London-van Der Waals Forces Research Articles

Interaction of Nanoparticles in Electrolyte Solutions.

The interaction between nanoparticles includes several components; however, the most frequently used are electrostatic, caused by overlapping double electrical layers, and London-van der Waals interactions, caused by quantum and thermodynamic fluctuations of electromagnetic fields. Only these two kinds of interaction are considered below. The electrostatic interaction is calculated based on the linearized Poisson-Boltzmann equation for particles with constant electrical potential of the surfaces (constant ζ potentials). An exact solution of the problem is obtained for both identical particles and particles of different sizes. For the London-van der Waals interaction, the screening of static fluctuations and the retardation of electromagnetic fields for the dispersive part of the interaction are taken into account. The total interaction energy for two particles was calculated for a range of possible nanoparticle sizes from 1 to 103 nm and electrolyte concentration from 10-2 to 10-6 mol/L. The predominance of the London-van der Waals force over the shielded electrostatic repulsion force was found at high electrolyte concentrations in the range from 10-2 to 10-3 mol/L at large interparticle distances.

Measurement of Van der Waals force using oscillating optical tweezers

We employ oscillating optical tweezers as a probe to measure the surface forces between polystyrene and silica. Thus, we modulate a trapped polystyrene particle with an external sinusoidal force in close proximity (∼80 nm) of a silica surface. The particle motion is influenced by several factors which include an increased drag force according to Faxen's correction, a spurious force that comes into play due to the diffusion coefficient of the medium becoming position dependent, and finally, the London-Van der Waals (LVdW) force which becomes substantial when the particle approaches the surface. By accounting for the other forces from the analytically known results, we are able to directly quantify the LVdW force from the experimentally measured amplitude of the oscillating particle. Thereby, we determine the Hamaker constant H for the LVdW force between polystyrene and silica, and obtain a good agreement with the value reported in the literature. Our method is general in nature and can be extended toward probing other surface effects or other interaction forces using oscillating optical tweezers.

Van der Waals Density Functional Theory vdW-DFq for Semihard Materials

There are a large number of materials with mild stiffness, which are not as soft as tissues and not as strong as metals. These semihard materials include energetic materials, molecular crystals, layered materials, and van der Waals crystals. The integrity and mechanical stability are mainly determined by the interactions between instantaneously induced dipoles, the so called London dispersion force or van der Waals force. It is challenging to accurately model the structural and mechanical properties of these semihard materials in the frame of density functional theory where the non-local correlation functionals are not well known. Here, we propose a van der Waals density functional named vdW-DFq to accurately model the density and geometry of semihard materials. Using β -cyclotetramethylene tetranitramine as a prototype, we adjust the enhancement factor of the exchange energy functional with generalized gradient approximations. We find this method to be simple and robust over a wide tuning range when calibrating the functional on-demand with experimental data. With a calibrated value q = 1.05 , the proposed vdW-DFq method shows good performance in predicting the geometries of 11 common energetic material molecular crystals and three typical layered van der Waals crystals. This success could be attributed to the similar electronic charge density gradients, suggesting a wide use in modeling semihard materials. This method could be useful in developing non-empirical density functional theories for semihard and soft materials.

London-van der Waals Force Field of a Chemically Patterned Surface To Enable Selective Adhesion.

The London-van der Waals (L-vdW) force between a particle and a surface strongly depends on the topography and the chemical properties of the interacting surfaces. Although a great deal of work has been done to understand the effect of topographical heterogeneity on the L-vdW adhesion, the role of chemical heterogeneity has been discussed only rarely. This study makes an attempt to quantify the magnitude and range of the L-vdW force acting on a spherical particle in the vicinity of a chemically patterned surface. Specifically, an ideal system of a smooth spherical particle approaching a surface composed of parallel stripes of chemically distinct materials with different Hamaker constants is considered. The L-vdW forces for such systems are determined by solving the London dispersion potential for the entire volumes of the adhering bodies from first principles, using Hamaker's microscopic approach. The computational results elucidate that a chemical interface can apply a tangential L-vdW force, in addition to the normal L-vdW force, on nearby particles. This can cause lateral motion of particles neighboring a chemically inhomogeneous surface. The magnitude of the tangential L-vdW force is found to be maximum when the particle is centered at the interface and shows a gradual drop as it moves away from this location. The magnitude and range of the tangential L-vdW force can be large for large colloidal particles in close contact with a chemically patterned surface whose materials have distinct Hamaker constants. This study suggests that the tangential L-vdW force field generated by a chemical interface can be utilized as a tool to manipulate the path of an approaching particle to facilitate selective adhesion.

