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[Kosuke Minami](https://orcid.org/0000-0003-4145-1118), [Kota Shiba](https://orcid.org/0000-0001-7775-0318), [Gaku Imamura](https://orcid.org/0000-0002-3130-7190), [Genki Yoshikawa](https://orcid.org/0000-0002-9136-8964)

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[Identification of gas species and their concentrations by using sorption kinetics of viscoelastic film](https://mdr.nims.go.jp/datasets/a1ec33af-dcb1-4602-ba1f-66666a1704c5)

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Identification of gas species and their concentrationsby using sorption kinetics of viscoelastic filmKosuke Minami1,2,*, Kota Shiba1, Gaku Imamura3 and Genki Yoshikawa1,41Research Center for Functional Materials, National Institute for Materials Science (NIMS), Tsukuba 305-0044 Japan2International Center for Young Scientists (ICYS), NIMS, Tsukuba 305-0044 Japan3International Research Center for Materials Nanoarchitectonics (MANA), NIMS, Tsukuba 305-0044 Japan4Graduate School of Pure and Applied Science, University of Tsukuba, Tsukuba 305-8571 Japan*Email: MINAMI.Kosuke@nims.go.jp; ORCiD: 0000-0003-4145-1118Abstract—Nanomechanical sensors and their arrays have beenattracting significant attention for detecting, distinguishing, andidentifying target analytes. In the static mode operation, sensingsignals are obtained by a concentration-dependent sorption-induced mechanical stress/strain. Recently, we derived an an-alytical solution, which is applicable to multistep injection-purge cycles in the static mode nanomechanical sensing withviscoelastic receptor layers. The model can be utilized for ex-tracting viscoelastic properties and the concentrations of analytesmore accurately by fitting a couple of injection purge curvesobtained from experimental data. Here, we show the utility ofthe optimized parameters directly not only for the identificationof gas species but also for their concentrations.Index Terms—gas identification, gas concentration identifica-tion, sorption kinetics, nanomechanical sensors, Membrane-typeSurface stress Sensor (MSS)I. INTRODUCTIONNanomechanical sensors have gained significant attention aspowerful tools for detecting target analytes [1]–[3], especiallyodors that are composed of a complex mixture of gaseousmolecules [4]–[6]. An array of nanomechanical sensors canbe potentially utilized as a sensing unit for artificial olfaction.In the so-called static operation, sensing signals are obtainedby measuring mechanical stress/strain induced by the sorptionof target molecules in a receptor material. The materials coatedon the nanomechanical sensors often exhibit viscoelastic na-ture, and hence the dynamic response of nanomechanicalsensing reflects the sorption kinetics along with the viscoelas-tic stress relaxation. On the basis of the theoretical modelproposed by Wenzel et al. [7], we recently derived the generalanalytical expression that includes the sorption kinetics and theviscoelastic stress relaxation [8]. This model is applicable tothe multistep injection-purge cycles without reaching a steady-state, allowing us to effectively analyze the sensor responsesand extract more accurate optimized parameters.In this study, we demonstrate the direct identification of gasspecies as well as their concentrations using the optimizedparameters obtained from the derived equation in [8]. Ourprevious report [9] clearly shows that one of the optimizedparameters can be utilized for the identification of gas speciesusing Wenzel’s model; however the model is limited foroptimizing the parameters accurately from the signal thatreaches a steady-state. In contrast to the model, our analyticalmodel [8] agrees well with sensor responses experimentallymeasured using a nanomechanical Membrane-type Surfacestress Sensor (MSS) [10] coated with viscoelastic materials.The curve fitting provides not only the several physical pa-rameters but also the features of the analyte species as wellas their concentrations, leading to the accurate identificationof the gas species and their concentrations without using anymultivariate analyses.II. GOVERNING EQUATIONSIn the case of the static mode operation of a micro-cantilever plate, the sorption-induced expansion makes thecantilever beam bend [1]. Several analytical solutions havebeen proposed for the theoretical formulations of the staticmode nanomechanical sensing, especially for a microcantilevermodel, which clearly shows that the signal responses ofthe nanomechanical sensors are directly proportional to theinternal strain ϵf .In the case of the sorption-induced nanomechanical sensing,there are several investigations using microcantilever sen-sors [7]. In the model, the concentration-dependent sorption-induced internal strain in a coating film ϵf (Cg) is approx-imated as ϵf = λCg (with λ = 13νa) for small volumeexpansion (i.e., ϵf ≪ 1), where νa is the specific volumeof the absorbed analyte. The absorption-induced