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.     

Evidence for the existence of an effective interfacial tension between miscible fluids: isobutyric acid-water and 1-butanol-water in a spinning-drop tensiometer

We report definitive evidence for an effective interfacial tension between two types of miscible fluids using spinning-drop tensiometry (SDT). Isobutyric acid (IBA) and water have an upper critical solution temperature (UCST) of 26.3 degrees C. We created a drop of the IBA-rich phase in the water-rich phase below the UCST and then increased the temperature above it. Long after the fluids have reached thermal equilibrium, the drop persists. By plotting the inverse of the drop radius cubed (r(-)(3)) vs the rotation rate squared (omega(2)), we confirmed that an interfacial tension exists and estimated its value. The transition between the miscible fluids remained sharp instead of becoming more diffuse, and the drop volume decreased with time. We observed droplet breakup via the Rayleigh-Tomotika instability above the UCST when the rotation rate was decreased by 80%, again demonstrating the existence of an effective interfacial tension. When pure IBA was injected into water above the UCST, drops formed inside the main drop even as the main drop decreased in volume with time. We also studied 1-butanol in water below the solubility limit. Effective interfacial tension values measured over time were practically constant, while the interface between the two phases remains sharp as the volume of the drop declines. The effective interfacial tension was found to be insensitive to changes in temperature and always larger than the equilibrium interfacial tension. Although these results may not apply to all miscible fluids, they clearly show that an effective interfacial tension can exist and be measured by SDT for some systems.     

Limiting conditions for applying the spherical section assumption in contact angle estimation

The shape of liquid drops on solid surfaces deviates from the spherical as tension decreases and gravity effects start affecting the drop shape. This paper attempts to define this deviation and estimates the dimensionless Eotvos number limits above which the deviation becomes "significant." The use of these limiting values can facilitate estimation of contact angle in the following manner. It is well known that the equilibrium contact angle made by a liquid drop on a solid surface can be estimated from measurements of two drop parameters. These parameters can be any two chosen from the drop volume, height, and wetted radius. In case the effect of gravity on the drop shape is negligible, simple algebraic relations derived from the spherical section assumption exist, from which the contact angle can be estimated. In systems where the "spherical section" assumption is invalid, the Laplace equation for the drop shape has been solved numerically with any two of the above parameters as the constraints, to obtain the contact angle. In this paper, Eotvos numbers at which the deviation of the drop profile from the spherical is significant enough to result in contact angle deviation of 1 degrees are estimated. The limiting values of Eotvos number, expressed as a function of the original contact angle made by the spherical profile, are obtained by solving the Laplace equation for the drop shape with the drop volume and wetted radius constraints for decreasing values of Interfacial tension. These limiting values are also estimated for different drop sizes and for cases where the drop phase is heavier (sessile) and lighter (buoyant) than the surrounding fluid. The independence of the Eotvos number estimates from the sign of the density difference as well as the drop size is shown. These Eotvos number limits can be used to check if the spherical section assumption, with the resulting simple algebraic relations, can be used for contact angle estimation and other shape-related analysis for a system.     

On the applicability of Young–Laplace equation for nanoscale liquid drops

Debates continue on the applicability of the Young–Laplace equation for droplets, vapor bubbles and gas bubbles in nanoscale. It is more meaningful to find the error range of the Young–Laplace equation in nanoscale instead of making the judgement of its applicability. To do this, for seven liquid argon drops (containing 800, 1000, 1200, 1400, 1600, 1800, or 2000 particles, respectively) at T = 78 K we determined the radius of surface of tension R_s and the corresponding surface tension γ_s by molecular dynamics simulation based on the expressions of R_s and γ_s in terms of the pressure distribution for droplets. Compared with the two-phase pressure difference directly obtained by MD simulation, the results show that the absolute values of relative error of two-phase pressure difference given by the Young–Laplace equation are between 0.0008 and 0.027, and the surface tension of the argon droplet increases with increasing radius of surface of tension, which supports that the Tolman length of Lennard-Jones droplets is positive and that Lennard-Jones vapor bubbles is negative. Besides, the logic error in the deduction of the expressions of the radius and the surface tension of surface of tension, and in terms of the pressure distribution for liquid drops in a certain literature is corrected.     

