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NASA NTRS2003

Modeling the Thermostructural Stability of Melt-infiltrated Sic/sic Composites

SiC/SiC composites developed by NASA with Sylramic-iBN fibers and melt-infiltrated (MI) SiC-Si matrices have demonstrated 1000-hour rupture life in air at 100 MPa and 1315OC. Recently it has been determined that a major factor controlling the long-term rupture life of these composites is not environment or stress, but an intrinsic microstructural and strength instability caused by a thermally-induced silicon attack of the Sic fibers. The objective of this paper is to present a simple diffusion-based analytical model which predicts well the observed effects of stress-free thermal exposure on the residual tensile strength of Sylramic-iBN/SiC-Si composites. The practical implications of the model for SiC/SiC composites with MI matrices are discussed.

DiCarlo, James A.↗

NASA NTRS1982

Influence of diffusion and convective transport on dendritic growth in dilute alloys

Experimentation has been carried out in which the kinetics and morphology of dendritic growth were measured as a function of thermal supercooling, solute concentration, and spatial orientation of the dendritic growth axis. The crystal growth system studied is succinonitrile, NC(CH2)2CN, with additions of argon (up to 0.1 mole percent). This system is especially useful as a model for alloy studies because kinetic data are available for high purity (7-9's) succinonitrile. The influence of the solute, at fixed thermal supercooling, is to increase the growth velocity and correspondingly decrease intrinsic crystal dimensions. Morphological measurements are described in detail relating tip size, perturbation wavelength, supercooling, and solute concentration. The analysis of these effects based on morphological stability theory is also discussed, and experiments permitting the separation of convective and diffusive heat transport during crystal growth of succinonitrile are described. The studies underscore the importance of gravitationally-induced buoyancy effects on crystal growth.

Glicksman, M. E.↗

NASA NTRS2002

Microscopic Foundation and Simulation of Coupled Carrier-Temperature Diffusions in Semiconductor Lasers

A typical semiconductor-based optoelectronic device, such as a diode laser, consists of three subsystems: an optical field, an electron-hole plasma (EHP), and a host crystal lattice. The physics of such a device involves the interplay of optical, electrical and thermal processes. A proper description of such a device requires that all three processes are treated on equal footing and in a self-consistent fashion. Furthermore, since a semiconductor laser has intrinsic spatial inhomogeneity, such a self-consistency naturally leads to a set of partial differential equations in space and time. There is a significant lacking of research interest and results on the transport aspects of optical devices in the literature with only a few exceptions. Even the most important carrier diffusion coefficient has not been properly derived and studied so far for optically excited plasma, while most of the work adopted results from electronics community where heavily doped semiconductors with mainly one type of carriers are dealt with. The corresponding transport equation for plasma energy or temperature has received even less attention. In this talk we describe our recent results on such a self-consistent derivation of temperature and carrier-density diffusion equations coupled with the lasing process. Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field. The equations derived above are implemented in various limiting cases to a typical diode laser to study the consequences of nonlinear diffusion and the cross diffusion terms on laser behavior, especially the dynamic behavior of a diode laser under modulation. Detailed results will be presented by comparing with the standard rate equation results.

Li, J.↗

NASA NTRS1996

Adjustment of Sensor Locations During Thermal Property Parameter Estimation

The temperature dependent thermal properties of a material may be evaluated from transient temperature histories using nonlinear parameter estimation techniques. The usual approach is to minimize the sum of the squared errors between measured and calculated temperatures at specific locations in the body. Temperature measurements are usually made with thermocouples and it is customary to take thermocouple locations as known and fixed during parameter estimation computations. In fact, thermocouple locations are never known exactly. Location errors on the order of the thermocouple wire diameter are intrinsic to most common instrumentation procedures (e.g., inserting a thermocouple into a drilled hole) and additional errors can be expected for delicate materials, difficult installations, large thermocouple beads, etc.. Thermocouple location errors are especially significant when estimating thermal properties of low diffusively materials which can sustain large temperature gradients during testing. In the present work, a parameter estimation formulation is presented which allows for the direct inclusion of thermocouple positions into the primary parameter estimation procedure. It is straightforward to set bounds on thermocouple locations which exclude non-physical locations and are consistent with installation tolerances. Furthermore, bounds may be tightened to an extent consistent with any independent verification of thermocouple location, such as x-raying, and so the procedure is entirely consonant with experimental information. A mathematical outline of the procedure is given and its implementation is illustrated through numerical examples characteristic of light-weight, high-temperature ceramic insulation during transient heating. The efficacy and the errors associated with the procedure are discussed.

