Effective Surface Energy Research Articles

Correlation of Effective Dispersive and Polar Surface Energies in Heterogeneous Self-Assembled Monolayer Coatings

We show, theoretically, that the measured effective dispersive and polar surface energies of a heterogeneous surface are correlated; the correlation, however, differs whether a Cassie or an Israelachvili and Gee model is assumed. Fluorocarbon self-assembled monolayers with varying coverage were grown on oxidized (100) silicon surfaces in a vapor phase process using five different precursors. Experimentally, effective surface energy components of the fluorocarbon self-assembled monolayers were determined from measured contact angles using the Owens-Wendt-Rabel-Kaelble method. We show that the correlation between the effective surface energy components of the heterogeneous surfaces coated with fluorocarbon self-assembled monolayers is in agreement with the Cassie model.

A new evaluation method of surface energy of ultra-thin film

A new method is proposed for evaluating the dispersive component of the effective surface energy of an ultra-thin film. The dispersive component is obtained by introducing a cut-off distance and integrating the corrected van der Waals pressure equation for a symmetric multilayer system. The cut-off distance is calculated using the experimentally determined surface energy of the substrate without an ultra-thin film. A stearic-acid Langmuir–Blodgett film on a glass plate was used as an ultra-thin film sample on a solid substrate. The dependences of the surface energy on the ultra-thin film thickness were investigated experimentally and theoretically, and the effectiveness of this method is discussed.

Generalization of Berreman’s model to the case of large amplitude of the grooves

We generalize Berreman's model to the case qA > or = 1 , where q is the wave vector of the surface structure and A its amplitude, to describe the alignment induced by a solid surface on a nematic liquid crystal. We show that, by taking into account correctly the elastic contribution to the surface energy connected with the surface topography, the effective surface energy is smaller than the one determined by Berreman, where the limiting surface is assumed flat and qA << 1 . The analysis is performed by assuming that the anchoring energy on the surface is strong, i.e., nematic molecules in contact with the limiting surface are tangent to it, for any bulk distortion. The generalization to the weak anchoring case is also presented.

Implications from the ratio of surface tension to bulk modulus and nearest neighbour distance, for planar surfaces

The theory of impact between nano-sized particles leads to the important non-dimensional grouping γ / aB , where γ , a and B are the effective surface energy, effective near neighbour distance, and effective bulk modulus for the impacting surfaces. A general, though formal, expression for γ / aB is obtained for a planar surface, and a modified Lennard-Jones analysis suggests that this grouping is of the order of several per cent. Bounds are suggested on this ratio, which are verified for many of the elements about their melting points, for several liquids at 298 K, and for the liquified noble gases. It is suggested that, at the atomic scale, the ratio between yield stress and the bulk modulus is also approximately equal to this grouping, which would make impacts between nano-scaled surfaces very much harder than for macroscopic impacts. However, γ / aB is material dependent and can vary by a factor of two or more about its median value. Subject to such variation, it is suggested that, to leading order, collisions between pure nanoscale particles depend primarily on the number of atoms in the clusters, and on a non-dimensional velocity scale, for low-velocity impacts. The expression for γ / aB is evaluated approximately in planar geometry by assuming that interactions between surface atoms (or molecules) only involve radial pair surface interactions.

Propane hydrate nucleation: Experimental investigation and correlation

In this work the nucleation kinetics of propane gas hydrate has been investigated experimentally using a stirred batch reactor. The experiments have been performed isothermally recording the pressure as a function of time. Experiments were conducted at different stirring rates, but in the same supersaturation region. The experiments showed that the gas dissolution rate rather than the induction time of propane hydrate is influenced by a change in agitation. This was especially valid at high stirring rates when the water surface was severely disturbed. Addition of polyvinylpyrrolidone (PVP) to the aqueous phase was found to reduce the gas dissolution rate slightly. However the induction times were prolonged quite substantially upon addition of PVP. The induction time data were correlated using a newly developed induction time model based on crystallization theory also capable of taking into account the presence of additives. In most cases reasonable agreement between the data and the model could be obtained. The results revealed that especially the effective surface energy between propane hydrate and water is likely to change when the stirring rate varies from very high to low. The prolongation of induction times according to the model is likely to be due to a change in the nuclei–substrate contact angle.

