Contribution To Surface Energy Research Articles

Elongated Quantum Dots of Ge on Si Growth Kinetics Modeling with Respect to the Additional Energy of Edges

In this paper refining of mathematical model for calculation of parameters of selforganised quantum dots (QDs) of Ge on Si grown by the method of molecular beam epitaxy (MBE) is done. Calculations of pyramidal and wedge-like clusters formation energy were conducted with respect to contributions of surface energy, additional edge energy, elastic strain relaxation, and decrease in the atoms attraction to substrate. With the help of well-known model based on the generalization of classical nucleation theory it was shown that elongated islands emerge later than pyramidal clusters. Calculations of QDs surface density and size distribution function for wedge-like clusters with different length to width ratio were performed. The absence of special geometry of islands for which surface density and average size of islands reach points of extremum that was predicted earlier by the model not taking into account energy of edges was revealed when considering the additional contribution of edge formation energy.

Geometry- and Length Scale-Dependent Deformation and Recovery on Micro- and Nanopatterned Shape Memory Polymer Surfaces.

Micro- and nanoscale surface textures, when optimally designed, present a unique approach to improve surface functionalities. Coupling surface texture with shape memory polymers may generate reversibly tuneable surface properties. A shape memory polyetherurethane is used to prepare various surface textures including 2 μm- and 200 nm-gratings, 250 nm-pillars and 200 nm-holes. The mechanical deformation via stretching and recovery of the surface texture are investigated as a function of length scales and shapes. Results show the 200 nm-grating exhibiting more deformation than 2 μm-grating. Grating imparts anisotropic and surface area-to-volume effects, causing different degree of deformation between gratings and pillars under the same applied macroscopic strain. Full distribution of stress within the film causes the holes to deform more substantially than the pillars. In the recovery study, unlike a nearly complete recovery for the gratings after 10 transformation cycles, the high contribution of surface energy impedes the recovery of holes and pillars. The surface textures are shown to perform a switchable wetting function. This study provides insights into how geometric features of shape memory surface patterns can be designed to modulate the shape programming and recovery, and how the control of reversibly deformable surface textures can be applied to transfer microdroplets.

Energy Budget of Liquid Drop Impact at Maximum Spreading: Numerical Simulations and Experiments.

The maximum spreading of an impinging droplet on a rigid surface is studied for low to high impact velocity, until the droplet starts splashing. We investigate experimentally and numerically the role of liquid properties, such as surface tension and viscosity, on drop impact using three liquids. It is found that the use of the experimental dynamic contact angle at maximum spreading in the Kistler model, which is used as a boundary condition for the CFD-VOF calculation, gives good agreement between experimental and numerical results. Analytical models commonly used to predict the boundary layer thickness and time at maximum spreading are found to be less correct, meaning that energy balance models relying on these relations have to be considered with care. The time of maximum spreading is found to depend on both the impact velocity and surface tension, and neither dependency is predicted correctly in common analytical models. The relative proportion of the viscous dissipation in the total energy budget increases with impact velocity with respect to surface energy. At high impact velocity, the contribution of surface energy, even before splashing, is still substantial, meaning that both surface energy and viscous dissipation have to be taken into account, and scaling laws depending only on viscous dissipation do not apply. At low impact velocity, viscous dissipation seems to play an important role in low-surface-tension liquids such as ethanol.

Thermo-coupled Surface Cauchy–Born theory: An engineering finite element approach to modeling of nanowire thermomechanical response

There are remarkable studies geared towards developing thermomechanical analyses of nanowires based on quasiharmonic and Molecular Dynamics simulations. These methods exhibit limited applicability due to the associated computational cost. In this study an engineering finite-temperature model based on Surface Cauchy–Born theory is developed, where surface energy is accounted for in the prediction of the thermomechanical response. This is achieved by using a temperature-dependent interatomic potential in the standard Cauchy–Born theory with a surface energy contribution. Simultaneous calculation of thermal and mechanical stresses is achieved by eliminating the diagonalization matrix of entropy in the quasiharmonic system. This leads to a reduction in the degrees of freedom by more than 99% in comparison with equivalent Molecular Dynamics models. For the purpose of validation, results obtained on copper and nickel nanowires through the proposed method are compared with those of the more involved Molecular Dynamics simulations. This comparison verifies the significant reduction in the computational process with an acceptable accuracy. Hence, the proposed method provides a promising engineering tool without compromising the underlying physics of the problem and has potential implications in the effective modeling of the nanoscale thermomechanical behavior.

