Indexes for evaluation of dynamic characteristics of pressure-sensitive paint based on pressure sensitivity and frequency response

Two evaluation indexes were proposed to select the optimal PSP for unsteady pressure measurement from various PSPs with different pressure sensitivity and frequency response. An effective sensitivity coefficient calculated by pressure sensitivity and gain attenuation due to the response delay was proposed. Furthermore, an effective amount of intensity change was recommended, which takes into account the emission intensity and the effective sensitivity coefficient, because the magnitude of the intensity of a PSP is also important for unsteady-pressure measurement with high-speed sampling. A total of five types of PC-PSPs developed in previous studies were compared: two types of fast-response PC-PSPs using Pt(II) meso-tetra (pentafluorophenyl) porphine (PtTFPP) with poly(isobutyl methacrylate) (poly(IBM)) and ruthenium complex with RTV silicone, respectively, and three types of PC-PSPs using PtTFPP with poly[1-trimethylsilyl)-1-propyne] (poly(TMSP)). A comparison was made using the proposed evaluation indexes under various pressure ranges. The results shows that poly(TMSP)-based PC-PSP has a high effective sensitivity coefficient at pressures less than 20 kPa. On the other hand, poly(IBM)-based PC-PSP has the highest effective sensitivity coefficient at a pressure of 100 kPa. The effective amount of intensity change of poly(TMSP)-based PC-PSP is the highest at 2 kPa, but that of poly(IBM)-based PC-PSP is the highest at a pressure higher than 5 kPa among the evaluated PC-PSPs due to its high luminescence intensity. A PSP with high emission intensity will provide high performance in terms of fluctuation of emission intensity detected by the photodetector when the excitation intensity and the exposure time are limited due to limitations of optical equipment or high-speed sampling.


