Surface Tension Relaxation Research Articles

Mechano-chemical AFM nanolithography of metallic thin films: A statistical analysis

A mechano-chemical atomic force microscope (AFM) nanolithography on a metallic thin film (50 nm in thickness) covered by a spin-coated soft polymeric mask layer (50–60 nm in thickness) has been introduced. The surface stochastic properties of initial grooves mechanically patterned on the mask layer (grooves before chemical wet-etching) and the lithographed patterns on the metallic thin film (the grooves after chemical wet-etching) have been investigated and compared by using the structure factor, power spectral density, and AFM tip deconvolution analyses. The effective shape of cross section of the before and after etching grooves have been determined by using the tip deconvolution surface analysis. The wet-etching process improved the shape of the grooves and also smoothed the surface within them. We have indicated that relaxation of the surface tension of the deposited mask layer after the AFM scribing is independent from surface density of the grooves and also their length scale. Based on the statistical analysis, it was found that increase of the width of the grooves after the wet-etching and also relaxation of surface tension of the mask layer resulted in a down limit in the size of the metallic nanowires made by the combined nanolithography method. An extrapolation of the analyzed statistical data has indicated that, in this method, the minimum obtainable width and length of the metallic nanowires are about 55 nm and 2 μm, respectively.

Surface tension and size effect in ferroelectric nanotubes

Using a thermodynamic model, linear stability analysis is performed on the associateddynamic Ginsburg–Landau equation for a ferroelectric nanotube. Analytic expressions ofthe transition temperature and Curie–Weiss relation are derived. The ferroelectricproperties of the tube are found to generally depend on its dimensions through effects ofthe surface tension and near-surface eigenstrain relaxation. Our results also show that thetransition temperature and polarization are both enhanced due to the dominance of theeffective radial pressures induced by the surface tension, resulting in a remnantpolarization and coercive field that may become larger than the bulk values.

An examination on the validity of the assumptions commonly made in dynamic surface tension measurement using a pendant bubble

Abstract The assumptions commonly made in dynamic surface tension (DST) measurement using the pendant bubble method are examined. A pendant bubble changes its shape in response to DST due to surfactant adsorption. The shape change induces motion in the bulk fluid during the relaxation of surface tension. Three assumptions motivated by which are: (i) negligible influence of the bulk fluid motion, (ii) uniform surface concentration along the bubble surface, and (iii) negligible convective effects in surfactant mass transfer. The first two are related to the validity of the use of the Young–Laplace equation for DST measurement, so that DST measurement can be conducted under the conditions of keeping a bubble nearly hydrostatic and of a constant surface tension at each instant in time. The last assures the transport process to be diffusion-dominated, so that genuine kinetics can be examined without being mediated by the bulk convection. This study invokes a dimensional analysis to inspect these assumptions via identifying relative importance among relevant effects. Experimental data are provided for justification. Criteria are not only established in line for validating these assumptions, but also guide in the choice of appropriate experimental conditions for conducting DST measurement.

A Theoretical Study on Surfactant Adsorption Kinetics: Effect of Bubble Shape on Dynamic Surface Tension

A planar or spherical fluid-liquid interface was commonly assumed on studying the surfactant adsorption kinetics for a pendant bubble in surfactant solutions. However, the shape of a pendant bubble deviates from a sphere unless the bubble's capillary constant is close to zero. Up to date, the literature has no report about the shape effect on the relaxation of surface tension due to the shape difference between a pendant bubble and a sphere. The dynamic surface tension (DST), based on the actual shape of a pendant bubble with a needle, of the diffusion-controlled process is simulated using a time-dependent finite element method in this work. The shape effect and the existence of a needle on DST are investigated. This numerical simulation resolves also the time-dependent bulk surfactant concentration. The depth of solution needed to satisfy the classical Ward-Tordai infinite-solution assumption was also studied. For a diffusion-controlled adsorption process, bubble shape and needle size are two major factors affecting the DST. The existence of a needle accelerates the bulk diffusion for a small bubble; however, the shape of a large pendant bubble decelerates the bulk diffusion. An example using this method on the DST data of C12E4 is illustrated at the end of this work.

