The Different Effect of Electron-Electron Interaction on the Spectrum of Atoms and Quantum Dots

The electron-electron scattering rate of single particle excitations in atoms is estimated and compared with the corresponding rate in quantum dots. It is found that in alkali atoms single particle excitations do not acquire a width due to electron-electron interaction, while in complex atoms they may. This width is typically smaller than the single particle level spacing, and hence does not affect the number of discrete single particle excitations resolved below the ionization threshold. This situation is contrasted with that of quantum dots where electron-electron interaction severely limits the number of resolved excitations. Unlike the case of quantum dots, the scattering rate in atoms is found to decrease with increasing excitation energy. The different effect of electron-electron interaction on the spectrum of quantum dots and atoms is traced to the different confining potentials in the two systems.Comment: 12 pages including 2 eps figure

Approximate analytic solution for electronic wave functions and energies in coupled quantum wells

A formalism is developed which results in simple analytic expressions for the electron energy splittings and the wave functions in coupled quantum well structures of the type employed in new laser and transistor configurations. The limits of validity of the formalism are explored

Reversed Hofmeister series - the rule rather than the exception

Over recent years, the supposedly universal Hofmeister series has been replaced by a diverse spectrum of direct, partially altered and reversed series. This review aims to provide a detailed understanding of the full spectrum by combining results from molecular dynamics simulations, Poisson–Boltzmann theory and AFM experiments. Primary insight into the origin of the Hofmeister series and its reversal is gained from simulation-derived ion–surface interaction potentials at surfaces containing non-polar, polar and charged functional groups for halide anions and alkali cations. In a second step, the detailed microscopic interactions of ions, water and functional surface groups are incorporated into Poisson–Boltzmann theory. This allows us to quantify ion-specific binding affinities to surface groups of varying polarity and charge, and to provide a connection to the experimentally measured long-ranged electrostatic forces that stabilize colloids, proteins and other particles against precipitation. Based on the stabilizing efficiency, the direct Hofmeister series is obtained for negatively charged hydrophobic surfaces. Hofmeister series reversal is induced by changing the sign of the surface charge from negative to positive, by changing the nature of the functional surface groups from hydrophobic to hydrophilic, by increasing the salt concentration, or by changing the pH. The resulting diverse spectrum reflects that alterations of Hofmeister series are the rule rather than the exception and originate from the variation of ion-surface interactions upon changing surface properties

Thermodynamics of Charge Regulation Near Surface Neutrality

The interaction between two adjacent charged surfaces immersed in aqueous solution is known to be affected by charge regulation - the modulation of surface charge as two charged surfaces approach each other. This phenomenon is particularly important near surface neutrality where the stability of objects such as colloids or biomolecules is jeopardized. Focusing on this ubiquitous case, we elucidate the underlying thermodynamics and show that charge regulation is governed in this case by surface entropy. We derive explicit expressions for charge regulation and formulate a new universal limiting law for the free energy of ion adsorption to the surfaces. The latter turns out to be proportional to $k_{B}T$, and independent of the association energy of ions to surface groups. These new results are applied to the analysis of unipolar as well as amphoteric surfaces such as oxides near their point of zero charge or proteins near their isoelectric point

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic amplitudes generally require simultaneous measurements of multiple harmonics to achieve satisfactory accuracy. In the present letter we address the mathematical challenge and derive accurate, explicit formulae for both conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM) each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range

Hydration Structure of a Single DNA Molecule Revealed by Frequency-Modulation Atomic Force Microscopy

Hydration interaction shapes biomolecules and is a dominant intermolecular force. Mapping the hydration patterns of biomolecules is therefore essential for understanding molecular processes in biology. Numerous studies have been devoted to this challenge, but current methods cannot map the hydration of single biomolecules, let alone do so under physiological conditions. Here, we show that frequency-modulation atomic force microscopy (FM-AFM) can fill this gap and generate 3D hydration maps of single DNA molecules under near-physiological conditions. Additionally, we present real-space images of DNA in which the double helix is resolved with unprecedented resolution, clearly revealing individual phosphate groups along the DNA backbone. FM-AFM therefore emerges as a powerful enabling tool in the study of individual biomolecules and their hydration under physiological conditions