Molecular features of nonionic detergents involved in the binding kinetics and solubilization efficiency, as studied in model (Langmuir films) and biological (Erythrocytes) membranes.

The effect of the nonionic detergents Brij-98 and Brij-58 over human erythrocytes was studied through quantitative hemolysis and in Langmuir films. Hemolytic tests revealed that Brijs are stronger membrane solubilizers than Triton X-100 (TX-100), with effective detergent/lipid ratios of 0.18 and 0.37 for Brij-98 and Brij-58, respectively. Experiments with Langmuir films provided significant information on the kinetics and thermodynamics of detergent-membrane interaction. The adsorption (ka) and desorption (kd) rate constants of Brijs were lower than those of TX-100. In the case of ka, that is probably due to their larger hydrophilic head (with twice (20) the oxyethylene units of TX-100). As for the thermodynamic binding constant, the linear and longer hydrophobic acyl chains of Brijs favor their stabilization in-between the lipids, through London van der Waals forces. Consequently, Kb,m values of Brij-98 (12,500 M-1) and Brij-58 (19,300 M-1) resulted higher than TX-100 (7500 M-1), in agreement with results from the hemolytic tests. Furthermore, Brij-58 binds with higher affinity than Brij-98 to bilayers and monolayers, despite its shorter (palmitic) hydrocarbon chain, showing that unsaturation restrains the detergent insertion into these environments. Our results provide significant information about the mechanism of interaction between Brijs and membranes, supporting their distinct solubilization effect.

DLVO THEORY OF COLLOID STABILITY

The Derjaguin–Landau–Verwey–Overbeek (DLVO) theory [1,2] has made it possible to discuss the stability of lyophobic colloids quantitatively. This theory is based on the interaction due to overlapping of electrical double layers and London–van der Waals forces between colloid particles.

Interactions between Halloysite Nanotubes and Poly(styrene sulfonate) in Solution

The interaction between halloysite nanotubes (HNT) and poly(styrene sulfonate) (PSS) in aqueous solution was investigated by dynamic light scattering. Dynamic behavior of HNT/PSS was observed with different salt, HNT, and PSS concentrations. The HNT colloids were stabilized by PSS over a wide range of HNT concentrations, and HNT suspension in dilute solution formed stable HNT/PSS particles. On the other hand, HNT particles aggregated as sediments at higher concentrations due to strong attraction among HNT rods, and HNT aggregates were stabilized by additional PSS. The interactions between HNT and PSS are described by the van der Waals–London force (VDWL). The stabilization process of HNT/PSS particles in salt solution was proposed by comparing the hydrodynamic radii and apparent intensities of samples. The results demonstrate that electrostatic, steric, and depletion stabilization processes are responsible for the stable dispersion of HNT even at high concentration.

Dispersion Forces and the Molecular Origin of Internal Friction in Protein.

Internal friction in macromolecules is one of the curious phenomena that control conformational changes and reaction rates. It is held here that dispersion interactions and London-van der Waals forces between nonbonded atoms are major contributors to internal friction. To demonstrate this, the flipping motion of aromatic rings of F10 and Y97 amino acid residues of cytochrome c has been studied in glycerol/water mixtures by cross relaxation-suppressed exchange nuclear magnetic resonance spectroscopy. The ring-flip rate is highly overdamped by glycerol, but this is not due to the effect of protein-solvent interactions on the Brownian dynamics of the protein, because glycerol cannot penetrate into the protein to slow the internal collective motions. Sound velocity in the protein under matching solvent conditions shows that glycerol exerts its effect by rather smothering the protein interior to produce reduced molecular compressibility and root-mean-square volume fluctuation (δVRMS), implying an increased number of dispersion interactions of nonbonded atoms. Hence, δVRMS can be used as a proxy for internal friction. By using the ansatz that internal friction is related to nonbonded interactions by the equation f(n) = f0 + f1n + f2n(2) + ..., where the variable n is the extent of nonbonded interactions with fi coefficients, the barrier to aromatic ring rotation is found to be flat. Also interesting is the appearance of a turnover region in the δVRMS dependence of the ring-flip rate, suggesting anomalous internal diffusion. We conclude that cohesive forces among nonbonded atoms are major contributors to the molecular origin of internal friction.

Long-range wetting transparency on top of layered metal-dielectric substrates.