Understanding the Buoy Effect of Surface-Enriched Pt Complexes in Ionic Liquids: A Combined ARXPS and Pendant Drop Study**

Recently, we demonstrated that Pt catalyst complexes dissolved in the ionic liquid (IL) [C₄C₁Im][PF₆] can be deliberately enriched at the IL surface by introducing perfluorinated substituents, which act like buoys dragging the metal complex towards the surface. Herein, we extend our previous angle-resolved X-ray photoelectron spectroscopy (ARXPS) studies at complex concentrations between 30 and 5 %_mol down to 1 %_mol and present complementary surface tension pendant drop (PD) measurements under ultraclean vacuum conditions. This combination allows for connecting the microscopic information on the IL/gas interface derived from ARXPS with the macroscopic property surface tension. The surface enrichment of the Pt complexes is found to be most pronounced at 1 %_mol. It also displays a strong temperature dependence, which was not observed for 5 %_mol and above, where the surface is already saturated with the complex. The surface enrichment deduced from ARXPS is also reflected by the pronounced decrease in surface tension with increasing concentration of the catalyst. We furthermore observe by ARXPS and PD a much stronger surface affinity of the buoy-complex as compared to the free ligands in solution. Our results are highly interesting for an optimum design of IL-based catalyst systems with large contact areas to the surrounding reactant/product phase, such as in supported IL phase (SILP) catalysis.     

Development of a new methodology to study drop shape and surface tension in electric fields

Development of a new methodology for the study of both shape and surface tension of conducting drops in an electric field is presented. This methodology, called axisymmetric drop shape analysis-electric fields (ADSA-EF), generates numerical drop profiles in an electrostatic field, for a given surface tension. Then, it calculates the true value of the surface tension by matching theoretical profiles to the shape of experimental drops, using the surface tension as an adjustable parameter. ADSA-EF can be employed to simulate and study drop shapes in the electric field and to determine its effect on liquid surface tension. The method can also be used to measure surface tension in microgravity, where current drop-shape techniques are not applicable. The axisymmetric shape of the drop is the only assumption made in the development of ADSA-EF. The new scheme is applicable when both gravity and electrostatic forces are present. Preliminary measurements using ADSA-EF suggest that the surface tension of water increases by about 2% when an electric field with the magnitude of 10(6) V/m is applied.     

Study of the surface and interfacial tensions in systems containing a low molar mass liquid crystal

The surface tension of a low molar mass liquid crystal (LMMLC), 4-cyano-4'-n-heptyloxybiphenyl (70CB), was measured as a function of temperature using the pendant drop method, forming drops of different volumes ranging from 5 to 11 mm³. Contact angles formed by drops of 70CB in the nematic and isotropic phases on plates of polystyrene (PS) and of a liquid crystal polymer (LCP), VECTRA A910, were also measured. Only large drops could be used for surface tension analysis. It was shown that in the nematic phase the surface tension of 70CB decreases with increasing temperature, and that in the isotropic phase the surface tension increases with increasing temperature. Using the values of contact angle and of surface tension of 7OCB it was possible to evaluate the interfacial energy between 7OCB and PS and between 7OCB and VECTRA. The interfacial energy between 7OCB and PS, and between 7OCB and VECTRA, decreased with increasing temperature for ranges of temperatures corresponding to both phases of 70CB.     

