Effect of added surfactant on convective assembly of monosized microspheres

Close-packed colloidal structures based on the size, packing, and surface activities of monosized microspheres and nanoparticles are useful in coatings for photonics,^1–4 solar cells,⁵ membranes,^6–10 cell capture devices,¹¹ etc. Most of these applications require a single layer of colloids in an ordered monolayer. Likewise, recent research shows the importance of fabricating a uniform monolayer coating for the synthesis of Janus particles.^12–14 Convective deposition has proven to be a robust technique for the fabrication of a monolayer from colloidal suspensions.^15–19 Rather than depositing a thin film of the suspension that eventually dries and deposits particles on the substrate, convective deposition utilizes a balance between the film formation and solvent evaporation. In this process, the particles are drawn toward an evaporating thin film by convection and they assemble into a close-packed structure. The close-packed structure is a result of convective steering^20,21 and/or capillary forces,^15,22,23 as observed in the “coffee ring effect.”²² The number of layers in the convective deposition is inversely correlated with the substrate velocity and depends on other experimental conditions, such as the evaporation rate, suspension's pH, ionic strength, and volume fraction. Producing a uniform crystalline monolayer of particles requires fine-tuning of all parameters, which becomes a foreseen limitation to process scale-up. This work demonstrates a method for reducing the process parameter sensitivity through the addition of a surfactant. Defects in the final structure, which result from a small deviation in processing conditions, are also reduced. Silica and polystyrene nanospheres are the most commonly used materials in the colloidal assembly due to their availability. Additionally, silica and polystyrene can be robustly modified with suitable functional groups to match a product need. Silica microspheres acquire a negative charge in the aqueous system, and thus, an anionic surfactant, in this study sodium dodecyl sulfate or SDS, was preferred over a cationic surfactant. The presence of SDS minimally alters the surface properties of silica, which helps us to isolate the effect of the surfactant. On the other hand, in the case of polystyrene particles, SDS has a strong affinity toward the particle surface, often a necessary addition to maintain the suspension stability.²⁴ 

Many previous studies have considered the effects of the surfactant on the stability of a colloidal suspension droplet^25,26 and the Marangoni flow induced as a result of surfactant concentration gradients over a thin film.^27–29 Recent research focuses on the reversing of the coffee ring effect due to Marangoni flow resulting from surface tension gradients^27,30–32 in a drying sessile drop. Additionally, researchers have investigated how a temperature gradient^33,34 or even a surface conductivity gradient³⁵ induces the Marangoni flow in thin films, similar to that found in tears of wine. Likewise, Yuan et al. used a surfactant to stabilize ultrathin films for depositing nanoparticles via the convective assembly.⁹ Berteloot et al.³⁶ first demonstrated the relationship between the coating film thickness and velocity via fluid mechanics using the lubrication theory. They show that the surface tension and curvature determine the pressure gradient, which is related to fluid velocity. There results assure that the presence of the surfactant will affect the coating since it changes both the surface tension and curvature. Here, we aim to demonstrate how the added surfactant alters the particle assembly mechanism, measure the leading order cause, and propose how this relates to previous theory.

Figure 1(a) shows the typical experimental setup used for convective deposition, where the meniscus of the suspension is confined in a space between the blade and substrate. The substrate is moved relative to the blade held at 45° using a linear motor (Harvard Instruments Co., Ltd.). This results in spreading suspension meniscus to form a thin film. The wetted suspension acts as the bulk particle source for the continuously produced thin film in this pseudo-steady state process. Particles flowing through evaporating the thin film orient into the close-packed structure by the convective steering and/or capillary forces.^15,23 The general relationship between a number of layers and the conditions of the convective assembly is given by the Nagayama equation,¹⁷ which assumes the pseudo-steady state flux balance between evaporation losses and convective flux in the thin film

Here, u_s is the substrate velocity (μm/s), J_e is the evaporative rate (μm/s), ϕ is the volume fraction of particles, β is the interaction parameter, d is the diameter of particles (μm), N is the number of layers in the assembly, and L is the drying length (mm). This equation assumes the balance between a convection flux and evaporation loss. The system is under pseudo-equilibrium with a sharp phase separation of nanoparticles from the uniformly suspended monolayer to a well-ordered structure as shown in Fig. 1(b). The solvent penetrates through the porous structure and eventually evaporates. The length of the wet particle assembly is known as the drying length, L. Under many conditions, L is an inverse function of the capillary number, as shown in previous work.³⁷ However, in the presence of a surfactant, this assumption of pseudo-steady mass balance may be insufficient in describing the expected thickness of deposited particles. Marangoni flow resulting from a local surface tension gradient along the free surface can play a crucial role in thin film hydrodynamics.^34,38 For instance, previous studies show that below a critical SDS concentration, the Marangoni effect observed in drying sessile droplets is weak, but then it is significant with regard to the internal droplet flow.^32,39 Our hypothesis is that the addition of a surfactant alters the surface energy along the continuously emerging interface during convective deposition, affecting the organization of particles.