Introduction
Pressure distribution is one of the most important characteristics in the field of fluid dynamics for the evaluation of fluid machinery and the elucidation of fluid phenomena.Pressure distribution is conventionally measured using pressure taps [1].On the one hand, pressure measurement with high spatial resolution using pressure taps requires the design and the manufacturing of a complex model that incorporates a large number of pressure taps with high spatial density.On the other hand, pressure-sensitive paints (PSPs) are used for measuring the pressure distribution on a model surface with non-intrusive and high spatial resolution [2].A PSP is a pressure sensor that uses a photophysical reaction and consists of a dye molecule and a binder that adsorbs the dye on a model surface.When a PSP is applied to a measurement target and illuminated with light of an appropriate wavelength, the dye is excited and emits luminescence with an intensity corresponding to the ambient oxygen concentration.It is possible to indirectly measure the ambient pressure by measuring the luminescence emission of a PSP with an optical sensor when the oxygen concentration is constant.A PSP is a wide-range, high-resolution, and nonintrusive pressure measurement technique compared to conventional measurement through pressure taps because each dye molecule coated on a model surface acts as a sensor.
Fast-response PSPs for the unsteady-pressure measurement have been rapidly developed using various types of porous binders [3][4][5].A thin layer chromatography (TLC) plate was first applied to a porous binder of a PSP, resulting in a response time of 25 µs [6].An anodized-aluminum PSP (AA-PSP), which is formed by anodizing an aluminum surface and forming an oxide film, has also been applied to the unsteadypressure measurement [7][8][9][10][11][12].Both TLC-PSPs and AA-PSPs have fast response times, but they are restricted by applicable materials and shapes.Once an AA-PSP is applied to aluminum, it is difficult to remove it without changing the shape of the aluminum.Therefore, a sprayable fast-response PSP has some advantages.Scroggin et al [13] first developed a porous binder consisting of polymers and solid particles by tape casting.Gregory et al [14] further developed a sprayable porous binder that was composed of polymer and solid particles.Furthermore, various PC-PSPs have been developed for unsteady-pressure measurement [15][16][17][18][19][20][21].Fast-response PSPs have been applied to the unsteady-pressure measurement [10,22].The mechanism of the time response of PSPs has also been studied [23][24][25][26][27].
Meanwhile, many studies on pressure measurement using a PSP have been conducted for pressure conditions of atmospheric pressure or higher.There is also a demand for pressure measurement using a PSP even at low pressure.One of these is compressible low-Reynolds-number flows that appear around high-speed fluid machines at low pressure.The compressible low-Reynolds-number flows are often found in aerospace engineering applications such as Mars probes [28,29] and unmanned aerial vehicles.Pressure measurement under compressible low-Reynolds-number conditions is more difficult than that under atmospheric pressure.The application of PSPs to unsteady-pressure measurement under low-pressure environments poses two major problems: the relative pressure sensitivity is low and time response is slow.
Firstly, low pressure is known to cause a decrease in the relative pressure sensitivity of conventional PSPs.Conventional pressure sensitivity [%/kPa] increases as the pressure decreases.However, this conventional pressure sensitivity does not take into account the decrease in pressure fluctuation caused by fluid phenomena due to the decrease in the ambient pressure.Nagata et al [30].indicates that the relative pressure sensitivity with respect to the ambient pressure decreases as the pressure decreases.This relative pressure sensitivity takes into account the pressure fluctuation caused by fluid phenomena, which decreases as the pressure decreases.Anyoji et al [31,32] used a PSP composed of palladium tetra(pentafluorophenyl) porphyrin (PdTFPP) and poly[1-trimethylsilyl)-1-propyne] (poly(TMSP)) [33] in a low-density wind tunnel.This PSP developed by Ono et al [34] has a high pressure sensitivity even in low-pressure conditions.They measured the pressure distribution on a flat plate in compressible low-Reynolds-number flows, when the Mach number of the freestream is M ≈ 0.2, the Reynolds number based on the freestream quantities is 4.0 × 10 3 ⩽ Re ⩽ 4.0 × 10 4 , and the pressure is in the range of 2-20 kPa.The poly(TMSP)based PSP was applied to a wing surface for other experiments in a low-density wind tunnel [35,36].Okudera et al [37] proposed adjusting the oxygen concentration and increasing the pressure sensitivity of the applied PSP.Nagata et al [38] measured the pressure distribution on the rotor blades with changing the oxygen concentration.
Secondly, the other of the two major problems is the slow time response for the time-resolved measurement of phenomena under low-pressure conditions.Kasai et al [39] evaluated the frequency response of three representative porous binders, a PC-PSP, an AA-PSP and a TLC-PSP, using a resonance tube at low pressure.The frequency response has been clarified to decrease because the lifetime of PSPs becomes longer at low pressure.Nagata et al [40] investigated the surface pressure distribution of a circular cylinder in 0.1 ⩽ M ⩽ 0.5 and 1, 000 ⩽ Re ⩽ 5, 000 using an AA-PSP in the low-density wind tunnel.The frequency response of this AA-PSP with tris(bathophenanthroline) ruthenium dichloride (Ru(dpp) 3 ) at low pressure was approximately the same as that at atmospheric pressure [39].On the other hand, the pressure sensitivity of this AA-PSP was lower than that of PtTFPP-based PC-PSP.They applied randomized singular value decomposition [41] to time-series PSP images and reduced noise due to a low signal-to-noise ratio (SNR).Therefore, the unsteady-pressure measurement at low pressure or low oxygen concentration is more difficult than the steady-pressure measurement at low pressure.
Pressure measurement is conventionally conducted near atmospheric pressure.Fast-response PSPs with high pressure sensitivity have been developed in this pressure range by individually evaluating the pressure sensitivity and time response of PSPs.However, the pressure sensitivity and time response under various pressure conditions, especially low pressure, show completely different performances depending on the type of PSPs [42].Therefore, it is necessary to consider them at the same time.Selecting the optimal PC-PSP from the perspective of ease of signal acquisition is desirable.Therefore, the effective sensitivity coefficient was introduced using the pressure sensitivity and the gain attenuation at an arbitrary frequency.This coefficient takes into account the static and dynamic characteristics and expresses the magnitude of the fluctuation of the intensity ratio at an arbitrary frequency.Furthermore, the effective amount of intensity change was proposed by multiplying the effective sensitivity coefficient by the luminescence intensity.These evaluation indexes enable us to compare PSPs considering the static/dynamic characteristics of PSPs and the luminescence intensity, which were conventionally considered separately.