Dynamic surface tension analysis of dodecyl sulfate association complexes

First, a novel calibration method is used to expand the current understanding of spherical drop growth and elongation that occurs during on-line measurements of surface pressure using the dynamic surface tension detector (DSTD). Using a novel surface tension calibration method, the drop radius is calculated as a function of time from experimental drop pressure data and compared to the theoretical drop radius calculated from volumetric flow rate. From this comparison, the drop volume at which the drop shape starts to deviate ( approximately 4 mul) from a spherical shape is readily observed and deviates more significantly by approximately 6 mul drop volume (5% deviation in the ideal spherical drop radius) for the capillary sensing tip employed in the DSTD. From this assessment of drop shape, an experimental method for precise drop detachment referred to as pneumatic drop detachment is employed at a drop volume of 2 mul (two second drops at 60 mul/min) in order to provide rapid dynamic surface tension measurements via the novel on-line calibration methodology. Second, the DSTD is used to observe and study kinetic information for surface-active molecules and association complexes adsorbing to an air-liquid drop interface. Dynamic surface tension measurements are made for sodium dodecyl sulfate (SDS) in the absence and presence of either tetra butyl ammonium (TBA) or chromium (III). Sensitive, indirect detection of chromium and other multiply charged metals at low concentrations is also investigated. The DSTD is utilized in examining the dynamic nature of SDS: cation association at the air-liquid interface of a growing drop. Either TBA or Cr(III) were found to substantially enhance the surface tension lowering of dodecyl sulfate (DS), but the surface tension lowering is accompanied by a considerable kinetic dependence. Essentially, the surface tension lowering of these DS: cation complexes is found to be a fairly slow process in the context of the two second DSTD measurement. The limit of detection for both SDS and chromium (III) is in the 300-400 part-per-billion (by mass) range.     

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.     

Contact line dynamics in the late-stage coalescence of diethylene glycol drops

We investigated the contact line dynamics of a composite drop formed as a result of the coalescence during the condensation of two diethylene glycol (DEG) drops at -4 degrees C on a silicon surface. The composite drop relaxes exponentially toward equilibrium with a typical relaxation time, tc, which depends on the equilibrium radius, R, of the composite drop. The value of tc is found to be in the range of 10-100 s for R approximately 1-4 microm. The relaxation dynamics is found to be larger by 6 orders of magnitude than that predicted by bulk hydrodynamics because of high dissipation in the contact line vicinity. Similar to low viscous liquids (water), this high dissipation can be attributed to an Arrhenius factor resulting from the phase change in the contact line vicinity and to the influence of surface defects that pin the contact line.     

The aggregation behavior of poly-(oxyethylene)-poly-(oxypropylene)-poly-(oxyethylene)-block-copolymers in aqueous solution

Aqueous solutions of blockcopolymers, consisting of a polyoxypropyleneblock (POP) with a polyoxyethylene-block (POE) at each side, were studied using surface and interfacial tension measurements, static and dynamic light scattering and smallangle neutron scattering techniques, electric birefringence, rheological and DSC-measurements. The compounds were commercial samples and had an approximate average composition EO₂₀PO₇₀EO₂₀, EO₁₈PO₅₈EO₁₈, and EO₁₀₆PO₆₉EO₁₀₆. All three compounds formed micelles above a critical concentration. The size of the micellar core is determined by the length of the hydrophobic poly-propyleneoxide block. The transfer energy of a propyleneoxide unit from the aqueous to the micellar phase is about 0.3 kT at room temperature and hence a quarter of the corresponding value for a CH₂-group.The aggregation number of the micelles increases strongly with increasing temperature while the hydrodynamic radius remains constant in first approximation. The smallangle neutron scattering (SANS) data show at higher concentrations a strong correlation peak. Both the SANS- and the light-scattering data can be interpreted on the basis of the theory of hard sphere particles.Solutions with a volume fraction beyond about 0.2 gellifie when the temperature is raised above a characteristic value that is at the lowest concentrations slightly above room temperature, shift to lower values with increasing concentrations. Below this gelation temperature DSC-measurements show a phase transition with enthalpies between 40J/g and 80J/g, which is probably due to the dehydration of the PO-groups; this transition can also be observed at low concentrations where no gelation takes place. The position of the correlation peak of the SANS-data is not affected by the gel formation. Some samples, however, show clear evidence of long-range order and seem therefore to consist of cubic liquid crystalline phases. The shear moduli of the gels can qualitatively be understood on the basis of hard sphere models.     

