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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 1,513 records · Page 84
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Modeling study of a proposed field calibration source using K-40 and high-Z targets for sodium iodide detectors

Calibration sources based on the primordial isotope potassium-40 ( 40 K) have reduced controls on the source’s activity due to its terrestrial ubiquity and very low specific activity. Potassium–40’s beta emissions and 1,460.8 keV gamma ray can be used to induce K-shell fluorescence x rays in high-Z metals between 60 and 80 keV. A gamma ray calibration source that uses potassium chloride salt and a high-Z metal to create a two-point calibration for a sodium iodide field gamma spectroscopy instrument is thus proposed. The calibration source was designed in collaboration with the Sandia National Laboratory using the Monte Carlo N-Particle eXtended (MCNPX) transport code. Two methods of x-ray production were explored. First, a thin high-Z layer (HZL) was interposed between the detector and the potassium chloride-urethane source matrix. Second, bismuth metal powder was homogeneously mixed with a urethane binding agent to form a potassium chloride-bismuth matrix (KBM). The bismuth-based source was selected as the development model because it is inexpensive, nontoxic, and outperforms the high-Z layer method in simulation. As a result, based on the MCNPX studies, sealing a mixture of bismuth powder and potassium chloride into a thin plastic case could provide a light, inexpensive field calibration source.

40K↗
DOE OSTI2021

Modeling Volatility-Based Aerosol Phase State Predictions in the Amazon Rainforest

Organic aerosol (OA) is a complex matrix of various constituents—fresh (primary organic aerosols—POA) and aged via oxidation (secondary organic aerosols—SOA), generated from biogenic, anthropogenic, and biomass burning sources. The viscosity of OA can be critical in influencing new particle formation, reactive uptake processes that impact evaporation-growth kinetics, and the lifetime of particles in the atmosphere. We report this work utilizes a well-defined relationship between volatility and viscosity for pure compounds, which we incorporated within the Weather Research and Forecasting Model coupled to chemistry (WRF-Chem) to simulate the phase state and viscosity of bulk OA during the dry-to-wet transition season (September–October) in the Amazon rainforest during 2014. Our simulations indicate spatial and temporal heterogeneity in aerosol phase state often not captured by global-scale models. We show the strong role of water associated with organic aerosol ($w_s$) as the dominant factor that can be used to quantitatively estimate OA viscosity. Analysis of WRF-Chem simulations across the entire atmospheric column indicates a strong inverse log-linear relationship between $w_s$ and OA viscosity with a correlation coefficient approaching 1, in the background and biomass burning-influenced conditions. At high altitudes where relative humidity (RH) and temperatures are low, our simulations indicate that OA exists in a semisolid-/solid-like phase state, consistent with previous studies. OA hygroscopicity is strongly correlated (ca. –0.8) with OA viscosity at RH ca. 30–50%, but this RH range is found mostly at low OA concentrations and the middle troposphere (ca. 6–10 km altitudes) in our simulated domain. OA hygroscopicity is uncorrelated with viscosity at higher-RH (near surface) and lower-RH (upper troposphere) regimes. At the urban site near surface, where day–night differences in RH are significant, RH is found to drive the phase state. At the background forested site near surface, where day–night RH differences are small, biomass burning-influenced OA is semisolid and a significant OA associated with background conditions is liquid-like. Simulations indicate a long tail of OA viscosity frequency distributions extending in the semisolid/solid regimes over background biogenic-influenced conditions due to the role of low-volatility OA components such as monoterpene oxidation products.

