...
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Effect of Substrate on Nucleation Rate of Two-Dimensional Colloidal Crystals Suxia Guo,*,† Jun Nozawa,*,† Masashi Mizukami,‡ Kazue Kurihara,‡ Akiko Toyotama,§ Junpei Yamanaka,§ Hiromasa Niinomi,† Junpei Okada,† and Satoshi Uda† Institute for Materials Research and ‡Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan § Graduate School of Pharmaceutical Sciences, Nagoya City University, 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan Downloaded via STATE UNIV NEW YORK PLATTSBURGH on May 14, 2019 at 15:53:30 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

S Supporting Information *

ABSTRACT: The effect of a substrate on the heterogeneous twodimensional (2D) nucleation of colloidal crystals has been investigated. Nucleation rates, J, of 2D colloidal crystals on uncoated cover glass, Ptcoated cover glass, and Au-coated cover glass are measured. Among the three substrates, the J of the uncoated cover glass is found to be the largest, while it is smallest for the Pt-coated cover glass under the same supersaturation conditions. The interfacial free energy change, Δσ, is obtained from the nucleation rate based on classical nucleation theory (CNT), indicating that uncoated cover glass possesses the smallest Δσ, while it is largest for the Pt-coated cover glass. Since Δσ originates from the bond energy in atomic crystals, we deduce that it is related to the interaction between colloidal particles and the substrate in a colloidal system. The interactions between a colloidal particle (polystyrene) and each substrate are determined with surface force measurements using atomic force microscopy (AFM). The results show that the adhesive force, which predominantly consists of the van der Waals force, between particles and uncoated cover glass, is the weakest, while that for the Pt-coated cover glass is the strongest. A larger attractive interaction between the colloidal particles and the substrate yields a higher Δσ, and thus a smaller J. The interaction between particles and substrate has a great influence on the heterogeneous nucleation rate of colloidal crystals.

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INTRODUCTION

It is well-known that colloidal crystals have unique optical features, which are expected to be applied to innovative optical functional devices. Two-dimensional (2D) colloidal crystals also possess versatile applications,10−12 among which “colloidal lithography” is a typical application. To produce surface patterning, 2D colloidal crystals are utilized as masks or templates in the processes of evaporation,13 deposition,14 etching,15 and imprinting.16 Furthermore, 2D colloidal crystals have been employed for fundamental studies as they are a promising model of phase transitions in atomic and molecular systems,17 such as for glass formation,18 liquid nucleation in crystals,19 and epitaxial growth.20 For these aforementioned applications, high quality 2D colloidal crystals are required.21 There are a variety of methods for fabricating 2D colloidal crystals, including solvent evaporation,22 spin coating,23 applying an electric field,24 and employing particles with attractive interaction.25 Many parameters, such as temperature, solvent, and humidity, are important to manipulate the quality of the resulting colloidal

The control of nucleation is critical for manipulating the number, size, perfection, and other characteristics of crystals.1 Heterogeneous nucleation on a substrate is the most common mode of crystallization in industry as well as in nature. Thus, the substrate plays a crucial role in the nucleation rate. Many efforts have been devoted to studying the effect of the substrate on nucleation; e.g., the effect of temperature of the substrate2 and the surface structure of the substrate3 have both been investigated. The substrate also plays a crucial role in the nucleation of colloidal crystals.4−6 Numerous studies on the substrate effect have been conducted. For instance, it was reported that the presence of a smooth hard wall drastically lowered the barrier for nucleation of colloidal crystals in a hard sphere system, where the critical Gibbs free energy for nucleation on the wall was lower than that for homogeneous nucleation by about 2 orders of magnitude.7 Arai et al. reported that a substrate in a supercooled liquid induced short-range translational ordering, the structure of which determined the final colloidal crystalline state such as bcc, hcp, or fcc.8 The effect of substrate curvature was also investigated, in which only seed particles exceeding a defined minimum size could promote nucleation.9 © XXXX American Chemical Society

Received: January 16, 2019 Revised: April 18, 2019 Published: April 25, 2019 A

DOI: 10.1021/acs.cgd.9b00069 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 1. (a) Cover glass (I), Au-coated cover glass (II), and Pt-coated cover glass (III) substrates. (b) Schematic illustration of the growth cell for the colloidal crystals. (c) Schematic illustration of the colloidal AFM probe for measuring interactions between the polystyrene particle and the substrate.