Effect of solution viscosity on dynamic surface tension detection

A dynamic surface tension detector (DSTD) was used to examine the molecular diffusion and surface adsorption characteristics of surface-active analytes as a function of solution viscosity. Dynamic surface tension is determined by measuring the differential pressure across the air/liquid interface of repeatedly growing and detaching drops. Continuous surface tension measurement throughout the entire drop growth is achieved for each eluting drop (at a rate of 30 drops/min for 2 μl drops), providing insight into the kinetic behavior of molecular diffusion and orientation processes at the air/liquid interface. Three-dimensional data are obtained through a calibration procedure previously developed, but extended herein for viscous solutions, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Thus, an analyte that lowers the surface tension results in an increase in surface pressure. The calibration procedure derived for the pressure-based DSTD was successfully extended and implemented in this report to experimentally determine standard surface pressures in solutions of varied viscosity. Analysis of analytes in viscous solution was performed at low analyte concentration, where the observed analyte surface activity indicates that the surface concentration is at or near equilibrium when in a water mobile phase (viscosity of 1.0 Cp). Two surface-active analytes, sodium dodecyl sulfate (SDS) and polyethylene glycol (MW 1470 g/mol, PEG 1470), were analyzed in solutions ranging from 0 to 60% (v/v) glycerol in water, corresponding to a viscosity range of 1.0-15.0 Cp. Finally, the diffusion-limited surface activity of SDS and PEG 1470 were observed in viscous solution, whereby an increase in viscosity resulted in a decreased surface pressure early in drop growth. The dynamic surface pressure results reported for SDS and PEG 1470 are found to correlate with solution viscosity and analyte diffusion coefficient via the Stokes-Einstein equation.     

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.     

Kinetisch-katalytische Bestimmungen in einem zweiphasensystem unter verwendung eines fallrohres

A rather simple method for kinetic-catalytic determinations is described, in which the reactants are dissolved in two immiscible liquid phases. Drops of the heavier phase fall through the lighter one contained in a vertical glass tube. As the drops fall, the reactants come into contact with each other at the interface, thus causing a change in the drops. The length of fall needed for completion of reaction is a measure of the concentration of the catalyst (e.g., decolorization of the drops in the determination of copper by the reaction between iron(III) and thiosulphate). If a gaseous reaction product is formed (e.g., N₂ or O₂) and adsorbed on the falling drop, then the drop stops falling and rises again. The depth of fall or the time needed for the drop to return to the upper end of the tube can be used as a measure for the concentration of catalyst (e.g., determination of thiosulphate with the iodine/azide reaction, or of copper as catalyst for the decomposition of hydrogen peroxide).     

THE RELATIONSHIP BETWEEN THE MOLAR PARTITION COEFFICIENT AND THE ULTRALOW INTERFACIAL TENSION MINIMUM IN A PETROLEUM SULFONATE/ HYDROCARBON/BRINE SYSTEM

The partitioning of a sodium petroleum sulfonate between heptane and brine yields surfactants with different molar absorptivity and λ_max values in the two phases, except near the point of minimum interfacial tension, e of the surfactant in the heptane phase increases sharply above the point of minimum interfacial tension between the two phases. The molar partition coefficient, M_H/M_W, for the surfactant between the heptane and brine phases is unity at surfactant concentrations in the brine phase below the point of minimum interfacial tension and drops sharply at concentrations above it. The critical micelle concentration of the surfactant in the aqueous phase equilibrated with the heptane phase is considerably below the concentration for minimum interfacial tension     

