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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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Higher derivative corrections to the entropic force from holography

Highlights: • We study higher derivative corrections to the entropic force from AdS/CFT. • We discuss how the entropic force changes with the shear viscosity to entropy density ratio at strong coupling. - Abstract: The entropic force has been recently argued to be responsible for dissociation of heavy quarkonia. In this paper, we analyze R{sup 2} corrections and R{sup 4} corrections to the entropic force, respectively. It is shown that for R{sup 2} corrections, increasing λ{sub GB} (Gauss–Bonnet factor) leads to increasing the entropic force. While for R{sup 4} corrections, increasing λ (’t Hooft coupling) leads to decreasing the entropic force. Also, we discuss how the entropic force changes with the shear viscosity to entropy density ratio, η∕s, at strong coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Cancer cachexia decreases specific force and accelerates fatigue in limb muscle

Highlights: •C-26 cancer cachexia causes a significant decrease in limb muscle absolute force. •C-26 cancer cachexia causes a significant decrease in limb muscle specific force. •C-26 cancer cachexia decreases fatigue resistance in the soleus muscle. •C-26 cancer cachexia prolongs time to peak twitch tension in limb muscle. •C-26 cancer cachexia prolongs one half twitch relaxation time in limb muscle. -- Abstract: Cancer cachexia is a complex metabolic syndrome that is characterized by the loss of skeletal muscle mass and weakness, which compromises physical function, reduces quality of life, and ultimately can lead to mortality. Experimental models of cancer cachexia have recapitulated this skeletal muscle atrophy and consequent decline in muscle force generating capacity. However, more recently, we provided evidence that during severe cancer cachexia muscle weakness in the diaphragm muscle cannot be entirely accounted for by the muscle atrophy. This indicates that muscle weakness is not just a consequence of muscle atrophy but that there is also significant contractile dysfunction. The current study aimed to determine whether contractile dysfunction is also present in limb muscles during severe Colon-26 (C26) carcinoma cachexia by studying the glycolytic extensor digitorum longus (EDL) muscle and the oxidative soleus muscle, which has an activity pattern that more closely resembles the diaphragm. Severe C-26 cancer cachexia caused significant muscle fiber atrophy and a reduction in maximum absolute force in both the EDL and soleus muscles. However, normalization to muscle cross sectional area further demonstrated a 13% decrease in maximum isometric specific force in the EDL and an even greater decrease (17%) in maximum isometric specific force in the soleus. Time to peak tension and half relaxation time were also significantly slowed in both the EDL and the solei from C-26 mice compared to controls. Since, in addition to postural control, the oxidative soleus is also important for normal locomotion, we further performed a fatigue trial in the soleus and found that the decrease in relative force was greater and more rapid in solei from C-26 mice compared to controls. These data demonstrate that severe cancer cachexia causes profound muscle weakness that is not entirely explained by the muscle atrophy. In addition, cancer cachexia decreases the fatigue resistance of the soleus muscle, a postural muscle typically resistant to fatigue. Thus, specifically targeting contractile dysfunction represents an additional means to counter muscle weakness in cancer cachexia, in addition to targeting the prevention of muscle atrophy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Forced running exercise attenuates hippocampal neurogenesis impairment and the neurocognitive deficits induced by whole-brain irradiation via the BDNF-mediated pathway

Highlights: •Forced exercise can ameliorate WBI induced cognitive impairment in our rat model. •Mature BDNF plays an important role in the effects of forced exercise. •Exercise may be a possible treatment of the radiation-induced cognitive impairment. -- Abstract: Cranial radiotherapy induces progressive and debilitating cognitive deficits, particularly in long-term cancer survivors, which may in part be caused by the reduction of hippocampal neurogenesis. Previous studies suggested that voluntary exercise can reduce the cognitive impairment caused by radiation therapy. However, there is no study on the effect of forced wheel exercise and little is known about the molecular mechanisms mediating the effect of exercise. In the present study, we investigated whether the forced running exercise after irradiation had the protective effects of the radiation-induced cognitive impairment. Sixty-four Male Sprague–Dawley rats received a single dose of 20 Gy or sham whole-brain irradiation (WBI), behavioral test was evaluated using open field test and Morris water maze at 2 months after irradiation. Half of the rats accepted a 3-week forced running exercise before the behavior detection. Immunofluorescence was used to evaluate the changes in hippocampal neurogenesis and Western blotting was used to assess changes in the levels of mature brain-derived neurotrophic factor (BDNF), phosphorylated tyrosine receptor kinase B (TrkB) receptor, protein kinase B (Akt), extracellular signal-regulated kinase (ERK), calcium-calmodulin dependent kinase (CaMKII), cAMP-calcium response element binding protein (CREB) in the BDNF–pCREB signaling. We found forced running exercise significantly prevented radiation-induced cognitive deficits, ameliorated the impairment of hippocampal neurogenesis and attenuated the down-regulation of these proteins. Moreover, exercise also increased behavioral performance, hippocampal neurogenesis and elevated BDNF–pCREB signaling in non-irradiation group. These results suggest that forced running exercise offers a potentially effective treatment for radiation-induced cognitive deficits.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Understanding syringeability and injectability of high molecular weight PEO solution through time-dependent force-distance profiles

