Effective osmotic cohesion due to the solvent molecules in a delocalized adsorbed monolayer.

A molecular thermodynamic model is derived for an uncharged delocalized surfactant monolayer adsorbed at a liquid interface, taking explicit account for the solvent molecules present in the monolayer. The model is based on the scaled particle theory of hard-disc mixtures, and is also extended to sticky discs (i.e. attraction between the adsorbed molecules). Upon compression of the adsorbed layer, the solvent is expelled from it. The respective osmotic effect on the equation of state is shown to be equivalent to an effective lateral depletion attraction between the surfactant molecules. This effective osmotic cohesion causes an increase of the value of the attraction parameter β of the monolayer. The smaller the size of the surfactant polar head group is, the larger the effective attraction the model predicts. This trend is verified with data for the adsorption at water|air surface of alcohols, undissociated acids, and hexaethylenglycol monoalkyl ethers. The proposed theory allows the amount of solvent in the monolayer to be estimated, which is shown to be important for the neutron reflectivity of the surface

Electrostatics of quadrupolarizable media

The classical macroscopic Maxwell equations are approximated. They are a corollary of the multipole expansion of the local electrostatic potential up to dipolar terms. But quadrupolarization of the medium should not be neglected if the molecules which build up the medium possess large quadrupole moment or do not have any dipole moment. If we include the quadrupolar terms in Maxwell equations we obtain the quadrupolar analogue of Poisson's equation: $\nabla^2 \phi - L^2_Q\nabla^4 \phi = - \rho / \varepsilon$. This equation is of the fourth order and it requires not only the two classical boundary conditions but also two additional ones: continuous electric field and the relation of the jump of the normal quadrupolarizability at the surface to the intrinsic normal surface dipole moment. The account of the quadrupole moment of the molecules leads to significant differences compared to the classical electrostatic theory

Energy of Liposome Patch Adhesion to the Pipet Glass Determined by Confocal Fluorescence Microscopy.

The formation of the gigaseal in the patch clamp technique is dependent on the adhesion between the cell or liposome membrane and the glass pipet. The adhesion results in a capillary force causing creep of the patch membrane up the pipet. The membrane can be immobilized by counteracting the capillary force by positive pressure applied to the patch pipet. We use this phenomenon to develop a method for static measurement of the adhesion free energy of the lipid bilayer to the glass. Confocal fluorescent microscopy is used to track the bilayer creep inside the pipet and measure the immobilization pressure at various salt concentrations and pH. The adhesion energy is simply related to this pressure. For the studied phospholipid bilayers, its values were in the 0.3-0.7 mJ/m2 range, increased with salt concentration, and had a maximum as a function of pH. This method offers a way to measure bilayer-glass adhesion energy in patch clamp experiments that is more precise than dynamic methods

Quadrupole terms in the Maxwell equations: Born energy, partial molar volume and entropy of ions. Debye-Hückel theory in a quadrupolarizable medium

A new equation of state relating the macroscopic quadrupole moment density $Q$ to the gradient of the field $\nabla E$ in an isotropic fluid is derived: $Q = \alpha_Q(\nabla E - U \nabla.E/3)$, where the quadrupolarizability $\alpha_Q$ is proportional to the squared molecular quadrupole moment. Using this equation of state, a generalized expression for the Born energy of an ion dissolved in quadrupolar solvent is obtained. It turns out that the potential and the energy of a point charge in a quadrupolar medium are finite. From the obtained Born energy, the partial molar volume and the partial molar entropy of a dissolved ion follow. Both are compared to experimental data for a large number of simple ions in aqueous solutions. From the comparison the value of the quadrupolar length $L_Q$ is determined, $L_Q = \sqrt{\alpha_Q/3\epsilon}= 1-2 {\AA}$. Further, the extended Debye-H\"uckel model is generalized to ions in a quadrupolar solvent. If quadrupole terms are allowed in the macroscopic Coulomb law, they result in suppression of the gradient of the electric field. In result, the electric double layer is slightly expanded. The activity coefficients obtained within this model involve three characteristic lengths: Debye length, ion radius and quadrupolar length $L_Q$. Comparison to experimental data shows that minimal distance between ions is equal to the sum of their bare ion radii; the concept for ion hydration as an obstacle for ions to come into contact is not needed for the understanding of the experimental data

The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential.