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

Modeling elasto-viscoplasticity in a consistent phase field framework

Existing continuum level phase field plasticity theories seek to solve plastic strain by minimizing the shear strain energy. However, rigorously speaking, for thermodynamic consistency it is required to minimize the total strain energy unless there is proof that hydrostatic strain energy is independent of plastic strain which is unfortunately absent. In this work, we extend the phase-field microelasticity theory of Khachaturyan et al. by minimizing the total elastic energy with constraint of incompressibility of plastic strain. We show that the flow rules derived from the Ginzburg-Landau type kinetic equation can be in line with Odqvist's law for viscoplasticity and Prandtl-Reuss theory. Free surfaces (external surfaces or internal cracks/voids) are treated in the model. Deformation caused by a misfitting spherical precipitate in an elasto-plastic matrix is studied by large-scale three-dimensional simulations in four different regimes in terms of the matrix: (a) elasto-perfectly-plastic, (b) elastoplastic with linear hardening, (c) elastoplastic with power-law hardening, and (d) elasto-perfectly-plastic with a free surface. The results are compared with analytical/numerical solutions of Lee et al. for (a-c) and analytical solution derived in this work for (d). Additionally, the J integral of a fixed crack is calculated in the phase-field model and discussed in the context of fracture mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Scaling dynamics in low-salt-rejection reverse osmosis for high-salinity produced water desalination: Mechanistic modeling and membrane autopsy

Membrane scaling remains a critical barrier to the reliable operation of desalination systems, particularly for hypersaline produced water (PW) treatment. This study fills the knowledge gap of autopsy-based model validation for PW desalination by elucidating scaling mechanisms in a Low-Salt-Rejection Reverse Osmosis (LSRRO) system through the integration of pilot-scale experimentation and complementary modeling approaches. A semi-empirical modeling framework was developed and applied to a multistage pilot LSRRO system equipped with nanofiltration and RO membranes treating high-salinity PW from the Permian Basin. Water quality analysis showed that total dissolved solids decreased from ~130,000 mg/L to ~1900 mg/L in the permeate, then further reduced to ~300 mg/L by a second-pass RO. Two different thermodynamic modeling approaches were evaluated: the first extends the LSRRO framework by incorporating system complexity and scaling phenomena, whereas the second method explicitly captures concentration polarization in localized supersaturation. Both methods illustrate the tendency for carbonate and sulfate scaling throughout the stages. Membrane autopsies revealed a silica-dominated deposit matrix, localized CaSO 4 at Stage 2, and minor barite/celestite despite their prominence in model predictions. Quantum-chemical calculations indicated silica scaling can be rationalized by favorable adsorption of H 4 SiO 4 on Fe-oxide surfaces (ΔG ≈ −44 kJ/mol), providing a kinetic pathway for interfacial inorganic polymerization even when bulk equilibrium predictions are conservative. Overall, the thermodynamic scaling modeling and membrane autopsy revealed heterogeneous, localized deposits with limited impact on LSRRO performance, while quantum analysis rationalized the thermodynamically unfavorable precipitation formation under bulk equilibrium, reconciling model–autopsy discrepancies. These insights support targeted pretreatment and silica-specific antiscalants to extend membrane lifetime and increase recovery, providing a transferable framework for hypersaline water desalination systems. The combined experimental–computational approach provides new mechanistic insight into scaling in hypersaline membrane systems and establishes a transferable framework for predicting and mitigating scaling in next-generation desalination technologies.

Low-salt-rejection reverse osmosis↗
DOE OSTI2017

Measurements of the production cross section of a $Z$ boson in association with jets in pp collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

Measurements of the production cross section of a Z boson in association with jets in proton–proton collisions at √s = 13 TeV are presented, using data corresponding to an integrated luminosity of 3.16 fb –1 collected by the ATLAS experiment at the CERN Large Hadron Collider in 2015. Inclusive and differential cross sections are measured for events containing a Z boson decaying to electrons or muons and produced in association with up to seven jets with p T > 30 GeV and |y| < 2.5. Predictions from different Monte Carlo generators based on leading-order and next-to-leading-order matrix elements for up to two additional partons interfaced with parton shower and fixed-order predictions at next-to-leading order and next-to-next-to-leading order are compared with the measured cross sections. Good agreement within the uncertainties is observed for most of the modelled quantities, in particular with the generators which use next-to-leading-order matrix elements and the more recent next-to-next-to-leading-order fixed-order predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Distributed and communication-efficient solutions to linear equations with special sparse structure

