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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Interaction energy and isosteric heat of adsorption between hydrogen and magnesium diboride

Hydrogen storage materials form a crucial research topic for future energy utilization employing hydrogen and among those of interest magnesium diboride (MgB 2 ) has shown its prevalence. In this study, a first-principles analytical adsorption model of one hydrogen molecule in the vicinity of various magnesium diboride crystal surfaces was developed in order to obtain surface thermodynamic properties as a function of molecular and lattice properties. Henry's law constant (K H ) and isosteric heat of adsorption (ΔH ads ) indicators of the affinity between a gaseous molecule and a solid surface are thus calculated. The results in this paper not only address questions pertaining to the first stage of hydrogen storage processes but also advance the understanding of physisorption thermodynamics of a neutral molecule (H 2 ) coming in contact with a layered metallic-like surface (MgB 2 ). Although the model is built from a framework of classical calculations, quantum effects are incorporated as the fractional charge of the ions on the free surfaces, which is essential for the calculation of analytic thermodynamic values that approximate calculations from other methods. To benchmark our theoretical models, periodic density functional calculations were performed to determine the interactions between H 2 and different MgB 2 surfaces from first-principles. By considering both the top and sublayers of MgB 2 in calculating interaction energy, we have analytically and computationally calculated the interaction energies of H 2 molecules and MgB 2 's terminated planes, and witnessed the strong dependence of interaction energies on surface charges. We have also observed a dipole flipping phenomenon which explains the discontinuity seen in the interaction energy graph of Mg(0001). Both analytical and computational results showed heat of adsorption at zero coverage varying at a very low range (<7 kJ mol -1 ).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field

We investigate the physics of charged-particle acceleration at spherical shocks moving into a uniform plasma containing a turbulent magnetic field with a uniform mean. This has applications to particle acceleration at astrophysical shocks, most notably, to supernovae blast waves. We numerically integrate the equations of motion of a large number of test protons moving under the influence of electric and magnetic fields determined from a kinematically defined plasma flow associated with a radially propagating blast wave. Distribution functions are determined from the positions and velocities of the protons. The unshocked plasma contains a magnetic field with a uniform mean and an irregular component having a Kolmogorov-like power spectrum. The field inside the blast wave is determined from Maxwell’s equations. The angle between the average magnetic field and unit normal to the shock varies with position along its surface. It is quasi-perpendicular to the unit normal near the sphere’s equator, and quasi-parallel to it near the poles. We find that the highest intensities of particles, accelerated by the shock, are at the poles of the blast wave. The particles “collect” at the poles as they approximately adhere to magnetic field lines that move poleward from their initial encounter with the shock at the equator, as the shock expands. The field lines at the poles have been connected to the shock the longest. We also find that the highest-energy protons are initially accelerated near the equator or near the quasi-perpendicular portion of the shock, where the acceleration is more rapid.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SU-E-J-238: First-Order Approximation of Time-Resolved 4DMRI From Cine 2DMRI and Respiratory-Correlated 4DMRI

Purpose: Cine 2DMRI is useful in MR-guided radiotherapy but it lacks volumetric information. We explore the feasibility of estimating timeresolved (TR) 4DMRI based on cine 2DMRI and respiratory-correlated (RC) 4DMRI though simulation. Methods: We hypothesize that a volumetric image during free breathing can be approximated by interpolation among 3DMRI image sets generated from a RC-4DMRI. Two patients’ RC-4DMRI with 4 or 5 phases were used to generate additional 3DMRI by interpolation. For each patient, six libraries were created to have total 5-to-35 3DMRI images by 0–6 equi-spaced tri-linear interpolation between adjacent and full-inhalation/full-exhalation phases. Sagittal cine 2DMRI were generated from reference 3DMRIs created from separate, unique interpolations from the original RC-4DMRI. To test if accurate 3DMRI could be generated through rigid registration of the cine 2DMRI to the 3DMRI libraries, each sagittal 2DMRI was registered to sagittal cuts in the same location in the 3DMRI within each library to identify the two best matches: one with greater lung volume and one with smaller. A final interpolation between the corresponding 3DMRI was then performed to produce the first-order-approximation (FOA) 3DMRI. The quality and performance of the FOA as a function of library size was assessed using both the difference in lung volume and average voxel intensity between the FOA and the reference 3DMRI. Results: The discrepancy between the FOA and reference 3DMRI decreases as the library size increases. The 3D lung volume difference decreases from 5–15% to 1–2% as the library size increases from 5 to 35 image sets. The average difference in lung voxel intensity decreases from 7–8 to 5–6 with the lung intensity being 0–135. Conclusion: This study indicates that the quality of FOA 3DMRI improves with increasing 3DMRI library size. On-going investigations will test this approach using actual cine 2DMRI and introduce a higher order approximation for improvements. This study is in part supported by NIH (U54CA137788 and U54CA132378)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Continuation of probability density functions using a generalized Lyapunov approach