The Nanocrystalline SnO2–TiO2 System‒Part II: Surface Energies and Thermodynamic Stability

The thermodynamic stability of nanocrystalline SnO2–TiO2 solid solutions was studied experimentally. Microcalorimetry of water adsorption revealed a systematic decrease in the surface energy with increasing Ti4+ content in the SnO2‐rich compositions, consistent with previous reports of Ti4+ segregation on the surface. The surface energy change was accompanied by an increase in the magnitude of the heat of water adsorption, also indicating a modification of the SnO2 surface by Ti4+. Supporting the water adsorption data, calculations using high‐temperature oxide melt solution calorimetry data also suggest a decrease in the interface energies. A thermodynamic analysis showed that the observed surface energy decrease is responsible for an increase in the stability of solid solutions in the nanophase regime. Although a miscibility gap is expected in this system from bulk phase diagrams, the surface energy contribution modifies the bulk trend and promotes extensive solid solutions when the surface area is above a critical value dependent on the surface energy and the bulk enthalpy of mixing.

Phytic acid layer template-assisted deposition of TiO2 film on titanium: Surface electronic properties, super-hydrophilicity and bending strength

Titanium dioxide film has received a great deal of attention, because of its excellent potentials and implications, in a variety of fields. Practically, the film is required to be well mechanically blended with the substrate (e.g. good compliance or flexibility) together with its surface properties to accomplish multiple functions. In this work, phytic acid (PA) layer template-assisted deposition of thin TiO2 film was implemented on titanium substrate to produce a good combination of surface properties and bending strength. Relatively smooth, homogenous and thin (ca. 800nm) anatase TiO2 films were obtained on the PA pre-templated Ti substrate. Significantly enhanced photoluminescence was observed on the PA template-deposited TiO2 as compared to the direct deposited TiO2. This is correlated with its higher carrier density in the space charge layer as disclosed by the Mott–Schottky investigation. Likewise, the prepared TiO2 films are super-hydrophilic (with water contact angle less than 5°), which is credited to the higher polar contribution of surface energy. Moreover, the PA template-deposited TiO2 film withstood plastic deformation up to 180° angle bending without failure. This template-assisted deposition of TiO2 film via surface-immobilized organic layer on rigid substrate suggests a promising route to enhance both its mechanical and physical performances.

Nanoscale superconductivity of γ-Ga islands grown by molecular beam epitaxy

We report on the preparation and superconductivity of metastable γ-Ga islands on Si (111) substrate. The Ga grows in a typical Volmer-Weber mode at a low temperature of 110 K, resulting in formation of Ga nanoislands at various sizes with the identical γ-phase. In-situ low temperature scanning tunneling spectra reveal quantized electronic states in ultrathin Ga islands. It is found that both the lateral size and thickness of the Ga islands strongly suppress the superconductivity. Due to substantial surface energy contribution, the transition temperature T c scales inversely with the island thickness and the minimum thickness for the occurrence of superconductivity is calculated to be two monolayers.

Study on the growth mechanism and optical properties of sputtered lead selenide thin films

Lead selenide thin films with different microstructure were deposited on Si (100) substrates using magnetron sputtering at 50°C, 150°C and 250°C, respectively. The crystal structure of the sputtered PbSe thin films varies from amorphous crystalline to columnar grain, and then to double-layer (nano-crystalline layer and columnar grain layer) structure as the deposition temperature increases, which is due to the dominating growth mode of the thin films changes from Frank–van der Merwe (or layer-by-layer) growth mode at 50°C to Volmer–Weber (or 3D island) growth mode at 150°C, and then to Stranski–Krastanow (or 3D island-on-wetting-layer) growth mode at 250°C. The growth mechanism of the sputtered PbSe thin films is mainly dominated by the surface and strain energy contributions. Moreover, the strain energy contribution is more prominent when the deposition temperature is less than 180°C, while, the surface energy contribution is more prominent when the deposition temperature is higher than 180°C. The absorption spectra of the sputtered PbSe thin films are in 3.1–5μm range. Besides, the sputtered PbSe thin film prepared at 250°C has two different optical band gaps due to its unique double-layer structure. According to the theoretical calculation results, the variation of the band gap with the deposition temperature is determined by the shift of the valence band maximum with the lattice constant.