In this paper we report two distributed and communication-efficient algorithms based on the multi-agent system are proposed to solve a system of linear equations with the Laplacian sparse system matrix. One algorithm is based on the gradient descent method in optimization. In this algorithm, the agents only share partial information instead of all of their collective state vectors to save significant communication. The other algorithm is obtained by approximating Newton’s method for a faster convergence rate. Although it requires twice as much communication as the first one, it is still communication-efficient given the low dimension of the information shared among agents. The convergence at a linear rate is proved for both algorithms, and a comprehensive comparison of their convergence rate, communication burden, and computation costs is also performed. The proposed algorithms can be applied to various systems to solve those problems that can be modeled as a system of linear equations with a Laplacian sparse system matrix. Simulation results with the electric power system illustrate their effectiveness.

42 ENGINEERING↗
DOE OSTI2021

Assessment the leaching characteristics and long-term leaching behavior of some radionuclides from synthesized zeolite cement matrix

Highlights: • Synthesis and characterization of zeolite cement synthesized from fly ash • Leaching tests were used to assess the release rate of {sup 85}Sr and {sup 60}Co radionuclides. • Simple mathematical models were used to detect leaching mechanisms. • Long-term leaching behavior of {sup 85}Sr and {sup 60}Co from cementitious matrix was assessed. The development of cementitious materials remains a vital goal to produce valuable products with good mechanical, physical and chemical properties suitable for the safe disposal of concentrated radionuclides resulted from the treatment of contaminated solutions. In this paper, zeolite cement with good properties was laboratory synthesized from industrial by-products fly ash and characterized using various characterization techniques. The leaching characteristics of strontium and cobalt radionuclides from the synthesized zeolite cement were scrutinized conforming with the standard leaching methodology of International Atomic Energy Authority (IAEA). A mechanical strength assessment was executed to characterize the extent of immobilization process of the solidified matrices. The cumulative leaching fraction (φ) of the two studied radionuclides was found to be less than 5% in all examined conditions, which implies the applicability of the IAEA-recommended methodology for estimating the diffusion coefficient. The experimental leaching data were regressed nonlinearly to various mathematical kinetic models to assess the controlling leaching mechanism and to determine the leaching parameters. The regression results indicated that strontium ({sup 85}Sr) and cobalt ({sup 60}Co) leaching resulted from two succeeding mechanisms: as first order kinetic reaction, and then diffusion. The calculated values of leachability indices signify that the performance of each of the studied matrices is within an acceptable range. A simplified mathematical model, rooted in the first order reaction and diffusion mechanisms, was simulated to predict the radionuclides leaching rates from zeolite cement matrices. By comparing the synthesized zeolite cement with other cementitious materials, it can be concluded that the synthesized material can be classified as an efficient material suitable to immobilize {sup 85}Sr and {sup 60}Co from radioactive wastes. The acquired findings demonstrated that the studied immobilized waste matrices have acceptable mechanical effectiveness.

36 MATERIALS SCIENCE↗
DOE OSTI2026

ReMU: regional minimal updating for model-based derivative-free optimization

Derivative-free optimization (DFO) problems are optimization problems where derivative information is unavailable or extremely difficult to obtain. Model-based DFO solvers have been applied extensively in scientific computing. Powell's NEWUOA (2004) [Powell, The NEWUOA software for unconstrained optimization without derivatives, in Large-Scale Nonlinear Optimization, Nonconvex Optimization and its Applications Vol. 83, G. Di Pillo and M. Roma, eds., Springer, 2006, pp. 255–297] and Wild's POUNDerS (2014) [Wild, Solving derivative-free nonlinear least squares problems with POUNDERS, in Advances and Trends in Optimization with Engineering Applications, T. Terlaky, M.F. Anjos, and S. Ahmed, eds., SIAM, 2017, pp. 529–540] explore the numerical power of the minimal norm Hessian (MNH) model for DFO and contributed to the open discussion on building better models with fewer data to achieve faster numerical convergence. Another decade later, we propose the regional minimal updating (ReMU) models, and extend the previous models into a broader class, including the H 2 norm models [Xie and Yuan, Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms, IMA J. Numer. Anal. 46 (2025), pp. 21–50]. This paper shows motivation behind ReMU models, computational details, theoretical and numerical results on particular extreme points and the barycentre of ReMU's weight coefficient region, and the associated KKT matrix error and distance. Novel metrics, such as the truncated Newton step error, are proposed to numerically understand the new models' properties. A new algorithmic strategy, based on iteratively adjusting the ReMU model type, is also proposed, and shows numerical advantages by combining and switching between the barycentric model and the classic least Frobenius norm model in an online fashion.