The effect of insect surface features on the adhesion of viscous capture threads spun by orb-weaving spiders

Spider orb-webs intercept a broad range of insects and their capture threads must adhere to a range of surface textures. In species of the Araneoidea clade, these capture threads are composed of viscid droplets whose size and spacing differ among species. To determine how droplet profile and insect surface texture interact, we measured the stickiness of viscous threads produced by four species using four insect surfaces that ranged from a smooth beetle elytra to the dorsal surface of a fly abdomen that was covered by large, widely spaced setae. The adhesion of threads to these surfaces differed by as much as 3.5-fold within a spider species and 2.1-fold for the same insect surface between spider species. However, 96% of these differences in stickiness was explained by four variables: the ratio of natural log of droplet volume to setal length, the natural log of droplet volume per mm of thread length, setal surface area, and the area of cuticle not excluded from thread contact by setae. Compared with previous measurements of primitive cribellar capture threads produced by orb weavers of the Deinopoidea clade, viscous threads performed more uniformly over the range of insect surfaces. They also held bug hemelytra, which were densely covered with fine setae, more securely, but held beetle elytra, fly wings and fly abdomens less securely than did viscous threads. Hemelytra may be held more securely because their setae more easily penetrate the viscous boundary layer to establish a greater area of interaction and, after having done so, offer more resistance as they are pulled through this layer. Finely textured surfaces may also have higher effective surface energies and therefore may interact more completely with viscous material.

Numerical simulation for the formation of nanostructures on the Stranski–Krastanow systems by surface undulation

The nanostructure formation of the Stranski–Krastanow (SK) systems is investigated by simulating the surface undulation of the systems driven by the surface diffusion mechanism. Of particular interest is how the surface undulation leads to the development of faceted nanostructures and wetting layers. The results reveal that the development exhibits three common features in the coarsening SK systems, while the development also results in distinct film morphologies, controlled by the maximum surface coverage of faceted islands. The maximum surface coverage depends on the film thickness, the ratio between the two characteristic lengths of the SK system, and the effective surface energy density of flat film.

Micromechanisms of cleavage fracture initiation from inclusions in ferritic welds: Part I. Quantification of local fracture behaviour observed in notched testpieces

Micromechanisms of cleavage fracture have been investigated in high strength weld metals with two types of microstructure. The local fracture stress was measured using notched bend testpieces, and by combining FEM predictions of local variations of local tensile stress and fractographic observations of initiation sites. The value of σ F( X 0) is significantly higher for weld metals with a lath-like microstructure. Inclusions have been found to be present in 82% of the initiation sites and undoubtedly they were usually responsible for the initiation of catastrophic cleavage fracture in both type of microstructures studied here. Local plasticity appears to be required to initiate cleavage fracture. An analysis of the potential difference between the local yield stress and the mean yield stress (from tensile testing) and the accuracy of predicted size of the plastic zone, suggests that these initiation sites are actually likely to be located inside the plastic zone. For a classical microstructure the value of the effective surface energy, γ p, was deduced to be approximately 9 J m −2; and for lath-like microstructures it was found to be approximately 13 J m −2.

Simulation of Vacancy Cluster Formation and Binding Energies in Single Crystal Germanium

AbstractResults are presented of the simulation of the properties of vacancy clusters in single crystal germanium. Classical molecular dynamics calculations based on a Stillinger and Weber potential were used in a theoretical investigation of different growth patterns of vacancy clusters Vi. The formation and binding energies of vacancy clusters have been studied in the range 1 ≤ i ≤ 35. The energetically favourable growth mode and an estimate of the effective surface energy was determined for a vacancy clusters containing up to 35 vacancies

Presence of intrinsic growth nuclei in overheated and undercooled liquid elements

Magnetic field texturing has already shown the possible existence of intrinsic solid nuclei above the melting temperature T m. The transfer of Δ n conduction electrons equalizing the Fermi energies of a particle containing n free electrons and the melt creates an interface electrostatic energy − ε v per volume unit that stabilizes tiny crystals above T m; they act as growth nuclei reducing the undercooling ratio θ=( T− T m)/ T m. The observed θ values and the effective dimensionless surface energies ( α 1ls) eff of 38 elements are used to calculate − ε v which is added to the Gibbs free energy change associated to a crystal formation. The ε v values are equal to 0.217(1−2.5 θ 2) multiplied by Δ H m/ V m the melting heat per volume unit. After melting these crystals above T m2=1.20 T m, θ could tend to the universal value −2/3. A simple formula based on the ε v values is predicting the linear decrease of Δ n/ n with θ and its disappearance for θ 0=−0.63. The free volume Δ V m/ V m and ε v also disappear for θ=−0.63 when Δ V m/ V m is equal to Δ n/ n. The surviving crystal radius is determined by a liquid droplet nucleation model in overheated crystals. A higher stability of tiny crystals is predicted from θ=0 to θ c. The strain energy density determines 0 < θ c⪡+0.2.