It has been recently shown that scores of physical and chemical phenomena (including spontaneous emission, scattering and Förster energy transfer) can be controlled by nonlocal dielectric environments provided by metamaterials with hyperbolic dispersion and simpler metal/dielectric structures. At this time, we have researched van der Waals interactions and experimentally studied wetting of several metallic, dielectric and composite multilayered substrates. We have found that the wetting angle of water on top of MgF2 is highly sensitive to the thickness of the MgF2 layer and the nature of the underlying substrate that could be positioned as far as ~100 nm beneath the water/MgF2 interface. We refer to this phenomenon as long range wetting transparency. The latter effect cannot be described in terms of the most basic model of dispersion van der Waals-London forces based on pair-wise summation of dipole-dipole interactions across an interface or a gap separating the two media. We infer that the experimentally observed gradual change of the wetting angle with increase of the thickness of the MgF2 layer can possibly be explained by the distance dependence of the Hamaker function (describing the strength of interaction), which originates from retardation of electromagnetic waves at the distances comparable to a wavelength.

Quantum Gravitational Force Between Polarizable Objects.

Since general relativity is a consistent low energy effective field theory, it is possible to compute quantum corrections to classical forces. Here we compute a quantum correction to the gravitational potential between a pair of polarizable objects. We study two distant bodies and compute a quantum force from their induced quadrupole moments due to two-graviton exchange. The effect is in close analogy to the Casimir-Polder and London-van der Waals forces between a pair of atoms from their induced dipole moments due to two photon exchange. The new effect is computed from the shift in vacuum energy of metric fluctuations due to the polarizability of the objects. We compute the potential energy at arbitrary distances compared to the wavelengths in the system, including the far and near regimes. In the far distance, or retarded, regime, the potential energy takes on a particularly simple form: V(r)=-3987ℏcG^{2}α_{1S}α_{2S}/(4πr^{11}), where α_{1S}, α_{2S} are the static gravitational quadrupole polarizabilities of each object. We provide estimates of this effect.

Surface energy and wettability of van der Waals structures.

The wetting behaviour of surfaces is believed to be affected by van der Waals (vdW) forces; however, there is no clear demonstration of this. With the isolation of two-dimensional vdW layered materials it is possible to test this hypothesis. In this paper, we report the wetting behaviour of vdW heterostructures which include chemical vapor deposition (CVD) grown graphene, molybdenum disulfide (MoS2) and tungsten disulfide (WS2) on few layers of hexagon boron nitride (h-BN) and SiO2/Si. Our study clearly shows that while this class of two-dimensional materials are not completely wetting transparent, there seems to be a significant amount of influence on their wetting properties by the underlying substrate due to dominant vdW forces. Contact angle measurements indicate that graphene and graphene-like layered transitional metal dichalcogenides invariably have intrinsically dispersive surfaces with a dominating London-vdW force-mediated wettability.

Vacuum Friction on a Rotating Pair of Atoms.

Zero-point quantum fluctuations of the electromagnetic vacuum create the widely known London-van der Waals attractive force between two atoms. Recently, there has been a revived interest in the interaction of rotating matter with the quantum vacuum. Here, we consider a rotating pair of atoms maintained by London-van der Waals forces and calculate the frictional torque they experience due to zero-point radiation. Using a semiclassical framework derived from the fluctuation dissipation theorem, we take into account the full electrostatic coupling between induced dipoles. Considering the case of zero temperature only, we find a braking torque proportional to the angular velocity and to the third power of the fine structure constant. Although very small compared to London-van der Waals attraction, the torque is strong enough to induce the formation of dimers in binary collisions. This new friction phenomenon at the atomic level should induce a paradigm change in the explanation of irreversibility.

Thermocapillary instability in an evaporating two-dimensional thin layer film

A novel two-dimensional model for the thermocapillary instability of a thin liquid film was developed and validated in the paper. The model incorporates a novel solution for the unperturbed velocity components and the thin film thickness (based on the boundary layer approach and balance equation) subject to evaporation under the boundary conditions of either mechanical interaction between the liquid and vapor phases or stationary vapor above the interphase boundary. A novel model for thermocapillary instability in a thin film was developed in frames of the linear perturbation method, i.e. modified Orr–Sommerfeld equation, taking into account the surface and London–van der Waals forces. The critical Reynolds number was computed by considering the two-dimensional disturbances, which according to the Squire’s theorem are more dangerous than the three-dimensional disturbances. For constant surface tension at the interphase interface, the unperturbed velocity profile is parabolic, and maximum increases, while the critical Reynolds number decreases with the decreasing capillary number. If the surface tension at the interphase interface depends on the temperature, the maximum of the undisturbed velocity profile increases with the decreasing capillary number and increasing modified Marangoni number, which entails more rapid decrease in the critical Reynolds number. It was also shown that the flow is destabilized by the increase in the temperature difference between the wall and the vapor, by the decrease in the absolute pressure and by the increase in the thermal conductivity. To confirm existence of different flow regimes in the nanofluid film, numerical simulations of capillary flow was performed, which exhibit qualitative consistence with the stability theory.