Figure 2. Nucleated 2D islands on different substrates, cover glass (a), Au-coated cover glass (b), and Pt-coated cover glass (c), under the same solution conditions, where Φ is 0.5% and the concentration of sodium polyacrylate is 0.15 g/L.

crystals. In particular, the substrate is one of the key factors in the nucleation of 2D colloidal crystals. In the conventional heteroepitaxial growth system, the impact of a substrate on the nucleation is measured by the change in interfacial free energy, Δσ, which consists of the interfacial energies between substrate/solid, σsub−solid, solid/ liquid, σsolid−liquid, and substrate/liquid, σsub−liquid.26 The Δσ is an important parameter to understand and control the nucleation rate and the growth mode of the thin film.27−29 Yet, the significance of the substrate on the crystallization of 2D colloids has not been taken into account. In general, the effect of the substrate has been ignored for the nucleation of 2D colloidal crystals even though they are grown on substrates of different materials. In our previous work, the generation of Δσ during nucleation was proposed. Two types of nucleation processes were recognized: conventional 2D nucleation and quasi-2D (q-2D) nucleation. The favored q-2D nucleation, which occurs with a smaller number of particles than that of 2D, was accounted for when Δσ was introduced into ΔG for the nucleation.30 We deduce that this is due to different particle−substrate interactions for the particles in the crystal and liquid phases. The polymer distribution around particles or surface charge of PS particles are probably not the same because the particle density for crystal and liquid phases is significantly different. Since the Δσ is dependent on the substrate material, we expected that nucleation and growth of colloidal crystals would vary when different substrates were employed. In the present study, to obtain a better understanding of the substrate effect, the nucleation of colloidal crystals on three different substrates, uncoated, Pt-coated, and Au-coated cover glasses, is examined. The nucleation rate, J, is measured for these three substrates, from which the Δσ value for each substrate is obtained. Since the Δσ originates from the bonding energy between the substrate and the crystals, the interaction

between particles and substrate is evaluated by surface force measurements.

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EXPERIMENTAL SECTION

The colloidal particles employed in the experiments were green fluorescent 500 nm monodispersed polystyrene spheres (PS) (Thermo Fisher Scientific). The zeta potential of the PS particles was measured as −47.1 ± 5.9 mV. A negatively charged sodium polyacrylate polymer (polymerization degree of 30 000−40 000) was dispersed into the PS suspensions as the depletant to generate an attractive force between the particles and the substrate as well as between the particles. The concentration of sodium polyacrylate was 0.15 g/L for all experiments. The volume fractions (Φ) of initial colloidal suspensions ranged from 0.05% to 1%. Three different substrates, uncoated, Au-coated, and Pt-coated cover glasses, were used (Figure 1a). A cover glass with a thickness of 0.12−0.17 mm was employed after cleaning with deionized water. Au or Pt thin layers (∼12 nm in thickness) were coated on the cover glass by the sputter coating technique (SC-701AT, Sanyu Electron Inc.). The solution was sealed in a growth cell composed of a silicone sheet as a spacer (2 mm thickness) and cover glass as a substrate as shown in Figure 1b. All of the experiments were performed under ambient conditions (ca. 25 °C). Colloidal crystallization is caused by a depletion attraction.31−33 Crystallization occurred on the substrates at the bottom of the cell, and was observed by inversed optical microscopy. An oil immersion lens (magnification = 100 and N.A. = 1.3) was utilized to achieve single particle resolution of 500 nm particles. The interaction forces between a polystyrene particle and a substrate were measured as a function of the surface separation distance (D) using colloidal probe atomic force microscopy.34,35 A schematic illustration of the setup is shown in Figure 1c. A commercial AFM (SPI3800-SPA400, SII NanoTechnology Inc.) in combination with a homemade closed fluid cell was used for the interaction forces measurement in aqueous solution. The colloidal probe was prepared by attaching a colloidal sphere (polystyrene, 10 μm in diameter) to the end of a cantilever (DNP-S, Bruker Nano Inc.) with UV curable resin (NOA61, Norland Products Inc.). The B

