Non-Perturbative Theory for Dispersion Self-Energy of Atoms

We go beyond the approximate series-expansions used in the dispersion theory of finite size atoms. We demonstrate that a correct, and non-perturbative, theory dramatically alters the dispersion selfenergies of atoms. The non-perturbed theory gives as much as 100% corrections compared to the traditional series expanded theory for the smaller noble gas atoms.Comment: 3 pages, no figures, 1 tabl

Effective Polarisability Models

Theories for the effective polarisability of a small particle in a medium are presented using different levels of approximation: we consider the virtual cavity, real cavity and the hard-sphere models as well as a continuous interpolation of the latter two. We present the respective hard-sphere and cavity radii as obtained from density-functional simulations as well as the resulting effective polarisabilities at discrete Matsubara frequencies. This enables us to account for macroscopic media in van der Waals interactions between molecules in water and their Casimir-Polder interaction with an interface

Distance-dependent sign-reversal in the Casimir-Lifshitz torque

The Casimir-Lifshitz torque between two biaxially polarizable anisotropic planar slabs is shown to exhibit a non-trivial sign-reversal in its rotational sense. The critical distance $a_c$ between the slabs that marks this reversal is characterized by the frequency $\omega_c\!\sim \!c/2a_c$ at which the in-planar polarizabilities along the two principal axes are equal. The two materials seek to align their principal axes of polarizabilities in one direction below $a_c$, while above $a_c$ their axes try to align rotated perpendicular relative to their previous minimum energy orientation. The sign-reversal disappears in the nonretarded limit. Our perturbative result, derived for the case when the differences in the relative polarizabilities are small, matches excellently with the exact theory for uniaxial materials. We illustrate our results for black phosphorus and phosphorene.Comment: 6 pages, 5 figures, accompanied by a supplementary materia

A study of finite-size, non-perturbative and anisotropic effects on the Lifshitz-van der Waals forces and torque with material dielectric responses from first-principles calculations

The van der Waals and the Casimir-Lifshitz forces are forces of attraction that exist between neutral polarizable bodies due to quantum fluctuations. They can be repulsive depending on the material properties and the geometry of the system. Since they are pervasive in nature, they encompass a great deal of relevance in the study of interaction between bodies in several different scenarios and background geometrical settings.   This doctoral thesis first addresses the important aspects of finite-size and the non-perturbative effects of the van der Waals interactions between two atoms or molecules. Going beyond the usual assumption of atoms and molecules as point particles and adopting a description of finite size, the divergence inherent in such interaction energies in the limit of zero separation distance between the two interacting atoms or molecules is removed. The attainment of finite interaction energy at such close separation distance facilitates the estimation of van der Waals force contribution to the binding energy of the molecules, and towards surfaces. This is particularly important for noble atoms. The interaction between a pair of helium (He) atoms and krypton (Kr) atoms, and between a pair of methane (CH$_4$) molecules considering its environmental relevance, is investigated in detail. The application of finite size further leads to finite self energies of the atoms. The full expression of the interaction energy, as is discussed in detail in this thesis, typically contains a logarithmic factor of the form $\ln(1 \pm x)$. Formerly, in evaluating the interaction energies, this factor is customarily series-expanded and truncated in the leading order with certain assumptions. This thesis explores the effect of using the full expression, which is referred herein as the non-perturbative (or, the non-expanded) theory, analytically wherever possible as well as numerically. The combined application of the finite-size theory and the non-perturbative theory results in as much as 100\,\% correction in the self energy of atoms in vacuum. This may give rise to significant physical consequences, for example, in the permeabilities of atoms across dielectric membranes.   The thesis next addresses the aspect of anisotropy in the Casimir-Polder interaction between a completely polarizable molecule and a dielectric slab polarizable in the normal direction. The formalism is applied to the study of preferential adsorption in the specific case of carbon dioxide (CO$_2$) and methane (CH$_4$) molecules interacting with amorphous silica slabs and thin gold films. Owing to its greater polarizability, the linearly polarizable CO$_2$ molecule is found to attract more towards the surfaces than the isotropically polarizable CH$_4$ molecule. In addition, the stable orientation of the CO$_2$ molecule with respect to the surface is determined to be the one in which the long, linear axis of the molecule is perpendicular to the surface. Further, the feature of Casimir torque which is a consequence of anisotropy in the interacting dielectric slabs is explored in the case of biaxial materials, in particular the bulk black phosphorus and its novel 2D counterpart phosphorene. The torque between a pair of phosphorus slabs, one face rotated with respect to the other, is observed to change sign at a particular separation distance which is determined by the crossing frequency of its planar dielectric components. This distance-dependent reversal of the sign of torque has never been observed before. The observation is verified with several other biaxial materials. This finding will help assist in the experimental detection of the Casimir torque, and can potentially be exploited in the future for designing nanodevices.   Another remarkable effect that is uncovered is the submersion of ice microcrystals under water governed by the balance of repulsive Lifshitz force from the vapor-water interface and the buoyant force of water. The repulsive effect is found to be enhanced by the presence of salt ions in the system. An exclusion zone ranging from 2 nm to 1 ${\mu}$m devoid of small ice particles is formed below the water surface. As the ice sphere grows in size, the buoyant force overcomes the Lifshitz force, and the ice sphere starts to float with a fraction of its volume above the water surface in accordance with the classical Archimedes principle. The combined impact of Lifshitz forces and double-layer interactions is further investigated in ice-water-CO$_2$ and vapor-water-CO$_2$ systems  employing different models of effective polarizability for ions, {\it viz.} the hardsphere model and Onsager's model. The CO$_2$ bubble is found to be repelled by the vapor-water interface and attracted towards the ice-water interface. The equilibrium thin film of water formed between vapor and ice surfaces varies in thickness depending on the model of effective polarizability and the type of salt present in the system. Further studies of the interaction energy in geometries comprising two molecules near an interface and molecule in a three-layer geometry are conducted which may be relevant for potential energy storage applications. The density functional theory (DFT) is employed to generate the frequency-dependent dielectric functions required for Lifshitz energy and force calculations.   Summing up, in the numerous contexts outlined above, the importance of the van der Waals and Lifshitz forces has been demonstrated. The studies in this thesis enable significant predictions related to these forces which may be verifiable by experiments.