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

What is a parton shower?

We consider idealized parton shower event generators that treat parton spin and color exactly, leaving aside the choice of practical approximations for spin and color. We investigate how the structure of such a parton shower generator is related to the structure of QCD. We argue that a parton shower with splitting functions proportional to ${{\alpha}}_{\mathrm{s}}$ can be viewed not just as a model, but as the lowest order approximation to a shower that is defined at any perturbative order. To support this argument, we present a formulation for a parton shower at order ${{\alpha}}_{\mathrm{s}}^{k}$ for any $k$. Since some of the input functions needed are specified by their properties but not calculated, this formulation does not provide a useful recipe for an order ${{\alpha}}_{\mathrm{s}}^{k}$ parton shower algorithm. However, in this formulation we see how the operators that generate the shower are related to operators that specify the infrared singularities of QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Evolution of Chain Dynamics and Oxidation States with Increasing Chain Length for a Donor–Acceptor-Conjugated Oligomer Series

While it is known that the chain length strongly affects the properties of π-conjugated polymers, the effects of chain length on the molecular structure, chain conformation, and oxidation state properties in donor–acceptor-type conjugated structures remain unclear. This limits our understanding of how the polymer molecular weight impacts material properties. Here, a discrete and monodisperse oligomer series (n = 3, 5, 7, 9, 15, and 21) and polymers (nPB), composed of the donor 3,4-propylenedioxythiophene (ProDOT), the acceptor benzothiadiazole (BTD), and methylthio end-capping groups, are synthesized by C–H-activated cross-coupling. The molecular structure, molecular weight, and dispersity of each oligomer/polymer are thoroughly characterized by nuclear magnetic resonance spectroscopy, mass spectrometry, and gel permeation chromatography. This series reveals a rod-to-coil transition at n = 15 and coil formation at polymer length scales of ~28 units via solution small-angle neutron scattering characterization. The oxidation states are deciphered via cyclic voltammetry, differential pulse voltammetry, spectroelectrochemistry, and density functional theory calculations. Oligomers 3–9 undergo successive one-electron oxidation steps, while 15 and higher undergo multielectron oxidations per step in CH 2 Cl 2 –TBAPF6 at a Pt ultramicroelectrode. The electronic transition of each oxidation state (1+, 2+, 3+, etc.) is tracked by absorption spectroscopy, revealing a “bipolaron to di-polaron” transition at n = 7 at which shorter oligomers prefer bipolaron formation and longer oligomers prefer di-polaron formation in their dication states. Furthermore, oxidized 15 has a lower electronic transition energy compared to its polymer homologue, as shown by spectroelectrochemistry, revealing a synergy between the chain length and the oxidation state properties. This study proves that the convergence limit between small molecule and polymer behavior occurs at approximately 15 units and highlights the property transitions that occur as a function of chain length for a donor–acceptor class of conjugated organic materials.

