# Size-dependent fluorescence of bioaerosols: Mathematical model using fluorescing and absorbing molecules in bacteria

## Abstract

This paper uses a mathematical model of fluorescent biological particles composed of bacteria and/or proteins (mostly as in Hill et al., 2013 [23]) to investigate the size-dependence of the total fluorescence emitted in all directions. The model applies to particles which have negligible reabsorption of fluorescence within the particle. The specific particles modeled here are composed of ovalbumin and of a generic Bacillus. The particles need not be spherical, and in some cases need not be homogeneous. However, the results calculated in this paper are for spherical homogeneous particles. Light absorbing and fluorescing molecules included in the model are amino acids, nucleic acids, and several coenzymes. Here the excitation wavelength is 266 nm. The emission range, 300 to 370 nm, encompasses the fluorescence of tryptophan. The fluorescence cross section (C _{F}) is calculated and compared with one set of published measured values. We investigate power law (Ad ^{y}) approximations to C _{F}, where d is diameter, and A and y are parameters adjusted to fit the data, and examine how y varies with d and composition, including the fraction as water. The particle's fluorescence efficiency (Q _{F}=C _{F}/geometric-cross-section) can be written for homogeneous particles as Q _{abs}R _{F}, where Qmore »

- Authors:

- US Army Research Lab., Adelphi, MD (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Silver Spring, MD (United States)

- Publication Date:

- Research Org.:
- Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1214684

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Quantitative Spectroscopy and Radiative Transfer

- Additional Journal Information:
- Journal Volume: 157; Journal Issue: C; Journal ID: ISSN 0022-4073

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; 54 ENVIRONMENTAL SCIENCES; Fluorescence; Bioaerosols; Aerosol characterization; Light scattering

### Citation Formats

```
Hill, Steven C., Williamson, Chatt C., Doughty, David C., Pan, Yong-Le, Santarpia, Joshua L., and Hill, Hanna H.
```*Size-dependent fluorescence of bioaerosols: Mathematical model using fluorescing and absorbing molecules in bacteria*. United States: N. p., 2015.
Web. doi:10.1016/j.jqsrt.2015.01.011.

```
Hill, Steven C., Williamson, Chatt C., Doughty, David C., Pan, Yong-Le, Santarpia, Joshua L., & Hill, Hanna H.
```*Size-dependent fluorescence of bioaerosols: Mathematical model using fluorescing and absorbing molecules in bacteria*. United States. doi:10.1016/j.jqsrt.2015.01.011.

```
Hill, Steven C., Williamson, Chatt C., Doughty, David C., Pan, Yong-Le, Santarpia, Joshua L., and Hill, Hanna H. Mon .
"Size-dependent fluorescence of bioaerosols: Mathematical model using fluorescing and absorbing molecules in bacteria". United States.
doi:10.1016/j.jqsrt.2015.01.011. https://www.osti.gov/servlets/purl/1214684.
```

```
@article{osti_1214684,
```

title = {Size-dependent fluorescence of bioaerosols: Mathematical model using fluorescing and absorbing molecules in bacteria},

author = {Hill, Steven C. and Williamson, Chatt C. and Doughty, David C. and Pan, Yong-Le and Santarpia, Joshua L. and Hill, Hanna H.},

abstractNote = {This paper uses a mathematical model of fluorescent biological particles composed of bacteria and/or proteins (mostly as in Hill et al., 2013 [23]) to investigate the size-dependence of the total fluorescence emitted in all directions. The model applies to particles which have negligible reabsorption of fluorescence within the particle. The specific particles modeled here are composed of ovalbumin and of a generic Bacillus. The particles need not be spherical, and in some cases need not be homogeneous. However, the results calculated in this paper are for spherical homogeneous particles. Light absorbing and fluorescing molecules included in the model are amino acids, nucleic acids, and several coenzymes. Here the excitation wavelength is 266 nm. The emission range, 300 to 370 nm, encompasses the fluorescence of tryptophan. The fluorescence cross section (CF) is calculated and compared with one set of published measured values. We investigate power law (Ady) approximations to CF, where d is diameter, and A and y are parameters adjusted to fit the data, and examine how y varies with d and composition, including the fraction as water. The particle's fluorescence efficiency (QF=CF/geometric-cross-section) can be written for homogeneous particles as QabsRF, where Qabs is the absorption efficiency, and RF, the fraction of the absorbed light emitted as fluorescence, is independent of size and shape. When QF is plotted vs. mid or mi(mr-1)d, where m=mr+imi is the complex refractive index, the plots for different fractions of water in the particle tend to overlap.},

doi = {10.1016/j.jqsrt.2015.01.011},

journal = {Journal of Quantitative Spectroscopy and Radiative Transfer},

number = C,

volume = 157,

place = {United States},

year = {Mon Feb 02 00:00:00 EST 2015},

month = {Mon Feb 02 00:00:00 EST 2015}

}

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