A study of finite-size and non-perturbative effects on the van der Waals and the Casimir-Polder forces

This licentiate thesis addresses two important aspects of the van der Waals and the Casimir-Polder ground-state and excited-state (resonance) interactions between two atoms or molecules. The first is the finite-size effect and the second is the non-perturbative effect. Going beyond the usual assumption of atoms and molecules as point particles and adopting a description of finite size, the divergence inherent in such interaction energies in the limit of zero separation distance between the two interacting atoms or molecules is removed. The attainment of finite interaction energy at such close separation distance facilitates the estimation of van der Waals force contribution to the binding energy of the molecules, and towards surfaces. This is particularly important for noble atoms. We investigate in detail for a pair of helium (He) atoms and krypton (Kr) atoms, and for a pair of methane (CH4) molecules considering its environmental importance. The application of finite size further leads to finite self energies of the atoms. The expression of the interaction energy, as is discussed in detail in this thesis, typically contains a logarithmic factor of the form ln(1-x). Formerly, in evaluating the interaction energies, this factor is customarily series-expanded and truncated in the leading order with certain assumptions. This thesis explores the effect of using the full expression, which we refer to as the non-perturbative (or, the non-expanded) theory, analytically wherever possible as well as numerically. The combined application of the finite-size theory and the non-perturbative theory results in as much as 100% correction in the self energy of atoms in vacuum. This may give rise to significant physical consequences, for example, in the permeabilities of atoms across dielectric membranes. The non-perturbative theory, in addition, exhibits interesting behaviour in the retarded resonance interaction.QC 20160509</p

A study of finite-size, non-perturbative and anisotropic effects on the Lifshitz-van der Waals forces and torque with material dielectric responses from first-principles calculations