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

Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Proposal for Universality in the Viscosity of Metallic Liquids

The range of magnitude of the liquid viscosity, η, as a function of temperature is one of the most impressive of any physical property, changing by approximately 17 orders of magnitude from its extrapolated value at infinite temperature (η o ) to that at the glass transition temperature, T g . We present experimental measurements of containerlessly processed metallic liquids that suggest that log(η/η o ) as a function of T A /T is a potentially universal scaled curve. In stark contrast to previous approaches, the scaling requires only two fitting parameters, which are on average predictable. The temperature T A corresponds to the onset of cooperative motion and is strongly correlated with T g , suggesting that the processes underlying the glass transition first appear in the high temperature liquid.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Assessment of TD-DFT and LF-DFT for study of d − d transitions in first row transition metal hexaaqua complexes

Herein, we present the systematic, comparative computational study of the d − d transitions in a series of first row transition metal hexaaqua complexes, [M(H{sub 2}O){sub 6}]{sup n+} (M{sup 2+/3+} = V {sup 2+/3+}, Cr{sup 2+/3+}, Mn{sup 2+/3+}, Fe{sup 2+/3+}, Co{sup 2+/3+}, Ni{sup 2+}) by the means of Time-dependent Density Functional Theory (TD-DFT) and Ligand Field Density Functional Theory (LF-DFT). Influence of various exchange-correlation (XC) approximations have been studied, and results have been compared to the experimental transition energies, as well as, to the previous high-level ab initio calculations. TD-DFT gives satisfactory results in the cases of d{sup 2}, d{sup 4}, and low-spin d{sup 6} complexes, but fails in the cases when transitions depend only on the ligand field splitting, and for states with strong character of double excitation. LF-DFT, as a non-empirical approach to the ligand field theory, takes into account in a balanced way both dynamic and non-dynamic correlation effects and hence accurately describes the multiplets of transition metal complexes, even in difficult cases such as sextet-quartet splitting in d{sup 5} complexes. Use of the XC functionals designed for the accurate description of the spin-state splitting, e.g., OPBE, OPBE0, or SSB-D, is found to be crucial for proper prediction of the spin-forbidden excitations by LF-DFT. It is shown that LF-DFT is a valuable alternative to both TD-DFT and ab initio methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Griffin: A MOOSE-based reactor physics application for multiphysics simulation of advanced nuclear reactors

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor physics application for multiphysics simulations of advanced reactor designs jointly developed by Idaho National Laboratory and Argonne National Laboratory. This paper summarizes the motivation, significance, architecture, design, and features of Griffin. Griffin offers flexible and extensible features to address the challenges associated with advanced reactor designs. These features range from fundamental particle transport to specific reactor physics tasks. The features cover a wide range including on-the-fly and traditional two-step cross-section generation methods, steady-state and transient transport solvers suitable for both heterogeneous and homogeneous models, high-fidelity depletion where thousands of isotopes can be tracked and low-fidelity depletion characterized by burnup, etc. The most fundamental aspect that sets Griffin apart from other reactor analysis codes is that it is developed based on the MOOSE framework. A modular development approach is strongly enforced, with multiphysics being an essential element considered since the beginning of Griffin’s development. Griffin links various MOOSE physics modules and couples to other MOOSE-based applications and non-MOOSE-based applications for multiphyiscs simulations. Griffin includes three modules: ISOXML for preparing and managing multigroup cross sections, radiation transport for solving the neutron transport equation, and reactor analysis for user-oriented reactor physics analysis functionalities. Griffin uses various finite element methods for spatial discretization, multigroup approximation for energy discretization and discrete ordinates method, spherical harmonics expansion method, and diffusion approximation for streaming direction discretization to solve the neutron transport equation. Griffin’s flexibility is evidenced through Griffin’s various applications to fast reactor, high-temperature reactor, pebble bed reactor, molten salt reactor, and microreactor designs. Griffin development follows the software quality assurance procedure for MOOSE-based applications and with software requirements consistent with the ASME NQA-1 standard. Griffin has been adopted into the reactor analysis system for the U.S. NRC and is in use at U.S. companies, universities and national laboratories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Learning high-dimensional parametric maps via reduced basis adaptive residual networks

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error estimates. A scalable neural network learning framework is thus to learn the nonlinear compressed reduced basis mapping. Unlike the reduced basis construction, however, neural network constructions are not guaranteed to reduce errors by adding representation power, making it difficult to achieve good practical performance. Inspired by recent approximation theory that connects ResNets to sequential minimizing flows, we present an adaptive ResNet construction algorithm. This algorithm allows for depth-wise enrichment of the neural network approximation, in a manner that can achieve good practical performance by first training a shallow network and then adapting. We prove universal approximation of the associated neural network class for $L^2_v$ functions on compact sets. Our overall framework allows for constructive means to detect appropriate breadth and depth, and related compact parametrizations of neural networks, significantly reducing the need for architectural hyperparameter tuning. Numerical experiments for parametric PDE problems and a 3D CFD wing design optimization parametric map demonstrate that the proposed methodology can achieve remarkably high accuracy for limited training data, and outperformed other neural network strategies we compared against.

