Ion distributions at charged aqueous surfaces: Synchrotron X-ray scattering studies

Surface sensitive synchrotron X-ray scattering studies were performed to obtain the distribution of monovalent ions next to a highly charged interface at room temperature. To control surface charge density, lipids, dihexadecyl hydrogen-phosphate (DHDP) and dimysteroyl phosphatidic acid (DMPA), were spread as monolayer materials at the air/water interface, containing $\mathrm{CsI}$ at various concentrations. Five decades in bulk concentrations ($\mathrm{CsI}$) are investigated, demonstrating that the interfacial distribution is strongly dependent on bulk concentration. We show that this is due to the strong binding constant of hydronium $\mathrm{H_{3}O^{+}}$ to the phosphate group, leading to proton-transfer back to the phosphate group and to a reduced surface charge. Using anomalous reflectivity off and at the $L_{3}$ $\mathrm{Cs^{+}}$ resonance, we provide spatial counterion ($\mathrm{Cs^{+}}$) distributions next to the negatively charged interfaces. The experimental ion distributions are in excellent agreement with a renormalized surface charge Poisson-Boltzmann theory for monovalent ions without fitting parameters or additional assumptions. Energy Scans at four fixed momentum transfers under specular reflectivity conditions near the $\mathrm{Cs^{+}}$ $L_{3}$ resonance were conducted on $10^{-3}\:\mathrm{M}$ $\mathrm{CsI}$ with DHDP monolayer materials on the surface. The energy scans exhibit a periodic dependence on photon momentum transfer. The ion distributions obtained from the analysis are in excellent agreement with those obtained from anomalous reflectivity measurements, providing further confirmation to the validity of the renormalized surface charge Poisson-Boltzmann theory for monovalent ions. Moreover, the dispersion corrections $f^{\prime}$ and $f^{\prime\prime}$ for $\mathrm{Cs^{+}}$ around $L_{3}$ resonance, revealing the local environment of a $\mathrm{Cs^{+}}$ ion in the solution at the interface, were extracted simultaneously with output of ion distributions. Another independent technique, X-ray fluorescence near total reflection was used to study ion adsorption at charged surfaces. Below the critical angle, the X-ray fluorescence spectra are only surface sensitive, providing the direct evidence of existence of $\mathrm{Cs^{+}}$ at the surface. Above the critical angle, combination of fluorescence spectra with and without the presence of monolayer materials yields the number of accumulated $\mathrm{Cs^{+}}$ per lipid at the surface. In addition, the fluorescence spectra collected as a function of incident X-ray energy near the $L_{3}$ edge provide the dispersion corrections, consistent with the results from the energy scans

Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet

Using the ambitwistor string, we complete the list of celestial OPE coefficients for supersymmetric theories. This uses the ambitwistor string worldsheet CFT to dynamically generate the OPE coefficients for maximally supersymmetric gauge theory, gravity and Einstein-Yang-Mills theories, including all helicity and orientation configurations. This extends previous purely bosonic results to include supersymmetry and provides explicit formulas which are, to the best of our knowledge, not in the literature. We also examine how the supersymmetric infinite dimensional soft algebras behave compared to the purely bosonic cases.Comment: v2, fixed typo, improved comment