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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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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Comment on “Thermodynamic Models for the (HClO 4 + NaClO 4 ){aq} and (HBr + NaBr){aq} Systems at 298.15 K and 0.1 MPa” Authored by Oakes, C. S., Ward, A. L., Chugunov, N. Journal of Chemical & Engineering Data , 68 , 2554–2562

Oakes et al. (2023) published a review article in this journal. In that paper, Oakes et al. (2023) developed thermodynamic models to describe electrolyte solutions for HClO 4 –NaClO 4 –H 2 O and HBr–NaBr–H 2 O systems, based on literature data. In their paper, previously published work from researchers in the field was criticized; some of it is ours. Here, in this brief Comment, we first comment on their models, and then we briefly provide a technical response to that criticism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Relating Geometric Nanoconfinement and Local Molecular Environment to Diffusion in Ionic Polymer Membranes

Understanding structure-diffusion relationships in ionic polymer membranes not only illuminates fundamental mechanisms for membrane transport, but also informs further membrane development. In this study, we employ NMR diffusometry and molecular dynamics (MD) simulations to investigate diffusion coefficients and activation energies of diffusion (Ea) for both a lithium-form perfluorosulfonic acid membrane and aqueous solutions of lithium triflate. NMR shows that, at high water/ion molar ratio (?), Ea for water diffusion is slightly lower in the membrane than in solution. Conversely, membrane transport exhibits much higher Ea at low hydration as compared to solutions. MD simulations of a model system consisting of carbon nanotubes with varying diameter reveal that Ea of diffusion clearly relates to both the geometric nanoconfinement of the hydrophilic pathways in the membrane as well as the local molecular environment. These results demonstrate that Ea of diffusion can serve as a revelatory tool for the study of molecular transport processes and the coupling of morphology with transport at the nanoscale. This study thus provides new insights and new experimental and computational models for understanding transport in a wide range of polymer membranes, such as those used in molecular separations applications.

Zhang, Rui↗
DOE OSTI2018

Impacts of glass composition, pH, and temperature on glass forward dissolution rate

Nuclear waste glasses dissolve at the forward dissolution rate (r f ) in very dilute aqueous solutions, which can isolate the impact of the glass composition from solution feedback and alteration product effects. While it has long been known that pH and temperature (T) strongly impact r f , the impacts of glass composition have remained uncertain. In this work, r f data from 19 nuclear waste glasses were used with the aim of identifying the effect of glass composition on r f . The r f values were modeled as: r f = k 0 10 –ηpH exp(-E a /RT), with k 0 , η, E a , and R, respectively, being the intrinsic rate constant, pH coefficient, apparent activation energy, and gas constant. However, no predictive correlation could be established between the individual model parameters (log[k 0 ], η, and E a ) and glass composition for the glasses considered in this study, an outcome that was attributed to the strong positive correlation between the log[$k_0$] and E a parameters. Therefore, a model was fitted directly to the combined r f from all 19 glasses. This approach showed that 90% of the variation in r f data could be accounted for solely by T and pH effects. Therefore, any composition effects must be relatively small. After normalizing for differences in pH and T, the only notable differences in r f between the glasses were found to correlate with variations in the fraction of glass forming tetrahedra contributed by tetrahedral boron, $f$([ 4 ]B), with an abrupt threshold at a high value of $f$([ 4 ]B) (~0.22), where higher r f are predicted with no discernable composition effects below the threshold.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Uncovering the hydride ion diffusion pathway in barium hydride via neutron spectroscopy

