Particle and substrate charge effects on colloidal self-assembly in a sessile drop

By direct video monitoring of dynamic colloidal self-assembly during solvent evaporation in a sessile drop, we investigated the effect of surface charge on the ordering of colloidal spheres. The in situ observations revealed that the interaction between charged colloidal spheres and substrates affects the mobility of colloidal spheres during convective self-assembly, playing an important role in the colloidal crystal growth process. Both ordered and disordered growth was observed depending on different chemical conditions mediated by surface charge and surfactant additions to the sessile drop system. These different self-assembly behaviors were explained by the Coulombic and hydrophobic interactions between surface-charged colloidal spheres and substrates.     

Axisymmetric drop shape analysis-constrained sessile drop (ADSA-CSD): a film balance technique for high collapse pressures

Collapse pressure of insoluble monolayers is a property determined from surface pressure/area isotherms. Such isotherms are commonly measured by a Langmuir film balance or a drop shape technique using a pendant drop constellation (ADSA-PD). Here, a different embodiment of a drop shape analysis, called axisymmetric drop shape analysis-constrained sessile drop (ADSA-CSD) is used as a film balance. It is shown that ADSA-CSD has certain advantages over conventional methods. The ability to measure very low surface tension values (e.g., <2 mJ/m2), an easier deposition procedure than in a pendant drop setup, and leak-proof design make the constrained sessile drop constellation a better choice than the pendant drop constellation in many situations. Results of compression isotherms are obtained on three different monolayers: octadecanol, dipalmitoyl-phosphatidyl-choline (DPPC), and dipalmitoyl-phosphatidyl-glycerol (DPPG). The collapse pressures are found to be reproducible and in agreement with previous methods. For example, the collapse pressure of DPPC is found to be 70.2 mJ/m2. Such values are not achievable with a pendant drop. The collapse pressure of octadecanol is found to be 61.3 mJ/m2, while that of DPPG is 59.0 mJ/m2. The physical reasons for these differences are discussed. The results also show a distinctive difference between the onset of collapse and the ultimate collapse pressure (ultimate strength) of these films. ADSA-CSD allows detailed study of this collapse region.     

Variational approach to wetting problems: Calculation of a shape of sessile liquid drop deposited on a solid substrate in external field

Analysis of the shape of sessile drops pinned to a solid substrate and exposed to the external potential is presented. Explicit expressions describing the drops’ shape are obtained with a calculus of variations for 2D and 3D wetting problems. The presented approach is applicable for analysis of electrowetting problems, the study of vibrated and centrifuged drops.     

Understanding (sessile/constrained) bubble and drop oscillations

The diffuse literature on drop oscillation is reviewed, with an emphasis on capillary wave oscillations of constrained drops. Based on the review, a unifying conceptual framework is presented for drop and bubble oscillations, which considers free and constrained drops/bubbles, oscillation of the surface or the bulk (i.e. center of mass) of the drop/bubble, as well as different types of restoring forces (surface tension, gravity, electromagnetic, etc). Experimental results (both from literature and from a new set of experiments studying sessile drops in cross flowing air) are used to test mathematical models from literature, using a novel whole profile analysis technique for the new experiments. The cause of oscillation (cross flowing air, vibrated surface, etc.) is seen not to affect oscillation frequency. In terms of models, simplified models are seen to poorly predict oscillation frequencies. The most advanced literature models are found to be relatively accurate at predicting frequency. However it is seen that no existing models are reliably accurate across a wide range of contact angles, indicating the need for advanced models/empirical relations especially for drops undergoing the lowest frequency mode of oscillation (the order 1 degree 1 non-axisymmetric ‘bending’ mode that corresponds to a lateral ‘rocking’ motion of the drop).     

