_Applied_  
_sciences_  
_Article_  
_Size Determination of Polystyrene Sub-Microspheres_  
_Using Transmission Spectroscopy_  
**[PERSON] 1,2\({}^{\copyright}\)**, [PERSON] 3\({}^{\copyright}\)**, [PERSON] 4,*, [PERSON] 5,  
**[PERSON] 5, [PERSON] 5\({}^{\copyright}\)**, [PERSON] 5, [PERSON] 6  
**and [PERSON] 2,*\({}^{\copyright}\)**  
1 Department of Physics, Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Hanoi 10000, Vietnam; [PERSON]L_ADDRESS]  
2 Department of Physics, Le Quy Don Technical University, Hanoi 10000, Vietnam  
3 University of Science and Technology of Hanoi, Vietnam Academy of Science and Technology, Hanoi 10000, Vietnam; [EMAIL_ADDRESS]  
4 Institute of Materials Science, Vietnam Academy of Science and Technology, Hanoi 10000, Vietnam  
5 Institute of Physics, Vietnam Academy of Science and Technology, Hanoi 10000, Vietnam; [EMAIL_ADDRESS] (L.H.T.N.); [EMAIL_ADDRESS] (N.T.N.); [EMAIL_ADDRESS] (D.V.); [EMAIL_ADDRESS] (H.Q.D).  
6 Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Hanoi 10000, Vietnam; [EMAIL_ADDRESS]  
* Correspondence: [EMAIL_ADDRESS] (K.X.B.); [EMAIL_ADDRESS] (H.M.N.); Tel.: +84-9061-112-521 (H.M.N.)  
Received: 30 June 2020; Accepted: 28 July 2020; Published: 29 July 2020  
**Featured Application: Polystyrene (PS) sub-microspheres have attracted much attention since they are the building blocks of many experiments, for example, in the preparation of photonics, for hybrid metal/dielectric plasmonic structures that have optical resonance in the visible/near-infrared range. Scanning electron microscopy (SEM), dynamic laser scattering (DLS), and nanoparticle tracking analysis (NTA) are widely used to determine the sizes of PS sub-microspheres. However, this equipment is not accessible for many labs, especially chemistry labs. This work demonstrates a simple method to estimate the sizes of PS sub-microspheres using a UV-vis spectrometer. This equipment is more common in labs and is routinely used to estimate the sizes of colloidal quantum dots (QDs) and metallic nanoparticles. Besides this, our proposed method does not require any curve fitting process; hence, it is applicable for researchers of other disciplines. This advantage makes the proposed method very convenient and practical for use in addition to other methods.**  
Nano/micro polystyrene (PS) beads have found many applications in different fields spanning from drug delivery, bio-diagnostics, and hybrid plasmonics to advanced photonics. The sizes of the PS beads are an important parameter, especially in plasmonic and photonic experiments. In this work, we demonstrate a quick and straightforward method to estimate the diameters of sub-microspheres (0.2 um to 0.8 um) using the transmission spectra of a close-packed monolayer of polystyrene beads on glass or quartz substrates. Experimental transmission spectra of the PS monolayers were verified against finite-difference time-domain (FDTD) simulation and showed good agreement. The effects of the substrates on the transmission spectra and, hence, the accuracy of the method were also studied by simulation, which showed that common transparent substrates only cause minor deviation of the PS bead sizes calculated by the proposed method.  
**Keywords:** photonic crystals; polystyrene sub-microspheres; finite-difference time-domain (FDTD)