Solid state materials possessing the ability for fast ionic diffusion of hydrogen have immense appeal for a wide range of energy-related applications. Ionic hydrogen transport research is dominated by proton conductors, but recently a few examples of hydride ion conductors have been observed as well. Barium hydride, BaH 2 , undergoes a structural phase transition around 775 K that leads to an order of magnitude increase in the ionic conductivity. This material provides a prototypical system to understand hydride ion diffusion and how the altered structure produced by the phase transition can have an enormous impact on the diffusion. We employ quasielastic and inelastic neutron scattering to probe the atomic scale diffusion mechanism and vibrational dynamics of hydride ions in both the low- and high-temperature phases. Jump lengths, residence times, diffusion coefficients, and activation energies are extracted and compared to the crystal structure to uncover the diffusion pathways. We find that the hydrogen jump distances, residence times, and energy barriers become reduced following the phase transition, allowing for the efficient conduction of hydride ions through a series of hydrogen jumps of length L = 3.1 Å.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Impacts of molecular architecture on the radiation-induced degradation and reaction kinetics of hydrophobic diglycolamides with the solvated electron and the dodecane radical cation

Given their proposed use as trivalent actinide–lanthanide separation ligands, the role of molecular architecture on the radiation robustness of diglycolamide (DGA) molecules has been investigated. This study examined three prototypical molecules with differences in their aliphatic chain architecture: N,N,N′,N′-tetra(n-octyl)diglycolamide (TODGA), N,N,N′,N′-tetra(2-ethylhexyl)diglycolamide (T2EHDGA), and N,N′-dimethyl-N,N′-dioctyldiglycolamide (DMDODGA). Rate coefficients and activation parameters are reported for the reactivity of each DGA with the solvated electron (e solv − ) and the corresponding dodecane radical cation (RH˙ + ) over the temperature range of 10.0 to 44.1 °C. These measurements indicate that DMDODGA is the most chemically reactive with both transient radicals, which may be attributed to this molecule's more accessible backbone. Complementary gamma dose accumulation studies (≤ 600 kGy) under envisioned process conditions—50 mM DGA in n-dodecane solvent—afforded dose constants for the loss of DGA of d = (3.41 ± 0.07) × 10 −3 , (4.19 ± 0.09) × 10 −3 , and (4.65 ± 0.09) × 10 −3 kGy −1 for T2EHDGA, DMDODGA, and TODGA, respectively. These dose constants indicate that varying DGA architecture affords subtle differences in chemical reactivity, leading to varying rates of radiolytic degradation under envisioned actinide–lanthanide separation conditions. However, more ambitious DGA frameworks, such as modifying the backbone, branching of the aliphatic chains, and/or changing the size of the chain may be required for larger gains in radiolytic longevity while optimizing actinide–lanthanide selectivity.

Arrhenius parameters↗
DOE OSTI2024

Localized basis set for plutonium

The implementation of optimal strictly localized atomic orbitals basis for plutonium (Pu) using norm-conserving pseudopotential density-functional theory (DFT) is presented. The basis set was applied to the α, β, γ, δ, δ', and ε phases of Pu, δ-Pu surface, and δ-PuGa alloys. The computed properties of the Pu phases and δ-Pu surface were in good agreement with both available experimental data and prior DFT calculations based on plane-wave methodologies. Results for the δ-PuGa alloys were also in good agreement with experimental data. Finally, the reliability of the basis set was further demonstrated by using ab initio molecular dynamics to model the diffusion coefficient and activation barrier for atomic diffusion in a δ-PuGa alloy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Study of Potentiometry for Monitoring Activity of GdCl 3 in Molten LiCl-KCl Salt

In pyroprocessing spent nuclear fuels by electrorefining in molten LiCl-KCl salt, it is desired to monitor in real time the UCl 3 concentration in the salt for safeguards purposes. Current chemical analysis of the highly radioactive salt for electrorefining by an inductively coupled plasma technique is inconvenient and usually time-consuming in generating the salt composition results. In this paper, we evaluated whether a simple potentiometry approach can be used for real-time monitoring the concentration of GdCl 3 , which was used as a surrogate for UCl 3 , in LiCl-KCl-GdCl 3 salt by measuring the open circuit potential of a Gd metal electrode with respect to a Ag/AgCl reference electrode (RE) when GdCl 3 salt was incrementally added to the LiCl-KCl salt. Additions of LaCl 3 , CeCl 3 and NdCl 3 salts were used for evaluating the effects of other chloride salts on the selectivity of the Gd metal electrode vs Ag/AgCl RE. While using potentiometry to determine GdCl 3 concentrations, Gd metal was unexpectedly observed to be unstable and dissolved in LiCl-KCl salt when GdCl 3 is present.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

Cu(In,Ga)Se 2 (CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. Here, we show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet, and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.