Milos, Frank S.↗

NASA NTRS1991

High performance etchant for thinning p(+)-InP and its application to p(+)n InP solar cell fabrication

An etchant, namely (o-H3PO4)u: (HNO3)v: (H2O2)t: (H2O)1-(u+v+t) is developed for thinning, after contacting, the p(+) emitter layer of p(+)n InP structures made by thermal diffusion. Varying u, v, and t, reproducible etch rates of 5 to 110 nm/min are obtained. After thinning the 0.6- to 2.5-micron thick p(+) InP layer down to 60-250 nm, specular surfaces are obtained at up to 80 nm/min etch rate. Due to its intrinsic qualities the resisual P-rich oxide after thinning the emitter layer provides surface passivation of p(+) InP surfaces and can also serve as a first-layer AR coating.

Faur, Maria↗

NASA NTRS2009

Solar Wind Ablation of Terrestrial Planet Atmospheres

Internal plasma sources usually arise in planetary magnetospheres as a product of stellar ablation processes. With the ignition of a new star and the onset of its ultraviolet and stellar wind emissions, much of the volatiles in the stellar system undergo a phase transition from gas to plasma. Condensation and accretion into a disk is replaced by radiation and stellar wind ablation of volatile materials from the system- Planets or smaller bodies that harbor intrinsic magnetic fields develop an apparent shield against direct stellar wind impact, but UV radiation still ionizes their gas phases, and the resulting internal plasmas serve to conduct currents to and from the central body along reconnected magnetic field linkages. Photoionization and thermalization of electrons warms the ionospheric topside, enhancing Jeans' escape of super-thermal particles, with ambipolar diffusion and acceleration. Moreover, observations and simulations of auroral processes at Earth indicate that solar wind energy dissipation is concentrated by the geomagnetic field by a factor of 10-100, enhancing heavy species plasma and gas escape from gravity, and providing more current carrying capacity. Thus internal plasmas enable coupling with the plasma, neutral gas and by extension, the entire body. The stellar wind is locally loaded and slowed to develop the required power. The internal source plasma is accelerated and heated, inflating the magnetosphere as it seeks escape, and is ultimately blown away in the stellar wind. Bodies with little sensible atmosphere may still produce an exosphere of sputtered matter when exposed to direct solar wind impact. Bodies with a magnetosphere and internal sources of plasma interact more strongly with the stellar wind owing to the magnetic linkage between the two created by reconnection.

Moore, Thomas Earle↗

NASA NTRS1990

Cellular structure of lean hydrogen flames in microgravity

Detailed, time-dependent, two-dimensional numerical simulations of premixed laminar flames have been used to study the initiation and subsequent development of cellular structures in lean hydrogen-air flames. The model includes detailed hydrogen-oxygen combustion with 24 elementary reactions of eight reactive species and a nitrogen diluent, molecular diffusion of all species, thermal conduction, viscosity, and convection. This model has been used to study the nonlinear evolution of cellular flame structure and shows that cell splitting, as observed in experiments, can be predicted numerically for sufficiently reactive mixtures. The structures that evolved also resembled the cellular structures observed in experiments. The present study shows that the 'cell-split limit' postulated from experimental observations is an intrinsic property of the mixture and that external factors such as heat losses are not necessary to cause this limit.