derivative-free trust-region methods↗
DOE OSTI2017

Relativistic R -matrix calculations for the electron-impact excitation of neutral molybdenum

A recent PISCES-B Mod experiment [Nishijima et al., J. Phys. B 43, 225701 (2010)] has revealed up to a factor of 5 discrepancy between measurement and the two existing theoretical models [Badnell et al., J. Phys. B 29, 3683 (1996); Bartschat et al., J. Phys. B 35, 2899 (2002)], providing important diagnostics for M O I . In the following paper we address this issue by employing a relativistic atomic structure and R -matrix scattering calculations to improve upon the available models for future applications and benchmark results against a recent Compact Toroidal Hybrid experiment [Hartwell et al., Fusion Sci. Technol. 72, 76 (2017)]. We determine the atomic structure of M O I using GRASP 0 , which implements the multiconfigurational Dirac-Fock method. Fine structure energies and radiative transition rates are presented and compared to existing experimental and theoretical values. The electron-impact excitation of M O I is investigated using the relativistic R -matrix method and the parallel versions of the Dirac atomic R -matrix codes. Electron-impact excitation cross sections are presented and compared to the few available theoretical cross sections. Throughout, our emphasis is on improving the results for the z 5 P$^{o}_{1, 2, 3}$ → a 5 S 2 , z 7 P$^{o}_{2, 3, 4}$ → a 7 S 3 and y 7 P$^{o}_{2, 3, 4}$ → a 7 S 3 electric dipole transitions of particular relevance for diagnostic work.

Smyth, R. T.↗
DOE OSTI2012

Discoidin domain receptor 2 (DDR2) regulates proliferation of endochondral cells in mice

Highlights: Black-Right-Pointing-Pointer Discoidin domain receptor 2 (DDR2) is a receptor tyrosine kinase. Black-Right-Pointing-Pointer DDR2 regulates cell proliferation, cell adhesion, migration, and extracellular matrix remodeling. Black-Right-Pointing-Pointer We produced in vitro and in vivo model to better understand the role of DDR2. Black-Right-Pointing-Pointer DDR2 might play an inhibitory role in the proliferation of chondrocyte. -- Abstract: Discoidin domain receptor 2 (DDR2) is a receptor tyrosine kinase that is activated by fibrillar collagens. DDR2 regulates cell proliferation, cell adhesion, migration, and extracellular matrix remodeling. The decrement of endogenous DDR2 represses osteoblastic marker gene expression and osteogenic differentiation in murine preosteoblastic cells, but the functions of DDR2 in chondrogenic cellular proliferation remain unclear. To better understand the role of DDR2 signaling in cellular proliferation in endochondral ossification, we inhibited Ddr2 expression via the inhibitory effect of miRNA on Ddr2 mRNA (miDdr2) and analyzed the cellular proliferation and differentiation in the prechondrocyte ATDC5 cell lines. To investigate DDR2's molecular role in endochondral cellular proliferation in vivo, we also produced transgenic mice in which the expression of truncated, kinase dead (KD) DDR2 protein is induced, and evaluated the DDR2 function in cellular proliferation in chondrocytes. Although the miDdr2-transfected ATDC5 cell lines retained normal differentiation ability, DDR2 reduction finally promoted cellular proliferation in proportion to the decreasing ratio of Ddr2 expression, and it also promoted earlier differentiation to cartilage cells by insulin induction. The layer of hypertrophic chondrocytes in KD Ddr2 transgenic mice was not significantly thicker than that of normal littermates, but the layer of proliferative chondrocytes in KD-Ddr2 transgenic mice was significantly thicker than that of normal littermates. Taken together, our data demonstrated that DDR2 might play a local and essential role in the proliferation of chondrocytes.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Exact relativistic expressions for polarization of incoherent Thomson scattering