14 SOLAR ENERGY↗
DOE OSTI2015

Understanding the Effect of Na in Improving the Performance of CuInSe 2 Based Photovoltaics

Cu(In,Ga)Se 2 (CIGS) thin film photovoltaic technology is in the early stages of commercialization with an annual manufacturing capacity over 1 GW and has demonstrated the highest module efficiency of any of the thin film technologies. However there still is a lack of fundamental understanding of the relationship between the material properties and solar cell device operation. It is well known that the incorporation of a small amount of Na into the CIGS film during processing is essential for high efficiency devices. However, there are conflicting explanations for how Na behaves at the atomic scale. This report investigates how Na is incorporated into the CIGS device structure and evaluates the diffusion of Na into CIGS grain boundaries (GBs) and bulk crystallites. Participants: This project was carried out at the Institute of Energy Conversion at the University of Delaware, collaborating with the Rockett group at the University of Illinois Urbana-Champagne. Significant Findings: The significant outcomes of this project for each task include; Task 1.0: Effect of Na in Devices Fabricated on PVD Deposited CIGS; Na diffusion occurs through the Mo back contact via GBs driven by the presence of oxygen; Na reversibly compensates donor defects in CIGS GBs,Task 2.0: Na Incorporation in Single Crystal CIGS; and bulk Na diffusion proceeds rapidly such that grains are Na-saturated immediately following CIGS thin film manufacture. Industry Guidance: The presented results offer interesting concepts for modification of manufacturing processes of CIGS-based PV modules. Possible approaches to improve control of Na uptake and uniformly increase levels in CIGS films are highlighted for processes that employ either soda-lime glass or NaF as the Na source. Concepts include the potential of O 2 or oxidative based treatments of Mo back contacts to improve Na diffusion through the metal film and increase Na uptake into the growing CIGS. This project has also offered fundamental understanding of the behavior of Na in CIGS grains and GBs, particularly the confirmation that CIGS grains will be saturated with Na immediately following manufacture Summary of Results: Most commercially available CIGS modules are fabricated on soda-lime glass coated with Mo as the back electric contact, and Na in the glass diffuses through the Mo layer into the CIGS during film growth. In Task 1 the transport of Na through Mo was evaluated using x-ray photoelectron surface spectroscopy along with diffusion modeling to obtain diffusion coefficients at several temperatures. It was determined that Na diffusion in Mo only occurs along GBs and that oxygen provides an additional driving force to enhance Na transport. Device data revealed that older Mo substrates with a greater amount of surface oxide resulted in slightly higher efficiencies due to enhanced Na incorporation caused by the oxide. This finding shows that Mo substrates could potentially undergo an oxidation treatment prior to CIGS deposition to further improve and control the incorporation of Na. To determine if in-grain Na affects device performance, in Task 1 Na was selectively removed from GBs using heat/rinse cycles. Due to the low temperature of this treatment, Na at GBS remained mobile while diffusion within the bulk was too slow for Na removal from the grain interiors. Changes in electrical properties were evaluated using conductivity and Seebeck coefficient measurements, with both decreasing as Na was removed to reach values similar to Na-free controls samples. This can be explained by the compensation of donor defects by Na, causing an increase in the free carrier concentration. Devices showed a decrease in open-circuit voltage after Na removal confirming that the beneficial effects of GB Na. The findings of this project will provide guidance for rational optimization of Na incorporation procedures in the manufacturing of CIGS solar cells. While it is known that Na segregates at CIGS GBs, the nature and role of Na diffusion into grain interiors was less clear. In Task 2, single crystal CuInSe 2 was used as a model system to represent the grain interiors of CIGS. Crystals processed by two different methods of different compositions and dislocation densities, were evaluated. Diffusion coefficients were obtained at two temperatures after Na diffusion, giving near identical values, ~2x10 11 cm 2 /s and ~6x10 11 cm2/s at 420°C and 480°C, respectively, for each crystal. Characterization confirmed that dislocation densities were too low to significantly impact the effective diffusion coefficient. The Cu-poor crystal had a higher solubility suggesting that Na diffusion is mediated by Cu-vacancies, but was not accompanied by an expected increase in diffusion coefficient. The activation energy for diffusion was similar to values expected for interstitial diffusion, but the large size of Na + ions should result in a solubility that is much lower than what was experimentally measured. A hybrid interstitial-substitutional mechanism is proposed that combines the fast diffusion of interstitial atoms with the high solubility common for substitutional impurities. Lattice diffusion of Na proceeds fast enough that CIGS grain interiors will have Na concentrations near the solubility limit of 1018 cm -3 when manufactured under standard conditions. Na and K treated epitaxial CIS films showed a significant increase in cathodoluminescence emission intensity, indicating a reduction of non-radiative recombination pathways, which is consistent with improvements in CIGS device performance, though the mechanism is not clear. Pathways forward: Despite the success of this project, there are a number of questions remaining related to further the understanding of the chemistry of Na in CIGS films and devices. These include further elucidation of the mechanisms of Na passivation in CIGS GBs, with identification of which defects are involved and confirmation of the possible effects of in-grain Na on device performance. To complete analysis of the cell structure, conformation of the presence and possible chemistries of Na at the CIGS/CdS junction and/or in the front transparent contacts, and its effects on device performance, is needed.