Stern-volmer relation
Pressure sensitivity of a PSP is theoretically described by the Stern-Volmer equation: where I is the emission intensity of a PSP at the pressure P and the subscript '0' shows the quantity under the condition without oxygen molecules; K(T) and K SV are the Stern-Volmer coefficients to the pressure and the oxygen concentration Y O2 , respectively; and S(T) is the solubility of oxygen molecules in a PSP binder, which depends on the temperature T of the binder.Equation ( 1) is normalized by the reference condition P ref and I ref in a typical wind-tunnel test because it is difficult to create completely oxygen-free conditions.The reference condition is conventional under wind-off conditions.Equation ( 1) is normalized by the reference parameters as the following equations: where A(T) and B(T) are the temperature-dependent Stern-Volmer coefficients due to thermal quenching.Here, the Stern-Volmer equation can be expressed in terms of the dimensionless numbers of the velocity and the pressure [30].
The pressure coefficient C P is described as in equation ( 5), assuming that the freestream pressure is the reference pressure P ref = P ∞ : where ρ ∞ and u ∞ are the gas density and the velocity of the mainstream, respectively.Equation ( 5) can be expressed by substituting the equation of state P = ρRT and the speed of sound a 2 = γRT as follows: where γ is the specific heat ratio and R is the gas constant.Furthermore, the following expression can be obtained by substituting equation ( 6) into equation ( 3): Equation ( 7) explains that I ref /I depends only on γ, M, and C P .This equation indicates that the normalized intensity of the PSP is independent of the ambient pressure.The C P distribution is almost the consistent value across similar flow structures with a moderate Reynolds number (Re > O(10 1 )) in shock-free flows.The γ is the constant when the gas species are the same as each other.Hence, variations in I ref /I with flow-induced pressure fluctuations ∆C P become larger at higher-M conditions.

Pressure sensitivity of PSP
The conventional pressure sensitivity S P of the PSP is defined as the gradient of the P − I ref /I curve: This parameter indicates the ambient pressure dependence of the change in the intensity ratio of the PSP emissions with respect to the pressure change.This pressure sensitivity of a PSP is higher at lower pressures and lower oxygen concentrations [32,43].Here, Nagata et al [30].introduced two parameters for the evaluation of a PSP that measures small pressure fluctuations under low-pressure conditions.The pressure evolution of the normalized pressure sensitivity, which is the local gradient of the Stern-Volmer curve B local , is calculated from the following equation [30]: where the ambient pressure was assumed to be equal to P ref in the present study.This parameter depicts the ambient pressure dependence of the intensity ratio of the PSP emissions on the pressure change normalized by the ambient pressure.
The second parameter is the change in the emission intensity ∆I PR (defined as S PR in the previous literature [30]), which is proportional to the ambient pressure, with respect to the pressure fluctuation ∆P: where P = (P ref + ∆P)/P ref = P/P ref .
The pressure fluctuation is normalized by the ambient pressure as the same as B local .The optimal ambient pressure in terms of maximizing these parameters can be derived analytically for the linear model in equation ( 3) by Okudera et al [37].As a parameter B local corresponds to B in the linear model, ∆I PR is described as the following equation, The optimal ambient pressure in terms of maximizing B is considered to be P ref = ∞ from equation ( 4).On the other hand, B is, in reality, not maximized at P ref = ∞ in cases where Henry's law is not applied, such as when the oxygen concentration in the polymer is saturated or when the polymer characteristic is dual sorption.

Frequency response
The frequency response against the sinusoidal pressure wave is conventionally evaluated using an acoustic resonance tube [44].The pressure fluctuations are sinusoidally approximated by the following equation.
The amplitude A P and the phase θ are calculated from the pressure fluctuations obtained by the PSP and the reference sensor.The gain and the phase delay ∆θ of the PSP are calculated using the following equations.
Here, the quantities with the subscripts 'PSP' and 'Sensor' represent those measured by the PSP and the reference sensor, respectively.In equation ( 13), A PSP /A Sensor (f) indicates the attenuation rate to the output of the reference sensor due to the low time response of the PSP.

