II.—The Van der Waals Force between a Proton and a Hydrogen Atom

The ability of scanning force microscopy to detect minute forces at high spatial resolution offers the possibility to systematically map the ever-present van der Waals (VDW) forces between probe and sample. Rigorously based on macroscopic quantum field theory the presented analysis involves an ab initio calculation of VDW forces in close relation to the experimental situation. It is shown that VDW forces directly reflect surface dielectric properties of the sample under investigation. Highly polar immersion liquids present between probe and sample are shown to significantly reduce VDW forces in magnitude. Additionally, some immersion media are found to cause a transition from attractive to repulsive interactions. The lateral resolution of VDW microscopy is estimated to be in the sub-100 nm range. First experimental aspects concerning VDW force detection are presented.

van der Waals effect on the nanoindentation response of free standing monolayer graphene

The main objective of this contribution is a constructive generalization of the holomorphic power and Laurent series expansions in ℂ to dimension 3 using the framework of hypercomplex function theory. This first article on hand deals with generalized Fourier and Taylor series expansions in the space of square integrable quaternion-valued functions which possess peculiar properties regarding the hypercomplex derivative and primitive. In analogy to the complex one-dimensional case, both series expansions are orthogonal series with respect to the unit ball in ℝ3 and their series coefficients can be explicitly (one-to-one) linked with each other. Finally, very compact and efficient representation formulae (recurrence, closed-form) for the elements of the orthogonal bases are presented.

A Comparison of Neutron Diffraction and Molecular Dynamics Structures: Hydroxyl Group and Water Molecule Orientations in Trypsin

The efforts of this thesis are directed towards understanding the physical driving forces that mediate membrane protein self-assembly processes within the native environment of membrane proteins, the bilayer milieu. While many defined determinants contribute to the energetics of membrane protein self-assembly, such as electrostatics, non-polar side-chain packing, hydrogen bonding, and solvophobic effects, the roles that these driving forces play have not been well characterized. The inability to describe the role of these physical driving forces in processes involving membrane proteins comes from the lack of quantitative thermodynamic measurements concerning membrane protein self-assembly equilibria within the lipid bilayer environment. These thermodynamic measurements would describe the free energy of self-assembly (∆G°) and the breakdown of this term into enthalpic (∆H°) and entropic components (∆S°). The studies within this thesis bridge the gaps in our knowledge of membrane protein self-assembly by quantifying the contributions of non-polar side-chain packing in the dimerization reaction of the large poly-topic membrane protein CLC-ec1 within lipid bilayers. An emphasis on describing non-polar side-chain packing was chosen due to membrane proteins commonly exhibiting the packing of transmembrane helices and surfaces lined with non-polar residues within lipid bilayers. Furthermore, non-polar side-chain packing is thought to be a significant contributor to membrane protein self-assembly, but its quantification has been limited. An emphasis is placed within the thesis on quantifying non-polar side-chain packing interactions in terms of van der Waals (VDW) interaction energies. Chapter 1 of this thesis describes the pertinent background of the driving forces thought to be involved in membrane protein self-assembly and provides an extensive review of the membrane protein CLC-ec1. The studies within this thesis employed a novel method, called the subunit capture method, to measure CLC-ec1 dimerization within membranes. Chapter 2 describes the subunit capture method and other methods commonly used throughout the thesis. Chapter 3 describes the first study, which characterizes the impact of removing non-polar side-chain contacts on the stoichiometry of the CLC-ec1 homodimer. Computational analysis of the dimerization interface of CLC-ec1 characterized non-polar side-chain packing by measuring the VDW interaction energies of side-chains within a structure of CLC-ec1 determined by x-ray crystallography. Subsequent experiments targeted non-polar side-chains exhibiting favorable VDW interaction energies by substituting 4-5 of the native residues at a time to the smaller residue alanine, depleting the favorable VDW interactions at the dimerization interface. The CLC-ec1 multiple alanine constructs revealed that the stoichiometry of CLC-ec1 is dependent upon the non-polar side-chains at the dimerization interface, as each construct becomes entirely monomeric in lipid bilayers. The studies also found that changes in CLC-ec1 stoichiometry occur in a solvent-dependent manner as three of the four CLC-ec1 multiple alanine constructs remain stable dimers in detergent micelles. Lastly, the study exposes a molecular hot-spot at residue 194, characterizing the substitution to alanine at that position as important for dimer stoichiometry in both detergents and lipids. The contents of Chapter 4 present the findings from a second study that sought answers to two questions. The study begins by posing the first question: Are protein-protein interactions driving the dimerization of CLC-ec1? To answer this question, we performed long all-atom molecular dynamics (MD) simulations to quantify the interactions of CLC-ec1 in a dimeric and monomeric state while embedded in a lipid bilayer. Through the quantification of VDW interaction energies, the measurements revealed that the interactions within each state are similar in magnitude. The findings from the MD simulations present VDW interactions as important to CLC-ec1 dimerization but not as a determinant that excessively stabilizes the CLC-ec1 dimer complex. The results from the analysis of the MD simulations allowed us to form the second question of the study: Will removing side-chain packing interactions at the dimerization interface destabilize the CLC-ec1 homodimer? The second question was thoroughly investigated by measuring the changes in dimerization free energy of CLC-ec1 constructs that contained single substitutions to alanine that generate cavities at the dimerization interface. The various changes in CLC-ec1 dimer stability due to the alanine substitutions were compared to the MD computational analysis to find no correlation between the two datasets. We conclude that while the CLC-ec1 single alanine substitutions destabilize the dimer complex, the removal of non-polar packing interactions from the dimer state of CLC-ec1 does not explain the measured changes in stability. The final chapter in this thesis, Chapter 5, presents a discussion of how the results obtained within this thesis fit into our current understanding of membrane protein self-assembly. Included in the discussion, we reason that CLC-ec1 may not have excessively favorable non-polar packing interactions at the CLC-ec1 dimerization interface in order to retain a flexible interface for function -related activities. Finally, Chapter 5 will conclude by posing a few future directions of study to answer new questions we have encountered while performing the work presented in this thesis.