14 SOLAR ENERGY↗
DOE OSTI2019

Short- and Intermediate-Range Structure and Dynamics of Fe-Ni-C Liquid Under Compression

Properties of liquid Fe alloys under high-pressure conditions are crucial for understanding the composition, thermal state, and dynamics of Earth’s core. Experiments on such liquids, however, are often performed under pressures far below those of the outer core, necessitating long extrapolations of experimental results to core conditions. Such estimates can be complicated by light elements possibly forming pressure-dependent molecular clusters that can significantly affect the physical properties of liquids as core conditions are approached. First-principles molecular dynamics simulations were employed to compute the properties of an Fe-Ni-C liquid with a composition of Fe 3.7 Ni 0.37 C at 1673 K and pressures from 0 to 67 GPa to benchmark computational methods on pressure effects on the structure and properties of the liquid relative to low pressure experimental results. The short-range structure is manifested by the coordination number (CN) of Fe/Ni-Fe/Ni being around 12, indicative of a nearly close-packed structure in the pressure range, and the CN of C-Fe/Ni gradual increasing from 6.5 to 8.5, indicative of an approximately octahedral to cubic transition as pressure increases. The Fe/Ni-Fe/Ni bond distance, however, is found to be 10 times more compressible than the C-Fe/Ni distance. The intermediate-range structure of Fe/Ni-Fe/Ni and C-Fe/Ni subsystems, described by a partial configurationally decomposed distribution function, undergoes substantial changes, characterized by a significant increase of the number of polyhedra that share 3 atoms with each other. Such dense configurations are related to an increased bulk modulus, decreased diffusion coefficient, decreased activation volume for diffusion, and increased shear viscosity. Reproducing the experimental observations at low pressures provides important support for modeling the liquid under the conditions relevant to the outer core.

58 GEOSCIENCES↗
NASA NTRS1977

Kinetics data for diffusion of outgas species from RTV 560

A detailed analytical and experimental study was made of the outgassing behavior of RTV 560 silicone rubber. The four outgas species which predominate in the temperature range of 285 K to 425 K were separately identified. The initial concentration of these species in the parent material and their bulk volatilities were determined. The diffusion coefficients and activation energy for diffusion of the two major species were deduced from outgassing rate data. It is shown that by using these data in a diffusion theory model, the outgassing rates of these major species can be predicted for arbitrary geometry and any temperature within the range studied.