Materials and preparation
Table 1 describes the prepared PC-PSP samples based on the previous literature [42].The following polymers, poly(isobutyl methacrylate) (poly(IBM)) [45,46] (Sigma Aldrich, USA), and RTV silicone [21] (Shin-Etsu Chemical, Japan), poly(TMSP) (Gelest, inc., USA) [42] were employed as the polymer for a binder.Hydrophobic TiO 2 particles with a diameter d of 15 nm and hydrophilic TiO 2 particles with d = 35 nm (Tayca Corporation, Japan) were used as particles.The particle mass content w particle within the binder is expressed as follows: where m particle and m polymer are the masses of particles and polymers, respectively.

Static and dynamic calibrations
The detailed setup and the data analysis method for static calibration and dynamic calibration under low-pressure conditions are described in the previous literature [42].Figure 1 shows a schematic illustration of the setup for the static calibration.The static characteristics of the PSPs were obtained by varying the pressure inside the chamber and the base temperature.Polymer/Ceramic PSPs using PtTFPP as a dye were excited by an ultraviolet light emitting diode (UV-LED; IL-106X, Hardsoft, Poland) with a center wavelength of 395 nm, while PC-PSP using Ru(dpp) 3 as a dye was excited by a blue LED (LEDA294-470, Hamamatsu Photonics, Japan) with a center wavelength of 470 nm.The luminescence intensity of the PSP coupon was detected by a 16-bit charge-coupled device (CCD) camera (ORCA II-BT 1024, Hamamatsu Photonics, Japan) with a camera lens (Nikkor 105 mm f/2.8, Nikon, Japan) and a bandpass filter of 640 ± 50 nm (PB0640/100, Asahi Spectra, Japan).The pressure P inside the chamber was varied in the range of 0.1-140 kPa by the pressure controller (DPI 515, Druck, UK), and the temperature T of the base on which the coupon was placed was varied in the range of 277-333 K by the temperature controller using Peltier elements (MT886-D1000, NetsuDenshi Kogyo, Japan).The accuracy of these pressure and temperature controllers was 30 Pa and 0.05 K, respectively.The luminescence intensity I under each condition was normalized with respect to the intensity under the reference condition of P ref = 10 kPa at T ref = 293 K.
The local Stern-Volmer coefficient introduced by Nagata et al [30] was calculated according to equation (9).The results of B local were moving averaged at a pressure higher than 16 kPa because B local is considered to be continuous in subsequent small pressure intervals.According to the previous study [42], B local were moving averaged with 22 points for PtTFPP-based PC-PSP using poly(TMSP) and hydrophilic particles and with 15 points for other PC-PSPs.The window size of the moving average was reduced at the endpoint on the high-pressure side.
The dynamic characteristics of PC-PSPs were investigated using an acoustic resonance tube [44].See in detail previous literature [39,42].Figure 2 shows a photograph and schematic illustration of the acoustic resonance tube.This acoustic resonance tube can generate sinusoidal pressure oscillations in a frequency range of 0.15-9.7 kHz using two types of speakers mounted at the end of the acoustic resonance tube: a speaker for low-frequency region of 0.15 ⩽ f ⩽ 2.8 [kHz] (TU-750, TOA Corporation, Japan) and a speaker for high-frequency region of 0.59 ⩽ f ⩽ 9.7 [kHz] (RX22, Peavey, USA).The number of input cycles from the power amplifier (Classic Pro CP600, Sound House inc., Japan) to the speakers was 4 × 2 10 .The other end of the acoustic  resonance tube was capped with a PSP sample with a pressure transducer in its center.Two types of pressure transducers were applied, depending on the pressure controlled by a pressure controller (CPC6000, Mensor, USA): CCQ-093-5A (Kulite, USA) in the range of 2-50 kPa and XCL-152-5SG (Kulite, USA) at 100 kPa.Installing a Peltier device (FPH1-12 706AC, Fujita Corporation, Japan) and a resistance temperature detector (R060-39, Chino Corporation, Japan) on the back of the PSP sample plate, the temperature of the sample plate was controlled by a Peltier controller (TD-1000A, Cell System Corporation, Japan).
The PSP coupon was excited with a UV laser (RV-1000TH, Ricoh, Japan) with a center wavelength of 400 nm.The distance between the UV-laser and the PSP coupon was approximately 400 mm.The emission intensity of the PSP was detected using a photomultiplier tube (PMT; H5784-02, Hamamatsu Photonics, Japan) equipped with a 640 ± 50 nm bandpass filter (PB0640/100, Asahi Spectra, Japan).The signals from the PMT and the pressure transducer were acquired simultaneously with a data-acquisition device (DAQ) (USB-6251, National Instruments, USA).The recorded signals were converted to pressure using an in-situ calibration result of the PSP at the lowest frequency of 0.15 kHz.The gain and the phase delay of the PSP signal were calculated according to equations ( 13) and ( 14) [44].The cutoff frequency was defined the frequency at which the gain attenuation was −3 dB.

