Investigation of self-assembled fractal porous-silica over a wide range of length scales using a combined small-angle scattering method

The unique structure of a set of self-assembled porous silica materials was characterized through a combined small-angle scattering (CSAS) method using small- and ultra-small angle neutron scattering as well as small-angle X-ray scattering. The porous silica specimens investigated were prepared by a sol-gel method under the presence of alkylketene dimer (AKD) template particles and through calcination, which leads to the development of porous silica having a mass-fractal structure over length scales from ~ 100 nm to ~ 10 μm. Furthermore, the specimens posses a hierarchical structure, which consist of a fractal porous structure, and also contain primary silica particles less than 10 nm in size, which form a continuous silica matrix. To characterize these complex structures, observation over a broad range of length scales is indispensable. We propose a CSAS technique that serves this purpose well.     

Multiple small-angle scattering—A review

Small-angle scattering (SAS) is a powerful experimental technique in condensed matter physics for studying structural features of inhomogeneities of colloidal dimensions. So far the technique has been largely exploited to study thin samples for which the single scattering approximation, for the radiation-matrix interaction, holds good. The single scattering approximation is invalid when the thickness of the sample exceeds the scattering mean free path. This situation calls for a guideline to analyse the scattering data having significant contribution from multiple scattering. Since multiple scattering broadens the scattering profile, the beam broadening nature of multiple scattering can also be exploited, by making the sample suitably thick, to study large size inhomogeneities which are otherwise inaccessible to a small-angle scattering set up because of its resolution constraints. The present article presents a review and extension of the theoretical basis for analysing multiple scattering data from the point of view of a recent formalism on multiple small-angle scattering. The formalism is valid for both monodisperse and polydisperse scattering media characterized by the presence of large size inhomogeneities in the matrix. It is shown that multiple scattering from a polydisperse sample can be described by a system of coupled integrodifferential equation. However, multiple scattering from a monodisperse sample can be described by a Fokker-Planck type of equation. These equations have been analysed with an emphasis laid on the nature of the structural information pertaining to the inhomogeneities which is extractable from the multiple scattering profile. When the linear dimension of inhomogeneities becomes comparable to the scattering mean free path of the radiation in the sample, the statistical nature of the medium becomes pronounced. The statistical nature of the medium modulates the scattering profile. The modulation effect could be broadening or narrowing of the profile depending upon the nature of the inhomogeneities and their population distribution. The limiting regimes of validity and the implications of various approximations, frequently used to analyse the scattering data, have been indicated.     

沙尘天气下激光信号的传输特性

以小角度近似为条件,利用逐级递归的方法推导了激光信号在沙尘天气下的辐射传输方程,得到了多次散射下的光强分布函数,以及波长和不对称因子对光强的影响。同时,通过比较不同散射相位函数及沙尘粒子的散射特性,采用了修正的TTHG(Two Term Henyey-Greenstein)散射相位函数,更加全面地反映了沙粒散射后光强的变化规律。研究结果表明,随着光学厚度的增加,散射光强呈现出先增大后减小的趋势,且多次散射的比重相比于单次散射而言逐渐增大。当散射次数超过3次以上时,接收光强的变化可以忽略不计。相对于Mie理论下的结果而言,采用小角度近似理论,从辐射传输的角度分析沙粒的散射特性误差更小,实现了准确描述沙尘天气下激光信号传输特性的目的。     

Positive deviation from debye‘s theory in small—angle x—ray scattering

The small-angle x-ray scattering (SAXS) resulting from a non-ideal two-phase system having sharply defined phase boundaries but with micro-fluctuations of electron density within any phase shows a positive deviation from Debye's theory. We have found a simple method suitable for fitting the slit-smeared SAXS data and correcting the positive deviation. The validity of this procedure is tested on porous ZrO_2 xerogel prepared using the sol-gel process.     

Spin chirality of polycrystalline MnSi, or, difficult way from rumours to the solid ground

Six different polycrystalline samples of MnSi were produced as a rapidly frozen melt after the single crystal growth in the Czochralski process. With the help of small-angle scattering of polarized neutrons we show that the magnetic spin chirality being scanned along the sample length oscillates strongly on a scale of 2-3 mm, revealing the volumes of the samples with high degree of an enantiomeric excess. The average chirality of the samples deviates from zero value.     