Opioid medications play a vital role in treating moderate to severe pain. Unfortunately, many drug misusers and abusers attempt to alter the formulations or properties of these drugs by manipulation, (e.g., crushing, chewing, smoking, snorting, injecting). The intravenous (IV) route is most dangerous to abusers, as the drugs directly enter the circulatory system and produce intense euphoria. To obtain a full understanding of the impact of syringe factors (e.g., needle gauge size, needle length, syringe barrel size), on the ease of injection, we undertook a comprehensive assessment of syringeability and injectability of manipulated abuse-deterrent formulations (ADFs). A texture analyzer-based testing method was developed for the measurement of the resistance force of pulling, holding, and pushing phases of injections. Results showed that the finer needle gauge sizes required higher injection force to withdraw drug solutions. In addition, the syringed liquid volume was highly dependent on needle gauge size, holding time, and sample viscosity. In most cases, a lower needle gauge number and a longer holding time increased the syringed volume. Needle length was highly correlated to injection force (R 2 = 0.99). Using longer needles to inject drug solution requires greater force. Furthermore, large barrel size was correlated to pushing force (R 2 = 0.99); thus, increasing the difficulty of pushing the plunger of a large syringe with one hand. Lastly, relationships between injection force, sample viscosity, and testing conditions were elucidated using a mathematical model, which could be used in the future to assess and predict injection force of solution samples.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Influence of Heave Plate Topology on Reaction Force

In this study, we explore the role of heave plate topology on fluid reaction forces using three, representative shapes: a hexagonal flat plate, a hexagonal conic with an open top, and the same with a closed top that encloses a fluid mass. We force each test article sinusoidally in a quiescent tank and decompose the reaction force using forms of the Morison equation for phase-invariant and phase-dependent parameterizations. We find that a flat plate generates 5.3 % more fluid reaction force than the open conic topology, and 21.4% more than the enclosed conic. Asymmetric topologies generate asymmetric reaction forces, but the magnitude of asymmetry is limited by nearly symmetric fluid inertia forces, which dominate over drag for these test articles. Additionally, we observe asymmetric vortex dynamics for the flat plate when the Keulegan-Carpenter number is between 1 and 2, accompanied by a shift in the phase of the peak force by of the oscillation period. As a consequence of this shift, the hydrodynamic coefficients estimated from the phase-dependent Morison equation decomposition are asymmetric, suggesting that phase-dependent representations may not provide physical insight in some hydrodynamic regimes.

added mass↗
DOE OSTI2019

Ab Initio Flexible Force Field for Metal–Organic Frameworks Using Dummy Model Coordination Bonds

We present force fields developed from periodic density functional theory (DFT) calculations that can be used in classical molecular simulations to model M–MOF-74 (M = Co, Fe, Mg, Mn, Ni, Zn) and its extended linker analogs. Our force fields are based on cationic dummy models (CDMs). These dummy models simplify the methodology required to tune the parameters and improve the accuracy of the force fields. We used our force fields to compare mechanical properties across the M–MOF-74 series and determine that increasing the size of the linker decreases the framework rigidity. In addition, we applied our force fields to an extended linker analog of Mg–MOF-74 and characterized the free energy of a previously reported deformation pattern in which the one-dimensional hexagonal channels of the framework become irregular. The free energy profiles confirm that the deformation is adsorbate induced and impossible to access solely by a pressure stimulus. On the basis of our results, we conclude that the force fields presented here and others that may be developed using our methodology are transferable across metal–organic framework series that share a metal center topology. Lastly, we believe that these force fields have the potential to be adapted for the study of complex problems in MOF chemistry, including defects and crystal growth, that have thus far been beyond the scope of classical molecular simulations.