Proposed evaluation indexes
It is necessary to consider the pressure sensitivity and time response of PSPs at the same time because they show completely different performances depending on the type of PSPs under various pressure conditions.The actual change in luminescence intensity may be small when a PSP has a fast response and low pressure sensitivity.In contrast, the actual change in luminescence intensity may be large when a PSP has a slow time response and high pressure sensitivity.In the present study, the static and dynamic characteristics of PSPs were evaluated from the perspective of ease of signal acquisition.Then, the effective sensitivity coefficient β e was proposed that is based on the pressure sensitivity and the gain attenuation at an arbitrary frequency f measured by the resonance tube as shown in equation (16).
where B local and A PSP /A Sensor (f) are the local Stern-Volmer coefficient [30] and the attenuation rate to the output of the reference sensor, respectively.This introduced coefficient takes into account the static and dynamic characteristics and expresses the effective sensitivity to changes in pressure at an arbitrary frequency.The magnitude of the luminescence intensity cannot be ignored in the actual unsteady-pressure measurements.Then, the effective amount of intensity change ∆I e was proposed by multiplying the effective sensitivity coefficient β e by the emission intensity I at an arbitrary pressure.
The static and dynamic characteristics of PSPs and the luminescence intensity of that, which are conventionally considered separately, can be compared by introducing these evaluation indexes above.
In the present study, B local with pressures of 2, 5, 10, 20, 20, 50, and 100 kPa at a temperature of 293 K was extracted from the results of the static calibration.The proposed evaluation indexes calculated using the gains at 1,934 and 5,020 Hz measured in the resonance tube are shown in the manuscript as the effective sensitivity coefficients at 2 and 5 kHz, respectively.The luminescence intensity of each sample was measured by the 16-bit CCD camera that was used for the static calibration.The f-number of the camera was set to 5.6.The luminescence intensity was measured using the same LED and LED current with different LED chips: one has a center wavelength of 395 nm for PtTFPP, and the other has a center wavelength of 462 nm for Ru(dpp) 3 .The luminescence intensity is assumed to be linear with respect to the duration of the camera exposure time.The luminescence intensity was compared when the camera exposure time was 490 µs for the phenomenon frequency of 2 kHz and 190 µs for the phenomenon frequency of 5 kHz, respectively.The effective sensitivity coefficient β e and the effective amount of intensity change ∆I e were calculated by substituting these B local , gain, and emission intensity into equations ( 16) and (17).Polymer/ceramic PSP using poly(IBM) around atmospheric pressure has the maximum B local , while PC-PSP using RTV and PC-PSP using poly(TMSP) have the maximum B local in the pressure range of 60-70 kPa and 10-20 kPa, respectively.According to Okudera et al [37], the partial pressure at which B local peaks is considered to depend on the solubility of oxygen and diffusivity.The permeability is calculated by multiplying the solubility and diffusivity.The oxygen permeability of PSP depends on the type of polymer.The high oxygen permeability of the polymer increases the oxygen concentration in the polymer even at low pressures.The oxygen concentration in the polymer increases as the pressure increases and eventually saturates.Therefore, a higher oxygen permeability is considered to decrease the pressure at which B local peaks.The oxygen permeability is considered to be the highest for poly(TMSP) and the lowest for poly(IBM).Here, B local of poly(TMSP)based PC-PSP became smaller as the particle mass content increases in the low-pressure range of 1-10 kPa. Figure 3(b) shows the dependence of the ambient pressure on the cutoff frequencies of PC-PSPs.The error bars of the cutoff frequency are the standard deviation in four times of the measurements.Polymer/ceramic PSP using Ru(dpp) 3 has a cutoff frequency of 10 kHz or higher at P ⩾ 5 kPa.Therefore, the cutoff frequencies for Ru(dpp) 3 -based PC-PSP at P ⩾ 5 kPa are not shown in figure 3(b).The standard deviation of Ru(dpp) 3based PC-PSP at P =2 kPa is large because the SNR in the dynamic calibration was low due to the low B local of approximately 0.1.The cutoff frequency of poly(TMSP)-based PC-PSP with 98 wt% particle mass content is between 4-6 kHz, and the cutoff frequency decreases as the pressure decreases at P ⩽ 20 kPa.On the other hand, the cutoff frequency of poly(TMSP)-based PC-PSP with a particle mass content of 95 wt% and PtTFPP-based PC-PSP using poly(IBM) is 4 kHz or less.Fast-response with a cutoff frequency of 4 kHz or more was achieved at a low pressure of 2 kPa even with PtTFPPbased PC-PSP using poly(TMSP) by increasing the particle mass content.Figure 3 shows that poly(TMSP)-based PC-PSP has the highest pressure sensitivity at a pressure less than 30 kPa, and poly(IBM)-based PC-PSP has the highest pressure sensitivity at a pressure higher than 30 kPa.On the other hand, Ru(dpp) 3 -based PC-PSP has the highest cutoff frequency in any pressure range.Figure 4 shows the emission intensity normalized by the intensity of poly(TMSP)-based PC-PSP with hydrophilic TiO 2 with a particle content of 98 wt% at each pressure.The error bars in figure 4 show the standard deviation of the normalized intensity in the analytical region on the sample coupons.This figure means the relative brightness based on the intensity of poly(TMSP)-based PC-PSP with hydrophilic TiO 2 with a particle mass content of 98 wt%.The relative intensity of poly(IBM)-based PC-PSP with hydrophilic TiO 2 is the highest at any pressure, especially at 20 kPa.In other words, poly(IBM)-based PC-PSP with hydrophilic TiO 2 is practical PC-PSP from the point of view of brightness.