42 ENGINEERING↗
DOE OSTI2020

Tight-binding study of beryllium

In this work, we have applied the Naval Research Laboratory Tight-binding (NRL-TB) Method to the hcp alkaline-earth metal Beryllium. This approach consists of fitting to energy band and total energy data generated by the Linearized Augmented Plane Wave (LAPW) for the fcc, bcc, sc, and hcp structures as a function of volume. First, we found that using the Generalized Gradient Approximation (GGA) for the input data secures a better agreement to experimental volumes than the LDA. Second, we found that including small volumes to the fit is needed to get TB parameters that are transferable enough to successfully predict the energies of structures that were not fitted, and to perform molecular dynamics (MD) simulations. The non-orthogonal Hamiltonian obtained, is successful in correctly predicting the hcp lattice as the ground state of Be and finding eight other structures, that were not fitted to LAPW, positioned at higher energies. In addition, the NRL-TB produces accurate energy bands, densities of states, elastic constants, the Bain path and several quantities derived from MD simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Mobilities of polydisperse hard spheres near a no-slip wall

In the article, we have derived an analytical formulation for far-field hydrodynamic interactions among unequal size hard spheres near a no-slip wall and have implemented the formulation in a Stokesian dynamics model to simulate a suspension of polydisperse particles in a semi-bounded domain. The formulation is based on the multipole expansion of the boundary integral of Stokes flow, and the mobility tensors are deduced from Fáxen’s law together with Green’s function for Stokes flow near a no-slip wall. Lubrication approximation is incorporated to account for the close-distance interactions between any two particles and also between the particles and the wall. The implementation is validated against previous formulations for equal size particles and against a boundary-element code for unequal size particles. The code can be used to simulate the Stokesian or Brownian interaction of unequal particles in presence of a no-slip wall. In the current study, we applied the Stokesian dynamics model to investigate the trajectories of two unequal hard spheres and their redistribution during sedimentation parallel to a wall. We further used it to demonstrate the cases of many-particle sedimentation toward or parallel to a wall.

catalysis (heterogeneous)↗
DOE OSTI2019

Investigating the role of water on CO2-Utica Shale interactions for carbon storage and shale gas extraction activities – Evidence for pore scale alterations

In this work, we probed the physical and chemical alteration of the carbonate-rich Utica Shale following CO 2 exposure when thin films of water were present at the shale surface. All reaction conditions were examined at 40 °C and CO 2 pressures up to 10.3 MPa for 14 days. CO 2 dissolution in the water layer at 2342 cm -1 and carbonate dissolution and precipitation at 1424, 874, and 712 cm -1 were discerned with in-situ Fourier Transform infrared spectroscopy (FT-IR). Significant etching and pitting from exposure to CO 2 and water were observed with feature relocation scanning electron microscopy (SEM). Application of the density function theory (DFT) for pore size analysis showed that micropores between approximately 0.9 and 2 nm disappeared while the mesopore volume increased after dissolution of carbonate. These results may provide new insights that carbonate rich shales such as the Utica may have a greater potential for alterations of pore space due to the reactivity of CO 2 which may affect 1) how CO 2 storage in shale formations plays a role in Carbon Capture and Storage (CCS) activities, 2) if CO 2 can be utilized as a potential fracturing agent, and 3) whether CO 2 is an effective fluid for enhanced hydrocarbon extraction.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗
DOE OSTI2016

Energetic, electronic and optical properties of lanthanide doped TiO{sub 2}: An ab initio LDA+U study

