Abstract
We have demonstrated and explored the effects of the hydrostatic pressure on a one-dimensional phononic crystal (1D PnC). In this regard, we designed the proposed 1D PnC structure with a stack of polycrystalline silicon (Si) and polymethyl methacrylate (PMMA) for four unit cells. A hydrostatic pressure (positive and negative) with values ranging from 0 to ± 5 GPa is applied on the PnC design. By using the well-known transfer matrix method (TMM), we have investigated the transmittance spectrum of the proposed PnC where the mechanical characteristics of PMMA are discussed in the presence of the applied hydrostatic pressure. The obtained results exhibit the tunability of the phononic band gap (PnBG) by controlling the applied hydrostatic pressure in the considered ultrasonic region. We found that the PnBG width is decreased and shifted towards the higher frequencies as the hydrostatic pressure increases. The decrease in the width of the PnBG could be due to the increase in the velocity of sound and Young's modulus of PMMA layer with increasing the pressure. The tunability feature of the PnBGs under hydrostatic pressure can be useful in different acoustic applications such as switches, transducers, filters, sound suppression, and sensors.
Similar content being viewed by others
Data availability
Requests should be addressed to any author.
Code availability
Not applicable.
References
Ahmed, A.M., Mehaney, A.: Ultra-high sensitive 1D porous silicon photonic crystal sensor based on the coupling of Tamm/Fano resonances in the mid-infrared region. Sci. Rep. 91(9), 1–9 (2019). https://doi.org/10.1038/s41598-019-43440-y
Aliev, G.N., Goller, B.: Quasi-periodic Fibonacci and periodic one-dimensional hypersonic phononic crystals of porous silicon: experiment and simulation. J. Appl. Phys. 116, 094903 (2014). https://doi.org/10.1063/1.4894620
Aly, A.H., Mehaney, A.: Enhancement of phononic band gaps in ternary/binary structure. Physica B Condens. Matter 407(21), 4262–4268 (2012). https://doi.org/10.1016/j.physb.2012.07.014
Aly, A.H., Mehaney, A., Abdel-Rahman, E.: Study of physical parameters on the properties of phononic band gaps. Int. J. Mod. Phys. B (2013). https://doi.org/10.1142/S0217979213500471
Cao, W., Qi, W.: Plane wave propagation in finite 2–2 composites. J. Appl. Phys. 78, 4627 (1998). https://doi.org/10.1063/1.360701
Darinskii, A.N., Shuvalov, A.L.: Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell. Phys. Rev. B 100, 184303 (2019). https://doi.org/10.1103/PhysRevB.100.184303
Dixit, M., Shaktawat, V., Sharma, K., Saxena, N.S., Sharma, T.P.: Mechanical characterization of polymethyl methacrylate and polycarbonate blends. AIP Conf. Proc. 1004, 311 (2008). https://doi.org/10.1063/1.2927574
Hussein, M.I., Hulbert, G.M., Scott, R.A.: Dispersive elastodynamics of 1D banded materials and structures: analysis. J. Sound Vib. 289, 779–806 (2006). https://doi.org/10.1016/J.JSV.2005.02.030
Ibarias, M., Zubov, Y., Arriaga, J., Krokhin, A.A.: Phononic crystal as a homogeneous viscous metamaterial. Phys. Rev. Res. 2, 022053 (2020). https://doi.org/10.1103/PhysRevResearch.2.022053
Ishiyama, C., Higo, Y.: Effects of humidity on Young’s modulus in poly(methyl methacrylate). J. Polym. Sci. Part B Polym. Phys. 40, 460–465 (2002). https://doi.org/10.1002/POLB.10107
Khateib, F., Mehaney, A., Aly, A.H.: Glycine sensor based on 1D defective phononic crystal structure. Opt. Quant. Electron. 52(11), 489 (2020)
Ko, Y.H., Kim, K.J., Ko, J.-H.: High-pressure sound velocity of PMMA studied by using brillouin spectroscopy. J. Korean Phys. Soc. 6312(63), 2358–2361 (2013). https://doi.org/10.3938/JKPS.63.2358
Lazcano, Z., Arriaga, J., Aliev, G.N.: Experimental and theoretical demonstration of acoustic Bloch oscillations in porous silicon structures. J. Appl. Phys. 115, 154505 (2014). https://doi.org/10.1063/1.4871535
Long, H., Cheng, Y., Zhang, T., Liu, X.: Wide-angle asymmetric acoustic absorber based on one-dimensional lossy Bragg stacks. J. Acoust. Soc. Am. 142, EL9 (2017). https://doi.org/10.1121/1.4991677
Malek, C., Aly, A.H., Alamri, A., Sabra, W.: Tunable PBGs with a cutoff frequency feature in Fibonacci quasi-periodic designs containing a superconductor material at THz region. Phys. Scr. (2021). https://doi.org/10.1088/1402-4896/ac0275
Matsushige, K., Radcliffe, S.V., Baer, E.: The mechanical behavior of poly(methyl methacrylate) under pressure. J. Polym. Sci. Polym. Phys. Ed. 14, 703–721 (1976). https://doi.org/10.1002/POL.1976.180140411
Mehaney, A., Ahmed, A.M.: Locally resonant phononic crystals at low frequencies based on porous SiC multilayer. Sci. Rep. 91(9), 1–12 (2019). https://doi.org/10.1038/s41598-019-51329-z
Mehaney, A., Elsayed, H.A.: Hydrostatic pressure effects on a one-dimensional defective phononic crystal comprising a polymer material. Solid State Commun. 322, 114054 (2020). https://doi.org/10.1016/J.SSC.2020.114054