The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poisson's classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gauss's relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension-of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of the bulk phases and the intrinsic polarization of the interface. The coefficient of the dielectro-Marangoni effect (surface flow due to gradient of the normal electric field) is found. A model of the Langevin type for the surface dipole moment and the intrinsic surface polarizability is presented.The work is funded by National Science fund through Contract No. 162 from 2015 with Sofia Universit

Comment on “A spherical cavity model for quadrupolar dielectrics” [J. Chem. Phys. 144, 114502 (2016)]

The dielectric properties of a fluid composed of molecules possessing both dipole and quadrupole moments are studied based on a model of the Onsager type (molecule in the centre of a spherical cavity). The dielectric permittivity ε and the macroscopic quadrupole polarizability αQ of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of αQ is to increase the reaction field, to bring forth reaction field gradient, to decrease the cavity field and to bring forth cavity field gradient. The effects from the quadrupole terms are significant in the case of small cavity size in a non-polar liquid. The quadrupoles in the medium are shown to have small but measurable effect on the dielectric permittivity of several liquids (Ar, Kr, Xe, CH4, N2, CO2, CS2, C6H6, H2O, CH3OH). The theory is used to calculate the macroscopic quadrupolarizabilities of these fluids as functions of pressure and temperature. The cavity radii are also determined for these liquids, and it is shown that they are functions of density only. This extension of Onsager’s theory will be important for non-polar solutions (fuel, crude oil, liquid CO2), especially at increased pressures

Improved methodology for performing the inverse Abel transform of flame images for color ratio pyrometry.

A new method is presented for performing the Abel inversion by fitting the line-of-sight projection of a predefined intensity distribution (FLiPPID) to the recorded 2D projections. The aim is to develop a methodology that is less prone to experimental noise when analyzing the projection of axisymmetric objects-in this case, co-flow diffusion flame images for color ratio pyrometry. A regression model is chosen for the light emission intensity distribution of the flame cross section as a function of radial distance from the flame center line. The forward Abel transform of this model function is fitted to the projected light intensity recorded by a color camera. For each of the three color channels, the model function requires three fitting parameters to match the radial intensity profile at each height above the burner. This results in a very smooth Abel inversion with no artifacts such as oscillations or negative values of the light source intensity, as is commonly observed for alternative Abel inversion techniques, such as the basis-set expansion or onion peeling. The advantages of the new FLiPPID method are illustrated by calculating the soot temperature and volume fraction profiles inside a co-flow diffusion flame, both being significantly smoother than those produced by the alternative inversion methods. The developed FLiPPID methodology can be applied to numerous other optical techniques for which smooth inverse Abel transforms are required

FLiPPID flame pyrometry Python code

Colour ratio pyrometry is an economic and rapid technique to obtain soot temperatures and volume fractions from colour photographs of flames. One of the key challenges is to reconstruct the light intensity at the flame cross section R(r,z) from its 2D projection recorded by the camera P(x,z), also known as the inverse Abel transform. In a recent project, our group developed a new Abel inversion method (FLiPPID) tailored to the analysis of co-flow diffusion flame images. Advantages over conventional methods are a less noisy image reconstruction and the suppression of nonphysical negative light intensities. The Python code for performing the image analysis is provided below. It can be used to compute 2D soot temperature and volume fraction profiles from colour photographs using different methods for the invers Abel transform (FLiPPID, BASEX, or onion peeling with combined with a Tikhonov regularisation). A more detailed description can be found in a recent preprint (https://como.cheng.cam.ac.uk/index.php?Page=Preprints&No=217) and publication as well as the comments within the Python code

Effect of the solvent quadrupolarizability on the strength of the hydrogen bond: Theory vs data for the Gibbs energy and enthalpy of homo- and heteroassociation between carboxylic acids and water.

A cavity model of the effect of a solvent on thermodynamic parameters of dimerization of polar species in non-polar liquids has been developed and compared to experimental data. Bulk solution data have been collected for stearic acid in cyclohexane and in toluene to quantify the extent of self-association of the acid in terms of the dimer self-dissociation constant, Kd. Composition and temperature-dependent experimental data have been collected to determine Kd, the enthalpy of dissociation, and temperature-dependent infrared molar absorption coefficients. The interaction of stearic acid with small amounts of water present in non-aqueous solvents is also addressed and quantified with a hetero-dissociation (or dehydration) constant, Kh. Existing data for acetic acid are also considered. The model connects Kd and Kh to the vapor-phase association equilibria. Solute dipole-solvent quadrupole interactions are shown to have a major effect on Kd in quadrupolar liquids, such as toluene, benzene, and CS2. This work provides important background as a prelude to adsorption studies of these additives from non-aqueous solvents to solid surfaces with relevance to commercial fluids, such as oil-based corrosion inhibitors and friction modifiers. Moreover, the presented theory of the solvent effect on Kd is a first step to generalization of standard implicit solvent models in computational chemistry (such as the polarizable continuum model) to media of significant quadrupolar strength. This is expected to be particularly important for polar species dissolved in CO2 relevant for carbon capture and storage where appropriate models do not currently exist.BP ICAM, BP Internationa