DOI: 10.1021/acs.cgd.9b00069 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 3. (a) Nucleation rate, J, at various ϕarea for three different substrates. (b) The ln J as a function of ln(ϕarea/ϕeq) for three different substrates. details of the surface force measurement are described in the Supporting Information. In this study, the area fraction, ϕarea, is employed to represent the surface concentration of the colloidal particles, which is defined as the area occupied by ad-particles in the observed area. The ϕarea is determined as the number of ad-particles on the substrate, N, multiplied by the area of the particle, Ω, divided by the observed area. The area of the formed colloidal crystals is not included in the observed area in the calculation of ϕarea.

glass has the largest J, while the Pt-coated substrate has the smallest J under the same ϕarea. We next analyzed the difference in J for different substrates from the thermodynamic viewpoint. In our previous work, the Gibbs free energy change, ΔG, for 2D nucleation was expressed in terms of the number of particles, n, taking the interfacial energy change, Δσ, into account30

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ΔG(n) = −nΔμ +

RESULTS AND DISCUSSION After mixing the polymer solution and the suspension, the particle concentration on the substrate gradually increase due to sedimentation of the particles by gravity and the depletion attraction between the particles and substrate which is induced by overlap of the depletion zones. Since 500 nm colloidal particles display strong Brownian motion, particles that do not form clusters return to solution after diffusion on the substrate. When the particle concentration reaches a certain value, nucleation occurs on the substrate. The nucleated first layer grows laterally and the 2D nucleation of the second layer occurs on the terrace. The nuclei grow into colloidal crystals with 3−5 layers by repeating the 2D nucleation. Figure 2 shows the nuclei formed 15 min after starting the experiment for the three different substrates under the same initial volume fraction, Φ. In Figure 2, there are many small disordered aggregates and ordered prenucleation clusters. The nuclei are identified by their sizes. The average particle number in small aggregates is about 10, while the typical critical nucleus size is 40. Therefore, small aggregates and nuclei are clearly identified by their size. Some of the small aggregates transform into prenucleation clusters that possess the same crystal structure as the nuclei. To identify nuclei, the evolution of the size of the prenucleation cluster is traced. Some that are smaller than the critical size will dissolve into the solution, while others that surpass a critical size will continue to grow. Thus, the critical number of particles is obtained as the maximum size that tends to dissolve. Among the three substrates, the number of nuclei on the uncoated cover glass is largest, while it is smallest for the Pt-coated cover glass. Thus, it is clear that the nucleation rate is dependent on the substrate material. The relationship between nucleation rate, J, and area fraction, ϕarea, which is introduced as the surface concentration of particles, for the three substrates is investigated. Figure 3a shows the J of 2D colloidal crystals as a function of ϕarea for three different substrates. Among the three substrates, cover

2 3 nΩ·Δσ + π

2 3 πa n · γ π

(1)

where a is the diameter of a colloid particle, Ω is the area per particle (equal to π(a/2)2), γ is the step free energy (line tension) of nuclei, and Δμ is the chemical potential difference between the bulk liquid and solid. Here, Δμ is a function of supersaturation, which is expressed as (ϕarea − ϕeq)/ϕeq, where ϕeq is the equilibrium concentration. The Δσ is the change in interfacial free energy, which is given by Δσ = σsub − solid + σsolid − liquid − σsub − liquid

(2)

where σ is the interfacial energy between each phase. The critical Gibbs free energy change, ΔG*, of the formation of critical nuclei leads to30 ΔG* =