The van der Waals and the Casimir-Lifshitz forces are forces of attraction that exist between neutral polarizable bodies due to quantum fluctuations. They can be repulsive depending on the material properties and the geometry of the system. Since they are pervasive in nature, they encompass a great deal of relevance in the study of interaction between bodies in several different scenarios and background geometrical settings.   This doctoral thesis first addresses the important aspects of finite-size and the non-perturbative effects of the van der Waals interactions between two atoms or molecules. Going beyond the usual assumption of atoms and molecules as point particles and adopting a description of finite size, the divergence inherent in such interaction energies in the limit of zero separation distance between the two interacting atoms or molecules is removed. The attainment of finite interaction energy at such close separation distance facilitates the estimation of van der Waals force contribution to the binding energy of the molecules, and towards surfaces. This is particularly important for noble atoms. The interaction between a pair of helium (He) atoms and krypton (Kr) atoms, and between a pair of methane (CH$_4$) molecules considering its environmental relevance, is investigated in detail. The application of finite size further leads to finite self energies of the atoms. The full expression of the interaction energy, as is discussed in detail in this thesis, typically contains a logarithmic factor of the form $\ln(1 \pm x)$. Formerly, in evaluating the interaction energies, this factor is customarily series-expanded and truncated in the leading order with certain assumptions. This thesis explores the effect of using the full expression, which is referred herein as the non-perturbative (or, the non-expanded) theory, analytically wherever possible as well as numerically. The combined application of the finite-size theory and the non-perturbative theory results in as much as 100\,\% correction in the self energy of atoms in vacuum. This may give rise to significant physical consequences, for example, in the permeabilities of atoms across dielectric membranes.   The thesis next addresses the aspect of anisotropy in the Casimir-Polder interaction between a completely polarizable molecule and a dielectric slab polarizable in the normal direction. The formalism is applied to the study of preferential adsorption in the specific case of carbon dioxide (CO$_2$) and methane (CH$_4$) molecules interacting with amorphous silica slabs and thin gold films. Owing to its greater polarizability, the linearly polarizable CO$_2$ molecule is found to attract more towards the surfaces than the isotropically polarizable CH$_4$ molecule. In addition, the stable orientation of the CO$_2$ molecule with respect to the surface is determined to be the one in which the long, linear axis of the molecule is perpendicular to the surface. Further, the feature of Casimir torque which is a consequence of anisotropy in the interacting dielectric slabs is explored in the case of biaxial materials, in particular the bulk black phosphorus and its novel 2D counterpart phosphorene. The torque between a pair of phosphorus slabs, one face rotated with respect to the other, is observed to change sign at a particular separation distance which is determined by the crossing frequency of its planar dielectric components. This distance-dependent reversal of the sign of torque has never been observed before. The observation is verified with several other biaxial materials. This finding will help assist in the experimental detection of the Casimir torque, and can potentially be exploited in the future for designing nanodevices.   Another remarkable effect that is uncovered is the submersion of ice microcrystals under water governed by the balance of repulsive Lifshitz force from the vapor-water interface and the buoyant force of water. The repulsive effect is found to be enhanced by the presence of salt ions in the system. An exclusion zone ranging from 2 nm to 1 ${\mu}$m devoid of small ice particles is formed below the water surface. As the ice sphere grows in size, the buoyant force overcomes the Lifshitz force, and the ice sphere starts to float with a fraction of its volume above the water surface in accordance with the classical Archimedes principle. The combined impact of Lifshitz forces and double-layer interactions is further investigated in ice-water-CO$_2$ and vapor-water-CO$_2$ systems  employing different models of effective polarizability for ions, {\it viz.} the hardsphere model and Onsager's model. The CO$_2$ bubble is found to be repelled by the vapor-water interface and attracted towards the ice-water interface. The equilibrium thin film of water formed between vapor and ice surfaces varies in thickness depending on the model of effective polarizability and the type of salt present in the system. Further studies of the interaction energy in geometries comprising two molecules near an interface and molecule in a three-layer geometry are conducted which may be relevant for potential energy storage applications. The density functional theory (DFT) is employed to generate the frequency-dependent dielectric functions required for Lifshitz energy and force calculations.   Summing up, in the numerous contexts outlined above, the importance of the van der Waals and Lifshitz forces has been demonstrated. The studies in this thesis enable significant predictions related to these forces which may be verifiable by experiments.

A study of finite-size, non-perturbative and anisotropic effects on the Lifshitz-van der Waals forces and torque with material dielectric responses from first-principles calculations