Comparison by proposed indexes 4.2.1. Effective sensitivity coefficient.
Figure 5 shows the effective sensitivity coefficient defined by equation ( 16) at each pressure for two different frequencies of 2 and 5 kHz. Figure 5(a) indicates that the effective sensitivity coefficient of poly(TMSP)-based PC-PSPs is the highest at P ⩽ 20 kPa, and that of poly(IBM)-based PC-PSPs is the highest at P ⩾ 50 kPa.The static and dynamic properties of even the same poly(TMSP) differ depending on the particle mass content and surface treatment of the particle.The effective sensitivity coefficient of poly(TMSP)-based PC-PSP with a hydrophilic particle mass content of 95 wt% is the highest at 2 kPa.Since PC-PSP using hydrophilic particles has a higher pressure sensitivity and faster response at lower pressure as shown in figure 3, PC-PSPs using hydrophilic TiO 2 have a higher β e at lower pressures.Furthermore, the β e of poly(TMSP)based PC-PSP is higher at 2 kPa when the particle mass content is lower.This is because poly(TMSP)-based PC-PSP with hydrophilic particle has higher pressure sensitivity at a lower particle mass content.The effective sensitivity coefficients for poly(TMSP)-based PC-PSPs using hydrophilic or hydrophobic TiO 2 with a particle mass content of 98 wt% is higher than that for poly(TMSP)-based PC-PSPs with a hydrophilic particle mass content of 95 wt% at 5 ⩽ P ⩽ 20 kPa.This is because the B local of PC-PSPs using hydrophilic or hydrophobic TiO 2 with a particle mass content of 98 wt% increases as the pressure increases in the pressure range of 5-20 kPa, and the β e becomes higher in poly(TMSP)-based PC-PSPs with hydrophilic TiO 2 with a particle content of 98 wt%, which have a high frequency response.Meanwhile, poly(IBM)-based PC-PSP shows the highest β e among them at a pressure higher than 50 kPa.Here, this PC-PSP has the highest pressure sensitivity at a pressure higher than 50 kPa.The PC-PSPs evaluated in the present study have a cutoff frequency of 2 kHz or higher.Thus, the influence of pressure sensitivity is larger than that of cutoff frequency when evaluating the effective sensitivity coefficient at a frequency of 2 kHz.
Figure 5(b) indicates the effective sensitivity at the frequency of 5 kHz.The effective sensitivity coefficient of poly(TMSP)-based PC-PSP is the highest among the evaluated PC-PSPs at P ⩽ 20 kPa, and the effective sensitivity coefficient of PC-PSPs using a polymer other than poly(TMSP) is the highest among them at P ⩾ 50 kPa.Polymer/Ceramic PSP with a hydrophilic particle mass content of 98 wt% has the highest effective sensitivity coefficient in the pressure range of 2-20 kPa because this PC-PSP has a high cutoff frequency and high pressure sensitivity at low pressure.The effective coefficient of Ru(dpp) 3 -based PC-PSP with hydrophilic TiO 2 is approximately the same as that of poly(TMSP)-based PC-PSP at 50 kPa.The pressure sensitivities of poly(TMSP)-based PC-PSPs decreases and that of Ru(dpp) 3 -based PC-PSP increase with increasing pressure under this condition.Furthermore, since the cutoff frequency of Ru(dpp) 3 -based PC-PSP is the highest under atmospheric pressure, this PC-PSP shows the highest β e at 50 kPa.At pressure of 100 kPa, poly(IBM)-based PC-PSPs, which has the highest pressure sensitivity, has the highest β e although its time response is lower than other PC-PSPs.The proposed effective sensitivity coefficient can compare PC-PSPs with different static and dynamic characteristics when the emission intensity is sufficiently high.

