3 Theoretical Models of Light Scattering and Absorption
55
spheres, and therefore one large sphere contains the same volume (and mass) of
material as eight small spheres. However, the surface area of one large sphere is
only four times that of one small sphere. Based upon our discussions of microscopic
light interactions (Sects. 3.3–3.5), we regard scattering as predominantly a surface
phenomenon, while absorption can occur anywhere within a particle. Thus, the eight
smaller particles, taken together, have essentially the same ability to absorb light as
the one large particle, but the eight small particles present more surface area to the
beam and have more ability to scatter light. The effect has been seen experimentally:
Devaux et al., for example, have conducted NIR reflectance experiments on mixtures
of two types of particles (wheat and rapeseed) and found that in mixtures containing
two different particle sizes, the smaller particles were more prominently represented
in the spectra than were the larger particles [17]. Consequently, when considering
the different types of particles that make up a sample, we must distinguish between
“types” of particles based not only upon composition, but also upon volume and
surface area.
The proposed criteria for the “representative layer” are:
• The volume fraction for each particle type is the same in the layer as in the sample
as a whole
• The cross-sectional surface areas of different particle types in the layer are in the
same proportion as they are in the sample as a whole
• The void fraction in the layer is the same as the void fraction of the sample as a
whole
• The layer is only one particle thick. (This means the representative layer does not
have a uniform thickness, as different particles have different sizes.)
The first three criteria ensure that the layer is representative of the sample as a
whole, in terms of physical properties that are important in determining outcomes
for interactions with light. The last criteria is included so that we can assume a
single interaction. A representative fraction of the light will interact with each of
the particles (or voids) present in the layer, but a given ray of light will only interact
with a given layer once. This means that we can assume the kinds of “microscopic”
models and phenomena described in Sects. 3.3–3.5 would apply to the representative
layer.
Mathematical expressions of these criteria can be found in [16] and [18]. Examples
of applications of the representative layer theory to real samples can be found in [19]
and [20].
3.10 Obtaining Linear Absorbance Data for Scattering
Samples
At this point, it is instructive to think back to Beer’s Law. The practical appeal of
the equation is that it is a simple linear relationship between the concentration of
the absorber (which is usually what we are trying to determine) and the absorbance
55
spheres, and therefore one large sphere contains the same volume (and mass) of
material as eight small spheres. However, the surface area of one large sphere is
only four times that of one small sphere. Based upon our discussions of microscopic
light interactions (Sects. 3.3–3.5), we regard scattering as predominantly a surface
phenomenon, while absorption can occur anywhere within a particle. Thus, the eight
smaller particles, taken together, have essentially the same ability to absorb light as
the one large particle, but the eight small particles present more surface area to the
beam and have more ability to scatter light. The effect has been seen experimentally:
Devaux et al., for example, have conducted NIR reflectance experiments on mixtures
of two types of particles (wheat and rapeseed) and found that in mixtures containing
two different particle sizes, the smaller particles were more prominently represented
in the spectra than were the larger particles [17]. Consequently, when considering
the different types of particles that make up a sample, we must distinguish between
“types” of particles based not only upon composition, but also upon volume and
surface area.
The proposed criteria for the “representative layer” are:
• The volume fraction for each particle type is the same in the layer as in the sample
as a whole
• The cross-sectional surface areas of different particle types in the layer are in the
same proportion as they are in the sample as a whole
• The void fraction in the layer is the same as the void fraction of the sample as a
whole
• The layer is only one particle thick. (This means the representative layer does not
have a uniform thickness, as different particles have different sizes.)
The first three criteria ensure that the layer is representative of the sample as a
whole, in terms of physical properties that are important in determining outcomes
for interactions with light. The last criteria is included so that we can assume a
single interaction. A representative fraction of the light will interact with each of
the particles (or voids) present in the layer, but a given ray of light will only interact
with a given layer once. This means that we can assume the kinds of “microscopic”
models and phenomena described in Sects. 3.3–3.5 would apply to the representative
layer.
Mathematical expressions of these criteria can be found in [16] and [18]. Examples
of applications of the representative layer theory to real samples can be found in [19]
and [20].
3.10 Obtaining Linear Absorbance Data for Scattering
Samples
At this point, it is instructive to think back to Beer’s Law. The practical appeal of
the equation is that it is a simple linear relationship between the concentration of
the absorber (which is usually what we are trying to determine) and the absorbance