Introduction

The present study aims to retrieve the spectral real part (or refraction index) and imaginary part (absorption index) of the complex index of refraction of microalgae from experimentally measured size distribution as well as absorption and scattering cross-sections. The green algae Chlamydomonas reinhardtii strain CC125 and its truncated chlorophyll antenna transformants tla1, tlaX, and tla1-CW+ as well as Botryococcus braunii, Chlorella sp., and Chlorococcum littorale were considered in this study. Finally, the results were used to retrieve the microalgae pigment concentrations and gain insight into their composition.

Analysis

In the present study, the different microalgae were assumed to be spherical. This assumption simplifies the calculations of their radiation characteristics by using the Lorenz–Mie theory instead of the T-matrix method. Moreover, despite their heterogeneous structure, microalgae were treated as homogeneous with some effective refraction and absorption indices. The different microalgae were treated as homogeneous spheres with an equivalent diameter such that their surface area was identical to that of their actual spheroidal shape assumed to be axisymmetric.  The equivalent diameter of the sphere having the same surface area as the spheroid is given by

where a and b are the major and minor diameters, respectively. The spheroid aspect ratio is defined as ε = a/b. Moreover, the number frequency of equivalent diameter ds is denoted by denoted by f(d_s) is defined as

where N(d_s) is the number of cells per unit volume of suspension having diameter between d_s and d_s+dd_s. The denominator on the right-hand side is the total cell concentration N_T expressed in total number of cells per m³ of suspension. The Lorenz-Mie theory predicts the absorption and scattering cross-sections denoted by C_abs,λ and C_sca,λ (expressed in m²) of an individual spherical cell of diameter d_s with complex index of refraction n_λ + ik_λ submerged in phosphate buffered saline (PBS) solution with refraction index n_PBS. Then, the absorption coefficient κ_λ and scattering coefficient σ_s,λ of a microorganism suspension with size distribution N(d_s) is expressed as

Here, C_abs,λ and C_sca,λ are the average absorption and scattering cross-sections of the microalgae in suspension (in m²), respectively. These average cross-sections can effectively be measured for typically polydisperse microalgae population. In fact, Berberoğlu et al.(2008) measured the average absorption and scattering cross-sections C_abs,λ and C_sca,λ for B. braunii, Chlorella sp., and C. littorale.  They also measured the average mass absorption C_abs,λ and scattering C_sca,λ cross-sections of C. reinhardtii and its mutants. These mass cross-sections were converted into C_abs,λ and C_sca,λ by the cells’ density and volume water fraction. Thus, the predictions from Lorenz-Mie theory could be directly compared with experimental data.

Results

Fig. 2 compares the effective refraction and absorptio nindices of C. reinhardtii CC 125 and its truncated chlorophyll antenna transformants tla1, tlaX, and tla1-CW+ between 400 and 750 nm. Overall, n_λ varied slightly from one strain to another.On the other hand, Fig. 2 clearly shows that the absorption index decreases from CC125 to tla1-CW+, tla1, and tlaX corresponding to a reduction in the size of their chlorophyll antenna. A significant decrease in k_λwas apparent for tlaX at wavelength 475 nm corresponding to a decrease in Chl b concentration caused by genetic engineering. In addition, tla1-CW+ features an absorption index larger than tla1 possibly due to the presence of a cell wall.

Fig. 2. Comparison of the retrieved refraction and absorption indices between 400 and 750 nm for the green algae C. reinhardtii CC 125 and its truncated chlorophyll antenna transformants tla1, tlaX, and tla1-CW+.

Fig. 3 shows the retrieved effective refraction and absorption indices for B. braunii, Chlorella sp., and C. littorale between 400 and 750 nm from the measured absorption and scattering cross-sections. Their refraction index n_λ varied slightly between 1.345 and 1.36. indicatesthat C. littorale had the largest absorption index k_λ while B. braunii and Chlorella sp. featured similar absorption indices across the PAR. Here also, k_λ features absorption peaks at 435, 475, and 676 nm corresponding to the absorption peaks of in vivo Chl a and Chl b. It is interesting to note that the absorption cross-section of B. braunii was larger than those of C. littorale and Chlorella sp. which were similar despite the fact that C. littorale were much smaller than B. braunii, and Chlorella sp. However,the dry mass fraction of Chl a+b was (a) 1.9% in C. littorale, (b) 0.22–0.56% in B. braunii, and (c) 0.4–1.41% in Chlorella sp.. This may explain why C. littorale had the largest absorption index k_λ and B.braunii and Chlorella sp. were found to have similar k_λ.

Fig. 3. Comparison of the retrieved refraction and absorption indices between 400 and 750 nm for B. braunii, Chlorella sp., and C. littorale.

Conclusion

This study presented and used a methodology to retrieve the spectral refraction and absorption indices of various biofuel producing microalgae from experimentally measured average absorption and scattering cross-sections between 400 and 750 nm. The microalgae were treated as spherical particles with equivalent diameter distributions calculated from experimentally measured major and minor diameter distributions. An inverse method was developed combining Lorenz-Mie theory as the forward method and genetic algorithm. The retrieved refraction and absorption indices were continuous function of wavelength with apparent absorption peaks corresponding to those of Chl a and Chl b. These optical properties can be used to predict the radiation characteristics of the species considered using Lorenz-Mie theory or the T-matrix method for a given size distribution and average aspect ratio.

Publications

E. Lee, R.-L. Heng, and L. Pilon, 2013. Optical Constants of C.reinhardtii, Its Truncated Chlorophyll Antenna Transformants, and Other Biofuel Producing Microalgae. Journal of Quantitative Spectroscopy and Radiation Transfer, Vol. 114, pp.122-135. doi:10.1016/j.jqsrt.2012.08.012. pdf

H. Berberoğlu, L. Pilon, and A. Melis, 2008. Radiation Characteristics of Chlamydomonas reinhardtiiCC125 and Its Truncated Chlorophyll Antenna Transformants tla1, tlaX, and 37RP1-tla1, International Journal of Hydrogen Energy, Vol. 33, No.22, pp. 6467–6483. doi:10.1016/j.ijhydene.2008.07.071 pdf