Effect of milling temperatures on surface area, surface energy and cohesion of pharmaceutical powders

Particle bulk and surface properties are influenced by the powder processing routes. This study demonstrates the effect of milling temperatures on the particle surface properties, particularly surface energy and surface area, and ultimately on powder cohesion. An active pharmaceutical ingredient (API) of industrial relevance (brivanib alaninate, BA) was used to demonstrate the effect of two different, but most commonly used milling temperatures (cryogenic vs. ambient). The surface energy of powders milled at both cryogenic and room temperatures increased with increasing milling cycles. The increase in surface energy could be related to the generation of surface amorphous regions. Cohesion for both cryogenic and room temperature milled powders was measured and found to increase with increasing milling cycles. For cryogenic milling, BA had a surface area ∼5× higher than the one obtained at room temperature. This was due to the brittle nature of this compound at cryogenic temperature. By decoupling average contributions of surface area and surface energy on cohesion by salinization post-milling, the average contribution of surface energy on cohesion for powders milled at room temperature was 83% and 55% at cryogenic temperature.

Fully Crystalline Faceted Fe-Au Core-Shell Nanoparticles.

Fe-Au core-shell nanoparticles displaying an original polyhedral morphology have been successfully synthesized through a physical route. Analyses using transmission electron microscopy show that the Au shell forms truncated pyramids epitaxially grown on the (100) facets of the iron cubic core. The evolution of the elastic energy and strain field in the nanoparticles as a function of their geometry and composition is calculated using the finite-element method. The stability of the remarkable centered core-shell morphology experimentally observed is attributed to the weak elastic energy resulting from the low misfit at the Fe/Au (100) interface compared to the surface energy contribution.

Contribution of surface energy and roughness to the wettability of polyamide 6 and polypropylene film in the plasma-induced process

Plasma-induced etching and chemical vapor coating processes are well-known technologies that modify the wetting properties of polymeric surfaces by engineering the surface roughness and surface energy. The contributing effect of plasma treatment for O2 etching and hexamethyldisiloxane (HMDSO) vapor coating on the wetting properties was investigated for polyamide 6 (PA6) and polypropylene (PP) substrates. The surface energy components of PA6 and PP were analyzed by the Owens–Wendt model, and were associated with the wettability of water and diiodomethane. With the introduction of roughness by the O2 etching process without HMDSO coating, the wettability of PA6 substrate was enhanced while that of PP was deteriorated when they were observed after 20 days aging. When the surface was etched for 7 min or longer with the subsequent coating with HMDSO, both PA6 and PP lost hydrophilic property, giving water contact angle of 180°. The wettability was examined for the varied treatment conditions and as a function of average nano-pillar length. This study helps better understand the interactions between the surface energy and roughness of polymeric materials, and their influence on surface wettability.

Interpolating function of the strain relief of epitaxial quantum dots via an alternative morphological descriptor

Assessing the equilibrium morphologies of self-assembled heteroepitaxial quantum dots requires the estimation of their elastic (volumetric), surface, and edge energy contribution, all of them being shape dependent. Due to the size and multifaceted morphology of these islands, the estimation of the first term is typically a time-consuming or complicated task. A general rule to predict it from the sole morphologies would guarantee a precious advantage in this field. Here we present an interpolating function to fulfill this purpose for the prototypical systems of Ge/Si and InAs/GaAs. The trend is first extracted from a systematic analysis of realistic shapes observed on (001) substrates. It is then tested and corroborated for selected vicinal (tilted) substrates. Finally, the deviations due to intermixing and the underlying wetting layer are quantified. Of fundamental importance in this process is the identification of a morphological descriptor more accurate than the widely adopted aspect ratio, the limitations of which are discussed.