Monte Carlo simulation for millimeter wave propagation and scattering in rain medium

As the operating frequencies of communications systems more higher into the millimeter wave range, the effects of multiple scattering in precipitation media become more significant. This paper treats the problems of electromagnetic multiple scattering in rain medium by the Monte Carlo method. The em wave is regarded as a Markov chain of photon collisions in a medium in which it is scattered and absorbed. For the sake of simplicity, the polarization is not taken into account, the above mentioned problems are described by the scale integro-diffierential equation of transfer. When the plane wave through a random medium with particle size distribution, the technique of weighted average is used to characterize the radiation intensity, including average scattering, absorption coefficients and phase function. The Monte Carlo simulation algorithms are done for the rain attenuation and reflectance at millimeter wavelength region. Our computational results are in good agreement with experimental data of rain attenuation.     

Terahertz Radiation Transport in Photonic Glasses

Multiple scattering of electromagnetic (EM) waves arises in disordered media with a refractive index varying on the scale of the wavelength. The diffusion approximation is a powerful tool to treat multiple scattering as a photon random walk, neglecting resonant phenomena. However, as the light intensity varies on a scale much smaller than the transport mean free path, resonances may occur in media formed by finite-size scatterers and break the diffusion approximation. The energy and phase velocity are very useful tools to reveal the onset of the resonant transport regime. In this paper the study of the propagation of terahertz (THz) waves through 3D random media by employing terahertz time-domain spectroscopy (THz-TDS) is addressed. Specifically, measurements of the electric field transmitted by samples of different thicknesses made of 1 mm diameter silica spheres dispersed in a paraffin matrix at different filling fractions are reported. This investigation has provided an accurate measurement of the EM field phase and, hence, information on the radiation propagation velocity that has enabled the first observation of a photonic glass at the THz range.     

不同表面激光双向反射分布函数的实验研究

根据粗糙面电磁散射理论讨论了粗糙表面双向反射分布函数（ＢＲＤＦ）和单位面积激光雷达截面的关系。测量不同粗糙度金板、铝基、钢基和涂层样片在０．６３μｍ的双向反射分布函数。分析了高度起伏均方根δ，斜率起伏均方根ｓ，介电常数对双向反射分布函数的影响。最后，将部分粗糙样片的双向反射分布函数理论计算结果与实验数据比较，两者有良好的吻合。     

X—射线荧光分析散函数法的原理及其应用：—Ⅲ.连续背景幂？…

本文在宽的基体变化范围内对波长为０．０８１ｎｍ的连续散射Ｘ－射线进行了研究,表明质量衰减系数与连续散射强度之间不再遵守传统散射内标法所假定的反比例关系,而是呈一种幂函数关系。理论证明和实验结果一致。提出了用０．０８１ｎｍ处的散射强度的函数校正基体效应的方法,用于地质样品中微量锶的测定,结果显示,在较大的基体变动范围内,本不与传统散射内标法相比准确度提高近４倍,克服了传统方法适应基体变化范围小的缺点     

Difference of optical properties between porous alumina and sapphire using two-substrate method at elevated temperature

We report on simultaneous measurements of the emittance, transmittance and reflectance of a porous alumina under same environment at 573 K, which has not been obtained. It is demonstrated that the correction of substrate radiation and multiple reflections is important for the accurate measurement of infrared (IR) optical properties of porous materials in a two-substrate method. We deduced the extinction, absorption and scattering coefficients of the alumina from the measured three quantities, based on the classical geometry model. The coefficients explain the difference of the IR optical properties between the alumina and the sapphire. The increasing reflectance of the alumina with thickness, unlike the sapphire, is attributed to the relatively high scattering coefficient at short wavelengths.     

Functional Ag porous films prepared by electrospinning

Face-centered cubic Ag porous films have been prepared directly from the heat treatment of AgNO₃-doped poly(vinyl alcohol) (PVA) electrospun nanofibers. Using Rhodamine B (RB) as the probing molecule, the surface-enhanced Raman scattering (SERS) effect of Ag porous films was demonstrated. The antibacterial activity of Ag porous films was also studied in this work. The propagation and biological activity of yeast cells were effectively inhibited by Ag porous films. These functional Ag porous films were expected to be applied in many fields, such as catalysis, diagnostics, sensors and antibacterial, etc.     