strain can,therefore, be assumed to be directly proportional to the analyteconcentration in the gas phase Cg .Among a large variety of materials, viscoelastic propertiesarise from dynamic differences on molecular rearrangements.Wenzel et al. proposed a theoretical model for a cantilever-typenanomechanical sensor coated with a viscoelastic material [7].The theoretical models are derived from the simplest three-parameter solid model:τrEUddtϵ(t) + ERϵ(t) = τrddtσ(t) + σ(t), (1)where EU and ER denote the unrelaxed (instantaneous) mod-ulus and relaxed (asymptotic) modulus, respectively, and τr isthe time constant of stress relaxation.For the derivation of the equations governing the con-centration of an analyte into a receptor material coated ona nanomechanical sensor during absorption/desorption pro-cesses, we assume a first-order absorption. The reaction rateof a concentration of an analyte in the coating film C(t) isgiven byddtC(t) =1τs[KpCg(t)− C(t)] , (2)where τs is diffusion time constant; Kp is known as thepartition coefficient in the case of a polymer coating film.In the case of gas sensing using nanomechanical sensors, thesample gas is usually introduced by carrier gas; subsequently,the gas line is switched to the purge gas line to promote thedesorption of the sample gases. Since the injection of analyteis generally controlled by the continuous flow of headspacegas or bubbling liquid samples, it can be assumed to behomogeneous in time. Thus, for the multistep injection-purgecycles, we consider a rectangular wave-like sequence (see alsoFig. 4 in [8]). Then, the concentration of an analyte in the gasphase Cg(t) can be described as a step function [8]:Cg(t) =0, t < t0Cg, t2(n−1) ≤ t < t2n−10, t2n−1 ≤ t < t2n(n = 1, 2, · · · ). (3)According to the formulation derived by Wenzel et al. [7],the derived general differential equation in Eq. (1) can beextended to the rectangular wave-like injection models. Substi-tuting Eq. (2) with Eq. (3) into Eq. (1), the general differentialequations of stress can be rewritten at the n-th injection andpurge processes as a step function [8]. Then, the recurrencerelations of the stresses between the n-th and (n+1)-th purgeand the relations between n-th purge and (n+1)-th injection canbe found. The recurrence formula can be solved, and hencethe stresses at the n-th injection and purge processes can beobtained asσ(t) =0, t < t0−σsat. + σsat.α2(n−1)∑i=0(−1)ie−t−tiτs+σsat.(1− α)2(n−1)∑i=0(−1)ie−t−tiτr ,t2(n−1) ≤ t < t2n−1σsat.α2n−1∑i=0(−1)ie−t−tiτs+σsat.(1− α)2n−1∑i=0(−1)ie−t−tiτr ,t2n−1 ≤ t < t2n, (4)withσsat. =ERλKpCg, (5a)α =1τs(EUER− τsτr)(1τs− 1τr)−1, (5b)where σsat. denotes the stress at the saturated or the equilib-rium state when the initial internal stress is zero [8]. TheFig. 1. Experimentally measured signal responses of PCL-coated MSS toODCB. (a) Fitting curves with optimized paramters calculated from eachconcentration (10, 20 and 30%). (b) Fitting curves with optimized prameterscalculated from 10% signal response. Corresponding γσsat. is multiplied by20%/10% and 30%/10%, respectively.models given in Eq. (4) are assumed to be proportional tothe concentration of analyte in the gas phase Cg and σsat. isrelated to the amplitude of the signal. Since the signal outputof the nanomechanical sensing is directly proportional to theconcentration C(t) as described above, the signal output isanalytically derived for the rectangular multistep injection-purge cycles with viscoelastic materials.III. EXPERIEMENTALA. Preparation of MSSIn this study, we used MSS as a sensing unit because ofthe high robustness and sensitivity [10]. The construction ofthe MSS chips and its working principle have been previouslyreported [10], [11]. Briefly, MSS consists of a silicon-basedmembrane suspended by four piezoresistive beams, composinga full Wheatstone bridge. The membrane is coated with areceptor material, which generates the surface stress causedby the sorption-induced expansion. The surface stress on themembrane is transduced to the four sensing beams as amplifieduniaxial stresses, resulting in the changes in the electricalresistance of the piezoresistors embedded in the beams.Polycaprolactone (PCL) and alkyl-functionalized nanopar-ticles (C18-STNPs) [4] were coated directly onto the MSSmembrane using an inkjet spotter (LabJet-500SP, MicrojetCorporation) equipped with a nozzle (IJHBS-300, MicrojetCorporation). Each receptor material was dissolved in N,N-dimethylformaide (DMF) at a concentration of 1 mg mL−1,and the resulting solutions were deposited onto each channelof the MSS. The injection speed, volume of a droplet, andnumbers of inkjet shots were fixed at ca. 5 m s−1, ca. 300pL, and 300 shots, respectively. A stage of the inkjet spotterwas heated at 80 °C to promote evaporation of DMF. Thethicknesses of the receptor layers were ca. 1 µm.B. SensingThe coated MSS chips were placed in a Teflon chamber,which was placed in an incubator with a controlled