Substitutional energies, thermodynamic charge transition levels and optical properties of lanthanide doped anatase TiO{sub 2} has been investigated using local density approximation with the Hubbard U correction (LDA+U) within the density functional theory formalism. All the lanthanides apart from La introduced impurity states in the host band gap on doping. The calculated substitutional energies indicate that it is possible to dope TiO{sub 2} with lanthanide ions. The optimal doping percentage was predicted to be ~3% and dopant levels resulting from Ce, Nd, Sm, Gd and Tm doping were found to possess negative U characteristics. In addition the calculated thermodynamic transition levels predicted Lu as not having any possible charge transitions within the host band gap. The calculated optical absorption coefficients indicate that lanthanide doping led to optical absorption in the visible regime. - Graphical abstract: Crystal structure of doped Sm doped TiO{sub 2} (RHS). Calculated PDOS and absorption spectra of Sm doped TiO{sub 2}. - Highlights: • Lanthanide doping significantly improved the optical properties of anatase TiO{sub 2}. • Lanthanide doping led to emission in the visible regions of the optical spectrum. • La, Ce, Pm, Sm, Eu, Gd, Tm, Yb and Lu doping gave good photocatalytic properties. • The optimum doping concentration in anatase TiO{sub 2} was found to be 2.78%.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Catalyzed oxidation of IG-110 nuclear graphite by simulated fission products Ag and Pd nanoparticles

To evaluate the stability of nuclear materials in high temperature gas reactors under air ingress conditions, catalytic oxidation of IG-110 graphite by two simulated fission products, metallic Pd and Ag, was studied in oxidative atmosphere and at temperatures up to 1000°C using an integrated furnace, mass spectroscopy and infrared spectroscopy system. Transmission electron microscopy and X-ray diffraction studies show that Pd and Ag nanoparticles were successfully introduced onto powdery IG-110 graphite through an impregnation and subsequent heat-treatment process. The combined mass spectroscopy and infrared spectroscopy methods allow simultaneous analysis of two gaseous products, CO and CO 2 , and separate measurements of activation energy for their formation reactions. It was found that the introduction of Pd or Ag to IG-110 graphite substantially catalyzed the oxidation of graphite, characteristic of decreased onset temperatures for the oxidation of graphite. Moreover, the catalytic effects by Pd and Ag are considerably different based on measured concentration ratios of CO 2 to CO as a function of oxidation temperatures. Ag makes the graphite oxidation commence at approximately 400°C with CO 2 being the dominant product. In contrast, Pd significantly increases the concentration ratio of CO 2 to CO at temperatures higher than approximately 690°C, although it decreases the onset temperature for the oxidation reaction to around 525°C. To understand the catalytic difference, the mechanism of the graphite oxidation was discussed based on the changes of surface oxygen species on Ag and Pd.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Probing Exciton Diffusion and Dissociation in Single-Walled Carbon Nanotube-C60 Heterojunctions

The efficiency of thin-film organic photovoltaic (OPV) devices relies heavily upon the transport of excitons to type-II heterojunction interfaces, where there is sufficient driving force for exciton dissociation and ultimately the formation of charge carriers. Semiconducting single-walled carbon nanotubes (SWCNTs) are strong near-infrared absorbers that form type-II heterojunctions with fullerenes such as C60. Although the efficiencies of SWCNT-fullerene OPV devices have climbed over the past few years, questions remain regarding the fundamental factors that currently limit their performance. In this study, we determine the exciton diffusion length in the C60 layer of SWCNT-C60 bilayer active layers using femtosecond transient absorption measurements. We demonstrate that hole transfer from photoexcited C60 molecules to SWCNTs can be tracked by the growth of narrow spectroscopic signatures of holes in the SWCNT 'reporter layer'. In bilayers with thick C60 layers, the SWCNT charge-related signatures display a slow rise over hundreds of picoseconds, reflecting exciton diffusion through the C60 layer to the interface. A model based on exciton diffusion with a Beer-Lambert excitation profile, as well as Monte Carlo simulations, gives the best fit to the data as a function of C60 layer thickness using an exciton diffusion length of approximately 5 nm.

14 SOLAR ENERGY↗

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