Patnaik, G.↗

NASA NTRS1986

IUE observations of interstellar hydrogen and deuterium toward Alpha Centauri B

A high dispersion profile is presented of the Lyman-alpha emission toward Alpha Cen B as recorded in two images taken with the IUE spacecraft. The spectra were examined with a three-parameter Gaussian or five-parameter solar-type profile to derive the intrinsic background stellar emission. Voight absorption profiles were calculated for the intervening H I and D I gas. A uniform, thermally broadened medium was assumed, with the calculations being based on the free stellar parameters of density, velocity dispersion and the bulk velocity of H I, and the density of D I. The use of a small aperture is shown to have been effective in eliminating geocoronal and interplanetary diffuse Ly-alpha contamination. The H I absorption profile toward Alpha Cen B is found to be equivalent to that toward Alpha Cen A, indicating that the H I profiles derived are essentially independent of stellar emission. Less success, however, was attained in obtaining any definitive D I profile, although an asymmetry in the blue and red wings of the Lyman-alpha emissions did show the presence of absorption by interstellar deuterium and allow setting a lower limit of 0.00001 for the D I/H I ratio.

Landsman, W. B.↗

NASA NTRS2001

Observations of O VI Emission from the Diffuse Interstellar Medium

We report the first Far Ultraviolet Spectroscopic Explorer (FUSE) measurements of diffuse O(VI) (lambda lambda 1032,1038) emission from the general diffuse interstellar medium outside of supernova remnants or superbubbles. We observed a 30 arcsec x 30 arcsec region of the sky centered at l = 315.0 deg and b = -41.3 deg. From the observed intensities (2930 +/- 290 (random) +/- 410 (systematic) and 1790 +/- 260 (random) +/- 250 (systematic) photons/sq cm/s/sr in the 1032 and 1038 angstrom emission lines, respectively), derived equations, and assumptions about the source location, we calculate the intrinsic intensity, electron density, thermal pressure, and emitting depth. The intensities are too large for the emission to originate solely in the Local Bubble. Thus, we conclude that the Galactic thick disk and lower halo also contribute. High velocity clouds are ruled out because there are none near the pointing direction. The calculated emitting depth is small, indicating that the O(VI)-bearing gas fills a small volume. The observations can also be used to estimate the cooling rate of the hot interstellar medium and constrain models. The data also yield the first intensity measurement of the C(II) 3s 2S(1/2) to 2p 2P(3/2) emission line at 1037 angstrom and place upper limits on the intensities of ultraviolet line emission from C(I), C(III), Si(II), S(III), S(IV), S(VI), and Fe(III).

Shelton, R. L.↗

NASA NTRS2003

Evolution and Transport of Water in the Upper Regolith of Mars

Long standing theoretical predictions [1-3], as well as recent spacecraft observations [4] indicate that large quantities of ice is present in the high latitudes upper decimeters to meters of the Martian regolith. At shallower depths and warmer locations small amounts of H2O, either adsorbed or free, may be present transiently. An understanding of the evolution of water based on theoretical and experimental considerations of the processes operating at the Martian environment is required. In particular, the porosity, diffusivity, and permeability of soils and their effect on water vapor transport under Mars-like conditions have been estimated, but experimental validation of such models is lacking. Goal: Three related mechanisms may affect water transport in the upper Martian regolith. 1) diffusion along a concentration gradient under isobaric conditions, 2) diffusion along a thermal gradient, which may give rise to a concentration gradient as ice sublimes or molecules desorb from the regolith, and 3) hydraulic flow, or mass motion in response to a pressure gradient. Our combined theoretical and experimental investigation seeks to disentangle these mechanisms and determine which process(es) are dominant in the upper regolith over various timescales. A detailed one-dimensional model of the upper regolith is being created which incorporates water adsorption/ desorption, condensation, porosity, diffusivity, and permeability effects. Certain factors such as diffusivity are difficult to determine theoretically due to the wide range of intrinsic grain properties such as particle sizes, shapes, packing densities, and emergent properties such as tortuosity. An experiment is being designed which will allow us to more accurately determine diffusivity, permeability, and water desorption isotherms for regolith simulants.