Dynamic Surface Tension Behavior in a Photoresponsive Surfactant System

The surface properties of a nonionic photoresponsive surfactant that incorporates the light-sensitive azobenzene group into its tail have been investigated. Cis-trans photoisomerization of this azobenzene group alters the ability of the surfactant to pack into adsorbed monolayers at an air/water interface or into aggregates in solution, thereby causing a significant variation in surface and bulk properties following a change in the illumination conditions. NMR studies indicate that a solution left in the dark for an extended period of time contains the trans isomer almost exclusively, whereas samples exposed to light of fixed wavelength eventually reach a photostationary equilibrium in which significant amounts of both isomers are present. At concentrations well above the cmc but under different illumination conditions (dark, UV light, visible light), freshly formed surfaces exhibit profoundly different surface tension trajectories as they approach essentially identical equilibrium states. This common equilibrium state corresponds to a surface saturated with the trans (more surface active) isomer. The dark sample shows a simple, single-step relaxation in surface tension after the creation of a fresh interface, whereas the UV and visible samples exhibit a more rapid initial decrease in tension, followed by a plateau of nearly constant tension, and finally end with a second relaxation to equilibrium. It is hypothesized that this behavior of the UV and visible samples is caused by competitive adsorption between the cis and trans isomers present in these mixtures. The cis surfactant reaches the interface more quickly, leading to an initially cis-dominated interface having a tension value corresponding to the intermediate plateau, but is ultimately displaced by the trans isomer. Fluorescence studies are used for cmc determination in the samples, and the results suggest that the two isomers segregate into distinct aggregate phases. The critical concentration associated with the formation of cis-rich aggregates is much larger than that of the trans-rich aggregates, which accounts for the faster diffusion of the cis isomer to a fresh interface. Models of the diffusion and adsorption of surfactant are developed. These consider the role of aggregates in the adsorption process by examining the limiting behavior of three aggregate properties: dissolution rate, mobility, and ability to incorporate into the interface. These models are used to analyze the surface tension relaxation of dark and UV samples, and the predictions are found to be in agreement with the observed characteristic relaxation time scales for these samples, though the results are inconclusive regarding the specific role of aggregates. High-intensity illumination focused on a surface saturated with surfactant is used to drive photoisomerization of the adsorbed surfactant, and rapid, substantial changes in surface tension result. These changes are consistent with proposed conformations of the adsorbed surfactant and with monolayer studies performed with a Langmuir film balance.

The spreading of a viscous microdrop on a solid surface

The spreading of a liquid microdrop across a solid surface is examined using the interface formation model. This model allows for variable surface tension at constant temperature and a flow induced Maragoni effect, by incorporating irreversible thermodynamics into the continuum model. The model is solved for small Capillary number and small Reynolds number. This problem has been considered before for much larger drops in Shikhmurzaev (Phys Fluids 9:266, 1997a), which examined the spreading of a drop for e = τ U CL/R ≪ 1, where U CL is the speed of the moving contact line across the solid surface, τ is the surface tension relaxation time of the viscous liquid, and R is a typical length scale for the size of the drop. This paper extends that work by examining e = O(1), which will be shown to be the appropriate scaling for very small liquid drops, on the scale of micrometres or less.

Study of the Surface Tension of the Aqueous Solutions of Dodecylamidoethyldimethylbenzylammonium Chloride

The dynamic and equilibrium surface tensions of aqueous dodecylamidoethyldimethylbenzylammonium chloride solutions of various concentrations at 16, 20, 25, 30, and 35°C are studied for the first time. The effects of the concentration and temperature on the surface tension relaxation are discussed. The possibility of two-dimensional phase transition and its effect on the dynamic behavior of surface tension are considered.

Oscillations of Sessile Drops of Surfactant Solutions on Solid Substrates with Differing Hydrophobicity

The paper reports results of experimental studies on the dynamic behavior of surfactant solution drops on substrates with differing hydrophobicity. Contact angle oscillations observed immediately after the drop deposition are studied, and a mechanistic interpretation of this phenomenon is put forward. The major emphasis is put on the physicochemical aspects of surfactant action, including the dynamic wetting enhancement and the effect of surface tension relaxation on the frequency of drop oscillation, which are characteristic of surfactant solutions. Appropriate scaling relations describing the drop dynamics are derived.