The dynamics of evaporating sessile droplets

Experiments on sessile drops evaporating in a normal atmosphere without an applied thermal gradient are reported and compared with an available theoretical model. The liquids used are alkanes; water; and, more recently, polydimethylsiloxane oligomers. The substrates are silicon wafers, completely wetted by the liquid. Experiments with hanging drops allow us first to discard any influence of convection in the gas phase on the drop dynamics. The model assumes the process to be controlled by the stationary diffusion of the evaporating molecules in the gas phase. For alkanes and water, and in a limited range of drop sizes where gravity can be ignored, the model accounts very well for the dynamics of the drop radius, and rather well for the contact angle. This is no longer the case with the polydimethylsiloxane oligomers, where the very small contact angles require a more elaborated analysis of the drop edge. The text was submitted by the authors in English.     

Two-dimensional colloidal aggregation: concentration effects

Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloidal aggregation in two dimensions were performed to elucidate the concentration dependence of the cluster fractal dimension and of the different average cluster sizes. Both on-lattice and off-lattice simulations were used to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned 2.5 orders of magnitude. In the DLCA case and in the flocculation regime, it was found that the fractal dimension shows a linear-type increase with the concentration phi, following the law: d(f)=d(fo)+aphi(c). For the on-lattice simulations the fractal dimension in the zero concentration limit, d(fo), was 1.451+/-0.002, while for the off-lattice simulations the same quantity took the value 1.445+/-0.003. The prefactor a and exponent c were for the on-lattice simulations equal to 0.633+/-0.021 and 1.046+/-0.032, while for the off-lattice simulations they were 1.005+/-0.059 and 0.999+/-0.045, respectively. For the exponents z and z', defining the increase of the weight-average (S(w)(t)) and number-average (S(n)(t)) cluster sizes as a function of time, we obtained in the DLCA case the laws: z=z(o)+bphi(d) and z'=z'(o)+b'phi(d'). For the on-lattice simulations, z(o), b, and d were equal to 0.593+/-0.008, 0.696+/-0.068, and 0.485+/-0.048, respectively, while for the off-lattice simulations they were 0.595+/-0.005, 0.807+/-0.093, and 0.599+/-0.051. In the case of the exponent z', the quantities z'(o), b', and d' were, for the on-lattice simulations, equal to 0.615+/-0.004, 0.814+/-0.081, and 0.620+/-0.043, respectively, while for the off-lattice algorithm they took the values 0.598+/-0.002, 0.855+/-0.035, and 0.610+/-0.018. In RLCA we have found again that the fractal dimension, in the flocculation regime, shows a similar linear-type increase with the concentration d(f)=d(fo)+aphi(c), with d(fo)=1.560+/-0.004, a=0.342+/-0.039, and c=1.000+/-0.112. In this RLCA case it was not possible to find a straight line in the log-log plots of S(w)(t) and S(n)(t) in the aggregation regime considered, and no exponents z and z' were defined. We argue however that for sufficiently long periods of time the cluster averages should tend to those for DLCA and, therefore, their exponents should coincide with z and z' of the DLCA case. Finally, we present the bell-shaped master curves for the scaling of the cluster size distribution function and their evolution when the concentration increases, for both the DLCA and RLCA cases.     

Triple-line behavior and wettability controlled by nanocoated substrates: influence on sessile drop evaporation

In this article, we investigate the influence of the surface properties of substrates on the evaporation process. Using various nanocoatings, it is possible to modify the surface properties of substrates, such as the roughness and the surface energy, while maintaining constant thermal properties. Experiments are conducted under atmospheric conditions with five fluids (methanol, ethanol, propanol, toluene and water) and four coatings (PFC, PTFE, SiOC, and SiO(x)). The various combinations of these fluids and coatings allow for a wide range of drop evaporation properties to be studied: the dynamics of the triple line, the volatility of fluids, and a large range of wettabilities (from 17 to 135°). The experimental data are in very good quantitative agreement with existing models of quasi-steady, diffusion-driven evaporation. The experimental results show that the dynamics of the evaporative rate are proportional to the dynamics of the wetting radius. Thus, the models succeed in describing the evaporative dynamics throughout the evaporation process regardless of the behavior of the triple line. Moreover, the use of various liquids reveals the validity of the models regardless of their volatility. The results also confirm the recent finding of a universal relation for the time evolution of the drop mass, independent of the drop size and initial contact angle. Finally, this study highlights the separate and coupled roles of the triple line and the wettability on the sessile drop evaporation process. Data reveal that the more wet and pinned a drop, the shorter the evaporation time.     