3 πa 2 γ 2 2Δμ − 3 a 2Δσ

(3)

ij ΔG* yz zz J = A expjjj− j kBT zz k {

and J is expressed as

(4)

where kB is the Boltzmann constant, T is the absolute temperature, and A is a kinetic prefactor, expressed as

( ) ΔU

K υ(T ) exp − k T , ΔU is the activation energy for one particle B

to migrate across the interface separating the nucleus and matrix, and Kυ(T) is the Zeldvich factor. The value of A is related to the attachment rate of the particles surrounding the critical nuclei, the Zeldvich factor, and the number density of

( ) ΔU

the colloidal particles. Since the term, exp − k T , is B

proportional to the diffusion coefficient, D, then D is also proportional to J. The effect of D on J was evaluated. The D values of particles for three substrates under low particle concentration were measured by using the equation MSD = ⟨(x − x0)⟩2 = 2Dt C

DOI: 10.1021/acs.cgd.9b00069 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 4. (a) Force−distance profiles between polystyrene particle and each substrate in pure water. A positive sign of the force corresponds to a repulsive interaction while a negative sign indicates an attractive force. Dashed lines indicate when the particle jumps into contact. (b) Statistics of adhesive forces between colloidal particles and three kinds of substrates. Red circles represent the value for uncoated cover glass, green triangles for Au-coated cover glass, and blue squares for Pt-coated cover glass.

driven by the vdW force.36 Since the strength of the depletion attraction depends on the size and density of the polymers,30 its value is independent of the substrate material, while the magunitude of the vdW force is dependent on the material. Therefore, to determine the vdW force between particles and each substrate, surface force measurements were conducted in pure water. The surface force measurement is a powerful method to measure very slight forces interacting between two substances with high sensitivity.37−39 All of the surface force measurements in this study were conducted in pure water instead of polymer added water. Since polymers easily adhere to the cantilever of the AFM, the measurement was challenging. However, because the depletion attraction is the same for all three substrates, the order of interaction between the particle and each substrate corresponds to that of the vdW force interaction. Figure 4a shows the force−distance profiles for the PS particle and three substrates in pure water measured during the approach process. The adhesive forces measured in the separation process are indicated at zero distance. The details of the measurements are described in the Supporting Information. Repulsive forces are observed in the distance range from several tens to 100 nm for all of the substrates, which are due to the electrostatic repulstion between the particle and substrates. As the substrate approaches the PS particle, the PS particle jumps into contact with the substrate, which is called “jump-in”, indicating that the gradient of the attractive force (vdW attraction) exceeds the stiffness of the cantilever. The jump-in is observed for all three substrates. After the approach process, the forces on the separation process are also measured, and “jump-out” is observed. The adhesive forces are determined as the force required for the jump-out to take place. The adhesive force consists of an electrostatic repulsion and the vdW force. However, since the vdW force is dominant at short distances, we regard the order of adhesive force for the three substrates as that of the vdW attraction. The adhesive forces for each substrate are shown in Figure 4b. The adhesive force for Pt-coated cover glass is the largest while that for the uncoated cover glass is the smallest. This magnitude order is the same as that for the Δσ values for each substrate determined from J. It is thus demonstrated that Δσ is based on the interaction between the particle and the substrate.

where MSD is mean square displacement, x is the displacement of a particle from its original position, and t is the observation time. The x and t are measured by in situ observations, in which 8 particles are traced over 120 s for each substrate. The results of D are (0.504 ± 0.21) × 10−12, (0.380 ± 0.05) × 10−12, and (0.384 ± 0.12) × 10−12 m2·s−1 for uncoated, Au-coated, and Pt-coated cover glass, respectively. Here, the J at ϕarea = 0.135 is 1.8 × 10−5, 4.2 × 10−5, and 9.9 × 10−5, for uncoated, Au-coated, and Pt-coated cover glass, respectively. The ratio of J for uncoated, Au-coated, and Ptcoated cover glass is 5:2:1. This difference is not accounted for by the variation of each D value; the difference in J is larger than that derived by D. While D is one of the parameters that affects J, Δσ is a more significant factor in colloidal crystals. Substituting eq 3 into the above equation yields ln J = ln A −

