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April 21, 2020 **Author:** Collin Roesler

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# Benchtop Spectrophotometry of Particulates on Filters (QFT in IS-mode)

#### 0.1 Benchtop Spectrophotometry of Particulate Matter Collected on Glass Fiber Filters (the Quantitative Filter Technique) Measured Internally-mounted in the Integrating Sphere (the QFT in IS-mode)

The size and shape of commercially available integrating spheres limits the geometric pathlength of cuvettes that can be internally mounted. Thus to obtain a strong signal to noise, the concentration of suspended matter in a 1-cm cuvette has to be much higher than is generally observed in aquatic systems. For this reason, discrete water samples are ﬁltered onto glass ﬁber ﬁlters (Whatman GF/F) and the absorbance of the ﬁlters is measured. The protocol is identical to that outlined above with the exception that the baseline/blank scans are performed with a blank ﬁlter through which a comparable volume of pure water has been ﬁltered (to ﬂatten the ﬁbers in a comparable manner to that of the sample ﬁlter). The ﬁlter is placed in the sample holder (same location as the cuvette), perpendicular to the sample beam with the top of the ﬁlter (particle side) facing the incoming sample beam. Thus the sample beam interacts with the particles prior to interacting with the ﬁlter. The computation of absorption is:

$$a=2.303\phantom{\rule{0.3em}{0ex}}\frac{Abs}{\ell}$$ |

where the geometric pathlength is computed from the measured sample volume ﬁltered (ml), and the eﬀective area of the ﬁlter ($c{m}^{2}$). The geometric pathlength can be thought of as a cylinder of water of cross section equal to the eﬀective ﬁlter area and length, $\ell $, suﬃcient to account for the volume ﬁltered (Figure 4). The geometric pathlength of the sample on the ﬁlter is equivalent to the length of the cylinder of the original suspension.

Comparisons between samples measured in cuvettes with those measured on ﬁlter pads indicates that there is an ampliﬁcation of the mean photon path through the ﬁlter in the original sample beam over that of the geometric path. This is called pathlength ampliﬁcation. It arises as photons scatter within the ﬁlter and particles before exiting into the sphere. It is not accounted for by the reference beam. Careful and extensive paired measurements have demonstrated that the ampliﬁcation is not negligible (Figure 5).

The pathlength ampliﬁcation must be corrected before the computation of absorption. The correction, derived empirically from the data in Figure 5A, is

$$Ab{s}_{s}=0.323\phantom{\rule{0.3em}{0ex}}Ab{s}_{f}^{1.0867}\phantom{\rule{0.3em}{0ex}},$$ |

where $Ab{s}_{s}$ is the absorbance (optical density) measured in suspension and $Ab{s}_{f}$ is the absorbance (optical density) measured on the ﬁlter pad. The absorption coeﬃcient is computed from the absorbance measured on the ﬁlter pad:

$$a=2.303\phantom{\rule{0.3em}{0ex}}\frac{0.323\phantom{\rule{0.3em}{0ex}}Ab{s}_{f}^{1.0867}}{\frac{{V}_{filt}}{\pi {r}_{eff}^{2}}}\phantom{\rule{0.3em}{0ex}}.$$ |

Historically, the QFT was employed measuring the ﬁlters in transmission mode (as in Figure 2 on the Benchtop Spectrophotometry of Solutions page, with the cuvette replaced by the ﬁlter). In addition to the pathlength ampliﬁcation within the ﬁlter, there was an additional error associated with the loss of nearly half the incident radiant power scattering in the backward direction (away from the detector). The correction for both the scattering loss and pathlength ampliﬁcation are determined from paired suspension measurements in internally-mounted cuvettes in the integrating sphere and ﬁltered particles on ﬁltered conﬁgured in transmission mode, $Ab{s}_{f-T}$ (Figure 5B):

$$Ab{s}_{s}=0.679\phantom{\rule{0.3em}{0ex}}Ab{s}_{f-T}^{1.2804}\phantom{\rule{0.3em}{0ex}}.$$ |

A simple linear relationship has been found relating the absorption measured on ﬁlters in transmission mode, $Ab{s}_{f-T}$, to that measured in the integrating sphere, $Ab{s}_{f-IS}$:

$$Ab{s}_{f-IS}=1.29\phantom{\rule{0.3em}{0ex}}Ab{s}_{f-T}+0.00205\phantom{\rule{0.3em}{0ex}}.$$ |

The linearity is only found for absorbance values less than 0.35 in the transmission mode, and 0.45 in integrating sphere mode (Figure 5C). Beyond that range, the relationship becomes non-linear.

While measuring the absorption by particles on the ﬁlter pad comes with measurement challenges and increased uncertainty, it does allow absorption to be determined on optically dilute samples. In addition, the particulate matter can be extracted with methanol (Kishino et al. (1985)) to remove the extractable phytoplankton pigments from the particulate matter. The scan of the extracted ﬁlter yields the absorbance by the non-algal particle fraction. After computing the absorption spectra for the particulate scan and the non-algal particle scan, the absorption by in vivo phytoplankton pigments (as they were, bound to proteins in the light harvesting complexes in the chloroplasts) can be computed by diﬀerence.