Inverse gas chromatography at infinite dilution, employing alkanes and alkenes as probes, has been used to characterize the surface properties of a series of smectites of varying chemical composition. The results of this study show that the acidic centers and the interlayer distances have a great influence on the specific interaction of the smectite surface with π-bonds of alkenes. High values of the specific interaction parameter, ɛπ, are caused by the existence of strong acidic centers that are connected with interlayer cations as well as with the chemical structure of the mineral sheets. On the other hand, alkanes, whose interaction with the smectites is predominantly dispersive, are unaffected by changes in the clays’ composition and/or structure.

The sorption properties of carbon-composite materials based on montmorillonite and hydrotalcite matrices have been studied using nitrogen adsorption isotherms and inverse gas chromatography. Carbon composite materials derived from both types of inorganic precursors contain pore structure accessible for adsorbate molecules. Adsorption capacity per unit mass of these composite adsorbents is larger in the case of hydrotalcite than in montmorillonite-based materials. Exposing these materials to ambient conditions results in their hydration. Subsequent water removal by heating under vacuum increases nitrogen adsorption capacity, which is explained by the opening of the adsorption space. The water content of hydrated samples and its effect on adsorption capacity is greater for the case of hydrotalcite-based materials. No direct relationship between carbon content and adsorption properties of the materials studied is observed.

The reactivity and stability of the edge faces of swelling clay minerals can be altered by layer charge and the stacking structure; however, these effects are poorly understood due to experimental limitations. The structure and stability of the montmorillonite {110}, {010}, {100}, and {130} edge faces with a layer charge of either y = 0.50 or y = 0.33 (e−/Si4O10) were investigated using first-principles calculations based on density functional theory. Stacked- and single-layer models were tested and compared to understand the effect of stacking on the stability of montmorillonite edge faces. Most stacked layers stabilize the edge faces by creating hydrogen bonds between the layers; therefore, the surface energy of the layers in the stacked-layer model is lower than in the single-layer model. This indicates that the estimates of edge face surface energy should consider the swelling conditions. Negative surface energies were calculated for these edge faces in the presence of chemisorbed water molecules. A high layer charge of 0.50 reduced the surface energy relative to that of the low layer charge of 0.33. The isomorphic substitution of Mg for Al increased the stability of interlayer Na ion positions, which were stable in the trigonal ring next to the Mg ions. The lowest surface energies of the {010} and {130} edge faces were characterized by the presence of Mg ions on edge faces, which had a strong cation adsorption site due to the local negative charge of the edges. The coordination numbers of O atoms around cations adsorbed to these edge faces were small in comparison to interlayers without water.

The present study considered the problem of halloysite nanoscroll synthesis by energy modeling of the formation of chrysotile and halloysite particles. The main aim of the study was to reveal an energy preference between scrolled and platy morphologies of the particles. Both hydrosilicates possess the ability to scroll spontaneously but relatively facile hydrothermal synthesis of the nanoscrolls is available only to the former, whereas halloysite forms mainly plates under the same conditions. This issue was investigated by a phenomenological energy model, taking into account: (1) strain energy due to the size difference between metal oxide and silica sheets; (2) surface-energy difference on the opposite sides of the layer; and (3) adhesion energy. Calculations showed that the halloysite layer had a significant scrolling potential due to the first energy component, but the surface-energy difference acted in the opposite direction and tried to unbend the layer. In contrast, these two actions were co-directional in chrysotile layers. In both cases, the formation of multi-layered plates became more energy favorable when the specific surface energy of the edges decreased. In the range 0.5–3 J/m2 for the specific surface energy, only halloysite layers showed an energy preference for platy particles over nanoscrolls, especially at small layer sizes. Certain processes, such as hydration, could reduce the corresponding specific surface energy value and, as a result, could stabilize the platy morphology of halloysite at the earliest stages of particle growth under hydrothermal conditions.

The special application environment puts forward the higher requirement of reliability of parts made from titanium alloy Ti–6Al–4V, which is closely related to the machining-induced residual stress. For the fact of the non-linear distribution of residual stress beneath the machined surface, distribution of peripheral milling-induced residual stress and its effect on fatigue performance of titanium alloy Ti–6Al–4V are still confusing. In the present study, residual stress profile induced by peripheral milling of Ti–6Al–4V is first studied. And then, energy criteria are proposed to characterise the whole state of the residual stress field. Finally, the effects of residual stress profile and surface energy on tensile–tensile fatigue performance of titanium alloy Ti–6Al–4V are discussed. The conclusions were drawn that the variation trend of surface residual stress (σr,Sur), maximum compressive residual stress (σC,ax), location (hr0) and response depth (hry) of residual stress profile with cutting parameters showed a similar pattern for both measure directions those parallel (σ1) and perpendicular (σ3) to the cutting direction. Cutting speed and feed rate have a main effect on surface residual stress, and the depth of cut has little effect on all the four key factors of residual stress profile. With the increase of cutting speed and feed rate, machining-induced surface energy tends to become larger. But increasing the depth of cut caused the strain energy stored in unit time to decrease. Furthermore, the effect of depth of cut on surface energy was weakened when the value of cutting depth becomes larger. Both the surface compressive residual stress and the maximum compressive residual stress are beneficial for prolonging the fatigue life, while large value of machining-induced surface energy leads to a decrease of fatigue life. Analysis of variance result shows that maximum residual compressive stress has a greater impact on fatigue life than other residual stress factors.