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

Capturing Deuteration Effects in a Molecular Mechanics Force Field: Deuterated THF and the THF–Water Miscibility Gap

Deuteration is a common chemical modification used in conjunction with experiments such as neutron scattering, NMR, and Fourier-transform infrared for the study of molecular systems. Under the Born–Oppenheimer (BO) approximation, while the underlying potential energy surface remains unchanged by isotopic substitutions, isotopic substitution still alters intramolecular vibrations, which in turn may alter intermolecular interactions. Molecular mechanics (MM) force fields used in classical molecular dynamics simulations are assumed to represent local approximations of the BO potential energy surfaces, and hence, MD simulations using simple isotopic mass substitutions should capture BO-compatible isotope effects. However, standard MM force-field parameterizations do not directly fit to the local harmonic quantum mechanical (QM) Hessian that describes the BO surface, but rather to QM normal-modes and/or mass-dependent internal-coordinate derived distortion energies. In this study, using tetrahydrofuran (THF)–water mixtures as our model system, we show that not only does a simple mass-substitution approach fail to capture an experimentally characterized deuteration effect (the loss of the closed-loop miscibility gap associated with the complete deuteration of THF) but also it is necessary to generate new MM force-field parameters that correctly describe isotopic dependent vibrations to capture the experimental deuteration effect. We show that the origin of this failure is a result of using mass-dependent features to fit the THF MM force field, which unintentionally biases the bonded terms of the force field to represent only the isotopologue used during the original force-field parameterization. In addition, we make use of our isotopologue-corrected force field for D 8 THF to examine the molecular origins of the isotope-dependent loss of the THF–water miscibility gap.

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

Force-Modulated C–C Reductive Elimination from Nickel Bis(polyfluorophenyl) Complexes

We have analyzed the rate of C(sp 2 )–C(sp 2 ) reductive elimination from nickel(II) bis(2,4,6-trifluorophenyl) complex-es (P–P)Ni(2,4,6-C 6 H 2 F 3 ) 2 containing either MeOBiPhep (3a) or macrocyclic bisphosphine ligand (3b-3e) as a func-tion of force applied to the biaryl backbone of these ligands through intramolecular tension generated by a molecular force probe. Nickel complexes 3 were isolated in 22-60% yield from reaction of bisphosphine with the bis(tetrahydrofuranyl) complex (THF) 2 Ni(2,4,6-C 6 H 2 F 3 ) 2 followed by chromatography. Thermolysis of complexes 3 in C 6 D 6 at 68 °C leads to first-order decay through > 3 half-lives to form 2,2',4,4',6,6'-hexaflurorobiphenyl as the exclusive fluorine-containing product in ≥93% yield. Whereas compressive forces up to –65 pN have no significant effect on the rate of reductive elimination, extension forces increase the rate of reductive elimination by a factor of three over a ~230 pN range of restoring forces relative to the strain-free MeOBiphep complex. Furthermore, the rate response of reductive elimination from nickel(II) bis(trifluorophenyl) complexes as a function of extension force is similar to the previously reported 2.8-fold increase in the rate of reductive elimination from platinum diaryl complexes (P–P)Pt(4-C 6 H 4 NMe 2 ) 2 over the same range of forces

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Force Field Development for Actinyl Ions via Quantum Mechanical Calculations: An Approach to Account for Many Body Solvation Effects

Advances in computational algorithms and methodologies make it possible to use highly accurate quantum mechanical calculations to develop force fields (pair-wise additive intermolecular potentials) for condensed phase simulations. Despite these advances, this approach faces numerous hurdles for the case of actinyl ions, AcO2n+ (high-oxidation-state actinide dioxo cations), mainly due to the complex electronic structure resulting from an interplay of s, p, d, and f valence orbitals. Traditional methods use a pair of molecules (“dimer”) to generate a potential energy surface (PES) for force field parametrization based on the assumption that many body polarization effects are negligible. We show that this is a poor approximation for aqueous phase uranyl ions and present an alternative approach for the development of actinyl ion force fields that includes important many body solvation effects. Force fields are developed for the UO22+ ion with the SPC/Fw, TIP3P, TIP4P, and TIP5P water models and are validated by carrying out detailed molecular simulations on the uranyl aqua ion, one of the most characterized actinide systems. It is shown that the force fields faithfully reproduce available experimental structural data and hydration free energies. Failure to account for solvation effects when generating PES leads to overbinding between UO22+ and water, resulting in incorrect hydration free energies and coordination numbers. A detailed analysis of arrangement of water molecules in the first and second solvation shell of UO22+ is presented. The use of a simple functional form involving the sum of Lennard-Jones + Coulomb potentials makes the new force field compatible with a large number of available molecular simulation engines and common force fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Surface summertime radiative forcing by shallow cumuli at the Atmospheric Radiation Measurement Southern Great Plains site

