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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

The computation of C-C and N-N bond dissociation energies for singly, doubly, and triply bonded systems

The bond dissociation energies (D sub e) of C2H2, C2H4, C2H6, N2, N2H2, and N2H4 are studied at various levels of correlation treatment. The convergence of D sub e with respect to the one particle basis is studied at the single reference modified coupled-pair functional (MCPF) level. At all levels of correlation treatment, the errors in the bond dissociation energies increase with the degree of multiple bond character. The multireference configuration interaction (MRCI) D sub e values, corrected for an estimate of higher excitations, are in excellent agreement with those determined using the size extensive averaged coupled pair functional (ACPF) method. It was found that the full valence complete active space self consistent field (CASSCF)/MRCI calculations are reproduced very well by MRCI calculations based on a CASSCF calculation that includes in the active space only those electrons involved in the C-C or N-N bonds. To achieve chemical accuracy (1 kcal/mole) for the D sub e values of the doubly bonded species C2H4 and N2H2 requires one particle basis sets including up through h angular momentum functions (l = 5) and a multireference treatment of electron correlation: still higher levels of calculation are required to achieve chemical accuracy for the triply bonded species C2H2 and N2.

Langhoff, Stephen R.↗
DOE OSTI2021

Quantifying multipoint ordering in alloys

A central problem in multicomponent lattice systems is to systematically quantify multipoint ordering. Ordering in such systems is often described in terms of pairs, even though this is not sufficient when three-point and higher-order interactions are included in the Hamiltonian. Current models and parameters for multipoint ordering are often only applicable for very specific cases or require approximating a subset of correlated occupational variables on a lattice as being uncorrelated. In this paper, cluster order parameters are introduced to systematically quantify arbitrary multipoint ordering motifs in substitutional systems through direct calculations of normalized cluster probabilities. These parameters can describe multipoint chemical ordering in crystal systems with multiple sublattices, multiple components, and systems with reduced symmetry. These are defined in this paper and applied to quantify four-point chemical ordering motifs in platinum/palladium alloy nanoparticles that are of practical interest to the synthesis of catalytic nanocages. Impacts of chemical ordering on nanocage stability are discussed. It is demonstrated that approximating four-point probabilities from superpositions of lower-order pair probabilities is not sufficient in cases where three- and four-body terms are included in the energy expression. Furthermore, conclusions about the formation mechanisms of nanocages may change significantly when using common pair approximations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Light–Induced Frenkel Defect Pair Formation Can Lead to Phase–Segregation of Otherwise Miscible Halide Perovskite Alloys

Alloys of ABX 3 halide perovskites (HP) exhibit unique phase behavior compared to traditional III-V and II-VI semiconductor alloys used in solar cells. While the latter typically have good mutual miscibility when their mixed components are size matched, and phase-segregate when size mismatched, HP alloys show good miscibility in the dark but can phase-segregate under light. Quantum mechanical calculations described herein reveal light-induced defect formation and migration hold the key. Specifically, the interaction between a halogen vacancy V X with halogen interstitial X i forming together a Frenkel-pair defect emerges as the enabler for phase-segregation in HP alloys. At a threshold bromine composition in the Br-I alloys, the photogenerated holes in the valence band localize, creating thereby a doubly-charged iodine Frenkel-pair (V I + I i ) 2+ . Faster migration of iodine over bromine interstitial into the vacant iodine V I site leads to the formation of iodine-rich and iodine-depleted regions, establishing phase-segregation. Removal of the mobile defects–the agent of segregation–by dark thermal annealing, supplies the opposing force, leading to reversal of phase-segregation. Furthermore, this atomistic understanding can enable some control of the phase-segregation by selecting substituting elements on the B site–such as replacing some Pb by Sn–that are unable to form stable Frenkel defects.

14 SOLAR ENERGY↗
NASA NTRS2012

Pathfinding the Flight Advanced Stirling Convertor Design with the ASC-E3

The Advanced Stirling Convertor (ASC) was initially developed by Sunpower, Inc. under contract to NASA Glenn Research Center (GRC) as a technology development project. The ASC technology fulfills NASA s need for high efficiency power convertors for future Radioisotope Power Systems (RPS). Early successful technology demonstrations between 2003 to 2005 eventually led to the expansion of the project including the decision in 2006 to use the ASC technology on the Advanced Stirling Radioisotope Generator (ASRG). Sunpower has delivered 22 ASC convertors of progressively mature designs to date to GRC. Currently, Sunpower with support from GRC, Lockheed Martin Space System Company (LMSSC), and the Department of Energy (DOE) is developing the flight ASC-F in parallel with the ASC-E3 pathfinders. Sunpower will deliver four pairs of ASC-E3 convertors to GRC which will be used for extended operation reliability assessment, independent validation and verification testing, system interaction tests, and to support LMSSC controller verification. The ASC-E3 and -F convertors are being built to the same design and processing documentation and the same product specification. The initial two pairs of ASC-E3 are built before the flight units and will validate design and processing changes prior to implementation on the ASC-F flight convertors. This paper provides a summary on development of the ASC technology and the status of the ASC-E3 build and how they serve the vital pathfinder role ahead of the flight build for ASRG. The ASRG is part of two of the three candidate missions being considered for selection for the Discovery 12 mission.

