Diffuse reflectance spectroscopy: a comparison of the theories

Simmons, E. L.

doi:10.1364/ao.14.001380

Cited by 212 publications

(99 citation statements)

References 25 publications

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“…The recently published modified particle model theory of Simmons [57] (Equations (93) and (94)) removes the discrepancy in the Melamed treatment. ~his modified particle model theory is thought by Simmons to be the most nearly correct of all diffuse refle~tance theories [39]. It may very well be true, but its general acceptance must of course await a tho~'ough testing under a variety of conditions by variOUS workers.…”

Section: S= --And K = --· U+a U+amentioning

confidence: 98%

“…If we take layer i to be the first layer and layer j to be the combination of all the other layers of an n-layer sample, we have (40) (39) In this approach it is assumed that the same isotropic solutions (eqs (36) and (37)) may be used for arbitrary angular distribu tions of scatter, so long as the scattering is averaged according to eqs (38) and (39). Blevin and Brown [38] have shown that the reflectance curves are essentially the same for isotropic scatter or for scatter according to the (42) where we have assumed that all layers are the same so the subscripts on l' and t can be dropped.…”

Section: Statistical Theorymentioning

confidence: 99%

“…From eq (11) we have the obvious restriction that K 2dx< 1. It is equally obvious that the equations do not apply when dx is made arbitrarily small, since the assumption of homogeneous layers requires it to be large compared with the dimension l of the scattering particles [14,39]. Thus we have [16] 1 l~dx<Kz which can alternatively be written We see that the attenuation due to absorption within a layer of thickness l must be very small compared with unity, and we are restricted to weakly absorbing and weakly scattering materials.…”

Section: S= --And K = --· U+a U+amentioning

confidence: 99%

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The interpretation of diffuse reflectance spectra

Hecht¹

1976

J. RES. NATL. BUR. STAN. SECT. A.

191

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Numerous treatments of the diffuse r efl ecting properties of scattering media have been d escribed. Many theories give an adequate account of the refl ectance for a specific set of conditions for which the model was constructed and the soluti on t ested experimentally. Only those models which are considered to be fairl y general are considered her e.It is conveni ent to di vide the theories into those based upon continuum models and those based upon s tatistical models. The continuum m odels typica ll y describe the scatterin g a nd absorbin g properties of a given m edium in t erm s of two phenomenological constants. These models may all be regarded as varying levels of approxima t e soluti on to the general equation of radi ative tra nsfer. This provides a convenient basis for compariso n of the various theories.The statistical models a re based upon a summa tion of transmittances a nd r efl ectances fr om individual l ayers or parti cles. Thus, ~o m e ass um ptions must be m ade abo ut the n ature of the fund amenta l units, and the validity of the ultim a te result will depend upon how closely these assumptions correspond with r eality. Only the statistical models lead to ex pressions fr om which absolute absorptivities and sca ttering coefficients can be calculat ed and r elated to the actual particle characteristics.The relationship between the various models will be discussed and the features which typify the ab~o rptivity and scatterin g coeffici ent according to each will be compared and related to the available experimental data. This leads t o a consideration of the charac teristics of appropriate model systems and standards.Key words: Absolute absorptivities; continuum models; diffuse reflectance; r adiative transfer; reflectance spectra; scatt ering coefficients ; statistical models. List of Principal Symbols UsedH-integral of Chandrasekhar (equation (35) ) (Note: Where a given letter is used in both capital and lower case form (e.g., r,R and t,T), the capital letter refers to the macroscopic observable and the lower case letter to the corresponding variable for an individual particle or layer of the material. A bar over a given symbol means the average value for that variable). (5)) scattering function (equation (2)) source func tion (eq ua tion (4)) absorptivity Kubelka-Munk absorption constant (equations (16) and (17) H(iJ.)

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Section: S= --And K = --· U+a U+amentioning

confidence: 98%

Section: Statistical Theorymentioning

confidence: 99%

Section: S= --And K = --· U+a U+amentioning

confidence: 99%

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The interpretation of diffuse reflectance spectra

Hecht¹

1976

J. RES. NATL. BUR. STAN. SECT. A.

191

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“…4B). The band gap of all powders are calculated according to the transformed Kubelka-Munk function vs the energy of light [43].In the case of X-Au-TiO 2 samples (Fig. 4A), there is no influence of gold on the band gap energy of TiO 2 (3.1 eV).…”

Section: Morphology and Structurementioning

confidence: 99%

One step synthesis of N-doped and Au-loaded TiO2 nanoparticles by laser pyrolysis: Application in photocatalysis

Bouhadoun

Guillard

Dapozze

et al. 2015

Applied Catalysis B: Environmental

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“…Based on our previous experience [34][35][36][37], the Kubelka-Munk method is a useful method. The optical absorption coefficient (a) calculated from the reflectance data using Kubelka-Munk equation [38][39][40][41] is expressed as:…”

Section: Resultsmentioning

confidence: 99%

Photoinduced deposition of gold nanoparticles on TiO2–WO3 nanotube films as efficient photoanodes for solar water splitting

Momeni

Ghayeb

2016

Appl. Phys. A

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Gold-modified TiO 2 -WO 3 nanotubes with different amounts of gold were obtained by two methods; photoassisted deposition and one-step electrochemical anodizing method. The morphology, crystallinity and elemental composition were studied by FE-SEM, XRD and EDX. The photoelectrochemical performance was examined under Xe light illumination in 1 M NaOH electrolyte. Characterization of the as-prepared TiO 2 -WO 3 samples indicated that sodium tungstate concentration in anodizing solution significantly influenced the morphology and photoelectrochemical activity of fabricated films. Also, photoelectrochemical characterizations show that the photocatalytic activity of Au/TiO 2 -WO 3 nanotubes was improved as compared with that of bare TiO 2 -WO 3 nanotubes. The experimental results showed that the photocatalytic activities of Au/TiO 2 -WO 3 were significantly affected by the amount of Au nanoparticles. The amount of gold nanoparticles was effectively controlled by time of photoreduction of the chloroauric acid solution. These new photoanodes showed enhanced high photocurrent density with good stability and are a highly promising photoanodes for photocatalytic hydrogen production.

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Diffuse reflectance spectroscopy: a comparison of the theories

Cited by 212 publications

References 25 publications

The interpretation of diffuse reflectance spectra

The interpretation of diffuse reflectance spectra

One step synthesis of N-doped and Au-loaded TiO2 nanoparticles by laser pyrolysis: Application in photocatalysis

Photoinduced deposition of gold nanoparticles on TiO2–WO3 nanotube films as efficient photoanodes for solar water splitting

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