Although shallow cumuli are common over large areas of the globe, their impact on the surface radiative forcing has not been carefully evaluated. This study addresses this shortcoming by analyzing data from days with shallow cumuli collected over eight summers (2000-2007) at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) Climate Research Facility (collectively ACRF) Southern Great Plains site. During periods with clouds, the average shortwave and longwave radiative forcings are 45.5 W m-2 and +11.6 W m-2, respectively. The forcing has been defined so that a negative (positive) forcing indicates a surface cooling (warming). On average, the shortwave forcing is negative, however, instances with positive shortwave forcing are observed approximately 20% of the time. These positive values of shortwave forcing are associated with three-dimensional radiative effects of the clouds. The three-dimensional effects are shown to be largest for intermediate cloud amounts. The magnitude of the three-dimensional effects decreased with averaging time, but it is not negligibly small even for large averaging times as long as four hours.

58 GEOSCIENCES↗
DOE OSTI2017

Force interacts with macromolecular structure in activation of TGF-β

Integrins are adhesion receptors that transmit force across the plasma membrane between extracellular ligands and the actin cytoskeleton. In activation of the transforming growth factor-β1 precursor (pro-TGF-β1), integrins bind to the prodomain, apply force, and release the TGF-β growth factor. However, we know little about how integrins bind macromolecular ligands in the extracellular matrix or transmit force to them. Here we show how integrin α V β 6 binds pro-TGF-β1 in an orientation biologically relevant for force-dependent release of TGF-β from latency. The conformation of the prodomain integrin-binding motif differs in the presence and absence of integrin binding; differences extend well outside the interface and illustrate how integrins can remodel extracellular matrix. Remodelled residues outside the interface stabilize the integrin-bound conformation, adopt a conformation similar to earlier-evolving family members, and show how macromolecular components outside the binding motif contribute to integrin recognition. Regions in and outside the highly interdigitated interface stabilize a specific integrin/pro-TGF-β orientation that defines the pathway through these macromolecules which actin-cytoskeleton-generated tensile force takes when applied through the integrin β-subunit. Simulations of force-dependent activation of TGF-β demonstrate evolutionary specializations for force application through the TGF-β prodomain and through the β- and not α-subunit of the integrin.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Long range electrostatic forces in ionic liquids

Ionic liquids are pure salts that are liquid under ambient conditions. As liquids composed solely of ions, the scientific consensus has been that ionic liquids have exceedingly high ionic strengths and thus very short Debye screening lengths. However, several recent experiments from laboratories around the world have reported data for the approach of two surfaces separated by ionic liquids which revealed remarkable long range forces that appear to be electrostatic in origin. Evidence has accumulated demonstrating long range surface forces for several different combinations of ionic liquids and electrically charged surfaces, as well as for concentrated mixtures of inorganic salts in solvent. The original interpretation of these forces, that ionic liquids could be envisioned as “dilute electrolytes,” was controversial, and the origin of long range forces in ionic liquids remains the subject of discussion. Here we seek to collate and examine the evidence for long range surface forces in ionic liquids, identify key outstanding questions, and explore possible mechanisms underlying the origin of these long range forces. Long range surface forces in ionic liquids and other highly concentrated electrolytes hold diverse implications from designing ionic liquids for energy storage applications to rationalizing electrostatic correlations in biological self-assembly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Piezoresistive cantilever force-clamp system

We present a microelectromechanical device-based tool, namely, a force-clamp system that sets or ''clamps'' the scaled force and can apply designed loading profiles (e.g., constant, sinusoidal) of a desired magnitude. The system implements a piezoresistive cantilever as a force sensor and the built-in capacitive sensor of a piezoelectric actuator as a displacement sensor, such that sample indentation depth can be directly calculated from the force and displacement signals. A programmable real-time controller operating at 100 kHz feedback calculates the driving voltage of the actuator. The system has two distinct modes: a force-clamp mode that controls the force applied to a sample and a displacement-clamp mode that controls the moving distance of the actuator. We demonstrate that the system has a large dynamic range (sub-nN up to tens of {mu}N force and nm up to tens of {mu}m displacement) in both air and water, and excellent dynamic response (fast response time, <2 ms and large bandwidth, 1 Hz up to 1 kHz). In addition, the system has been specifically designed to be integrated with other instruments such as a microscope with patch-clamp electronics. We demonstrate the capabilities of the system by using it to calibrate the stiffness and sensitivity of an electrostatic actuator and to measure the mechanics of a living, freely moving Caenorhabditis elegans nematode.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2013