We observe an appreciable effect on coating patterns with added SDS, similar to that found in drying of sessile droplets.³² Figure 2 shows the dependence of the surface morphology as a function of the deposition rate and surfactant concentration. There is differing behavior for the range of monolayer velocities for a given set of parameters (ϕ − 0.2, RH − 20%, and T − 23 °C) at different SDS concentrations. Without the added surfactant, the number of layers is correlated with the substrate velocity as (N ∼ 1/u_s²),³⁷ and thus, a small deviation from an ideal velocity typically leads to sub-monolayer deposition at higher velocity, and lower substrate velocity results in areas of multilayers. In practice, without the added surfactant, an ideal monolayer can only be obtained over a very narrow range of substrate velocities. This sensitivity of the deposition speed makes the process less desirable. Our previous work shows that an addition of surface charge⁴⁰ or high frequency mechanical vibration⁴¹ allows a wider monolayer velocity range. However, changing the surface charge cannot be implemented in situations where the surface properties are critical to the performance of the assembled particles, and it is non-trivial to add a prescribed vibration during the deposition. Here, we have shown a similar enhancement of the monolayer range using SDS.

In this analysis, the concentration is reported as w/w% of SDS, ξ, and the critical micelle concentration (CMC) concentration for SDS is ξ = 0.23. The monolayer range is narrow and relatively unaffected at lower SDS concentrations of 0 ≤ ξ ≤ 0.1, as expected. The range of deposition speed resulting from the monolayer expands with a further increase in the SDS concentration. The monolayer range expands as ξ → 1, surpassing the critical micelle concentration. Previous studies have noticed a similar sharp transition in the Marangoni recirculation as the concentration nears the CMC, for example, Still et al. observed an increase in the Marangoni recirculation for ξ > 0.5.³² In this system, the Marangoni stresses are present at the air–liquid interface altering velocity in the direction of deposition. Not shown here, at much higher SDS concentrations (ξ > 2), the deposition process still forms ordered layers of particles, but they are marred by the deposition of dried regions of solid SDS, apparently resulting in streaks due to the local change in topology and surface chemistry. To demonstrate the robustness of monolayer coatings with the added surfactant, Fig. 3(a) displays a continuous monolayer deposition across a broad region of deposition velocities, ranging from u_s = 83.3 mm/s down to u_s = 25 mm/s from left to right. The discontinuity lines in the deposition are only the result of changing the substrate velocity and are caused by temporary particle accumulation. The smooth and continuous color bands validate the uniform coating at different velocities. It shows a clear transition from the slight submonolayer to monolayer and from the monolayer to slight multilayer deposition. Figure 3(b) shows the microstructure obtained at different monolayer velocities. To quantify the morphology of the particle assembly, ρ and Ψ₆ were calculated for each deposition. Figure 3(c) shows the general quality of monolayers for all values of ξ. The particle density fluctuates but stays just slightly below the expected value of ρ = π/sqrt(12) ≈ 0.906, as expected due to defects that result in imperfect deposition and small polydispersity in the particle size. Likewise, the Ψ₆ values are uniformly high for all monolayer deposition speeds and the multilayer deposition.

These observations point toward the significant change in the mode of the particle assembly at higher SDS concentrations. The Marangoni stress alters the otherwise simple mass balance between the evaporation and convection as described in the Nagayama equation. This results in the change of the behavior of the characteristic drying length where the liquid extends into the porous structure and evaporates. In order to quantify the effect of Marangoni stress on deposition, we analyzed a variation in the drying length with the surfactant amount. As shown in previous work, for the evaporation dominant system, the drying length, L, varies as an inverse function of the substrate velocity (1/u_s).³⁷ L depends on the initial solvent penetration velocity into the particle bed. Figure 4 shows a progressive shortening of the drying length with increasing ξ. For ξ = 0, the drying length varies inversely with the substrate velocity. With increasing ξ, the dependence of the drying length on the substrate velocity is weaker. For ξ = 1, the drying length is essentially independent of the substrate velocity. We believe, here, that the flow is likely governed by the Marangoni stresses at the interface due to the presence of the surfactant. Additionally, for ξ = 1, the drying length is much shorter, perhaps due to continuous depinning of a contact line resulting from lower surface energy. Though the drying length changes as a function of the surfactant concentration, this alone cannot explain why the monolayer deposition is preferred in this system. We hypothesize that the Marangoni stress acts as a flow control feedback like system, which allows just enough suspension from the bulk meniscus to obtain the monolayer (as illustrated in Fig. 5). This feedback loop broadens the monolayer velocity range. A significant widening of monolayer velocity increases the flexibility of this process. As noted above, we fail to obtain a uniform coating for ξ > 2.

Surprisingly, the effect of the surfactant on the particle assembly has not previously been explored in detail but likely resides in many experiments with latex particles and other surfactant stabilized suspensions. This study of the surfactant impact on convective deposition without changing the actual surface properties of particles is a clear indication that the added surfactant alters the assembly. The drastic decrease in the drying length indicates the existence of Marangoni stress resulting from a surfactant concentration gradient on the interface. This effect is only observed at concentrations above CMC. The counter flow and/or buildup of surfactant invokes a depinning of the contact line, which broadens the often-desirable range of monolayer deposition. What remains unclear is how the Marangoni stress directly cancels out the effect of faster substrate velocity to maintain monolayer coating conditions over a relatively wide range of deposition rates. It suggests that there is a balance of stress altering the streamlines in such a way that it negates the faster flow conditions at higher velocities. It is also serendipitous that not only are monolayer conditions maintained over a larger range of processing conditions, but also monolayers have a high degree of order that is independent of the surfactant concentration. These results suggest that in many cases, where appropriate, the added surfactant can aid in producing larger-scale monolayer structures without a high degree of sensitivity to the operating conditions.

This material is based upon the work supported by the National Science Foundation (NSF) Scalable Nanomanufacturing Program under Grant No. 1120399.

The authors declare no competing financial interest.