Wong, Wayne A.↗
NASA NTRS2012

Pathfinding the Flight Advanced Stirling Convertor Design with the ASC-E3

The Advanced Stirling Convertor (ASC) was initially developed by Sunpower, Inc. under contract to NASA Glenn Research Center (GRC) as a technology development project. The ASC technology fulfills NASA's need for high efficiency power convertors for future Radioisotope Power Systems (RPS). Early successful technology demonstrations between 2003 to 2005 eventually led to the expansion of the project including the decision in 2006 to use the ASC technology on the Advanced Stirling Radioisotope Generator (ASRG). Sunpower has delivered 22 ASC convertors of progressively mature designs to date to GRC. Currently, Sunpower with support from GRC, Lockheed Martin Space System Company (LMSSC), and the Department of Energy (DOE) is developing the flight ASC-F in parallel with the ASC-E3 pathfinders. Sunpower will deliver four pairs of ASC-E3 convertors to GRC which will be used for extended operation reliability assessment, independent validation and verification testing, system interaction tests, and to support LMSSC controller verification. The ASC-E3 and -F convertors are being built to the same design and processing documentation and the same product specification. The initial two pairs of ASC-E3 are built before the flight units and will validate design and processing changes prior to implementation on the ASC-F flight convertors. This paper provides a summary on development of the ASC technology and the status of the ASC-E3 build and how they serve the vital pathfinder role ahead of the flight build for ASRG. The ASRG is part of two of the three candidate missions being considered for selection for the Discovery 12 mission.

Wong, Wayne A.↗
DOE OSTI2014

Double-Wronskian solitons and rogue waves for the inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma

Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us to investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed. -- Highlights: •Double-Wronskian soliton solutions are obtained and proof is finished by virtue of some double Wronskian identities. •Asymptotic analysis is applied for us to investigate the interaction between the two solitons. •First- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation. •Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Multiwavelength analysis of annihilating dark matter as the origin of the gamma-ray emission from M31

Indirect detection of dark matter (DM) by multiwavelength astronomical observations provides a promising avenue for probing the particle nature of DM. In the case of DM consisting of weakly interacting massive particles (WIMPs), self-annihilation ultimately produces various observable products including e ± pairs and gamma rays. The gamma rays can be detected directly, while the e ± pairs can be detected by radio emission from synchrotron radiation or X rays and soft gamma rays from inverse Compton scattering. An intriguing region to search for astrophysical signs of DM is the Galactic center (GC) of the Milky Way, due in part to an observed excess of gamma rays that could be DM. A recent observation by the Fermi-LAT collaboration of a similar excess in the central region of the Andromeda galaxy (M31) leads us to explore the possibility of a DM-induced signal there as well. We use the RX-DMFIT tool to perform a multifrequency analysis of potential DM annihilation emissions in M31. We consider WIMP particle models consistent with the GC excess and calculate the expected emission across the electromagnetic spectrum in comparison with available observational data from M31. We find that the particle models that best fit the M31 excess favor lower masses than the GC excess. The best-fitting models are for a $b\bar{b}$ final state with M χ = 11 GeV and $\langle$σv$\rangle$ = 2.6 × 10 -26 cm 3 s -1 , as well as an evenly mixed $\bar{b}$b/τ + τ - final state with M χ = 5.8 GeV and $\langle$σv$\rangle$ = 2.03 × 10 -26 cm 3 s -1 . For conservative estimates of the diffusion and magnetic field models the expected radio emissions appear to be in tension with currently available data in the central region of M31, although this constraint has a fairly strong dependence on the values chosen for parameters describing the magnetic field strength and geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Solution of the Skyrme-Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) HFODD (v2.73y): A new version of the program

Here, we describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Current density partitioning in time-dependent current density functional theory

We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

The computation of C-C and N-N bond dissociation energies for singly, doubly, and triply bonded systems

The bond dissociation energies (De) of C2H2, C2H4, C2H6, N2, N2H2, and N2H4 are studied at various levels of correlation treatment. The convergence of De with respect to the one-particle basis is studied at the single-reference modified coupled-pair-functional (MCPF)level. At all levels of correlation treatment, the errors in the bond dissociation energies increase with the degree of multiple bond character. The multireference configuration-interaction (MRCI) De values, corrected for an estimate of higher excitations, are in excellent agreement with those determined using the size-extensive averaged-coupled-pair-functional (ACPF) method. The full-valence complete-active-space self-consistent-field (CASSCF)/MRCI calculations are reproduced very well by MRCI calculations based on a CASSCF calculation that includes in the active space only those electrons involved in the C-C or N-N bonds.