Micromechanisms of cleavage fracture initiation from inclusions in ferritic welds: Part II. Quantification of local fracture behaviour observed in fatigue pre-cracked testpieces

The quantification of the local fracture behaviour and the fracture toughness of high strength low alloy weld metals have been studied using fatigue pre-cracked CTOD testpieces. In CTOD testpieces, when brittle fracture occurs, with or without prior stable crack growth, cleavage usually starts from an inclusion located at the initiation site within allotriomorphic ferrite for weld metals with a classical microstructure, or within bainite or martensite packets in weld metals with a lath-like microstructure. The mean value of fracture stress, σ F( X 0), when evaluated using CTOD testpieces, has proved to be higher than when it is evaluated using SENB testpieces. This is deduced to be as a direct consequence of the reduction of the inclusion size found at initiation sites in CTOD testpieces. The effective surface energy here was evaluated to be approximately 8.6 J m −2, for the weld metal with a classical microstructure and 14 J m −2, for the weld metal with a lath-like microstructure. These values are closely similar to the values of the effective surface energy evaluated using SENB testpieces.

Analytical determination of the surface energy of sub-5nm head-disk interfaces accounting for multilayer effects

In this work, a five-layer HDI configuration was employed to derive a simple way to relate the multilayer Hamaker constant to an effective surface energy of the HDI. Specifically, the five layers of the HDI include two layers on the slider [diamondlike carbon (DLC) overcoat, Al2O3–TiC] and two layers on the disk (lubricant, DLC overcoat) as well as the air gap (or flying height). Following the formulation for two equivalent homogeneous surfaces, one can derive the effective surface energy of the five-layer model. To investigate the effect of the topmost layer thicknesses of the slider and disk on the surface energy, they were first varied from 2 to 5nm and from 0.5 to 2nm, respectively. It was found that the surface energy depends largely on the disk lubricant thickness while it has little dependence on the slider DLC thickness. Lubricant pickup by the slider and its effect on the surface energy was also investigated and it was found that the overall surface energy of the interface is lower when there is lubricant pickup.

Ab initio atomic-scale modelling of iodine effects on hcp zirconium

In order to elucidate possible mechanisms of stress corrosion cracking of nuclear power plant cladding material, we have investigated the iodine–zirconium interactions using ab initio atomic-scale calculations. We show that for the gas pressure estimated during the reactor power transients, the reduction of the zirconium effective free surface energy induced by the adsorption of atomic iodine is significant (more than 80%). Furthermore, for given iodine partial pressure, the surface energy reduction for the basal planes is higher than for the prismatic ones, in agreement with the experimental observation of a cleavage along the basal planes. We have also estimated the iodine surface diffusion coefficient, and its high value (about 10−6 cm2 s−1 at 600 K) indicates that iodine is mobile enough to follow the crack tip during the cracking experiments reproduced in laboratory conditions. Our results clearly rule out the influence of absorbed iodine during the cracking process, its equilibrium concentration being totally negligible.

Dependency of Fracture Toughness of Plasma Sprayed Al&lt;SUB&gt;2&lt;/SUB&gt; O&lt;SUB&gt;3&lt;/SUB&gt; Coatings on Lamellar Structure

The fracture toughness of plasma-sprayed Al2O3 coatings in terms of critical strain energy release rate GIc was investigated using a tapered double cantilever beam (TDCB) approach. This approach makes the fracture toughness be measured only using the critical fracture load disregarding crack length during test. The Al2O3 coatings were deposited under different spray distances and plasma powers to clarify the effect of spray parameters on the GIc of the coatings. The fracture surfaces were examined using scanning electron microscope. On the basis of an idealized layer microstructure model for thermal sprayed coatings, the theoretical relationship between the cohesive fracture toughness and microstructure is proposed. The correlation between the calculated fracture toughness and observed value is examined. It was found that the fracture toughness of plasma sprayed Al2O3 coatings is not significantly influenced by spray distance up to 110 mm, and further increase in spray distance to 130 mm resulted in large decrease in the fracture toughness of the coatings. The GIc value predicted based on the proposed model using lamellar interface mean bonding ratio and the effective surface energy of bulk ceramics agreed well with the observed GIc data. Such agreement evidently shows that the fracture toughness of thermally sprayed ceramic coatings at the direction along coating surface is determined by lamellar interface bonding.