The amorphous carbon thin films were deposited by the ion beam sputtering deposition technique on Ni–Cu alloy substrates. The effect of sputtering ion beam energy on wettabillity, surface, and structural properties of thin films was examined. The sputtering ion beam energy was varied over a wide range from 2 to 5 keV. Raman spectra showed that the values of ID/IG ratio and the ‘G’ peak position have a reduction trend by increasing the argon ion beam energy while the surface roughness increased due to the resputtering effect. The wettability and surface energy of a-C carbon films were studied by contact angle measurements in relation to structure and topography. The deposited films showed a relatively high water contact angle (CA) that decreases from 87° to 75°. The X-ray photoelectron spectroscopy showed that the value of sp3/sp2 bond content of a-C thin films deposited with the highest argon ion beam energy of 5 keV was about 0.8. Furthermore, the optical band gap followed similar trends of the structural properties.

We consider general surface energies, which areweighted integrals over a closed surface with a weight functiondepending on the position, the unit normal andthe mean curvature of the surface. Energiesof this form have applications in many areas, such as materials science,biology and image processing. Often one is interested in findinga surface that minimizes such an energy, which entails finding its firstvariation with respect to perturbations of the surface.We present a concise derivation of the first variation of thegeneral surface energy using tools from shape differential calculus.We first derive a scalar strong form and nexta vector weak form of the first variation. The latter reveals thevariational structure of the first variation, avoids dealingexplicitly with the tangential gradient of the unit normal,and thus can be easily discretized using parametric finite elements.Our results are valid for surfaces in any number of dimensionsand unify all previous results derived for specific examples ofsuch surface energies.

Let $K:=SO\left(2\right)A_1\cup SO\left(2\right)A_2\dots SO\left(2\right)A_{N}$ where $A_1,A_2,\dots, A_{N}$ are matrices of non-zero determinant. Weestablish a sharp relation between the following two minimisationproblems in two dimensions. Firstly the N-well problem with surface energy. Let $p\in\left[1,2\right]$ , $\Omega\subset \mathbb{R}^2$ be a convex polytopal region. Define $$I^p_{\epsilon}\left(u\right)=\int_{\Omega} d^p\left(Du\left(z\right),K\right)+\epsilon\left|D^2u\left(z\right)\right|^2 {\rm d}L^2 z$$ and let A F denote the subspace of functions in $W^{2,2}\left(\Omega\right)$ that satisfy the affine boundary conditionDu=F on $\partial \Omega$ (in the sense of trace), where $F\not\inK$ . We consider the scaling (with respect to ϵ) of $$m^p_{\epsilon}:=\inf_{u\in A_F} I^p_{\epsilon}\left(u\right).$$ Secondly the finite element approximation to the N-well problemwithout surface energy. We will show there exists a space of functions $\mathcal{D}_F^{h}$ whereeach function $v\in \mathcal{D}_F^{h}$ is piecewise affine on a regular(non-degenerate) h-triangulation and satisfies the affine boundarycondition v=lF on $\partial \Omega$ (where l F is affine with $Dl_F=F$ ) such that for $$\alpha_p\left(h\right):=\inf_{v\in \mathcal{D}_F^{h}}\int_{\Omega}d^p\left(Dv\left(z\right),K\right) {\rm d}L^2 z$$ there exists positive constants $\mathcal{C}_1<1<\mathcal{C}_2$ (depending on $A_1,\dots, A_{N}$ , p) for which the following holds true $$\mathcal{C}_1\alpha_p\left(\sqrt{\epsilon}\right)\leq m^p_{\epsilon}\leq\mathcal{C}_2\alpha_p\left(\sqrt{\epsilon}\right) \text{ for all }\epsilon>0.$$

This paper discusses the asymptotic behaviour, and in particular the critical singularities, of the generating functions for Pólya walks with a given fraction of visits to a hyperplane when the walk is or is not constrained to be on one side of that hyperplane. The three-dimensional case has applications in physics and chemistry.