Hudson, T. L.↗

NASA NTRS1995

ROSAT PSPC and HRI observations of the composite starburst/Seyfert 2 galaxy NGC 1672

The nearby barred spiral galaxy NGC 1672 has been observed with the Position Sensitive Proportional Counter (PSPC) and High Resolution Imager (HRI) instruments on board the ROSAT X-ray satellite. NGC 1672 is thought to have an obscured Seyfert nucleus, and it has strong starburst activity as well. Three bright X-ray sources with luminosities 1-2 x 10(exp 40) erg/s are clearly identified with NGC 1672. The strongest lies at the nucleus, and the other two lie at the ends of NGC 1672's prominent bar, locations that are also bright in H alpha and near-infrared images. The nuclear source is resolved by the HRI on about the scale of the recently identified nuclear ring, and one of the sources at the ends of the bar is also probably resolved. The X-ray spectrum of the nuclear source is quite soft, having a Raymond-Smith plasma temperature of approximately equals 0.7 keV and little evidence for intrinsic absorption. The ROSAT band X-ray flux of the nuclear source appears to be dominated not by X-ray binary emission but rather by diffuse gas emission. The absorption and emission properties of the sources, as well as their spatial extents, lead us to models of superbubbles driven by supernovae. However, the large density and emission measure of the nuclear X-ray source stretch the limits that can be comfortably accommodated by these models. We do not detect direct emission from the putative Seyfert nucleus, although an alternative model for the nuclear source is thermal emission from gas that is photoionized by a hidden Seyfert nucleus. The spectra of the other two X-ray sources are harder than that of the nuclear source, and have similar difficulties with regard to superbubble models.

Brandt, W. N.↗

NASA NTRS1992

IRAS and the Boston University Arecibo Galactic H I Survey: A catalog of cloud properties

The Infrared Astronomy Satellite (IRAS) Galactic Plane Surface Brightness Images were used to identify infrared emission associated with cool, diffuse H I clouds detected by the Boston University-Arecibo Galactic H I Survey. These clouds are associated with galactic star clusters, H II regions, and molecular clouds. Using emission-absorption experiments toward galactic H II regions, we determined the H I properties of cool H I clouds seen in absorption against the thermal continuum, including their kinematic distances. Correlations were then made between IRAS sources and these H II regions, thus some of the spatial confusion associated with the IRAS fields near the galactic plane was resolved since the distances to these sources was known. Because we can also correlate the BU-Arecibo clouds with existing CO surveys, these results will allow us to determine the intrinsic properties of the gas (neutral and ionized atomic as well as molecular) and dust for interstellar clouds in the inner galaxy. For the IRAS-identified H II region sample, we have established the far infrared (FIR) luminosities and galactic distribution of these sources.

Bania, Thomas M.↗

NASA NTRSDate not supplied

Updates on the Predictive Materials Modeling Software Tools

Updates on NASA‘s efforts to build a Predictive Material Modeling (PMM) framework from the micro-scale to the macro-scale are presented in this abstract. The PMM effort is part of the Entry Systems Modeling (ESM) project under NASA’s Game Changing Development (GCD) program. To reduce the need for extensive testing and accelerate the design cycle process, ESM is developing simulation and modeling tools that enable the characterization of the properties of thermal protection materials and their response to extremely hot plasma. The Porous Microstructure Analysis (PuMA) software has been developed to compute effective material properties and perform material response simulations on digitized microstructures of porous media. PuMA is able to import three-dimensional digital images obtained from X-ray microtomography or to generate artificial microstructures that mimic real materials. PuMA also provides a module for interactive 3D visualizations. Version 3, which was recently released as open-source, includes modules to compute simple morphological properties such as porosity, volume fractions, pore diameter, and specific surface area. Additional capabilities include the determination of effective thermal and electrical conductivity (both radiative and solid conduction - including the ability to simulate local anisotropy for the latter); effective diffusivity and tortuosity from the continuum to the rarefied regime; techniques to determine the local material orientation, as well as mechanical properties (elasticity coefficients), and permeability. Computed properties are then used to inform a macro-scale material response model, such as those implemented in the Porous material Analysis Toolbox based on OpenFOAM (PATO) software developed within ESM. The computational model in PATO is a generic heat and mass transfer model for porous reactive materials containing several solid phases and a single gas phase. The detailed chemical interactions occurring between the solid phases and the gas phase are modeled at the pore scale, assuming Local Thermal Equilibrium. Recent efforts include the development of a mechanical erosion model as well as a unified model allowing an intrinsic coupling between fluid and material. Comparison to flight data (Mars Science Laboratory [MSL] Entry Descent and Landing Instrument [MEDLI] and Mars 2020 MEDLI2) is critical in order to validate these computational tools. Examples of ablative material response using the code will be presented, including 3D simulations of the full-scale heatshield of the MSL capsule. The simulations demonstrated the ability of the modern material response code, PATO, to handle the material response of geometrically complex and large domains through the use of massively parallel computations.