We present a derivation of the degree of polarization for incoherent Thomson scattering (TS) using Mueller matrix formalism. An exact analytic solution is obtained for spectrum-integrated matrix elements. The solution is valid for the full range of incident polarizations, scattering angles, and electron thermal motion from non-relativistic to ultra-relativistic. It is based on a newly developed theoretical model, a finite transit time (FTT) correction to previous theoretical work on TS polarization. The Mueller matrix elements are substantially different from previous calculations without the FTT correction, even to the lowest linear order in T e =m e c 2 <<1. Mathematically, the derivation is a unique example of fully analytical integration of the 3D scattering operator over a relativistic Maxwellian distribution function; experimentally, the results have application to the use of the polarization properties of Thomson scattered light as a method of electron temperature measurement. The results can also be used as a reliable tool for benchmarking and verification of numerical codes for frequency resolved properties of TS polarization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Understanding grain boundary segregation under irradiation: A mesoscale modeling study

Grain boundaries (GBs) are an important component in the design of irradiation resistant materials as they play a crucial role as point defect sinks for non-equilibrium vacancies and self-interstitials. However, in the presence of sustained point defect fluxes, the coupled transport of atomic components with inherently different diffusivities often leads to radiation-induced segregation (RIS), with undesired effects on properties such as intergranular corrosion and stress-assisted cracking. In this talk, we investigate the fundamental mechanisms leading to GB segregation in BCC FeCr-based alloys using multiscale modeling and experiments. A phase-field model is employed to account for both thermodynamic and kinetic segregation mechanisms. The full Onsager transport matrix is derived using kinetic Monte Carlo, molecular dynamics, and kinetic cluster expansion (KineCluE) calculations. The thermodynamics of GB segregation is described via an atomic density-based modification to the CALPHAD free energy. The modeling predictions are then compared against segregation data from atom probe characterization for various temperatures, compositions, and neutron irradiation conditions. We will conclude by discussing the utility of the multiscale modeling approach to shed light on the fundamental mechanisms leading to solute-GB interaction.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microstructural development in DED stainless steels: applying welding models to elucidate the impact of processing and alloy composition

Austenitic stainless steel microstructures produced by directed energy deposition (DED)are analogous to those developed during welding, particularly high energy density welding. To better understand microstructural development during DED, theories of microstructural evolution,which have been established to contextualize weld microstructures, are applied in this study to microstructural development in DED austenitic stainless steels. Phenomenological welding models that describe the development of oxide inclusions, compositional microsegregation, ferrite,matrix austenite grains, and dislocation substructures are utilized to clarify microstructural evolution during deposition of austenitic stainless steels. Two different alloys, 304L and 316L, arecompared to demonstrate the broad applicability of this framework for understanding microstmctural development during the DED process. Despite differences in grain morphology and solidification mode for these two alloys (which can be attributed to compositional differences),similar tensile properties are achieved. It is the fine-scale compositional segregation and dislocation structures that ultimately determine the strength of these materials. The evolution of microsegregation and dislocation structures is shown to be dependent on the rapid solidification and thermomechanical history of the DED processing method and not the composition of the starting material.