Nano-metrology of porous structures — I Comparison of measured neutron scattering with calculated scattering to access pore lattice,diameter, and wall parameters,using models of extended arrays of regular or randomised pores

Neutron scattering offers a length-scale-independent method of probing structured matter on an atomic scale through nano-scale to meso-scale. A protocol is presented that provides a versatile method of determining structure, by comparison of measured and calculated neutron scattering, for any structural distribution that can be described algebraically or numerically, requiring no particular model other than the model of the structure, and needing no adjustable parameters other than the scale and other parameters describing the physical model. The method enables the direct comparison of measured and calculated scattering from structured matter: from simple finite and infinite bodies, from extended regular array of pores, or from extended arrays of pores with a partially randomised character. Examples are given for the radial distributions of a range of regular bodies, of large arrays of highly ordered porous materials such as templated SBA-15 and MCM-41 silicas, as well as for more disordered materials such as sol–gel silicas. Monte Carlo integration of the calculated scattering for ensembles of up to about 100,000 pores has been studied using these techniques. The method enables the calculation of the solid–solid density correlation function G(r)$G\left(r\right)$ for model systems, and hence, by Fourier transformation, the expected scattering. Example measured scattering is compared with the calculated scattering, with further data presented in a related paper. The technique allows the direct calculation and comparison with measurement of all three of the main pore structural parameters: lattice spacing, pore diameter, and pore-wall thickness. Example SBA-15 wide and small angle neutron scattering (SANS) data, measured on NIMROD (the Near and InterMediate Range Order Diffractometer at ISIS), is used as an initial evaluation of the applicability of the techniques. The method is also applicable to determining structure by comparing calculating with measured diffraction broadening, and an example is given using SBA-15 diffraction data, measured on D20, at the Institut Laue-Langevin (ILL), Grenoble.     

Taking into account channels of focused intensity losses for refractive optics elements

Methods are proposed for taking into account intensity losses due to random deviations of composition profiles and due to small-angle scattering effects in amorphous materials and wide-angle scattering effects in polycrystalline materials. Experimental data are presented on the study of polycrystalline-diamond lenses using a synchrotron radiation beam.     

Investigation of multiple ultrasmall-angle neutron scattering with the aid of a double-crystal diffractometer

A method of multiple small-angle neutron scattering (MSANS), used to obtain information about inhomogeneities of substances, is considered. Experimental schemes and theory of a double-crystal diffractometer intended for measuring multiple small-angle neutron scattering are described. Methods used to approximate MSANS angular distributions at a low concentration of inhomogeneities and based on Moliére’s theory are reviewed. Their applicability is demonstrated for the examples ofMSANS spectra of samples from ferromagnetic iron-nickel alloys, aluminum powders, and high-T _c superconductor ceramic materials. Theoretical and experimental investigations of interference effects that manifest themselves in multiple small-angle neutron scattering on systems containing high concentrations of scatterers are reported.     

A small-angle X-ray scattering study of the isotropic and nematic phases of V2O5 suspensions

We report small-angle X-ray scattering experiments performed in both the isotropic and nematic phases of aqueous V₂O₅ suspensions. We show that the scattering in the isotropic phase can be well described in the whole accessible q-range by only considering the form factor of non-interacting ribbons. We investigate the influence of concentration and pH on the dimensions of V₂O₅ ribbons and show that these parameters do not have any significant effect, as long as the system stays well within the chemical stability domain of the ribbons. We then show that nematic single domains display an anisotropic small-angle scattering pattern, even at scattering vectors small compared to that at which a characteristic correlation peak is observed. This feature is expected for a nematic phase, but was rarely observed. We finally try to describe this scattering within the framework of theories developed for the structure factor of a nematic polymer, and we reach the conclusion that chain ends are certainly important to understand this pattern. Received 21 July 1999 and Received in final form 17 December 1999     

Radiation Transfer in a Binary, Stochastic Medium with Strongly Fluctuating Parameters

The propagation of radiation in a three-dimensional, inhomogeneous, stochastic, scattering medium and in an equivalent homogeneous medium has been investigated by the small-angle iteration method. The statistical structure of the scattering parameters of a three-dimensional medium has been described within the framework of the two-dimensional Poisson process and the binary Markov process. The analytical data obtained point to the fact that the three-dimensional inhomogeneity of a stochastic medium significantly influences the radiation transfer in it.     

Diagnostics of density fluctuations by enhanced scattering with frequency-tunable microwave sources

The enhanced scattering diagnostics method based on the scattering of microwaves close to the upper hybrid resonance in the plasma has a high sensitivity and spatial resolution and makes it possible to observe the plasma density fluctuations with characteristic scale-lengths much smaller than the wavelength of the probing radiation in vacuum. Good spatial resolution for spatial positioning of the scattering volume by fast tuning of the source frequency ±5% around the reference frequency in the range 100–300 GHz at high power makes this diagnostic method particularly suitable for fluctuation and high energy particle measurements in tokamak plasmas with relatively flat density and temperature profiles.     