Underwater adhesion of abalone: The role of van der Waals and capillary forces

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean’s stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

Characterisation of inter-particle forces within agglomerated metallurgical powders

The present paper investigated the effects of the electrostatic and non-electrostatic interactions on the water wettability of a surface. Based on this aim, examinations are performed on the molybdenum disulfide (MoS2) as possible nanostructure surface. The results obtained through calculating the water contact angle on the MoS2 surface indicate which this surface is a weak hydrophobic substrate. The present simulations illustrate that the electrostatic interactions have little impact on the wettability amount of the MoS2 substrate. However, the molybdenum disulfide is composed of two charged parts with significant values. In addition, it is observed that the relation between density, van der Waals and electrostatic interactions is different from each other. It have been observed that the van der Waals interactions have direct relationship with water density while there is not anything between the electrostatic interactions and water density peak. The Obtained results via simulation demonstrate that the effectiveness of electrostatic interactions on the wettability depends on the sigma in the Lennard–Jones equation. In the other words, the role of electrostatic and van der Waals interactions on the wettability are not indissociable from each other and this method is sufficient in nanostructure systems.Graphic abstract

The interaction of silicene with MoS2 surfaces has an important role in determining many properties of these systems. However, the intricate nature of silicene-based systems presents significant challenges for both experimental and computational investigations, often resulting in conflicting reports in the literature. Using molecular dynamics simulations with hybrid potentials, this work investigates the epitaxial growth of silicene on an MoS2 substrate using a vapor-deposition-like method. The findings reveal that silicene can achieve stability on an MoS2 substrate in an AB low-buckled configuration when both van der Waals and covalent interactions are considered. In this configuration, the silicene layer exhibits numerous defects, which can be significantly reduced by increasing the substrate temperature. In contrast, when only van der Waals interactions are accounted for, the system becomes unstable, leading to the collapse of the silicene structure into a three-dimensional disordered arrangement of Si atoms. A similar instability is observed in a heterostructure where a silicene sheet is intercalated between two MoS2 layers. These results, combined with the lattice mismatch observed between silicene and MoS2, suggest that van der Waals interactions alone are insufficient to ensure the mechanical stability of silicene.