A simple and rapid method for the determination of the surface equations of state and adsorption isotherms for efficient surfactants

A simple and fast method for determination of adsorption isotherms for highly surface-active surfactants is presented. Efficient surfactants often have critical micelle concentrations <0.1 mM and the determination of surface tension isotherms involves measurements at very low bulk concentrations where long equilibration times, solution depletion and trace impurities can seriously compromise accuracy. In the method described here, a bubble of known surface area, A1, and surface excess concentration, Γ1, is expanded rapidly to a new surface area, A2. The surface tension at the new surface excess, Γ2 = Γ1A1/A2, is evaluated by extrapolation of the surface tension relaxation profile to t = 0. It is shown empirically that the choice of t = 0 to correct for adsorption of the surfactant to the growing bubble is ⅔ of the bubble growth time. The equation of state σ(Γ) when combined with equilibrium surface tension measurements in the vicinity of the c.m.c. is sufficient to define completely the adsorption isotherm. This method is then applied to the determination of the adsorption isotherms of the non-ionic surfactants C12E5 and C12E3 and the cationic surfactant C16TAB in the presence of 0.1 M NaBr.

Fluorescence Evidence That a Phase Transition Causes the Induction Time in the Reduction in Dynamic Tension during Surfactant Adsorption to a Clean Air/Water Interface and a Kinetic–Diffusive Transport Model for the Phase-Induced Induction

An aqueous soluble surfactant adsorbing from solution onto an initially clean air/water interface often exhibits an induction period in the surface tension relaxation in which, as the adsorption begins, the tension remains near the clean interface value for an extended period of time before decreasing rapidly to the equilibrium value. In this study, using a model nonionic soluble surfactant, C 14E 6(CH 3(CH 2) 13–(OCH 2CH 2) 6–OH), we present direct fluorescence evidence that this induction is due to a first-order phase transition from a gaseous (G) to a liquid expanded (LE) phase that the assembling monolayer undergoes at constant surface pressure. An open channel flow cell is initially filled with water, and onto its air/water interface is spread an insoluble amphiphilic dye that fluoresces upon irradiation in the LE phase and whose fluorescence is quenched in the G phase. An aqueous solution of C 14E 6 is then allowed to flow through the channel. We observe the immediate appearance of bright islands of the LE phase growing in a dark (G) background, confirming the presence of the G/LE phase transition. These islands eventually occupy the entire surface, after which the interface remains uniformly bright. We correlate this phase transition to the induction period by simultaneously measuring the tension of the interface of the open channel, and verifying that as the islands grow the tension remains at the clean value until the bright LE phase occupies the entire surface, whereupon the tension rapidly decreases. We further develop a phase transition surfactant transport model for the induction period in which surfactant diffuses toward and kinetically adsorbs onto the surface, and then rapidly equilibrates between the G and LE phases. For our model surfactant C 14E 6, we independently measure the surface concentration of the nucleating LE phase, the LE phase surfactant equation of state, the kinetic rate constants for adsorption into the LE phase, and the bulk diffusion coefficient. Using these measurements, we predict induction times for adsorption onto a clean surface without convection. We also measure these induction times in tension relaxation for adsorption onto a pendant bubble using axisymmetric shape analysis, and demonstrate agreement with the simulations with no adjustable constants.

Adsorption Relaxation for Nonionic Surfactants under Mixed Barrier-Diffusion and Micellization-Diffusion Control

Relaxation processes of surfactant adsorption and surface tension, which are characterized by two specific relaxation times, are theoretically investigated. We are dealing with fluid interfaces and small initial deviations from equilibrium. For surfactant concentrations below the critical micellization concentration (CMC), we consider adsorption under mixed barrier-diffusion control. General analytical expressions are derived, which are convenient for both numerical computations and asymptotic analysis. Series expansions for the short- and long-time limit are derived. The results imply that the short-time asymptotics is controlled by the adsorption barrier, whereas the long-time asymptotics is always dominated by diffusion. Furthermore, for surfactant concentrations above the CMC, adsorption under mixed micellization-diffusion control is considered. Again, a general analytical expression is derived for the relaxation of surfactant adsorption and surface tension, whose long- and short-time asymptotics are deduced. The derived equations show that at the short times the relaxation is completely controlled by the diffusion, whereas the long-time asymptotics is affected by both demicellization and diffusion. The micellar effect is manifested as an exponential (rather than square-root) decay of the perturbation. The derived expressions are applied to process available experimental data for the nonionic surfactant Triton X-100 and to determine the respective demicellization rate constant.