The van der Waals and the Casimir-Lifshitz forces are forces of attraction that exist between neutral polarizable bodies due to quantum fluctuations. They can be repulsive depending on the material properties and the geometry of the system. Since they are pervasive in nature, they encompass a great deal of relevance in the study of interaction between bodies in several different scenarios and background geometrical settings.   This doctoral thesis first addresses the important aspects of finite-size and the non-perturbative effects of the van der Waals interactions between two atoms or molecules. Going beyond the usual assumption of atoms and molecules as point particles and adopting a description of finite size, the divergence inherent in such interaction energies in the limit of zero separation distance between the two interacting atoms or molecules is removed. The attainment of finite interaction energy at such close separation distance facilitates the estimation of van der Waals force contribution to the binding energy of the molecules, and towards surfaces. This is particularly important for noble atoms. The interaction between a pair of helium (He) atoms and krypton (Kr) atoms, and between a pair of methane (CH$_4$) molecules considering its environmental relevance, is investigated in detail. The application of finite size further leads to finite self energies of the atoms. The full expression of the interaction energy, as is discussed in detail in this thesis, typically contains a logarithmic factor of the form $\ln(1 \pm x)$. Formerly, in evaluating the interaction energies, this factor is customarily series-expanded and truncated in the leading order with certain assumptions. This thesis explores the effect of using the full expression, which is referred herein as the non-perturbative (or, the non-expanded) theory, analytically wherever possible as well as numerically. The combined application of the finite-size theory and the non-perturbative theory results in as much as 100\,\% correction in the self energy of atoms in vacuum. This may give rise to significant physical consequences, for example, in the permeabilities of atoms across dielectric membranes.   The thesis next addresses the aspect of anisotropy in the Casimir-Polder interaction between a completely polarizable molecule and a dielectric slab polarizable in the normal direction. The formalism is applied to the study of preferential adsorption in the specific case of carbon dioxide (CO$_2$) and methane (CH$_4$) molecules interacting with amorphous silica slabs and thin gold films. Owing to its greater polarizability, the linearly polarizable CO$_2$ molecule is found to attract more towards the surfaces than the isotropically polarizable CH$_4$ molecule. In addition, the stable orientation of the CO$_2$ molecule with respect to the surface is determined to be the one in which the long, linear axis of the molecule is perpendicular to the surface. Further, the feature of Casimir torque which is a consequence of anisotropy in the interacting dielectric slabs is explored in the case of biaxial materials, in particular the bulk black phosphorus and its novel 2D counterpart phosphorene. The torque between a pair of phosphorus slabs, one face rotated with respect to the other, is observed to change sign at a particular separation distance which is determined by the crossing frequency of its planar dielectric components. This distance-dependent reversal of the sign of torque has never been observed before. The observation is verified with several other biaxial materials. This finding will help assist in the experimental detection of the Casimir torque, and can potentially be exploited in the future for designing nanodevices.   Another remarkable effect that is uncovered is the submersion of ice microcrystals under water governed by the balance of repulsive Lifshitz force from the vapor-water interface and the buoyant force of water. The repulsive effect is found to be enhanced by the presence of salt ions in the system. An exclusion zone ranging from 2 nm to 1 ${\mu}$m devoid of small ice particles is formed below the water surface. As the ice sphere grows in size, the buoyant force overcomes the Lifshitz force, and the ice sphere starts to float with a fraction of its volume above the water surface in accordance with the classical Archimedes principle. The combined impact of Lifshitz forces and double-layer interactions is further investigated in ice-water-CO$_2$ and vapor-water-CO$_2$ systems  employing different models of effective polarizability for ions, {\it viz.} the hardsphere model and Onsager's model. The CO$_2$ bubble is found to be repelled by the vapor-water interface and attracted towards the ice-water interface. The equilibrium thin film of water formed between vapor and ice surfaces varies in thickness depending on the model of effective polarizability and the type of salt present in the system. Further studies of the interaction energy in geometries comprising two molecules near an interface and molecule in a three-layer geometry are conducted which may be relevant for potential energy storage applications. The density functional theory (DFT) is employed to generate the frequency-dependent dielectric functions required for Lifshitz energy and force calculations.   Summing up, in the numerous contexts outlined above, the importance of the van der Waals and Lifshitz forces has been demonstrated. The studies in this thesis enable significant predictions related to these forces which may be verifiable by experiments.

Non-monotonic phase behaviour of a mixture containing non-adsorbing particles and polymerising rod-like molecules

Hypothesis: Previous works have shown that many-body interactions induced by dispersants with increasing correlation length will generate a diminishing two-phase region [Soft Matter 14, 6921 (2018)]. We conjecture that the attenuation of the depletion attraction due to many-body interactions is a ubiquitous phenomenon in medium-induced interactions. We propose mixtures of colloidal particles and rod-like polymers as a feasible experimental system for verifying these predictions, since the intra-molecular correlations are not screened in a good solvent for rod-like polymers as they are in flexible polymers. The length of the rods can grow and become the dominant length scale that determines the range of the depletion interactions for the imbedded non-adsorbing particles. Simulations: We study many-body depletion forces induced by polymerizing rod-like polymers on spherical non-adsorbing colloids, using Metropolis Monte Carlo simulations. We also employ a simple mean-field theory to further justify our numerical predictions. Findings: We demonstrate that the phase diagram displays the same qualitative features that have previously been predicted by many-body theory, for mixtures containing flexible polymers under theta solvent conditions. The contraction of the particle two-phase region that we observe, as the correlation length increases beyond some specific value, could be a signature of the weakening of the depletion caused by many-body effects