Mehaney, A., Nagaty, A., Aly, A.H.: Glucose and Hydrogen peroxide concentrations measurement using 1D defective phononic crystal sensor. Plasmonics (2021a). https://doi.org/10.1007/s11468-021-01435-4
Mehaney, A., Shehatah, A.A., Ahmed, A.M.: Modeling of phononic crystal cavity for sensing different biodiesel fuels with high sensitivity. Mater. Chem. Phys. 257, 123774 (2021b). https://doi.org/10.1016/J.MATCHEMPHYS.2020.123774
Ngoepe, P.E., Lambson, E.F., Saunders, G.A., Bridge, B.: The elastic behaviour under hydrostatic pressure of poly(methyl methacrylate) and its fully deuterated form. J. Mater. Sci. 2511(25), 4654–4657 (1990). https://doi.org/10.1007/BF01129921
Nomura, M.: Phononic band engineering for thermal conduction control and similarity with photonic band engineering. Microsyst. Technol. 223(22), 473–480 (2015). https://doi.org/10.1007/S00542-015-2569-5
Palaz, S., Ozer, Z., Ahundov, C., Mamedov, A.M., Ozbay, E.: Multiferroic based 2D phononic crystals: band structure and wave propagations. Ferroelectrics 544, 88–95 (2019). https://doi.org/10.1080/00150193.2019.1598193
Sabra, W., Aly, A.H.: A comparative study of the effective surface impedance of an HTc superconducting thin film from visible to mid-IR region. Opt. Quant. Electron. 53, 416 (2021). https://doi.org/10.1007/s11082-021-03072-x
Sauer, J.A., Mears, D.R., Pae, K.D.: Effects of hydrostatic pressure on the mechanical behaviour of polytetrafluoroethylene and polycarbonate. Eur. Polym. J. 6, 1015–1032 (1970). https://doi.org/10.1016/0014-3057(70)90034-0
Sayed, F.A., Elsayed, H.A., Aly, A.H.: Optical properties of photonic crystals based on graphene nanocomposite within visible and IR wavelengths. Opt. Quant. Electron. 52, 464 (2020)
Sun, Y., Yu, Y., Zuo, Y., Qiu, L., Dong, M., Ye, J., Yang, J.: Band gap and experimental study in phononic crystals with super-cell structure. Results Phys. 13, 102200 (2019). https://doi.org/10.1016/J.RINP.2019.102200
Taya, S.A., Ramahi, O.M., Abutailkh, M.A., Doghmosh, N., Nassar, Z.M., Upadhyay, A., Colak, I.: Investigation of bandgap properties in one-dimensional binary superconductor–dielectric photonic crystal: TE case. Indian J. Phys. (2021a). https://doi.org/10.1007/s12648-021-02151-9
Taya, S.A., Abutailkh, M.A., Colak, I., Ramahi, O.M.: Modelling of three tunable multichannel filters using Ag metal as a defect layer in a photonic crystal. Opt. Quant. Electron. 53, 644 (2021b). https://doi.org/10.1007/s11082-021-03307-x
Taya, S.A., Doghmosh, N., Abutailkh, M.A., Upadhyay, A., Nassara, Z.M., Colak, I.: and Ilhami Colak “Properties of band gap for p-polarized wave propagating in a binary superconductor-dielectric photonic crystal. Optik 243, 167505 (2021c). https://doi.org/10.1016/j.ijleo.2021.167505
Taya, S.A., Daher, M.G., Colak, I., et al.: Highly sensitive nano-sensor based on a binary photonic crystal for the detection of mycobacterium tuberculosis bacteria. J. Mater. Sci. Mater. Electron. 32, 28406–28416 (2021d)
Upadhyay, A., Singh, S., Sharma, D., Taya, S.A.: An ultra-high birefringent and nonlinear decahedron photonic crystal fiber employing molybdenum disulphide (MoS2): A numerical analysis. Mater. Sci. Eng. B 270, 115236 (2021). https://doi.org/10.1016/j.mseb.2021.115236
Vasseur, J.O., Deymier, P.A., Khelif, A., Lambin, P., Djafari-Rouhani, B., Akjouj, A., Dobrzynski, L., Fettouhi, N., Zemmouri, J.: Phononic crystal with low filling fraction and absolute acoustic band gap in the audible frequency range: a theoretical and experimental study. Phys. Rev. E 65, 056608 (2002). https://doi.org/10.1103/PhysRevE.65.056608
Zheng, M., Wei, P.J.: Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces. Int. J. Miner. Metall. Mater. 16, 608–614 (2009). https://doi.org/10.1016/S1674-4799(09)60105-9
Acknowledgements
The author thanks the reviewers and editors for improving this article. This work/manuscript/paper was produced with the financial support of the Academy of Scientific Research and Technology of Egypt; ScienceUP/GradeUp initiative: Grant Agreement No. (7859) and No. (7860). Its contents are the sole responsibility of the authors and do not necessarily reflect the views of the Academy of Scientific Research and Technology.
Author information
Authors and Affiliations
Contributions
All authors co-implemented the computer code, co-performed the numerical simulations, co-analyzed the data, co-wrote and revised the main manuscript text. All authors contributed equally.
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Consent to participate
Not applicable.
Consent for publication
Not applicable.
Research involving human and animal rights
This article does not contain any studies involving animals or human participants performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mehaney, A., Ahmed, A.M., Elsayed, H.A. et al. Hydrostatic pressure effects for controlling the phononic band gap properties in a perfect phononic crystal. Opt Quant Electron 54, 94 (2022). https://doi.org/10.1007/s11082-021-03484-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-021-03484-9