Dynamics of PEO−PPO−PEO and PPO−PEO−PPO Triblock Copolymers at the Air/Water Interface upon Thermal Stimulation

Dynamics of PEO−PPO−PEO and PPO−PEO−PPO at the air/water interface upon thermal stimulation is studied with a fast surface light scattering (SLS) technique, in terms of the dynamic surface tension recovery relaxation of the copolymer solutions in response to a short-pulsed temperature jump. The characteristic of the surface tension relaxation is examined pertaining to the structure, molecular weight, and concentration of the block copolymers at the air/water interface. The surface tension relaxation time of the copolymer surfactants is found to be monotonically related to the molecular weight of the PEO blocks suggesting that thermal sensitivity in surface tension of the copolymer solutions be due to a conformation change of PEO chains in the copolymers at the air/water interfaces upon the temperature change.

Effect of surface-tension relaxation on the spectrum of motions of a liquid with charged free surface

The spectrum of capillary-relaxational motions of a charged free liquid surface is analyzed. The analysis takes into account the effect of surface-tension relaxation and the existence of two relaxation times due to different physical mechanisms. Each relaxation mechanism is associated with certain liquid wave motions. Motions due to different relaxation processes interact with each other and with capillary-gravity waves through nonlinear mechanisms.

Adsorption and Desorption Kinetics of C12E4 on Perturbed Interfaces

Two processes for the mass transport of C12E4 in a quiescent surfactant solution were studied: (i) the desorption of C12E4 out of a suddenly compressed interface; (ii) the adsorption of C12E4 onto a suddenly expanded air−water interface. A video-enhanced pendant bubble tensiometer was used for the measurement of surface tension relaxation due to the adsorption or desorption of surfactant molecules. Both processes were found to be diffusion-controlled at dilute concentration but diffusive-kinetic mixed-controlled at more elevated bulk concentration for C12E4. Rate constants of adsorption/desorption were evaluated from the comparison between the surface tension profiles and the theoretical profiles predicted from the Frumkin model. The values of the kinetic rate constants of C12E4 obtained from these two experiments are nearly the same. A theoretical simulation was also performed to confirm the shifting mechanism (J. Chem. Eng. Jpn. 1996, 29, 634) for C12E4 for both desorption and expansion processes.

Adsorption Kinetics of Ionic Surfactants after a Large Initial Perturbation. Effect of Surface Elasticity

This theoretical study is devoted to the relaxation of surface tension of an ionic surfactant solution for submicellar concentrations. The effects of added nonamphiphilic electrolyte and counterion binding are taken into account. We consider a large initial deviation from equilibrium, which is defined as the formation of a new interface: there is no adsorbed surfactant and electric double layer at the initial moment. Next, the surfactant solution and its interface are allowed to relax without any subsequent perturbation. The electrodiffusion equations, which describe the adsorption kinetics, are nonlinear, and it is impossible to find a general analytical solution, especially in the case of large initial deviations. Nevertheless, the problem can be linearized in the asymptotic case of long times. The derived theoretical expressions show that the relaxation times in the cases of large and small initial perturbations are numerically close to each other. For that reason the relaxation time can be considered as a general kinetic property of the adsorption monolayer. The theory predicts also the slope of the experimental plot of dynamic surface tension vs inverse square root of time; this makes the theory useful for interpretation of experimental data. The theoretical expressions involve the surface (Gibbs) elasticity, whose definition for adsorption monolayers of soluble ionic surfactants is discussed in detail. The Gibbs elasticity of such monolayers is found to increase strongly with the rise of salt concentration. The derived asymptotic expressions are verified against an exact computer solution of the electrodiffusion problem, and excellent agreement is found.