Effective amount of intensity change.
The effective amount of intensity change at 2 and 5 kHz is indicated in figure 6.The values of the maximum effective amount of intensity change at 2 kHz are nearly three times larger than that at 5 kHz.The lower frequency result in the higher intensity fluctuation that can be detected by the photodetector.Figure 6(a) shows that the effective amount of intensity change of PC-PSPs excluding Ru(dpp) 3 -based PC-PSP show almost the same characteristics at a frequency of 2 kHz as each other at pressure of 2 kPa.There is considered to be no difference in the effective amount of intensity change between poly(TMSP)-based PC-PSPs with a high β e and poly(IBM)-based PC-PSP with a high luminescence intensity, when measuring the phenomenon at a low frequency of 2 kHz and a low pressure of 2 kPa.On the other hand, the magnitude of the gain due to the response delay of the PSP affects the ∆I e at a high frequency of 5 kHz and low pressure of 2 kPa.Since poly(TMSP)-based PC-PSP with hydrophilic TiO 2 with a particle mass content of 98 wt% has the highest β e among them, poly(TMSP)-based PC-PSP with hydrophilic TiO 2 has the highest ∆I e among them for the unsteady-pressure measurement of the phenomenon of 5 kHz (figure 6(b)).Polymer/Ceramic PSP using poly(IBM) with hydrophilic TiO 2 indicates the highest performance for measuring the phenomenon of both 2 and 5 kHz at P ⩾ 5 kPa.This is because the luminescence intensity of this PC-PSP is higher than that of any poly(TMSP)-based PC-PSP at low pressure (figure 4) due to the lower pressure sensitivity of this PC-PSP at low pressure.
A PC-PSP with the β e differs from that with the highest ∆I e , as shown in figures 5 and 6.In other words, these parameters suggest that, even if a high-speed phenomenon is measured, it is important to select a PSP depending on whether the measurement can be performed with sufficient emission intensity or not.