Instantaneous shifted‐excitation Raman difference spectroscopy (iSERDS)

Shifted‐excitation Raman difference spectroscopy (SERDS) is an experimental method to recover spontaneous Raman spectra despite the presence of strong fluorescence interference. The common scheme requires a tunable laser source and recording two spectra after each other. In this paper, an approach for instantaneous SERDS (iSERDS) is presented utilizing a broadband light source. The broadband radiation is spatially dispersed in the focal plane inside the object of investigation. The generated scattering signal is imaged onto the slit of an imaging spectrograph. The individual pixel lines on the detector represent Raman spectra with slightly shifted excitation wavelength and hence allow SERDS spectra to be derived. The proposed iSERDS technique is a suitable approach for obtaining Raman spectra from fluorescing samples provided they are homogenous on the length scale of the measurement volume. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple-scattering in radar systems: A review

Although extensively studied within the lidar community, the multiple scattering phenomenon has always been considered a rare curiosity by radar meteorologists. Up to few years ago its appearance has only been associated with two- or three-body-scattering features (e.g. hail flares and mirror images) involving highly reflective surfaces.Recent atmospheric research aimed at better understanding of the water cycle and the role played by clouds and precipitation in affecting the Earth's climate has driven the deployment of high frequency radars in space. Examples are the TRMM 13.5 GHz, the CloudSat 94 GHz, the upcoming EarthCARE 94 GHz, and the GPM dual 13-35 GHz radars. These systems are able to detect the vertical distribution of hydrometeors and thus provide crucial feedbacks for radiation and climate studies. The shift towards higher frequencies increases the sensitivity to hydrometeors, improves the spatial resolution and reduces the size and weight of the radar systems. On the other hand, higher frequency radars are affected by stronger extinction, especially in the presence of large precipitating particles (e.g. raindrops or hail particles), which may eventually drive the signal below the minimum detection threshold. In such circumstances the interpretation of the radar equation via the single scattering approximation may be problematic. Errors will be large when the radiation emitted from the radar after interacting more than once with the medium still contributes substantially to the received power. This is the case if the transport mean-free-path becomes comparable with the instrument footprint (determined by the antenna beam-width and the platform altitude).This situation resembles to what has already been experienced in lidar observations, but with a predominance of wide- versus small-angle scattering events. At millimeter wavelengths, hydrometeors diffuse radiation rather isotropically compared to the visible or near infrared region where scattering is predominantly in the forward direction. A complete understanding of radiation transport modeling and data analysis methods under wide-angle multiple scattering conditions is mandatory for a correct interpretation of echoes observed by space-borne millimeter radars.This paper reviews the status of research in this field. Different numerical techniques currently implemented to account for higher order scattering are reviewed and their weaknesses and strengths highlighted. Examples of simulated radar backscattering profiles are provided with particular emphasis given to situations in which the multiple scattering contributions become comparable or overwhelm the single scattering signal. We show evidences of multiple scattering effects from air-borne and from CloudSat observations, i.e. unique signatures which cannot be explained by single scattering theory. Ideas how to identify and tackle the multiple scattering effects are discussed. Finally perspectives and suggestions for future work are outlined.This work represents a reference-guide for studies focused at modeling the radiation transport and at interpreting data from high frequency space-borne radar systems that probe highly opaque scattering media such as thick ice clouds or precipitating clouds.     

Optical properties of pigmented coatings taking into account particle interactions

A T-matrix approach is used to obtain the orientation-averaged scattering and absorption cross sections of randomly oriented particle clusters, and the average angular distribution of the radiation scattered by them. The coefficients involved in the expansion of the phase function are obtained from this T-matrix approach, and used in a multiple scattering formalism to characterize the angular distribution of the diffuse radiation propagating through a particulate coating perpendicularly illuminated with collimated visible radiation. Asymmetry between forward and backward propagating diffuse radiation intensities is taken into account by means of this multiple scattering approach, which is based on solving the radiative transfer equation for successive scattering order contributions. A four-flux model is applied to compute the reflectance in terms of wavelength of the incident radiation and particle concentration. An application of the formalism is carried out to predict the optical properties of titanium dioxide pigmented polymer coatings, in terms of the pigment volume fraction and the degree of aggregation.