Capillary rise of surfactant solutions

The capillary flow of surfactant solutions in hydrophobic and hydrophilic capillaries has been studied. The results obtained are discussed in the light of surface tension relaxation and adsorption phenomena. Modes of surfactant transport and effects of surfactant adsorption, aggregation, and monomer–micelle interconversion on the capillary rise dynamics are further analyzed in the framework of a theoretical model. This provides a self-consistent and quantitatively correct picture of the experimental results. In the case of hydrophobic capillaries, two limiting types of dynamic behavior are adsorption-controlled rise and diffusion-controlled rise. In some cases, slow relaxation of adsorbed layers at the liquid/solid interface can cause a drift of the rise height over a long time under quasi-equilibrium conditions. A slow relaxation, as compared to the capillary rise rate, of the liquid/vapor interface may also produce a maximum in the rise s. time curve. This behavior was, for instance, seen for a surfactant solution penetrating into a hydrophilic capillary.

Effect of dynamic surface tension on the growth rate of the Tonks-Frenkel instability

By means of a numerical analysis of the dispersion equation for capillary motions of a liquid with a charged flat free surface subjected to relaxation of the surface tension, it is shown that the growth rate of the instability of the free surface of the liquid decreases as the characteristic relaxation time of the surface tension increases and the Tonks-Frenkel parameter decreases. The instability itself occurs in a limited range of wave numbers whose width is also determined by the value of the Tonks-Frenkel parameter.

Surface Tension Relaxation of Poly(N-isopropylacrylamide) at the Air/Water Solution Interface As Probed by Surface Laser Light Scattering

Surface laser light scattering (SLLS) is used to investigate the surface relaxation dynamics at the interface of the air/poly(N-isopropylacrylamide) (PNIPAM)−water solution. The SLLS data yields a result consistent with a model invoking three consecutive regions in the surface relaxation process. In the region where the surface tension undergoes a rapid change, a line width maximum is found. The line width maximum is due to a strong coupling of the capillary wave with the surface longitudinal wave associated with the surface dilational modulus, as a result of rapid segmental motion of the polymer chains at the interface.

Adsorption Kinetics of C10E8 at the Air−Water Interface

The adsorption of C10E8 onto a clean air−water interface and the desorption out of an overcrowded interface due to a sudden shrinkage of a pendant bubble in a quiescent surfactant solution are studied. Video-enhanced pendant bubble tensiometry is employed for the measurement of the relaxation in surface tension. Relaxation profiles of surface tension for C10E8 molecules absorbing onto a freshly created air−water interface and desorbing out of a compressed air−water interface are obtained. The adsorption of C10E8 is found to be anticooperative from the equilibrium surface tension data compared with the prediction of the Frumkin model. The controlling mechanism of the adsorption process changes as a function of bulk concentration; it shifts from diffusion control at dilute concentration to mixed diffusive-kinetic control at more elevated bulk concentration. It is also confirmed that the desorption of C10E8 out of a compressed interface is a mixed diffusive-kinetic controlled process. Comparison is made for the entire relaxation period of the tension data and the model predictions. Values of the diffusivity and the adsorption/desorption rate constants of C10E8 are calculated from these dynamic surface tension profiles. The values of the kinetic rate constants obtained from the desorption experiment are the same as that obtained from the clean adsorption experiment.

Adsorption Kinetics of 1-Octanol at the Air−Water Interface

The adsorption of 1-octanol at an air−water interface is studied theoretically and experimentally. A video-enhanced pendant bubble tensiometry is utilized for the measurement of relaxation of surface tension. Two types of processes were investigated: the adsorption onto an initially clean air−water interface and the desorption out of a suddenly compressed interface which is originally at equilibrium. A theoretical simulation using the equilibrium surface tension is performed and it is concluded that there is no shift in controlling mechanism for the adsorption of 1-octanol molecules from an aqueous phase onto an initially clean air−water surface. The adsorption of 1-octanol onto a clean air-water interface is verified experimentally to be a diffusion-controlled process. A diffusion coefficient was computed by comparing these adsorption profiles with numerical solutions of bulk surfactant diffusion equation and the generalized Frumkin adsorption model. The re-equilibration of a compressed interface agrees...