Conclusions
In the present study, two evaluation indexes were newly proposed for selection of a PSP suitable for a certain environment.These indexes consider both the static and the dynamic properties of PSPs.One is the effective sensitivity coefficient, which takes into account the local Stern-Volmer coefficient and the gain attenuation due to the response delay.The other is the effective amount of intensity change, which is the effective sensitivity coefficient multiplied by the luminescence intensity.If the emission intensity is sufficiently high due to the conditions of the measuring equipment, it is appropriate to select only on the basis of the effective sensitivity coefficient.On the contrary, the effective amount of intensity change is more reasonable to select the PSP when the excitation intensity and the exposure time are limited, such as when measuring high-speed phenomena.
Five types of PC-PSPs were compared using the proposed evaluation indexes at the target frequencies of 2 and 5 kHz in the pressure range of 2-100 kPa.It showed that poly(TMSP)based PC-PSP has the maximum effective sensitivity coefficient at a pressure less than 20 kPa, while PC-PSPs using RTV or poly(IBM) have the maximum effective sensitivity coefficient at a pressure higher than 50 kPa.Unlike the effective sensitivity coefficient, poly(TMSP)-based PC-PSP has the highest effective amount of intensity changes at a low pressure of 2 kPa, and poly(IBM)-based PC-PSP for both measurement frequencies has the highest effective amount of intensity change in the pressure range of 5-100 kPa.The effective amount of intensity changes shows that a PSP with a high luminescence intensity will be suitable for measurement at that pressure, although the PSP has a low pressure sensitivity and a low time response.

Appendix. Calibration curves of frequency response of PC-PSP
The frequency responses of poly(TMSP)-based PC-PSPs with hydrophilic TiO 2 and hydrophobic TiO 2 are shown in figures A.1 and A.2. Figure A.1 shows that the phase delay is approximately constant at all pressures.On the other hand, the gain in clearly decreases at 2 kPa, but the difference in the gain is negligible at 5-20 kPa.The gain of 500-3,000 Hz at 100 kPa is smaller than that at other pressures.Then, the cutoff frequency at 100 kPa is slightly lower than at other pressures.The reason why the gain at 100 kPa at 500-3,000 Hz is smaller than that at other pressures was not elucidated and is a subject of future work.

Figure 3 (
Figure 3(a) shows the local Stern-Volmer coefficient of the fabricated PC-PSPs.The pressure range for maximum B local depends on the type of polymer in each PC-PSP.Polymer/ceramic PSP using poly(IBM) around atmospheric pressure has the maximum B local , while PC-PSP using RTV and PC-PSP using poly(TMSP) have the maximum B local in the pressure range of 60-70 kPa and 10-20 kPa, respectively.According to Okudera et al[37], the partial pressure at which B local peaks is considered to depend on the solubility of oxygen and diffusivity.The permeability is calculated by multiplying the solubility and diffusivity.The oxygen permeability of PSP depends on the type of polymer.The high oxygen permeability of the polymer increases the oxygen concentration in the polymer even at low pressures.The oxygen concentration in the polymer increases as the pressure increases and eventually saturates.Therefore, a higher oxygen permeability is considered to decrease the pressure at which B local peaks.The oxygen permeability is considered to be the highest for poly(TMSP)

Figure 3 .
Figure 3. Conventional characteristic at each pressure and 293 K: (a) pressure characteristics and (b) cutoff frequency.Cutoff frequencies of Ru(dpp) 3 -based PC-PSP are 10 kHz or higher at P ⩾ 5 kPa and are not shown in this figure.

Figure 4 .
Figure 4. Normalized intensity of fast PSP at each pressure normalized by the luminescence intensity of Pt-TMSP-hydrophilic.

Figure 5 .
Figure 5. Effective sensitivity for each pressure at (a) 2 kHz and (b) 5 kHz.

Figure 6 .
Figure 6.Effective amount of intensity change for each pressure at (a) 2 kHz and (b) 5 kHz.

Figure A. 1 .
Figure A.1.Bode plots of PC-PSP using poly(TMSP) and hydrophilic TiO 2 with a particle mass content of 98 wt% at T ref = 293 K: (a) Gain and (b) Phase.

Figure A. 2 .
Figure A.2. Bode plots of PC-PSP using poly(TMSP) and hydrophobic TiO 2 with a particle mass content of 98 wt% at T ref = 293 K: (a) Gain and (b) Phase.

Table 1 .
Conditions for preparing PC-PSP.