Distributed force probe bending model of critical dimension atomic force microscopy bias

Critical dimension atomic force microscopy (CD-AFM) is a widely used reference metrology technique. To characterize modern semiconductor devices, small and flexible probes, often 15 to 20 nm in diameter, are used. Recent studies have reported uncontrolled and significant probe-to-probe bias variation during linewidth and sidewall angle measurements. To understand the source of these variations, tip-sample interactions between high aspect ratio features and small flexible probes, and their influence on measurement bias, should be carefully studied. Using theoretical and experimental procedures, one-dimensional (1-D) and two-dimensional (2-D) models of cylindrical probe bending relevant to carbon nanotube (CNT) AFM probes were developed and tested. An earlier 1-D bending model was refined, and a new 2-D distributed force (DF) model was developed. Contributions from several factors were considered, including: probe misalignment, CNT tip apex diameter variation, probe bending before snapping, and distributed van der Waals-London force. A method for extracting Hamaker probe-surface interaction energy from experimental probe-bending data was developed. Comparison of the new 2-D model with 1-D single point force (SPF) model revealed a difference of about 28% in probe bending. A simple linear relation between biases predicted by the 1-D SPF and 2-D DF models was found. The results suggest that probe bending can be on the order of several nanometers and can partially explain the observed CD-AFM probe-to-probe variation. New 2-D and three-dimensional CD-AFM data analysis software is needed to take full advantage of the new bias correction modeling capabilities.

Determination of Hamaker constants of polymeric nanoparticles in organic solvents by asymmetrical flow field-flow fractionation

Interaction forces between all objects are either of repulsive or attractive nature. Concerning attractive interactions, the determination of dispersion forces are of special interest since they appear in all colloidal systems and have a crucial influence on the properties and processes in these systems. One possibility to link theory and experiment is the description of the London–Van der Waals forces in terms of the Hamaker constant, which leads to the challenging problem of calculating the van der Waals interaction energies between colloidal particles. Hence, the determination of a Hamaker constant for a given material is needed when interfacial phenomena such as adhesion are discussed in terms of the total potential energy between particles and substrates. In this work, the asymmetrical flow field-flow fractionation (AF-FFF) in combination with a Newton algorithm based iteration process was used for the determination of Hamaker constants of different nanoparticles in toluene.

A generalization of the dipolar force

The static dipolar force is generalized to time-dependent classical distributions of dipoles and electromagnetic fields. This force may exhibit a remarkable resonance character for induced dipoles, related to the pole structure of the polarizabilities. The resonance phenomenon is illustrated for two macroscopic polarizable bodies, with mutually induced polarizations, using the well-known Lorentz-Drude model for the dielectric response with optical dispersion and a characteristic (resonance) frequency. Specifically, the calculations are performed for distances much longer than the dimension of the bodies (“point-like” bodies), but shorter than the characteristic wavelength (sub-wavelength, stationary, near-field regime). The polarizations are induced via a localized external field acting upon only one body. The force is practically vanishing for distinct substances and acquires a non-vanishing value for identical substances. It falls off as the 7-th power of the distance, being reminiscent of the van der Waals-London force. The conditions of validity of this resonance phenomenon are emphasized. Particular cases corresponding to independent external fields or two isolated, interacting bodies (closed system) are also analyzed, with similar conclusions regarding the resonance character of the force.

Role of long- and short-range hydrophobic, hydrophilic and charged residues contact network in protein’s structural organization