3 πa 2 γ 2 (2kBT ln ϕarea /ϕeq − 3 a 2Δσ )kBT

(5)

Here, the ϕeq is determined experimentally as ϕarea where the growth rate of steps of 2D islands is zero, assuming that Δμ is only used for growth kinetics. The ϕeq for uncoated, Aucoated, and Pt-coated cover glass are 1.1%, 0.9%, and 0.95%, respectively. The values in Figure 3a are replotted based on eq 5 as shown in Figure 3b. The Δσ is obtained from Figure 3b by fitting eq 5. The values of Δσ on the uncoated, Au-coated, and Pt-coated cover glass are determined to be 0.83 ± 0.07, 1.39 ± 0.13, and 1.47 ± 0.11 [kBT/a2], respectively. The errors of the Δσ values for Au and Pt overlap. Here, Δσ is also determined by the number of particles in the critical size. The Δσ values for uncoated, Au-coated, and Pt-coated cover glass are 1.07 ± 0.06, 1.55 ± 0.05, and 2.20 ± 0.10 [kBT/a2], respectively. The magnitude order of Δσ for the three substrates is consistent with that obtained by J. In the atomic system, Δσ is dependent on the bonding energy between the substrate and a formed crystal. We deduce that the Δσ for colloidal crystals is related to the strength of the interaction between particles and the substrate. The interaction between particles and substrate in a polymer solution mainly consists of the depletion attraction and the vdW force. The vdW force plays the dominant role for the interaction between submicron-sized particles and substrate, e.g., the adsorption of a silica particle onto hydrogel surfaces is D

DOI: 10.1021/acs.cgd.9b00069 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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roughnesses on Au-coated and Pt-coated cover glass that are used in the nucleation experiment are measured by AFM to be 0.84 ± 0.08 and 0.29 ± 0.04 nm. The roughness of the Ptcoated cover glass is smaller than that of the Au coating. Thus, the surface force measurements for different substrates with approximately the same roughness were conducted. The adhesive force of Pt-coated cover glass with a roughness of 1.11 ± 0.06 nm was compared to that of Au with nearly the same roughness (0.84 ± 0.08 nm). The adhesive force of the Pt-coated cover glass is measured to be 17.30 ± 1.25 mN/m (force profile is shown in Figure S2 in the Supporting Information), which is less than that of the Au-coated cover glass. The greater roughness of the substrate yields less adhesive force, which is suggested by the relationship between the strength of the vdW force and roughness.47 If the influence of roughness is taken into account, the order of measured forces is in accordance with the calculation results based on eq 6 for the coated samples. The J on a Pt-coated substrate with a roughness of 0.63 ± 0.09 nm (similar to the Au-coated cover glass) was measured to evaluate the effect of roughness on J. The J on the Pt-coated cover glass was slightly larger than that on the Au-coated cover glass under the same supersaturation. This result is consistent with magnitude of the relationship of the Hamaker constants between Pt and Au. The relationship between nucleation rate and strength of the vdW force that depends on the roughness is confirmed experimentally in a qualitative manner. Here, it should be noted that, to the best of our knowledge, this is the first time that surface force measurements between polystyrene colloidal particles and Au and Pt films over water medium have been conducted. These results are applicable to not only colloidal crystallization, but also to various surface chemistry fields that include surfaces of polystrene, Au or Pt. We have studied the effect of substrates on the J of 2D colloidal crystals. The value of Δσ is relevant to the strength of the interaction between particles and substrates. We demonstrated that Δσ for colloidal crystals could be controlled by changing the substrate material or its roughness, which leads to further control of J.