Implementation and examination of a new drop shape analysis algorithm to measure contact angle and surface tension from the diameters of two sessile drops

The performance of a new algorithm developed to measure contact angle and surface tension of sessile drops is examined. To calculate the contact angle and surface tension, the new algorithm (ADSA-TD) requires the radius (contact or equatorial) and volume of two sessile drops of different sizes that are placed on the same surface. Initially, the algorithm was tested using synthetic drops (synthetic or theoretical drops are produced by numerical integration of the Laplace equation). The radii and volumes of synthetic drops were used as ADSA-TD inputs. The calculated contact angle (θ) and surface tension (γ) by ADSA-TD matched perfectly the assumed values of θ and γ used to produce the synthetic drops, confirming theoretically the validity of the new algorithm. In the next step, the sensitivity of the algorithm to input errors was examined. It was shown experimentally that both calculated contact angle and surface tension are affected by the errors in volume and radius. Besides the error in input values, it was shown that the size difference between the paired drops and the differences in their contact angles would affect the output of ADSA-TD. As it turns out, the calculated surface tension is so sensitive to the above factors that ADSA-TD does not appear to be promising as a surface tension measurement technique. However, ADSA-TD produced acceptable contact angle values as compared to measurements made by other proven techniques such as axisymmetric drop shape analysis-profile. Thus, ADSA-TD may be of interest as a contact angle measurement technique which does not require the liquid surface tension as input.     

Kinetics of colloidal templating using emulsion drop consolidation

The emulsion templating of ordered colloidal microsphere assemblies by Manoharan et al. involves a consolidation process where dispersed phase fluid is transported from droplets into a continuous phase. Consolidation can be approximated as a diffusion process with moving boundaries. The kinetics of consolidation are investigated here by following droplet shrinkage with time as a prelude to understanding rate effects on assembly structure. Consolidation kinetics are influenced by liquid diffusivity, the number of colloidal particles in a droplet, and the surfactant concentration. While surfactant exhibits little effect well below its critical micelle concentration (CMC) value, it significantly slows consolidation above the CMC. For a specific continuous phase (i.e., silicone oil and fluorinated silicone oil), with proper scalings, the droplet size shrinks with time following a power law independent of droplet diameter, surfactant concentrations, and particle number concentration. The power law exponent varies from 1/2 to 2/3 with different continuous oil phases as a result of concentration and interfacial effects. This study leads to an improved understanding of colloidal microstructure development at interfaces that can be applied in novel materials synthesis and drug delivery areas.     

Comparison of sessile drop and captive bubble methods on rough homogeneous surfaces: a numerical study

Quasi-static experiments using sessile drops and captive bubbles are the most employed methods for measuring advancing and receding contact angles on real surfaces. These observable contact angles are the most easily accessible and reproducible. However, some properties of practical surfaces induce certain phenomena that cause a built-in uncertainty in the estimation of advancing and receding contact angles. These phenomena are well known in surface thermodynamics as stick-slip phenomena. Following the work of Marmur (Marmur, A. Colloids Surf., A 1998, 136, 209-215), where the stick-slip effects were studied with regard to sessile drops and captive bubbles on heterogeneous surfaces, we developed a novel extension of this study by adding the effects of roughness to both methods for contact angle measurement. We found that the symmetry between the surface roughness problem and the chemical heterogeneity problem breaks down for drops and bubbles subjected to stick-slip effects.     