The origin of ferroelectricity in Hf1−xZrxO2: A computational investigation and a surface energy model

The structural, thermal, and dielectric properties of the ferroelectric phase of HfO2, ZrO2, and Hf0.5Zr0.5O2 (HZO) are investigated with carefully validated density functional computations. We find that the free bulk energy of the ferroelectric orthorhombic Pca21 phase is unfavorable compared to the monoclinic P21/c and the orthorhombic Pbca phase for all investigated stoichiometries in the Hf1−xZrxO2 system. To explain the existence of the ferroelectric phase in nanoscale thin films, we explore the Gibbs/Helmholtz free energies as a function of stress and film strain and find them unlikely to become minimal in HZO films for technological relevant conditions. To assess the contribution of surface energy to the phase stability, we parameterize a model, interpolating between existing data, and find the Helmholtz free energy of ferroelectric grains minimal for a range of size and stoichiometry. From the model, we predict undoped HfO2 to be ferroelectric for a grain size of about 4 nm and epitaxial HZO below 5 nm. Furthermore, we calculate the strength of an applied electric field necessary to cause the antiferroelectric phase transformation in ZrO2 from the P42/nmc phase as 1 MV/cm in agreement with experimental data, explaining the mechanism of field induced phase transformation.

On the Stability of Rotating Drops.

We consider the equilibrium and stability of rotating axisymmetric fluid drops by appealing to a variational principle that characterizes the equilibria as stationary states of a functional containing surface energy and rotational energy contributions, augmented by a volume constraint. The linear stability of a drop is determined by solving the eigenvalue problem associated with the second variation of the energy functional. We compute equilibria corresponding to both oblate and prolate shapes, as well as toroidal shapes, and track their evolution with rotation rate. The stability results are obtained for two cases: (i) a prescribed rotational rate of the system (“driven drops”), or (ii) a prescribed angular momentum (“isolated drops”). For families of axisymmetric drops instabilities may occur for either axisymmetric or non-axisymmetric perturbations; the latter correspond to bifurcation points where non-axisymmetric shapes are possible. We employ an angle-arc length formulation of the problem which allows the computation of equilibrium shapes that are not single-valued in spherical coordinates. We are able to illustrate the transition from spheroidal drops with a strong indentation on the rotation axis to toroidal drops that do not extend to the rotation axis. Toroidal drops with a large aspect ratio (major radius to minor radius) are subject to azimuthal instabilities with higher mode numbers that are analogous to the Rayleigh instability of a cylindrical interface. Prolate spheroidal shapes occur if a drop of lower density rotates within a denser medium; these drops appear to be linearly stable. This work is motivated by recent investigations of toroidal tissue clusters that are observed to climb conical obstacles after self-assembly [Nurse et al., Journal of Applied Mechanics 79 (2012) 051013].

Polymeric Droplets on Soft Surfaces: From Neumann’s Triangle to Young’s Law

Shape deformation of polymeric droplets on gel-like surfaces is studied by using a combination of the molecular dynamics simulations and theoretical calculations. On the basis of the results of molecular dynamics simulations, we have developed a theoretical model of droplet shape deformation on elastic surfaces which takes into account surface and elastic energy contributions. Analysis of simulation results in the framework of this model shows that the equilibrium droplet shape is controlled by the dimensionless parameter γSL/GSa, where γSL is the surface tension of the substrate/liquid interface, GS is the shear modulus of the substrate, and a is the contact radius of polymeric droplet. This parameter describes crossover between Neumann’s triangle conditions for liquid droplets on liquid substrates and Young’s law for droplets on rigid substrates. In the limit when the elastocapillary length is much larger than the contact radius, γSL/GS ≫ a, we recover the Neumann’s triangle conditions for liquid droplets floating on liquid substrates. However, in the opposite limit, γSL/GS ≪ a, our model reproduces Young’s law. The model predictions are in a very good agreement with simulation results and experimental data.