The interaction of the ground states of two closed-shell systems (atom or molecule) is usually repulsive except for a weak long-range van der Waals or electrostatic interaction. But the interaction of an excited state with the ground state of the same fragments can form a strong chemical bond. The bound excited state has been called an excimer or exciplex state and the bound to continuum transition defines an excimer emission system [2.1]. In the case of degenerate open-shell fragments (e.g., P-states, etc.) more than one molecular state will correlate with the degenerate asymptote. Some or all of the curves may be essentially repulsive, but there may also be a bound ground state. The excited state of the open-shell fragment interacting with a ground state fragment can also yield strongly bound molecular states which can be defined as excimer states. The analysis of excimer emission systems in this chapter assumes that the lower repulsive state always arises from ground state fragments which may, however, be degenerate. Rare gas atoms interacting in their ground state provides an example of a single repulsive curve arising from a non-degenerate asymptote. The interaction of two hydrogen atoms in their ground 2 S states will, on the other hand, yield two states a \(^1\Sigma _g^ + \) and a \(^3\Sigma _u^ + \) which are, respectively, strongly bound and repulsive. By generalizing the definition of an excimer emission system to include degenerate asymptotic ground states, we would include almost all possible chemical systems. In order to keep the review within limits, we have restricted consideration to the interactions of either rare gas or Group II atoms with other atomic species for which excimer emission systems have been found and were originally suggested as laser candidates [2.2]. Only two triatomic classes of excimers have been included which are again based on rare gas or Group II molecule fragments.

An explicit numerical-analytical method is demonstrated for accurate solving the Schrödinger equation in those cases when this equation reducible to a system of n coupled ordinary differential equations with singular points. Fundamental system of solutions is constructed as algebraic combinations of power series, power functions and logarithmic function in the neighbourhood of the regular singular point and as asymptotic expansions of solutions in the neighbourhood of the irregular singular point. The method is based on the calculation of recurrent sequences of constant matrices of coefficients in power series and in inverse power series in asymptotic expansions using derived recurrent relations, that makes possible to calculate solutions at any given point using only algebraic computations and elementary functions. In turn it makes possible to solve accurately the eigenvalue problem and scattering problem and to derive analytical expressions for the wavefunctions. The method is applied to calculations of energies and wavefunctions of the discrete spectrum and wave functions of the continuous spectrum of the hydrogen-like atoms and of acceptors in semiconductors.

As miniaturization progresses, pattern collapse during the drying step of wet cleaning processes has become a critical issue in the semiconductor industry. In this study, we used reactive molecular dynamics simulations to analyze pattern collapse, with a focus on bondings and reactions. To simulate pattern deformation during the drying process of wet cleaning, we created a FinFET model as a HAR structure. The surface of this model was terminated with hydrogen atoms. The widths between the patterns were changed in order to create a Laplace pressure difference when water molecules were placed on the surface. The model was simulated by placing water molecules up to half the height of the pattern. As a result, the pattern was deformed. Furthermore, by removing water molecules and changing the Laplace pressure balance, it was found that the pattern contacted each other at the tip. The pattern remained in contact when water molecules were removed from the model. In the contact area, the covalent bonds, such as Si-Si and Si-O-Si, were not formed, but instead, hydrogen-to-hydrogen van der Waals bonds were formed between patterns. We calculated the total van der Waals forces between hydrogen atoms at the contact surfaces using the Hamaker equation and calculated the elastic force of the patterns using the beam deflection formula. Our calculations showed that the total van der Waals forces between hydrogen atoms at the contact surfaces were larger than the elastic force of the patterns, indicating that van der Waals forces could be a factor in maintaining the contact of the patterns.

The van der Waals interaction energy between two closed-shell systems can be approximated as the sum of the Hartree-Fock (HF) and dispersion interaction energies. The dispersion energy is given as a power series in ${R}^{\mathrm{\ensuremath{-}}n}$ when the interaction potential is expanded in the multipole operators of the asymptotic systems. This series is convergent only if the overlap of the systems is explicitly considered. This paper will describe the calculation of the induced-dipole--induced-dipole dispersion interaction including the anisotropic damping due to charge overlap. The He-${\mathrm{H}}_{2}$, Ne-${\mathrm{H}}_{2}$, and Ar-${\mathrm{H}}_{2}$ systems were considered and the van der Waals potentials were constructed with use of available HF interaction potentials.

The van der Waals interaction between carbon nanotubes leads to forming the agglomerates. If the nanotubes are the same diameters and legths they are associated into regular structure like a crystal. However, the van der Waals forces also result to some deformation of the nanotubes. This work presents the analysis of the influence of the nanotubes’ diameters and the symmetry of their arrangement on the nanotube deformation and intertube distances.