Simultaneous monitoring of protein adsorption at the solid–liquid interface from sessile solution droplets by ellipsometry and axisymmetric drop shape analysis by profile

In this paper two in situ techniques are combined to simultaneously examine protein adsorption at the solid–liquid interface from sessile solution droplets. With axisymmetric drop shape analysis by profile (ADSA-P) the change in solid–liquid interfacial tension is determined, while ellipsometry is employed to measure the amount of protein adsorbed from the same solution droplet at the solid–liquid interface. Three proteins (human serum albumin (HSA), immunoglobulin G (IgG) and fibrinogen (Fb)) were dissolved to a concentration of 0.05 mg ml⁻¹ in PBS (pH 7) and sessile droplets were placed for 2 h on a 47.8 nm thick gold coating on glass. The gold coated glass was positioned onto a quartz prism with immersion oil. The prism was aligned in a rotating analyser ellipsometer and the optical beam was thus allowed to be reflected at the hydrophobic gold surface. The ADSA-P set-up was built in 90° cross-beamed set-up around the prism. By combining the results for the adsorbed amounts and the interfacial tension changes over the two hour adsorption period, two stages in the adsorption process could be distinguished. In the first stage, the adsorbed amounts increase in correspondence with the interfacial tension changes, indicating that the interfacial tension changes are caused by adsorption, whereas in the second stage interfacial tension changes continue despite the adsorbed amounts being constant. Consequently, the second stage must be associated with conformational changes of the adsorbed proteins. For HSA and Fb, the conformational contribution to the interfacial tension changes (7.8 and 5.3 mJ m⁻², respectively) were approximately 2-fold the adsorption contribution, while for IgG both were equal around 3 mJ m⁻².     

Symmetry-controlled colloidal nanocrystals: nonhydrolytic chemical synthesis and shape determining parameters

Since inorganic nanocrystals exhibit unique shape-dependent nanoscale properties and can be utilized as basic building blocks for futuristic nanodevices, a systematic study on the shape control of these nanocrystals remains an important subject in materials and physical chemistry. In this feature article, we overview the recent progress on the synthetic development of symmetry-controlled colloidal nanocrystals of semiconductor and metal oxide, which are prepared through nonhydrolytic chemical routes. We describe their shape-guiding processes and illustrate the detailed key factors controlling their growth by examining various case studies of zero-dimensional spheres and cubes, one-dimensional rods, and quasi multidimensional structures such as disks, multipods, and stars. Specifically, the crystalline phase of nucleating seeds, surface energy, kinetic vs thermodynamic growth, and selective adhesion processes of capping ligands are found to be most crucial for the determination of the nanocrystal shape.     

Interfacial tension of liquids from the height and contact angle of a single sessile drop

The height of a sessile drop of liquid when placed on a smooth solid surface increases as the drop volume increases, until it reaches a limiting value for a very large drop. The magnitude of the height and the contact angle depends on the different physical properties of the system. A large value for the contact angle is often associated with a large value for height and vice versa. From the data of measured limiting height, Z _Θ ^∞ and contact angle,Θ, the surface or interfacial tension,γ, can be estimated using the following equation: $$\gamma = \Delta \rho \cdot g \cdot (Z_\Theta ^\infty )^2 /2(1 - \cos (\Theta ))$$ whereΔ? is the density difference between the sessile drop and that of its surrounding medium,g is the gravitational force of acceleration. In this study, the magnitude ofγ of water for various systems is estimated. These values agree with the literature values. Furthermore, the values ofγ for various liquid₁/ solid/liquid₂ systems agree with data from other methods. Thus, the above equation is valid for different liquid-solid systems. It is further shown that very accurate measurements of contact angle,Θ, can be carried out for systems in which Z _Θ Δ _? andγ are known. The variation ofΘ with the height and volume of the sessile drop is analyzed for different systems.     

Formation and dynamics of capillary-flow-induced colloidal rings

We have directly observed the ring formation of colloidal particles of 1 μm diameter at the contact lines of air, water, and oil using a laser scanning confocal microscope. Colloidal rings form and grow through the transport of particles induced by capillary flow due to water evaporation. In addition, we observe the sudden "jump in" of particles into the ring and the "depletion" of particles in the ring. Particle-tracking experiment shows that the particles within the ring exhibit 1D-like motion along the circular ring geometry, and the pair correlation function of the ring configuration suggests an equilibrium interparticle distance of approximately 2.8 μm. It is also found that the structure and formation speed of the colloidal rings can be controlled by accelerating water evaporation by the addition of methanol as a cosolvent.     