36 MATERIALS SCIENCE↗
DOE OSTI2024

On the applicability of the Redlich-Kister framework for viscosity estimation of molten halide salt mixtures

For molten halide salt mixtures already being utilized or under consideration for carbon-free energy production systems, it is crucial that their viscosity is well understood so that system thermal hydraulics can be reliably assessed. Because of the difficulty in accurately measuring molten halide viscosity and the sheer size of the matrix of possible higher order salt mixtures that may be of interest to the energy industry, there are several gaps in the quantified understanding of molten halide viscosity across this matrix. As such, both first-principles and semi-empirical modeling techniques may be crucial for rapidly assessing this broad, complex compositional domain. Herein, the Redlich-Kister framework is applied to assess the feasibility of broadly interpolating and estimating the viscosity of several pseudobinary and pseudoternary molten halide salt systems that may be of key interest to the energy industry. The framework is based on the assumption that an ideal component and a nonideal component collectively describe the viscosity as a function of composition and temperature for a given molten halide system. Three different ideal models were considered for the ideal component, including Grunburg-Nissan, Katti-Chaudhri, and Gambill methods. Regarding the pseudobinary interpolations, the Redlich-Kister models with either the Grunburg-Nissan or Katti-Chaudhri models as the ideal component resulted in either highly (average error less than 5%) or reasonably (average error less than 15%) accurate interpolations of pseudobinary halide viscosity; BeF 2 - or UF 4 -bearing salts tended to result in reasonably accurate interpolations, whereas other pseudobinary mixtures tended to show high accuracy. Regarding the pseudoternary extrapolations, the Redlich-Kister framework shows reasonable success at estimating the extent to which a pseudoternary system may indicate deviations from ideal Grunburg-Nissan mixing, where discrepancies with comparative experimental data generally stay within 30%. Finally, the primary reasons identified for such discrepancies are (1) inaccuracy in the underlying experimental data, (2) different complexation behavior in the higher order systems compared to the pseudobinary subsystems, and (3) extrapolation into temperatures too far out of the domain, which is valid for the underlying experimental data feeding the Redlich-Kister model.

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

Moisture-induced autonomous surface potential oscillations for energy harvesting

A variety of autonomous oscillations in nature such as heartbeats and some biochemical reactions have been widely studied and utilized for applications in the fields of bioscience and engineering. Here, we report a unique phenomenon of moisture-induced electrical potential oscillations on polymers, poly([2-(methacryloyloxy)ethyl] dimethyl-(3-sulfopropyl) ammonium hydroxide-co-acrylic acid), during the diffusion of water molecules. Chemical reactions are modeled by kinetic simulations while system dynamic equations and the stability matrix are analyzed to show the chaotic nature of the system which oscillates with hidden attractors to induce the autonomous surface potential oscillation. Using moisture in the ambient environment as the activation source, this self-excited chemoelectrical reaction could have broad influences and usages in surface-reaction based devices and systems. As a proof-of-concept demonstration, an energy harvester is constructed and achieved the continuous energy production for more than 15,000 seconds with an energy density of 16.8 mJ/cm 2 . A 2-Volts output voltage has been produced to power a liquid crystal display toward practical applications with five energy harvesters connected in series.

42 ENGINEERING↗
DOE OSTI2012

Explicit formulas for generalized harmonic perturbations of the infinite quantum well with an application to Mathieu equations

We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

On the relationship between the classical Dicke-Jaynes-Cummings-Gaudin model and the nonlinear Schroedinger equation

In this paper, the relationship between the classical Dicke-Jaynes-Cummings-Gaudin (DJCG) model and the nonlinear Schroedinger (NLS) equation is studied. It is shown that the classical DJCG model is equivalent to a stationary NLS equation. Moreover, the standard NLS equation can be solved by the classical DJCG model and a suitably chosen higher order flow. Further, it is also shown that classical DJCG model can be transformed into the classical Gaudin spin model in an external magnetic field through a deformation of Lax matrix. Finally, the separated variables are constructed on the common level sets of Casimir functions and the generalized action-angle coordinates are introduced via the Hamilton-Jacobi equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the number of relaxation modes or “folding pathways” that contribute to the evolution of the state populations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