Liu, C. K.↗
NASA NTRS1984

Identification and control of structures in space

The derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE) is reported and the equations of motion of a similar structure orbiting the earth are also derived. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is proposed whereby the quantities defining the rigid-body maneuver are assumed to be relatively large, with the elastic deformations and deviations from the rigid-body maneuver being relatively small. The perturbation equations have the form of linear equations with time-dependent coefficients. An active control technique can then be formulated to permit maneuvering of the spacecraft and simultaneously suppressing the elastic vibration.

Meirovitch, L.↗
NASA NTRS1985

Maneuvering of flexible spacecraft with application to SCOLE

This paper is concerned with the derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE). For future reference, the equations of motion of a similar structure orbiting the earth are also derived. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is presented where the quantities defining the rigid-body maneuver are assumed to be relatively large, with the elastic deformations and deviations from the rigid-body maneuver being relatively small. The perturbation equations have the form of linear, non-self-adjoint equations with time-dependent coefficients. An active control technique can then be formulated to permit maneuvering of the spacecraft and simultaneously suppressing the elastic vibration.

Meirovitch, L.↗
NASA NTRS1989

Analysis of finite phased arrays of circular microstrip patches

A method is presented for analyzing a finite planar array of circular microstrip patches fed by coaxial probes. The self- and mutual impedances between array elements are calculated using the method of moments with the dyadic Green's function for a dielectric layer on a ground plane. The patch circuits are determined by using the reaction integral equation. The active input impedance as well as the active element pattern of the array are computed from a knowledge of the resultant patch currents. The calculated results for two-element and eight-element linear arrays are in good agreement with experimental data. The active reflection coefficient and element pattern for the center and edge elements of a two-dimensional array as a function of scan angle are also presented.

Deshpande, Manohar D.↗
NASA NTRS2002

NASA IKONOS Characterization Methodologies

The objectives of IKONOS characterization are to: 1) Perform spatial characterization by measuring edge response of IKONOS images to evaluate Modulation Transfer Function (MTF); 2) Perform geolocational accuracy assessment of IKONOS imagery using surveyed geodetic targets; 3) Perform radiometric vicarious calibrations of IKONOS imagery and compare with Space Imaging calibration coefficients. Calibration activities conducted in West Texas, and at Stennis Space Center, Mississippi and Lunar Lake, Nevada are profiled in this viewgraph presentation.

Pagnutti, Mary↗
NASA NTRS2009

UAVSAR Phased Array Aperture

This paper describes the development of a patch antenna array for an L-band repeat-pass interferometric synthetic aperture radar (InSAR) instrument that is to be flown on an unmanned aerial vehicle (UAV). The antenna operates at a center frequency of 1.2575 GHz and with a bandwidth of 80 MHz, consistent with a number of radar instruments that JPL has previously flown. The antenna is designed to radiate orthogonal linear polarizations in order to facilitate fully-polarimetric measurements. Beam-pointing requirements for repeat-pass SAR interferometry necessitate electronic scanning in azimuth over a range of -20degrees in order to compensate for aircraft yaw. Beam-steering is accomplished by transmit/receive (T/R) modules and a beamforming network implemented in a stripline circuit board. This paper, while providing an overview of phased array architecture, focuses on the electromagnetic design of the antenna tiles and associated interconnects. An important aspect of the design of this antenna is that it has an amplitude taper of 10dB in the elevation direction. This is to reduce multipath reflections from the wing that would otherwise be detrimental to interferometric radar measurements. This taper is provided by coupling networks in the interconnect circuits as opposed to attenuating the output of the T/R modules. Details are given of material choices and fabrication techniques that meet the demanding environmental conditions that the antenna must operate in. Predicted array performance is reported in terms of co-polarized and crosspolarized far-field antenna patterns, and also in terms of active reflection coefficient.