Characterization of colloidal hematite particle shape and dispersion behavior

An elliptically polarized light scattering (EPLS) technique for the size and shape characterization of ellipsoidal hematite particles is presented. The hematite particles are synthesized by aging aqueous FeCl(3) or Fe(NO(3))(3) solutions at 100 degrees C. Different reaction conditions create particles of aspect ratios between 1 (spherical) and 8 (elongated). Cross-sectional diameter and aspect ratio are observed as a function of reaction (aging) time. Growth of the elongated particles, as well as their fractal aggregation behavior, is characterized using EPLS and comparisons are made with photon correlation spectroscopy and TEM measurements.     

Total Gaussian curvature,drop shapes and the range of applicability of drop shape techniques

Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.     

Nonequilibrium inertial dynamics of colloidal systems

We consider the properties of a one-dimensional fluid of Brownian inertial hard-core particles, whose microscopic dynamics is partially damped by a heat bath. Direct interactions among the particles are represented as binary, instantaneous elastic collisions. Collisions with the heat bath are accounted for by a Fokker-Planck collision operator, whereas direct collisions among the particles are treated by a well known method of kinetic theory, the revised Enskog theory. By means of a time multiple time-scale method we derive the evolution equation for the average density. Remarkably, for large values of the friction parameter and/or of the mass of the particles we obtain the same equation as the one derived within the dynamic density functional theory (DDF). In addition, at moderate values of the friction constant, the present method allows to study the inertial effects not accounted for by DDF method. Finally, a numerical test of these corrections is provided.     

Computer simulations of nematic drops: coupling between drop shape and nematic order

We perform Monte Carlo computer simulations of nematic drops in equilibrium with their vapor using a Gay-Berne interaction between the rod-like molecules. To generate the drops, we initially perform NPT simulations close to the nematic-vapor coexistence region, allow the system to equilibrate and subsequently induce a sudden volume expansion, followed with NVT simulations. The resultant drops coexist with their vapor and are generally not spherical but elongated, have the rod-like particles tangentially aligned at the surface and an overall nematic orientation along the main axis of the drop. We find that the drop eccentricity increases with increasing molecular elongation, κ. For small κ the nematic texture in the drop is bipolar with two surface defects, or boojums, maximizing their distance along this same axis. For sufficiently high κ, the shape of the drop becomes singular in the vicinity of the defects, and there is a crossover to an almost homogeneous texture; this reflects a transition from a spheroidal to a spindle-like drop.     

Dynamics of a disturbed sessile drop measured by atomic force microscopy (AFM)

A new method for studying the dynamics of a sessile drop by atomic force microscopy (AFM) is demonstrated. A hydrophobic microsphere (radius, r ～ 20-30 μm) is brought into contact with a small sessile water drop resting on a polytetrafluoroethylene (PTFE) surface. When the microsphere touches the liquid surface, the meniscus rises onto it because of capillary forces. Although the microsphere volume is 6 orders of magnitude smaller than the drop, it excites the normal resonance modes of the liquid interface. The sphere is pinned at the interface, whose small (<100 nm) oscillations are readily measured with AFM. Resonance oscillation frequencies were measured for drop volumes between 5 and 200 μL. The results for the two lowest normal modes are quantitatively consistent with continuum calculations for the natural frequency of hemispherical drops with no adjustable parameters. The method may enable sensitive measurements of volume, surface tension, and viscosity of small drops.     

Impact dynamics of colloidal quantum dot solids

We use aerosol techniques to investigate the cohesive and granular properties of solids composed of colloidal semiconductor nanocrystals (quantum dot solids). We form spherical agglomerates of nanocrystals with a nebulizer and direct them toward a carbon substrate at low (~0.01 m/s) or high (~100 m/s) velocities. We then study the morphology of the deposit (i.e., the "splat") after impact. By varying the size of the agglomerate and the spacing between the nanocrystals within it, we observe influences on the mechanical properties of the quantum dot solid. We observe a liquid-to-solid transition as the nanocrystals become more densely packed. Agglomerates with weakly interacting nanocrystals exhibit liquidlike splashing and coalescence of overlapping splats. More dense agglomerates exhibit arching and thickening effects, which is behavior typical of granular materials.