Elastic beam over an adhesive wavy foundation

The adhesive behavior of a thin infinitely long elastic beam resting over a wavy rigid foundation with wavelength λ is studied. Three governing parameters have been identified describing the physical and geometrical properties of the system: the dimensionless surface energy γ̃=γ/Es, the dimensionless amplitude h̃=h/λ of the substrate, and thickness of the beam s̃=s/λ. Analyzing the variation of the total energy of the system as a function of the governing parameters three different adhesive regimes have been individuated: full adhesion, partial adhesion, and no adhesion (point contact). An effective surface energy has been considered showing that the effect of surface waviness could be beneficial in increasing the adhesive strength of the system. In particular for γ̃=1.0 and s̃=0.1, it has been evaluated a maximum effective interface energy of about 1.4γ under full contact conditions. Larger amplifications are expected for higher γ̃ and smaller s̃.

X-ray synchrotron study of liquid-vapor interfaces at short length scales: effect of long-range forces and bending energies.

We have investigated the small-scale structure of the liquid-vapor interface using synchrotron x-ray scattering for liquids with different molecular structures and interactions. The effective momentum-dependent surface energy first decreases from its macroscopic value due to the effect of long-range forces, and then increases with increasing wave vector. The results are analyzed using a recent density functional theory. The large wave-vector increase is attributed to a bending energy for which local and nonlocal contributions are equally important.

The effective surface energy of heterogeneous solids measured by inverse gas chromatography at infinite dilution

Inverse gas chromatography (IGC) at infinite dilution has been widely used to access the nonspecific surface free energy of solid materials. Since most practical surfaces are heterogeneous, the effective surface energy given by IGC at infinite dilution is somehow averaged over the whole sample surface, but the rule of averaging has thus far not been established. To address this problem, infinite dilution IGC analysis was carried out on mixtures of known heterogeneity. These materials are obtained by mixing two types of solid particles with significantly different surface energies as characterized individually with IGC, and results are obtained for binary combinations in varying proportions. It is found that when all surface components have the same accessibility by probe molecules, the effective surface energy of such a heterogeneous surface is related to the surface energy distribution by a square root linear relationship, σ eff LW =∑ iφ i σ i LW , where σ i LW refers to the nonspecific (Lifshitz–van der Waals) surface energy of patches i, and φ i to their area fraction.

Influence of surface roughness on the adhesion of elastic films

It is shown that a self-affine roughness at the junction of an elastic film and a hard solid substrate influences considerably the adhesion of the elastic film, especially for small roughness exponents H (H<0.5) and/or large long wavelength roughness ratios w/xi with w being the rms roughness amplitude and xi being the in-plane roughness correlation length. Analytical calculations of the local surface slope allows an estimate of the roughness effects on the adhesion energy more precisely than those presented in earlier works (especially for roughness exponents H<0.5). For weak surface roughness the elastic energy contribution is significant on the film effective surface energy deltagamma(eff) and on pull-off force for elastic modulus E in the range of GPa. Moreover, in the case of partial contact an estimation of the pull-off force shows that it strongly decreases with reducing contact area due to surface.

Statistical analysis of ice fracture characteristics

This paper addresses the fracture toughness and strength characteristics of ice taken from Notoro Lagoon in the Okhotsk Sea close to Hokkaido. Experimental values of tensile and bending strengths, and fracture toughness of sea ice conformed to Weibull statistical distribution. The proposed model predicts variation in fracture toughness as a function of the statistical distribution of ice grain sizes, effective surface energy, and elastic constants of ice. A very good agreement between experimental cumulative probability of fracture toughness and predicted distribution of fracture toughness of sea ice has been found. Computing the Weibull stress of sea ice, the dependence of fracture probability on stress intensity factor has been established. This result is in very good agreement with the presented method for the prediction of fracture toughness of sea ice.

Factors affecting the shape of the ductile-to-brittle transition

This paper uses a statistical model of cleavage fracture to examine the effect of various material parameters on the mean toughnesses of ferritic steels in the transition region. Individually, changes in the flow properties, in the effective surface energy, and in the distribution of particles from which cleavage is initiated, all affect the curvature of the mean fracture toughness ( K c) versus temperature ( T) curve. The range of applicability of the Master Curve description of K c versus T is due to real metallurgical processes causing counteracting changes in more than one parameter at a time. As a result, if the Master Curve is applicable before irradiation hardening, plastic deformation or tempering, then it may well remain applicable after these processes. It will not apply both before and after segregation (intergranular failure) or warm prestressing. The study also illuminates the differences between plates, welds and forgings in their response to irradiation or thermo-mechanical processing.