material modeling↗

NASA NTRS2000

General Purpose Fortran Program for Discrete-Ordinate-Method Radiative Transfer in Scattering and Emitting Layered Media: An Update of DISORT

This update reports a state-of-the-art discrete ordinate algorithm for monochromatic unpolarized radiative transfer in non-isothermal, vertically inhomogeneous, but horizontally homogeneous media. The physical processes included are Planckian thermal emission, scattering with arbitrary phase function, absorption, and surface bidirectional reflection. The system may be driven by parallel or isotropic diffuse radiation incident at the top boundary, as well as by internal thermal sources and thermal emission from the boundaries. Radiances, fluxes, and mean intensities are returned at user-specified angles and levels. DISORT has enjoyed considerable popularity in the atmospheric science and other communities since its introduction in 1988. Several new DISORT features are described in this update: intensity correction algorithms designed to compensate for the 8-M forward-peak scaling and obtain accurate intensities even in low orders of approximation; a more general surface bidirectional reflection option; and an exponential-linear approximation of the Planck function allowing more accurate solutions in the presence of large temperature gradients. DISORT has been designed to be an exemplar of good scientific software as well as a program of intrinsic utility. An extraordinary effort has been made to make it numerically well-conditioned, error-resistant, and user-friendly, and to take advantage of robust existing software tools. A thorough test suite is provided to verify the program both against published results, and for consistency where there are no published results. This careful attention to software design has been just as important in DISORT's popularity as its powerful algorithmic content.

Tsay, Si-Chee↗

NASA NTRS2001

Filtration Combustion in Smoldering and SHS

Smolder waves and SHS (self-propagating high-temperature synthesis) waves are both examples of filtration combustion waves propagating in porous media. Smoldering combustion is important for the study of fire safety. Smoldering itself can cause damage, its products are toxic and it can also lead to the more dangerous gas phase combustion which corresponds to faster propagation at higher temperatures. In SHS , a porous solid sample, consisting of a finely ground powder mixture of reactants, is ignited at one end. A high temperature thermal wave, having a frontal structure, then propagates through the sample converting reactants to products. The SHS technology appears to enjoy a number of advantages over the conventional technology, in which the sample is placed in a furnace and "baked" until it is "well done". The advantages include shorter synthesis times, greater economy, in that the internal energy of the reactions is employed rather than the costly external energy of the furnace, purer products, simpler equipment and no intrinsic limitation on the size of the sample to be synthesized as exists in the conventional technology. When delivery of reactants through the pores to the reaction site is an important aspect of the combustion process, it is referred to as filtration combustion. The two types of filtration combustion have a similar mathematical formulation, describing the ignition, propagation and extinction of combustion waves in porous media. The goal in each case, however, is different. In smoldering the desired goal is to prevent propagation, whereas in SHS the goal is to ensure propagation of the combustion wave, leading to the synthesis of desired products. In addition, the scales in the two areas of application differ. Smoldering generally occurs at lower temperatures and propagation velocities than in SHS nevertheless, the two applications have much in common so that what is learned fit make application can be used to advantage in the other. In porous media, melting often occurs ahead of the propagating combustion wave. In certain cases there is so much melting that the porous solid structure is destroyed, e.g., by melting and a suspension arises, consisting of a liquid bath containing solid particles and/or gas bubbles. The resulting combustion wave is referred to as a liquid flame. We have considered a number of problems involving filtration combustion. Here, we describe four such studies: (A) rapid buoyant filtration combustion waves; (B) diffusion driven combustion waves; (C) rapidly propagating liquid flames in gravitational fields; and (D) gas-phase influence on liquid flames in gravitational fields.

Matkowsky, Bernard J.↗

NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