Hydrophobic and Electrostatic Interactions in Adsorption at Interfaces: · Relation to the Nature of Liquid Surfaces

Electrostatic .and .hydrophobic interactions of ions near interfaces are examined in relation to the nature and structure of surfaces of. liquids, esp~cia.lly that of water. The superficial excess entropy and energy of liquid surfaces is calculated from surface tension data, aind Stefan\u27s ratio is evaluated for several liquid interfaces. Stefan\u27s ratio is related to the ratio of co-ord~nation number of surface molecules to that for bulk molecules and leads to information on surface structure. Stefan\u27•s ratio is ca. 0.5 for non-polar liquids but is near 0.1 for H-\u27bonded liquids. The superficial excess entropy is related to the cohesive energy density and to co-ordination i,n the surface. Short-range ·effects in adsorption of ions at air/water interfaces are determined by the structure of the liquid surface and by electrostatic polarization energy near the interface. Based on the Born equation, relations are · deduced for ionic adsorption near liquid interfaces. By studying the adsorption of a series of propylamine perchloratesat the air/water interface and the correspond1ng surface potential changes, the relaEve . importance of hydrophobic and electrosrtatic ion-solvent interaction effects was investigated. Methods for investig~ting the entropy of water at charged interfaces are discussed and a theory of entropy of water· in the double-layer is reviewed

Hydrophobic and Electrostatic Interactions in Adsorption at Interfaces: · Relation to the Nature of Liquid Surfaces

Electrostatic .and .hydrophobic interactions of ions near interfaces are examined in relation to the nature and structure of surfaces of. liquids, esp~cia.lly that of water. The superficial excess entropy and energy of liquid surfaces is calculated from surface tension data, aind Stefan\u27s ratio is evaluated for several liquid interfaces. Stefan\u27s ratio is related to the ratio of co-ord~nation number of surface molecules to that for bulk molecules and leads to information on surface structure. Stefan\u27•s ratio is ca. 0.5 for non-polar liquids but is near 0.1 for H-\u27bonded liquids. The superficial excess entropy is related to the cohesive energy density and to co-ordination i,n the surface. Short-range ·effects in adsorption of ions at air/water interfaces are determined by the structure of the liquid surface and by electrostatic polarization energy near the interface. Based on the Born equation, relations are · deduced for ionic adsorption near liquid interfaces. By studying the adsorption of a series of propylamine perchloratesat the air/water interface and the correspond1ng surface potential changes, the relaEve . importance of hydrophobic and electrosrtatic ion-solvent interaction effects was investigated. Methods for investig~ting the entropy of water at charged interfaces are discussed and a theory of entropy of water· in the double-layer is reviewed

Electrostatic interactions mediated by polarizable counterions: weak and strong coupling limits

We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.Comment: 25 pages, 7 figure

CSR engagement in SMEs – tactical or strategic?

Research aim and objectives: The aim of the research was to determine what (if any), Corporate Social Responsibility (CSR) activities small and medium-sized enterprises (SMEs) engage in, including their motivations for undertaking such activities, but also their rationale for not doing so. For those engaging, the objective was to ascertain the perceived benefit these activities provide, and whether this was a strategic or tactical decision for the organisation. For those not engaging, the objective was to understand their reasons for none engagement. Theoretical framework: This paper engages with the strategic CSR literature in framing CSR activities as a set of tools which can address a range of strategic priorities to the long-term benefit of the organisation. Design/methodology: The study surveyed a range of firms in the East Midlands of the UK, in both manufacturing and service sectors and across the spectrum of different-sized organisations over three different years (2017, 2018 and 2020). Respondent numbers ranged from 277 (2017), 280 (2018) and 421 (2020). Similar questions were asked across the three years encompassing a range of CSR-related activities and rationales for engagement or none engagement. Findings: There has been a growth in interest in CSR activities in the region over the surveyed period. Firm size correlates with increased activity (larger firms engaging more than smaller ones). Different types of activities are associated with different firm sizes: the more common reason for engagement in micro/small businesses is particularly “personal link with a cause/ altruism;” there is a willingness to build community links in medium businesses, while staff development is slightly more prominent in larger businesses. Larger businesses perceive CSR activities as more important to achieve their long-term strategic goals, and they are more likely to increase their investment in CSR as a result. Practical/social implications: As perceptions of the need for businesses to support their communities continues to grow, awareness on the positive impact of CSR activities in SMEs in achieving strategic objectives needs to be encouraged as a gateway to more sustained investment in CSR in a wider range of SMEs. Key words

Entropy and Entanglement in Quantum Ground States

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length, and we present strong evidence supporting a conjecture that there exist such systems with arbitrarily large entropy. However, we then show that, under an assumption on the density of states which is believed to be satisfied by many physical systems such as the fractional quantum Hall effect, that an efficient matrix product state representation of the ground state exists in any dimension. Finally, we comment on the implications for numerical simulation.Comment: 7 pages, no figure

Dynamical Quantum Phase Transitions in the Transverse Field Ising Model

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.Comment: 4+4 pages, 4 figures, Appendix adde

A new Euclidean tight 6-design

We give a new example of Euclidean tight 6-design in $\mathbb R^{22}$.Comment: 9 page

Solvent Structure and Molecular Orientation in the Double-Layer at the Mercury- Water Interface

Solvent structure and molecular orientation in the Hg-water interphase is an important and previously little investigated aspect of the electrical double-layer at charged metal interfaces. By using pyrazine and pyridine in critical comparative experiments on a) changes of surface dipole potential difference (Esin and Markov effects), b) surface pressure changes and c) charge dependence of free energy of adsorption, it is shown how the surface dipole contribution from oriented solvent molecules may be evaluated together with the charge-dependent distribution function for water orientation. In the case of pyridine, orientation of the adsorbate molecule itself occurs in a manner dependent on surface charge on the metal and interaction with oriented and bulk solvent molecules

Solvent Structure and Molecular Orientation in the Double-Layer at the Mercury- Water Interface

Solvent structure and molecular orientation in the Hg-water interphase is an important and previously little investigated aspect of the electrical double-layer at charged metal interfaces. By using pyrazine and pyridine in critical comparative experiments on a) changes of surface dipole potential difference (Esin and Markov effects), b) surface pressure changes and c) charge dependence of free energy of adsorption, it is shown how the surface dipole contribution from oriented solvent molecules may be evaluated together with the charge-dependent distribution function for water orientation. In the case of pyridine, orientation of the adsorbate molecule itself occurs in a manner dependent on surface charge on the metal and interaction with oriented and bulk solvent molecules

Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction