Indian Journal of Geo-Marine Sciences Vol. 41(6), December 2012, pp. 557-562 An investigation on the behaviour of PDMS as a membrane material for underwater acoustic sensing M. F. A. Rahman, M. R. Arshad, A.A. Manaf & M.I.H. Yaacob, Underwater Robotic Research Group(URRG), School of Electrical & Electronics Engineering, Universiti Sains Malaysia Engineering Campus, 14300 Nibong Tebal, Penang, MALAYSIA [E-mail:-mohdfaizal07@yahoo.com] Received 26 July 2012; revised 17 August 2012 Present study consists the behaviour of Polydimethylsiloxane (PDMS) as a vibrating membrane for acoustic signal detection application. Modelling and simulation work was performed using ANSYS 12.1. Theory of acoustic impedance showed that PDMS acting as an acoustic membrane is acoustically matched when operated in water rather than air with 96.7% energy transfer efficiency. Effect of hydrostatic pressure on the membrane deflection was studied for a very shallow application with depth level ranging from 0 to 1m. Effect of PDMS structural geometry on its deflection behaviour was also studied by varying the radius and thickness of the membrane structure. Finally, according to the deflection theory, the type of membrane deflection was classified based on the variation of radius to thickness ratio of the membrane as well as the applied pressure. [Keywords: Acoustic sensor, PDMS membrane, Hydrostatic effect, Deflection theory] Introduction In underwater or undersea technology, acoustic signal plays an important role in enabling many applications such as for the purpose of military, sea monitoring and exploration, imaging, control, underwater robotic and communication. Acoustic technology is a preferred method for underwater wireless application due to several advantages over its counterpart; radio and optical waves. Radio waves normally need large antenna and high power for its operation, while optical approach always suffers from scattering effect during underwater transmission 1. The operation of acoustic system basically depends on how well the signal is to be transmitted and received between each subcomponent that forms the whole system. The performance criteria of underwater system depends on many parameters such as frequency, depth, range, power consumption, energy efficiency, transmit response and receive sensitivity 2,3. Acoustic sensing is one of the main area that gains much attention in this underwater technology. It deals with the utilisation of a sensing device that is able to capture the transmitted signal at certain boundary condition and specification. Researchers have allocated much of their time and effort exploring in this area, owing to its prospective use in the future. Ability to successfully implement this technology will help to boost the performance of many underwater applications beyond the human capability. Apart from that, miniaturisation becomes another factor of consideration in acoustic sensor design due to its advantages in mass production, low power consumption and massive cost reduction. This miniaturization trend becomes viable due to the advancement in microfabrication technology and continues to be an active research in acoustic sensing field since a decade ago 4,5. In microsensing technology, one of the main parameter that directly influences the performance of a sensor is the receive sensitivity. For a membranebased acoustic sensor, receive sensitivity depends on the amount of membrane deflection in response to a signal. For such sensor, the more the membrane get deflected, the higher sensitivity it will achieve 6. Such deflection not only depends solely on the signal pressure, but other parameters such as bias voltage, noise and hydrostatic pressure are among the main contributing factors that need to be addressed properly. Membrane material and structural geometry are two design variables that contribute to the receive sensitivity and thus affects the operating performance. Therefore, proper selection of material used as a membrane and its design geometry are vital in designing a device with remarkable performance.
558 INDIAN J. MAR. SCI., VOL. 41(6), DECEMBER 2012 In terms of the membrane deflection, its behaviour or characteristic can be classified either into small or large based on the theory of deflection 7. The classification is based on the ratio between the deflection and its thickness. The classification is significant in estimating the non linearity effect and the validity of the solution. According to the theory, the membrane deflection of less than 1/5 or 0.2 of the thickness is classified as small deflection or thin plate, while for higher deflection up to three times of the membrane thickness, large deflection or thick plate is applicable 7,8. Materials and Methods Material for vibrating membrane: PDMS Currently, in microscale technology, Silicon Nitride (Si 3 N 4 ) is the most common material used for the membrane-based acoustic sensor due to its microfabrication practicality. Using the material, the thin layer membrane can be realised from the microfabrication process such as LPCVD 9,10. However, the advancement in microfluidic technology has offered an alternative membrane material for such microscale device. The use of PDMS as the membrane in many microfluidic devices such as in microvalves and micropump application has suggested its suitability to be used for microacoustic sensing as well 11,12. Compared to Silicon Nitride, PDMS has a lower Young Modulus which indicates its advantage in terms of deflection behaviour over Silicon Nitride. In addition, via microfluidic fabrication technology, this material is found to be easier to be developed through softlitography process 13. The sample preparation process is simpler and involves less fabrication steps. One of the interesting features governed by PDMS is the controllable strength of its material properties through a controlled ratio of its mixture during preparation process. Different ratio of sample mixing will yield different properties of the end product 14. Acoustic impedance is another important factor of choosing PDMS as a membrane for underwater application. In some application, the acoustic impedance mismatch requires the application of matching layer to reduce the acoustic difference between two different medium materials where the signal is propagating. Implementation of multilayer device consists of several matching layers could cause another problem such as reducing the bandwidth. The availability of suitable matching layer also becomes a problem in some cases. In addition, for a device operating at very high frequency, the need for a very thin matching layer is sometimes impractical due to some limitation in fabrication process 15. Large acoustic impedance difference causes the energy not to be transferred efficiently. Material with similar acoustic impedance thus improves the efficiency in terms of energy transfer, and consequently increases the vibration amplitude. Fig. 1 shows how different acoustic impedance affects the energy transfer. Better impedance matching between PDMS and water has been obtained from theoretical calculation in order to predict the energy transfer efficiency. Equation 1 is used to estimate the acoustic impedance for an acoustic signal that is travelling through different medium. The acoustic impedance represents the opposition to the sound propagation within a medium such as: Z = pv Rayls (1) where: kg p = materials density 3 m m V = acoustic velocity 2 s By knowing the acoustic impedance for each medium of acoustic wave propagation, the energy transfer efficiency can be obtained based on the Fig. 1 Reflected and transmitted energy passed through different medium of propagation.
RAHMAN et al: BEHAVIOUR OF PDMS AS A MEMBRANE MATERAIL 559 reflection coefficient which is given in Equation 2. The coefficient represents the energy reflected at the overlapping surface between two medium of acoustic propagation. Table 2 shows the material properties of air, water and PDMS which are used to obtain the respective parameter. 2 Z 2 Z1 R = (2) Z 2 + Z1 where: Z 2 = Acoustic impedance of medium 2 Z 1 = Acoustic impedance of medium 1 The selection of PDMS has an effect of reducing the need for matching layer as proposed by 16. This will in turn avoids the unnecessary layer and simplify the fabrication process. Depth analysis of membrane deflection (hydrostatic pressure effect) This work was first performed to study the static deflection characteristic of the membrane at different water depth level. A range of 0 to 1m was chosen as underwater depth due to the targeted application is for a very shallow operation. Theoretically, at every depth level, the membrane will experience different water pressure due to hydrostatic force. At 0 m surface level, the only pressure considered acting on the membrane is only due to atmospheric pressure. The deeper it goes underwater, the membrane will experience an additional pressure due to hydrostatic force. The hydrostatic pressure depends on water density, gravitational attraction and underwater depth and is given by Equation 3. Phyd = ρgh (3) where: ρ = water density (kg/m 3 ) G = gravitational force (N) h = underwater depth (m) Thus, at static condition, the amount of pressure acting the on the membrane will be a combination of atmospheric and hydrostatic pressure as given in Equation 4. P tot = P atm + P hyd (4) where P atm is taken as 101.325 kpa. Using ANSYS 12.1, SHELL208 element was selected to represent a 2D axisymmetry thin layer of the membrane. Axisymmetry model was used in order to simplify the computational task of the programming. Based on Equation 3 and 4, a hydrostatic pressure was applied in order to study the behaviour of membrane deflection at different underwater depths. By setting the end node to be fixed, the model was divided into 10 nodes per division to enable the data to be collected at each related node. The model is based on geometry setup given in Table 1. The deflection data at every node was then extracted to plot the deflection behaviour of the membrane at specified geometry. Fig. 2 shows the schematic diagram of the axisymmetry model. Membrane geometry effect The task was continued with the investigation on the effect of different radius and thickness parameter on the deflection profile of the membrane model. For thickness analysis, the parameter was varied from 100 to 1000 µm with radius was fixed to 5000 µm. On the other hand, for radius analysis, the parameter was varied between 1000 to 5000 µm with thickness of 500 µm. Both parameters were then modified at several set of ratio and the deflection behaviour at each ratio was plotted. For this analysis, the deflection was taken as the ratio of maximum deflection over its respective thickness. This analysis was carried out to study the effect of geometry ratio that determines the Layer Table 1 Membrane geometry specification Vibrating Membrane ANSYS Element SHELL208 (2D Axisymmetry) Elastic Modulus (kpa ) 400 Poisson ration 0.5 Radius (µm) 5000 Thickness (µm) 1000 Fig. 2 Schematic diagram of axisymmetry model.
560 INDIAN J. MAR. SCI., VOL. 41(6), DECEMBER 2012 deflection region. All analysis were based on 1MPa applied pressure. Pressure Response Using the specification given in Table 1, the applied pressure were then varied between 100 to 2000 MPa to investigate the membrane response upon the pressure range. The pressure range was assumed to represent the actual acoustic pressure signal. This pressure range was predetermined based on the value that will exhibit the transition from small deflection to large deflection region. The response was analysed to find the threshold pressure that separate the small and large deflection assumption for the PDMS membrane based on the theory of deflection. Results and Discussions Acoustic Impedance Acoustic impedance leads to the determination of energy transfer efficiency between different medium of propagation. Table 2 shows the acoustic impedance between two common medium of acoustic signal transmission; air and water and the PDMS acting as a membrane. Different acoustic impedance will affect the transmission of the signal. Table 3 shows the calculated reflected and transmitted energy percentage to indicate their energy efficiency between different propagation medium. All parameters were calculated based on Equation 3 and 4. From the table, we found that the energy transfer is very efficient if the PDMS is used as a sensing membrane in water environment or in immersion application, with nearly 97% efficiency. With approximately 3.3% of reflected energy between water and PDMS, it indicates that most of the energy will be transferred to the membrane, thus producing the maximum deflection. Implementing PDMS as a membrane for airborne application however only yields 0.01% efficiency. Hydrostatic pressure effect Fig. 3 shows the simulation result of membrane 2D axisymmetry model at different depth of underwater operation. As expected, the deeper it goes underwater, the more deflection it will experience. The depth seems to deform the original flat shape of the membrane. The deflection is non linear along the radial axis with maximum deflection to occur at the centre of the membrane. The result shows that through this range of depth, the membrane will have about 28 to 30 nm deflection at its centre. Comparing the maximum deflection to the thickness of the membrane, at this depth level, the variation is very small. This suggests that hydrostatic pressure at this range is not significant in deforming the membrane initial shape. The model however does not predict the deflection caused by the total pressure. Deflection profile in underwater depth analysis only considers the environmental pressure (atmospheric and hydrostatic) by excluding the real signal pressure. Therefore, further analysis need to be performed to investigate on the deflection due to overall pressure including both transmitted and environmental pressure. Membrane geometry effect Fig. 4 shows the deflection behaviour of centre node which represents the maximum displacement of the membrane when the thickness was varied from 100 µm to 1000 µm. Initially the changes are almost linear before arriving at a point where the centre deflection starts to increase in non linear manner. This happens at the thickness of 300 µm. Through this range of thickness the maximum deflection varies from 0.27 µm to 119 µm. Fig. 5 shows the deflection Table 2 Acoustic properties of air, water and PDMS Medium Air Water PDMS Density, p (kg/m 3 ) 1.2 1053 969 Sound speed, V (m/s 2 ) 334 1490 1119 Acoustic Impedance, Z (Rayls) 400.8 1568970 1084311 Propagation Medium Table 3 Reflection coefficient Reflected Coefficient, R Reflected (%) Efficiency (0.01) Air to PDMS 0.999 99.9 0.01 Water to PDMS 0.033 3.3 96.7 Fig. 3 2D Axisymmetric radial deflection profile.
RAHMAN et al: BEHAVIOUR OF PDMS AS A MEMBRANE MATERAIL 561 Fig. 4 The relationship between the membrane thickness and the maximum deflection. Fig. 6 The relationship between the structural ratio (radius over thickness) and the deflection ratio (maximum deflection over thickness). Fig. 7 The relationship between the pressure signal and the deflection ratio (maximum deflection over thickness). Fig. 5 The relationship between the membrane radius and the maximum deflection. results of the membrane when the radius was varied. It is found that the relationship is not linear over the range. With the applied pressure of 1 MPa at thickness fixed to 500 µm, the centre deflection increase from 0.007 µm to 28 µm. Both results indicates that in predicting the behaviour of membrane deflection, geometry factor need to be consider thoroughly due to the non linearity behaviour. The effect of radius to thickness ratio on the deflection percentage is depicted in Fig 6. This analysis is useful in estimating either at the proposed specification, the deflection undergo a small or large deflection according to the plate deflection theory. By referring to Fig. 6, when the radius to thickness ratio is less than 27:1, the deflection to thickness ratio is less than 1/5 or 0.2, suggesting that this is the threshold region where small defection theory is applicable. Going beyond this point, large deflection theory should be considered where the PDMS membrane starts to lose its linearity behaviour. Pressure response Fig. 7 shows the relationship between the applied pressure on the deflection ratio (maximum deflection over thickness). The analysis is aimed to predict the threshold pressure where the PDMS membrane starts to leave the small deflection region assumption. It is found that at the deflection ratio of 0.2 the corresponding pressure is about 750 MPa or 271 db. In real application, most of the underwater projector is operating below than this pressure signal. This suggests that, the small deflection theory is still applicable for the PDMS membrane operating at this given geometry specification without suffering the non linear load-deflection relationship. Throughout the previous investigation, the suitability of the PDMS as a membrane for underwater sensing application can be summarised and justified as follows: 1. PDMS is good as an underwater sensing membrane due to its acoustic impedance which is closely matched the acoustic impedance of the transmission medium.
562 INDIAN J. MAR. SCI., VOL. 41(6), DECEMBER 2012 2. At the selected range of underwater depth, PDMS exhibits only a very small initial deflection. 3. There is a possibility to manipulate the structural geometry of the PDMS membrane as well as the applied signal pressure in order to ensure the membrane can be operated in small deflection region according to the existing plate theory. Conclusion The deflection behaviour of a PDMS membrane and its suitability for underwater operation has been successfully studied through several modelling and simulation works. It consists the study of underwater acoustic properties, depth analysis, structural geometry effect and pressure response based on the plate deflection theory. Acoustic property of PDMS makes it a suitable material candidate to be used as a sensing membrane for underwater application due to similarity of the acoustic impedance between the membrane s material and the underwater environment. Depth analysis gives an overview on the amount of initial static deflection caused by the hydrostatic pressure. Geometry analysis gives the relationship between the deflection and structural parameter such as radius and thickness. Through this work as well, the maximum deflection can be predicted by selecting a suitable ratio between the membrane radius and thickness. Therefore, the sensitivity of a membrane-based sensor which depends on the membrane s displacement can be controlled and designed by combining all these relevant factors. Acknowledgement This work was supported and funded by the USM Research University Grant Scheme (1001/PELECT/814168) References 1 Stojanovic, M., Underwater Acoustic Communication, Wiley Encyclopedia of Electrical and Electronic Engineering, (1997) 1-33. 2 Preisig J., Acoustic Propagation Considerations for Underwater Acoustic Communications Network Development, ACM Press, 11 ( 2006) 1-5 3 Akyildiz I.F., Pompili D., Melodia T., Underwater acoustic sensor network:research challenges, Ad Hoc Networks, 3 (2005) 257-279 4 Arshad M.R., Recent Advancement in Sensor Technology for Underwater Applications, Indian Journal of Marine Sciences, 38 ( 2009) 267-273 5 Yaacob M.I.H., Arshad M.R., Manaf A.A., Review on MEMS Based Acoustic Transducer for Underwater Application, paper presented at the Proc. of the Electrical and Electronic Postgraduate Colloqium, (2009) 1-5. 6 Caronti A., Caliano G., Carotenuto R., Savoia A., Pappalardo M., Cianci E., Foglietti V., Capacitive Micromachined Ultrasonic Transducer (CMUT) Arrays for Medical Imaging, Microelectronics Journal, 37 (2006) 770-777. 7 Eaton W.P., Bitsie F., Smith J.H., Plummer D.W, A New Analytical Solution for Diaphragm Deflection and its Application to a Surface Micromachined Pressure Sensor, paper presented at the International Conference on Modeling and Simulation of Microsystems, (1999) 640-643. 8 Lee J.S., Lucyszyn S., Design and Pressure Analysis for Bulk-micromachined Electrthermal Hydraulic Microactuators using a PCM, Sensors and Actuators A, 133 (2007) 294-300 9 Ko S.C., Kim Y.C., Lee S.S., Choi S.H., Kim S.R., Piezoelectric Membrane Acoustic Devices, paper presented at the IEEE Conference of MEMS, (2002) 296-299. 10 Ballantine D.S., White R.M., Martin S.J., Ricco A.J., Zellers E.T., Frye G.C., Wahltjen H., Acoustic Wave Sensors: Theory, Design and Physico-Chemical Applications, Academic Press, USA, 1997. 11 Au A.K., Lai H., Utela B.R, Folch A., Microvalves and Micropumps for BioMEMS, Micromachines, 2 (2011) 179-220. 12 Zhang C., Xing D., Li Y., Micropumps, microvalves and micromixers within PCR microfluidic chips: Advances and trends, Biotechnology Advances,25 (2007) 483-514. 13 Suk J.W., Cho J., Capillary Flow control using Hydrophobic Patterns, Journal of Micromechanics and Microengineering, 17(2007) 11-15. 14 Thangawng A.L., Ruoff R.S., Swartz M.A., Glucksberg M.R., Biomedical Microdevices, (2007) 587-595 15 Ladabaum I., Jin X., Soh H.T., Atalar A., Khuri-Yakub B.T., Surface Micromachined Capacitive Ultrasonic Transducers, IEEE Trans. on Ultrasonics, Ferroelectrics and Frequency Bontrol, 45 (1998) 678-690. 16 Persson H.W., Hertz C.H., Acoustic Impedance Matching of medical ultrasound Transducers, Ultrasonics, 23 (1985) 83-89.