Only hydrophilic substrates are employed in the present study. When a hydrophobic substrate is used, the nucleation rate will be smaller. It was reported that surface force measurements suggest a stronger interaction between PS and hydrophobic substrates, which is due to the formation of a bridging air bubble between PS and the substrate.40 A larger Δσ for a hydrophobic substrate is obtained by the stronger interaction, which leads to a smaller nucleation rate. Here, it should be mentioned that an image-charge is induced by the metal conducting substrates of Pt and Au. There are reports on the effect of the image-charge on particle interaction, e.g., the effect of the image-charge on the 2D colloidal crystallization at an oil-aqueous interface41 and the intensity of the particle interaction, in which the value of zeta potential is changed.42,43 In the present study, since the surface force measurement includes all of the interactions that are working between particles and substrate, the effect of the image-charge is included in the results. Though we cannot differentiate the effect of the image-charge quantitatively, the relationship between Δσ and particle interaction is not changed. In general, the vdW force can also be estimated by calculations using the Hamaker constant of individual materials. The vdW force between particles and a plate is given by44 FvdW = −

AHR 6D2

(6)

where AH is the Hamaker constant between a colloidal particle and a plate in a solution medium, R is the radius of one colloidal particle, and D is the distance between the particle surface and a plate. AH is calculated using individual Hamaker constants of polystyrene, water, and each substrate as44 AH = ( A11 −

A 22 )( A33 −

A 22 )

(7)

where A11, A22, and A33 are the Hamaker constants of the colloidal particle, water, and substrate, respectively. The following values are used for the calculations: polystyrene, A11 = 6.6 × 10−20 J;44 water, A22 = 3.7 × 10−20 J;45 glass, Au, and Pt, A33 = 6.3 × 10−20, 38 × 10−20, and 20 × 10−20 J, respectively.46 The combined Hamaker constants of eq 7 for uncoated, Au-coated, and Pt-coated cover glass are calculated to be 0.4 × 10−20, 2.7 × 10−20, and 1.6 × 10−20 J, respectively. The combined Hamaker constant, Δσ, and adhesive forces for the three substrates are summarized in Table 1.

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SUMMARY Nucleation rates, J, of 2D colloidal crystals on cover glass, Ptcoated cover glass, and Au-coated cover glass have been measured. Different J values for each substrate are determined, from which different values of Δσ are obtained. From the surface force measurements, it is revealed that Δσ is of relevance to the interaction between particles and substrates. The larger attractive interaction between colloidal particles and substrate yields a higher Δσ and hence larger ΔG*, leading to a smaller J. We clearly demonstrate that the type of substrate and its roughness are crucial parameters for controlling the nucleation rate of colloidal crystals. Our findings will contribute to extensive applications of colloidal crystals such as in colloidal epitaxy and lithography grown on any substrate.

Table 1. Values of Combined AH, Adhesive Forces, and Δσ on Three Substrates substrates

AH (10−20 J)

adhesive force (mN/m)

Δσ (kBT/a2)

cover glass Au Pt

0.4 2.7 1.6

1.61 ± 0.10 19.12 ± 1.77 56.93 ± 3.38

0.83 ± 0.07 1.39 ± 0.13 1.47 ± 0.11

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Among the three substrates, the calculated van der Waals interaction between PS particles and Au-coated cover glass is the largest. This is not consistent with the surface force measurements and Δσ values determined from J. This inconsistency is likely caused by the roughness of the coated substrate since the vdW force is dependent on roughness.47 We then conducted the surface force measurements for different substrates with similar roughness. The average surface

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.9b00069. Surface force measurements (PDF) E

DOI: 10.1021/acs.cgd.9b00069 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (S. Guo). *E-mail: [email protected] (J. Nozawa). ORCID

Suxia Guo: 0000-0002-8567-6557 Jun Nozawa: 0000-0001-7735-3515 Kazue Kurihara: 0000-0002-7299-1371 Hiromasa Niinomi: 0000-0001-7003-5434 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by JSPS KAKENHI Grant Number 18K05054 and the China Scholarship Council (CSC).

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REFERENCES

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DOI: 10.1021/acs.cgd.9b00069 Cryst. Growth Des. XXXX, XXX, XXX−XXX