Unmanned Aerial Vehicle (UAV)↗
DOE OSTI2026

Affinity and Treatment of LDR Organics in Low Activity Waste by Cementitious Materials – 26109

The physiochemical interactions between organic contaminants, minerals, and polymer additives in grout/cementitious materials are being identified. This research supports a proposed Resource Conservation and Recovery Act (RCRA) treatment variance relevant to the Land Disposal Restriction (LDR) organics present in Hanford tank waste. It provides the technical basis to address the aspects documented by the Environmental Protection Agency in a draft memo necessary to establish that organics can be immobilized/stabilized in a cementitious matrix. The organic species may interact with cementitious minerals, including slag, fly ash, cement, and other components/dopants like activated carbon. A list of 132 reasonably expected LDR organics associated with Hanford tank waste (RPP-RPT-63493, Rev 1a) was screened by functional groups, octanol-water partitioning coefficients, and detection frequency in Hanford tank waste samples. A subset of 15 compounds spanning the identified properties was tested using sorption and leachate tests. These compounds were subjected to traditional batch sorption tests and leaching tests on/from Cast Stone cementitious material with and without activated carbon (a potential organic adsorption additive). The interactions between organic compounds were observed in traditional batch sorption and modified TCLP leachate tests for surrogate Cast Stone material with and without activated carbon addition. Specifically, phthalic acid (negatively charged) and 4-chloroaniline (polar) sorbed strongly to unmodified Cast Stone, while a group of three phenolic compounds (2,4,6-Trichlorophenol, Pentachlorophenol, o-Cresol) sorbed to and were retained by Cast Stone with a 1% activated carbon amendment. Mixtures of these compounds demonstrated visible retention of the organics within the matrix with a quantifiable affinity of the organics to the cement. This novel testing supports the notion that organics within Hanford tank waste would be retained onto the cement phase with the addition of simple materials easily added to the formulation as part of the treatment process. To further provide additional support to this claim, models employing Flory-Huggins theory in conjunction with macromolecular and organic molecule solubility parameters and species activity coefficients are being utilized to better understand these interactions. Within this context, Van Krevelen (VK) and Hansen organic and polymer solubility parameters were used to inform the Flory-Huggins interaction parameter, allowing for a quantifiable method of evaluating polymer-solvent compatibility and, by extension, interactions with proposed binding additives (e.g., activated carbon). These models and measurement should test the hypothesis for our systems understanding and applicability of Flory-Huggins theory, and whether the prediction of organics in the polymer phase versus the aqueous phase can be confidently made using this strategy. The estimation of the organic molecular activity coefficient in these high salt-saturated aqueous systems is another factor that will be assessed. This project aims to predict and understand complicated organic interactions in these heterogenous systems, guiding optimal treatment and stabilization methodologies.

Jolin, Will [Savannah River National Laboratory (S↗
DOE OSTI2017

The frequency-dependent response of single aerosol particles to vapour phase oscillations and its application in measuring diffusion coefficients

A new method for measuring diffusion in the condensed phase of single aerosol particles is proposed and demonstrated. The technique is based on the frequency-dependent response of a binary particle to oscillations in the vapour phase of one of its chemical components. Here, we discuss how this physical situation allows for what would typically be a non-linear boundary value problem to be approximately reduced to a linear boundary value problem. For the case of aqueous aerosol particles, we investigate the accuracy of the closed-form analytical solution to this linear problem through a comparison with the numerical solution of the full problem. Then, using experimentally measured whispering gallery modes to track the frequency-dependent response of aqueous particles to relative humidity oscillations, we determine diffusion coefficients as a function of water activity. The measured diffusion coefficients are compared to previously reported values found using the two common experiments: (i) the analysis of the sorption/desorption of water from a particle after a step-wise change to the surrounding relative humidity and (ii) the isotopic exchange of water between a particle and the vapour phase. The technique presented here has two main strengths: first, when compared to the sorption/desorption experiment, it does not require the numerical evaluation of a boundary value problem during the fitting process as a closed-form expression is available. Second, when compared to the isotope exchange experiment, it does not require the use of labeled molecules. Therefore, the frequency-dependent experiment retains the advantages of these two commonly used methods but does not suffer from their drawbacks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