Collisional effects on nonlinear ion drag force for small grains

The ion drag force arising from plasma flow past an embedded spherical grain is calculated self-consistently and non-linearly using particle in cell codes, accounting for ion-neutral collisions. Using ion velocity distribution appropriate for ion drift driven by a force field gives wake potential and force greatly different from a shifted Maxwellian distribution, regardless of collisionality. The low-collisionality forces are shown to be consistent with estimates based upon cross-sections for scattering in a Yukawa (shielded) grain field, but only if non-linear shielding length is used. Finite collisionality initially enhances the drag force, but only by up to a factor of 2. Larger collisionality eventually reduces the drag force. In the collisional regime, the drift distribution gives larger drag than the shift distribution even at velocities where their collisionless drags are equal. Comprehensive practical analytic formulas for force that fit the calculations are provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Graphene thickness dependent adhesion force and its correlation to surface roughness

In this paper, adhesion force of graphene layers on 300 nm silicon oxide is studied. A simple model for measuring adhesion force for a flat surface with sub-nanometer roughness was developed and is shown that small surface roughness decreases adhesion force while large roughness results in an effectively larger adhesion forces. We also show that surface roughness over scales comparable to the tip radius increase by nearly a factor of two, the effective adhesion force measured by the atomic force microscopy. Thus, we demonstrate that surface roughness is an important parameter that should be taken into account in analyzing the adhesion force measurement results.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Effect of particle-particle interactions on the acoustic radiation force in an ultrasonic standing wave

Ultrasonic standing waves are widely used for separation applications. In MEMS applications, a half wavelength standing wave field is generated perpendicular to a laminar flow. The acoustic radiation force exerted on the particle drives the particle to the center of the MEMS channel, where concentrated particles are harvested. In macro-scale applications, the ultrasonic standing wave spans multiple wavelengths. Examples of such applications are oil/water emulsion splitting [1], and blood/lipid separation [2]. In macro-scale applications, particles are typically trapped in the standing wave, resulting in clumping or coalescence of particles/droplets. Subsequent gravitational settling results in separation of the secondary phase. An often used expression for the radiation force on a particle is that derived by Gorkov [3]. The assumptions are that the particle size is small relative to the wavelength, and therefore, only monopole and dipole scattering contributions are used to calculate the radiation force. This framework seems satisfactory for MEMS scale applications where each particle is treated separately by the standing wave, and concentrations are typically low. In macro-scale applications, particle concentration is high, and particle clumping or droplet coalescence results in particle sizes not necessarily small relative to the wavelength. Ilinskii et al. developed a framework for calculation of the acoustic radiation force valid for any size particle [4]. However, this model does not take into account particle to particle effects, which can become important as particle concentration increases. It is known that an acoustic radiation force on a particle or a droplet is determined by the local field. An acoustic radiation force expression is developed that includes the effect of particle to particle interaction. The case of two neighboring particles is considered. The approach is based on sound scattering by the particles. The acoustic field at the location of one particle then consists of two components, the incident sound wave and the scattered field generated by the neighboring particle. The radiation force calculation then includes the contributions of these two fields and incorporates the mutual particle influence. In this investigation the droplet/particle influence on each other has been analyzed theoretically by using the method developed by Gorkov and modified by Ilinskii et al.

42 ENGINEERING↗
DOE OSTI2015

A test on reactive force fields for the study of silica dimerization reactions

We studied silica dimerization reactions in the gas and aqueous phase by density functional theory (DFT) and reactive force fields based on two parameterizations of ReaxFF. For each method (both ReaxFF force fields and DFT), we performed constrained geometry optimizations, which were subsequently evaluated in single point energy calculations using the other two methods. Standard fitting procedures typically compare the force field energies and geometries with those from quantum mechanical data after a geometry optimization. The initial configurations for the force field optimization are usually the minimum energy structures of the ab initio database. Hence, the ab initio method dictates which structures are being examined and force field parameters are being adjusted in order to minimize the differences with the ab initio data. As a result, this approach will not exclude the possibility that the force field predicts stable geometries or low transition states which are realistically very high in energy and, therefore, never considered by the ab initio method. Our analysis reveals the existence of such unphysical geometries even at unreactive conditions where the distance between the reactants is large. To test the effect of these discrepancies, we launched molecular dynamics simulations using DFT and ReaxFF and observed spurious reactions for both ReaxFF force fields. Our results suggest that the standard procedures for parameter fitting need to be improved by a mutual comparative method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this paper, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (l E ) with salt concentration c s and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, l E ~ c s -0.5 as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Inspired by Cohen’s extraction of Warner’s force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