Langhoff, Stephen R.↗
DOE OSTI2013

Defining efficient enzyme-cofactor pairs for bioorthogonal profiling of protein methylation

Protein methyltransferase (PMT)-mediated posttranslational modification of histone and nonhistone substrates modulates stability, localization, and interacting partners of target proteins in diverse cellular contexts. These events play critical roles in normal biological processes and are frequently deregulated in human diseases. In the course of identifying substrates of individual PMTs, bioorthogonal profiling of protein methylation (BPPM) has demonstrated its merits. In this approach, specific PMTs are engineered to process S-adenosyl-L-methionine (SAM) analogs as cofactor surrogates and label their substrates with distinct chemical modifications for target elucidation. Despite the proof-of-concept advancement of BPPM, few efforts have been made to explore its generality. With two cancer-relevant PMTs, EuHMT1 (GLP1/KMT1D) and EuHMT2 (G9a/KMT1C), as models, we defined the key structural features of engineered PMTs and matched SAM analogs that can render the orthogonal enzyme–cofactor pairs for efficient catalysis. Here we have demonstrated that the presence of sulfonium-β-sp 2 carbon and flexible, medium-sized sulfonium-δ-substituents are crucial for SAM analogs as BPPM reagents. The bulky cofactors can be accommodated by tailoring the conserved Y1211/Y1154 residues and nearby hydrophobic cavities of EuHMT1/2. Profiling proteome-wide substrates with BPPM allowed identification of >500 targets of EuHMT1/2 with representative targets validated using native EuHMT1/2 and SAM. This finding indicates that EuHMT1/2 may regulate many cellular events previously unrecognized to be modulated by methylation. The present work, therefore, paves the way to a broader application of the BPPM technology to profile methylomes of diverse PMTs and elucidate their downstream functions.

Islam, Kabirul↗
DOE OSTI2015

Superconductivity: The persistence of pairs

Superconductivity stems from a weak attraction between electrons that causes them to form bound pairs and behave much like bosons. These so-called Cooper pairs are phase coherent, which leads to the astonishing properties of zero electrical resistance and magnetic flux expulsion typical of superconducting materials. This coherent state may be qualitatively understood within the Bose–Einstein condensate (BEC) model, which predicts that a gas of interacting bosons will become unstable below a critical temperature and condense into a phase of matter with a macroscopic, coherent population in the lowest energy state, as happens in 4 He or cold atomic gases. The successful theory proposed by Bardeen, Cooper and Schrieffer (BCS) predicts that at the superconducting transition temperature T c , electrons simultaneously form pairs and condense, with no sign of pairing above T c . Theorists have long surmised that the BCS and BEC models are opposite limits of a single theory and that strong interactions or low density can, in principle, drive the system to a paired state at a temperature Tpair higher than T c , making the transition to the superconducting state BEC-like (Fig. 1). Yet most superconductors to date are reasonably well described by BCS theory or its extensions, and there has been scant evidence in electronic materials for the existence of pairing independent of the full superconducting state (though an active debate rages over the cuprate superconductors). Writing in Nature, Jeremy Levy and colleagues have now used ingenious nanostructured devices to provide evidence for electron pairing1. Perhaps surprisingly, the material they have studied is a venerable, yet enigmatic, low-temperature superconductor, SrTiO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation

Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H{sub 2}, and eliminates delocalization errors in H{sub 2}{sup +} and other single-bond systems. It gives surprisingly good non-bonded interaction energies – competitive with the ph-RPA – with the correct R{sup −6} asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Preparation of Core-Shell Coordination Molecular Assemblies via the Enrichment of Structure-Directing "Codes" of Bridging Ligands and Metathesis of Metal Units

A series of molybdenum- and copper-based MOPs were synthesized through coordination-driven process of a bridging ligand (3,3'-PDBAD, L-1) and dimetal paddlewheel clusters. Three conformers of the ligand exist with an ideal bridging angle between the two carboxylate groups of 0 degrees (H-2 zeta-L(1)), 120 degrees (H-2 beta-L-1), and of 90 degrees (H-2 beta-L-1), respectively. At ambient or lower temperature, (HL1)-L-2 and Mo-2(OAc)(4) or Cu-2(OAc)(4) were crystallized into a molecular square with ?-L-1 and Mo-2/Cu-2 units. With proper temperature elevation, not only the molecular square with ?-L-1 but also a lantern-shaped cage with a-L-1 formed simultaneously. Similar to how Watson-Crick pairs stabilize the helical structure of duplex DNA, the core-shell molecular assembly possesses favorable H-bonding interaction sites. This is dictated by the ligand conformation in the shell, coding for the formation and providing stabilization of the central lantern shaped core, which was not observed without this complementary interaction. On the basis of the crystallographic implications, a heterobimetallic cage was obtained through a postsynthetic metal ion metathesis, showing different reactivity of coordination bonds in the core and shell. As an innovative synthetic strategy, the site-selective metathesis broadens the structural diversity and properties of coordination assemblies.