BackgroundThe three-dimensional structure of a protein can be described as a graph where nodes represent residues and the strength of non-covalent interactions between them are edges. These protein contact networks can be separated into long and short-range interactions networks depending on the positions of amino acids in primary structure. Long-range interactions play a distinct role in determining the tertiary structure of a protein while short-range interactions could largely contribute to the secondary structure formations. In addition, physico chemical properties and the linear arrangement of amino acids of the primary structure of a protein determines its three dimensional structure. Here, we present an extensive analysis of protein contact subnetworks based on the London van der Waals interactions of amino acids at different length scales. We further subdivided those networks in hydrophobic, hydrophilic and charged residues networks and have tried to correlate their influence in the overall topology and organization of a protein.ResultsThe largest connected component (LCC) of long (LRN)-, short (SRN)- and all-range (ARN) networks within proteins exhibit a transition behaviour when plotted against different interaction strengths of edges among amino acid nodes. While short-range networks having chain like structures exhibit highly cooperative transition; long- and all-range networks, which are more similar to each other, have non-chain like structures and show less cooperativity. Further, the hydrophobic residues subnetworks in long- and all-range networks have similar transition behaviours with all residues all-range networks, but the hydrophilic and charged residues networks don’t. While the nature of transitions of LCC’s sizes is same in SRNs for thermophiles and mesophiles, there exists a clear difference in LRNs. The presence of larger size of interconnected long-range interactions in thermophiles than mesophiles, even at higher interaction strength between amino acids, give extra stability to the tertiary structure of the thermophiles. All the subnetworks at different length scales (ARNs, LRNs and SRNs) show assortativity mixing property of their participating amino acids. While there exists a significant higher percentage of hydrophobic subclusters over others in ARNs and LRNs; we do not find the assortative mixing behaviour of any the subclusters in SRNs. The clustering coefficient of hydrophobic subclusters in long-range network is the highest among types of subnetworks. There exist highly cliquish hydrophobic nodes followed by charged nodes in LRNs and ARNs; on the other hand, we observe the highest dominance of charged residues cliques in short-range networks. Studies on the perimeter of the cliques also show higher occurrences of hydrophobic and charged residues’ cliques.ConclusionsThe simple framework of protein contact networks and their subnetworks based on London van der Waals force is able to capture several known properties of protein structure as well as can unravel several new features. The thermophiles do not only have the higher number of long-range interactions; they also have larger cluster of connected residues at higher interaction strengths among amino acids, than their mesophilic counterparts. It can reestablish the significant role of long-range hydrophobic clusters in protein folding and stabilization; at the same time, it shed light on the higher communication ability of hydrophobic subnetworks over the others. The results give an indication of the controlling role of hydrophobic subclusters in determining protein’s folding rate. The occurrences of higher perimeters of hydrophobic and charged cliques imply the role of charged residues as well as hydrophobic residues in stabilizing the distant part of primary structure of a protein through London van der Waals interaction.

Interfacial thin films rupture and self-similarity

Two superposed thin layers of fluids are prone to interfacial instabilities due to London-van der Waals forces. Evolution equations for the film thicknesses are derived using lubrication theory. Using the intrinsic scales, for a single layer, results in a system with parametric dependence of four ratios of the two layers: surface tension, Hamaker constant, viscosity, and film thickness. In contrast to the single layer case, the bilayer system has two unstable eigenmodes: squeezing and bending. For some particular parameter regimes, the system exhibits the avoided crossing behavior, where the two eigenmodes are interchanged. Based on numerical analysis, the system evolves into four different rupture states: basal layer rupture, upper layer rupture, double layer rupture, and mixed layer rupture. The ratio of Hamaker constants and the relative film thickness of the two layers control the system dynamics. Remarkably, the line of avoided crossing demarks the transition region of mode mixing and energy transfer, affecting the scaling of the dynamical regime map consequentially. Asymptotic and numerical analyses are used to examine the self-similar ruptures and to extract the power law scalings for both the basal layer rupture and the upper layer rupture. The scaling laws for the basal layer rupture are the same as those of the single layer on top of a substrate. The scaling laws for the upper layer rupture are different: the lateral length scale decreases according to (tr-t)1/3 and the film thickness decreases according to (tr-t)1/6.

ELECTROMAGNETIC EIGENMODES IN MATTER. VAN DER WAALS-LONDON AND CASIMIR FORCES

We derive van der Waals-London and Casimir forces by calculating the eigenmodes of the electromagnetic fleld interacting with two semi-inflnite bodies (two halves of space) with parallel separated by distance d. We adopt simple models for metals and dielectrics, well-known in the elementary theory of dispersion. In the non-retarded (Coulomb) limit we get a d i3 -force (van der Waals-London force), arising from the zero-point energy (vacuum ∞uctuations) of the surface plasmon modes. When retardation is included we obtain a d i4 -(Casimir) force, arising from the zero- point energy of the surface plasmon-polariton modes (evanescent modes) for metals, and from propagating (polaritonic) modes for identical dielectrics. The same Casimir force is also obtained for \flxed surfaces boundary conditions, irrespective of the pair of bodies. The approach is based on the equation of motion of the polarization and the electromagnetic potentials, which lead to coupled integral equations. These equations are solved, and their relevant eigenfrequencies branches are identifled.

Amendment to published paper: "Turbulent coagulation model considering effects of London-van der Waals force and wettability"

This paper is to correct a mistake in the authors' previous paper (Nakaoka et al., Progress in Computational Fluid Dynamics, 2008, 8(5), 270-275), which originated in the solution procedure of the population-balance (PB) equation.