Phase stability in nanoscale material systems: extension from bulk phase diagrams

Phase diagrams of multi-component systems are critical for the development and engineering of material alloys for all technological applications. At nano dimensions, surfaces (and interfaces) play a significant role in changing equilibrium thermodynamics and phase stability. In this work, it is shown that these surfaces at small dimensions affect the relative equilibrium thermodynamics of the different phases. The CALPHAD approach for material surfaces (also termed "nano-CALPHAD") is employed to investigate these changes in three binary systems by calculating their phase diagrams at nano dimensions and comparing them with their bulk counterparts. The surface energy contribution, which is the dominant factor in causing these changes, is evaluated using the spherical particle approximation. It is first validated with the Au-Si system for which experimental data on phase stability of spherical nano-sized particles is available, and then extended to calculate phase diagrams of similarly sized particles of Ge-Si and Al-Cu. Additionally, the surface energies of the associated compounds are calculated using DFT, and integrated into the thermodynamic model of the respective binary systems. In this work we found changes in miscibilities, reaction compositions of about 5 at%, and solubility temperatures ranging from 100-200 K for particles of sizes 5 nm, indicating the importance of phase equilibrium analysis at nano dimensions.

Decoupling the contribution of surface energy and surface area on the cohesion of pharmaceutical powders.

Surface area and surface energy of pharmaceutical powders are affected by milling and may influence formulation, performance and handling. This study aims to decouple the contribution of surface area and surface energy, and to quantify each of these factors, on cohesion. Mefenamic acid was processed by cryogenic milling. Surface energy heterogeneity was determined using a Surface Energy Analyser (SEA) and cohesion measured using a uniaxial compression test. To decouple the surface area and surface energy contributions, milled mefenamic acid was "normalised" by silanisation with methyl groups, confirmed using X-ray Photoelectron Spectroscopy. Both dispersive and acid-base surface energies were found to increase with increasing milling time. Cohesion was also found to increase with increasing milling time. Silanised mefenamic acid possessed a homogenous surface with a surface energy of 33.1 ± 1.4mJ/m(2) , for all milled samples. The cohesion for silanised mefenamic acid was greatly reduced, and the difference in the cohesion can be attributed solely to the increase in surface area. For mefenamic acid, the contribution from surface energy and surface area on cohesion was quantified to be 57% and 43%, respectively. Here, we report an approach for decoupling and quantifying the contribution from surface area and surface energy on powder cohesion.

A Phase-Field Approach for Wetting Phenomena of Multiphase Droplets on Solid Surfaces

We study the equilibrium wetting behavior of immiscible multiphase systems on a flat, solid substrate. We present numerical computations which are based on a vector-valued multiphase-field model of Allen-Cahn type, with a new boundary condition, based on appropriately designed surface energy contributions in order to ensure the right contact angles at multiphase junctions. Experimental investigations are carried out to validate the method and to support the numerical results.

Crystallization in Carbon Nanostructures

We investigate ground state configurations for atomic potentials including both two- and three-body nearest-neighbor interaction terms. The aim is to prove that such potentials may describe crystallization in carbon nanostructures such as graphene, nanotubes, and fullerenes. We give conditions in order to prove that planar energy minimizers are necessarily honeycomb, namely graphene patches. Moreover, we provide an explicit formula for the ground state energy which exactly quantifies the lower-order surface energy contribution. This allows us to give some description of the geometry of ground states. By recasting the minimization problem in three-space dimensions, we prove that ground states are necessarily nonplanar and, in particular, rolled-up structures like nanotubes are energetically favorable. Eventually, we check that the C20 and C60 fullerenes are strict local minimizers, hence stable.

Direct Measurement of Fusion Enthalpy of LaAlO3 and Comparison of Energetics of Melt, Glass, and Amorphous Thin Films

Enthalpy of fusion and melting temperature of perovskite LaAlO3 were measured using thermal analysis method as 124 ± 10 kJ/mol at 2134 ± 10°C, providing a value of 52 ± 4 J·(mol·K)−1 for entropy of fusion. Crystallization enthalpy of amorphous LaAlO3 thin films was found to change from −24 to −17 kJ/mol with decrease in film thickness from 100 to 20 nm. Differences in energetics of amorphous LaAlO3 films and glass cannot be explained exclusively by surface energy contribution but must reflect differences in structure between films and glasses in this system.