Park, J↗
DOE OSTI2021

Extracting the number of short-range correlated nucleon pairs from inclusive electron scattering data

The extraction of the relative abundances of short-range correlated (SRC) nucleon pairs from inclusive electron scattering is studied using the generalized contact formalism (GCF) with several nuclear interaction models. GCF calculations can reproduce the observed scaling of the cross-section ratios for nuclei relative to deuterium at high xB and large Q 2 , a 2 =(σ A /A)/(σ d /2). In the nonrelativistic instant-form formulation, the calculation is very sensitive to the model parameters and only reproduces the data using parameters that are inconsistent with ab initio many-body calculations. Using a light-cone GCF formulation significantly decreases this sensitivity and improves the agreement with ab initio calculations. The ratio of similar mass isotopes, such as 40 Ca and 48 Ca, should be sensitive to the nuclear asymmetry dependence of SRCs, but is found to also be sensitive to low-energy nuclear structure. Thus the empirical association of SRC pair abundances with the measured a2 values is only accurate to about 20%. Finally, improving this will require cross-section calculations that reproduce the data while properly accounting for both nuclear structure and relativistic effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Magnetic Interactions in Substitutional Core-Doped Graphene Nanoribbons

The design of a spin imbalance within the crystallographic unit cell of bottom-up engineered 1D graphene nanoribbons (GNRs) gives rise to nonzero magnetic moments within each cell. Here, we demonstrate the bottom-up assembly and spectroscopic characterization of a one-dimensional Kondo spin chain formed by a chevron-type GNR (cGNR) physisorbed on Au(111). Substitutional nitrogen core doping introduces a pair of low-lying occupied states per monomer within the semiconducting gap of cGNRs. Charging resulting from the interaction with the gold substrate quenches one electronic state for each monomer, leaving behind a 1D chain of radical cations commensurate with the unit cell of the ribbon. In this work, scanning tunneling microscopy (STM) and spectroscopy (STS) reveal the signature of a Kondo resonance emerging from the interaction of $\textit{S}$ = 1/2 spin centers in each monomer core with itinerant electrons in the Au substrate. STM tip lift-off experiments locally reduce the effective screening of the unpaired radical cation being lifted, revealing a robust exchange coupling between neighboring spin centers. First-principles DFT-LSDA calculations support the presence of magnetic moments in the core of this GNR when it is placed on Au.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Nucleon-pair approximation for nuclei from spherical to deformed regions

Here we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provide a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by S D G pairs) reproduce the nuclear shape evolution in the N = 26 isotones, Ca 46 , Ti 48 , Cr 50 , and Fe 52 , and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: Ti 44 – 48 , Cr 48 , Cr 50 , Fe 52 , Zn 60 – 64 , Ge 64 , 66 , Mo 84 , and Xe 108 – 112 . Finally, using the S D G I -pair approximation we describe low-lying states of Ba 112 , 114 , cases difficult to reach by conventional configuration-interaction methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Charge Regulation Stabilizes the Formation of Ionic Liquid‐Based Amphiphilic Oligomer Droplet Interface Bilayers

Amphiphilic charged oligomers (oligodimethylsiloxane – methylimidazolium cation, ODMS-MIM (+) ), assemble into bilayers using the droplet interface bilayer (DIB) platform, possess similar size and functionality as phospholipid bilayers, but exhibit increased stability. The oligomer ionic headgroups (MIM (+) ) are covalently bound to monodisperse, short-chain (n = 13) hydrophobic tails (ODMS). These self-assemble as monolayer brushes at the oil–aqueous interface of water droplets that are influenced by both the charged cationic headgroups, and the nature of the covalently attached tails in the organic phase. Charge regulation (CR) stabilizes the formation of ordered, molecularly close-packed brush phases, which results in highly insulating, stable DIB membranes, with contributions from specific ion-pairing effects, Debye screening, and voltage-dependent electrocompressive stresses. In the oil phase, interactions between hexadecane, a good solvent for ODMS, and the hydrophobic tails result in extended waiting times for bilayer formation compared to phospholipid DIBs, for which hexadecane is a poor solvent. Close agreement between experimental values and predictions for two key parameters, the critical membrane thickness, h c , and maximal grafted headgroup density, Γ 0 , validate an electrostatic CR model consisting of adsorption and partial neutralization of counterions at a charged interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