超疏水表面上冷凝液滴发生弹跳的机制与条件分析

使用液滴合并前后的体积和表面自由能守恒作为两个限制条件,确定了合并液滴的初始形状,即为偏离平衡态的亚稳态液滴,具有缩小其底半径而向平衡态液滴转变的推动力.进而分析了液滴变形过程中的推动力和三相线(TPCL)上的滞后阻力,建立了液滴变形的动态方程并进行了差分求解.如果液滴能够变形至底半径为0mm的状态,则根据该状态下液滴重心上移的速度确定液滴的弹跳高度.不同表面上冷凝液滴合并后的变形行为的计算结果表明,光滑表面上的液滴合并后,液滴只能发生有限的变形,一般都在达到平衡态之前就停止了变形,因此冷凝液滴不会发生弹跳;粗糙表面上的Wenzel态液滴的三相线上的滞后阻力更大,因而液滴更难以变形和弹跳;具有微纳二级结构表面上只润湿微米结构,但不润湿纳米结构的部分Wenzel态液滴能够变形至Cassie态,但没有明显的弹跳;只有在纳米或微纳二级结构表面上的较小Cassie态液滴合并后,液滴易于变形至底半径为0mm的状态并发生弹跳.因此,Cassie态合并液滴处于亚稳态,并且其三相线上的移动阻力很小,是导致冷凝液滴弹跳的关键因素.     

Determination,by dynamic surface-tension analysis,of the molar mass of proteins denatured in guanidine thiocyanate

A drop-based dynamic surface-tension detector (DSTD) has been used to study the dynamic surface tension behavior of proteins denatured in guanidine thiocyanate (GndSCN). The dynamic surface tension at the air–liquid interface is obtained by measuring the internal pressure of drops that grow and detach at a specified rate. In the method the sample of interest is injected and subsequently flows to the DSTD-sensing capillary tip. For this work, a novel DSTD calibration procedure utilizing two distinct mobile phases is applied. Here, the mobile phases are aqueous with different constituents, for example GndSCN and phosphate buffer, either added or omitted. The dual-mobile phase calibration procedure gives the analyst the capability of making protein measurements in a GndSCN–phosphate buffer mobile phase, while measuring a calibration standard in another mobile phase, such as water, in which the surface tension of the calibration standard is readily available. Results are presented with drop volumes of either 2 L (i.e. 2-s drops) or 7 L (i.e. 7-s drops) for proteins varying in molar mass from 12,000 to 330,000 g mol^–1. We demonstrate that the DSTD can be used to determine the molar mass of proteins denatured in GndSCN. The method applies a regime where the denatured protein is detected by surface-active properties, and selectivity with regard to molar mass is contained in the dynamic component of the DSTD signal. The dynamic surface pressure signals of the denatured proteins suggest that diffusion plays a large role in the kinetics of the surface activity. The limit of detection for the denatured proteins studied ranged from 3 mg L^–1 to 14 mg L^–1. The DSTD, coupled with the novel dual-mobile phase calibration procedure, can be used to investigate the fundamental properties of proteins. Insight into the behavior at the air–liquid interface for native and denatured proteins is achieved; this is a novel tool for studying protein denaturation, complementary to other common approaches such as spectroscopy and calorimetry. Furthermore, the reported method could be widely applied to the study of effects on the interfacial properties of proteins after a variety of chemical and physical modifications that are possible with the dual-mobile phase calibration procedure.     

Gamma irradiation effect on chain segment motion and charge detrapping in polyamide 610

Gamma irradiation effect on the chain segment motion and charge detrapping in polyamide 610 was investigated by means of thermally stimulated depolarization current (TSDC), wide-angle X-ray diffraction (WAXD), differential scanning calorimetry (DSC) and gel fraction. There are four current peaks (named α, ρ₁, ρ₂ and ρ₃ peak, respectively) in TSDC spectra of polyamide 610. The α peak corresponds to the glass transition, the ρ₁ peak is attributed to space charge trapped in the amorphous phase, the ρ₂ peak is originated from space charge trapped in the interphase between crystalline and amorphous regions and the ρ₃ peak is originated from space charge trapped in crystalline phase. With the increase of irradiation dose from 1.5 to 2 MGy, ρ₁ and ρ₂ peaks gradually merge into one single peak. With the increase of irradiation dose the degree of crosslinking in amorphous phase is more than that in interphase and then the trap depth of interphase is gradually close to that of amorphous phase. By analyzing the characteristic parameters of these peaks, it is found that gamma irradiation can reduce the mobility of chain segments and increase structural defects in polyamide 610. In addition, irradiation increases the stability of trapped charge in both amorphous phase and interphase, but not affecting the stability of trapped charge in crystalline phase.