temper-ature of 25.00 ± 0.02 °C. The chamber was connected to agas system consisting of two mass flow controllers (MFCs),a mixing chamber, a purging gas line, and a vial for asolvent liquid. The vapor of each solvent was produced bybubbling carrier gas. Pure nitrogen gas was used as carrierand purging gases. The total flow rate was maintained at 100mL min−1 during the experiments. The duration time wasprecisely controlled and the concentrations of the four differentsolvent vapors were controlled using MFC-1 at Pa/P0 of 0.1,0.2, and 0.3, where Pa and P0 denote the partial vapor pressureand saturated vapor pressure of the solvent, respectively (TableI). Before measuring MSS signals, pure nitrogen gas wasintroduced into the MSS chamber for 1 min. Subsequently,MFC-1 (injection line) was switched on/off at each durationtime (10 [s]) with a controlled total flow rate of 100 mLmin−1 using MFC-2 for up to 20 injection-purge cycles toobtain constant gas concentration given in Eq. (3). Data weremeasured with a bridge voltage of –0.5 V and recorded witha sampling rate of 100 Hz. The data collection program wasdesigned using LabVIEW (NI Corporation).TABLE ICONCENTRATIONS OF GASES USED IN THIS STUDYVOC P0 [ppm] a Pa/P0 [ppm] b10% 20% 30%Water 31300 3130 6270 9400Ethanol 86300 8630 17300 25900n-Dodecane 196 19.6 39.1 58.71,2-dichlorobenzene 1950 195 390 585aSaturated vapor pressure in the unit of ppm is estimated by using Antoine equation [12].bEach concentration of vapor is calculated from saturated vapor pressure.C. Curve fitting and estimation of parametersTo extract coating film properties from experimental data,we used least squares methods with trust region reflectivealgorithm using Python 3 with SciPy module. The amplitudeconstant σsat., the diffusion time constant τs, the relaxationtime constant τr, and the ratio of unrelaxed and relaxed moduliEU/ER in addition to the time when the first injection starts(t0) were optimized using the derived formula in this study.IV. RESULTS AND DISCUSSIONA. Estimation of parametersFigure 1a shows one of the fitting results for the signal re-sponses of PCL-coated MSS to 1,2-dichlorobenzene (ODCB)in different concentrations. The signal responses with differentconcentrations are well fitted with the derived equations for thefive injection-purge cycles [8]. Importantly, the analyte/coatingpair shows the amplitude parameter γσsat. proportional tothe concentrations of analytes, where γ is a proportionalityfactor. As shown in Fig. 1b, the signal responses of differentconcentrations (20% and 30%) can be entirely predicted withthe fitting parameters extracted from the 10% signal responseby simply multiplying the amplitude parameter γσsat.. Thegood agreement of the concentration dependence demonstratesthat the predictive capabilities of the theoretical models.When the measured signal responses are short (e.g., 30 s),then the parameters extracted from the experimental resultsFig. 2. Fitting accuracy between a single injection signal response andmultistep injection-purge cycles. (a,b) Signal responses of PCL-coated MSSto ODCB are shown (Pa/P0 = 30%) for a single injection (a) andmultistep injection-purge cycles (b). Red colored signal responses are usedfor optimizing each fitting curve, and blue colored signal responses are entiresignal output. Black dashed lines are the corresponding fitting curves.cannot predict the entire signal responses (Fig. 2). Even if thesignal response seems to reach the steady-state, the parametersextracted from a single injection procedure do not fit well tothe experimental result (Fig. 2a). Conversely, in the case of themultistep injection-purge cycle system, the curves predicted bythe extracted parameters fit well with the experimental results,even if the duration is relatively short (e.g., 90 s) as can be seenin Fig. 2b. Therefore, the optimized parameters extracted froma couple of injection-purge cycles can be clearly predicted bythe experimental responses.B. Identification of gas species and their concentrationsAmong the intrinsic parameters, the diffusion constant τsis informative for gas identification as it reflects the physic-ochemical interaction between a receptor material and a gas.In our previous reports [9], we demonstrated that the two dif-ferent time constants obtained from two different viscoelasticmaterial-coated MSS can be utilized for the gas identification;however, the model for optimizing the parameters in [9] wasbased on the Wenzel’s model [7], so that the signal responseshave to reach the steady-state. In contrast, the present modelfor the multistep injection-purge cycles allows us to optimizethe fitting parameters, including τs and γσsat., more accurately.Figure 3 shows the plot of the two diffusion time constantsobtained from two different materials-coated MSS for variousvolatile organic compounds (VOCs). It is clearly shown thateach VOC forms well-separated clusters, even when the signalresponses are obtained from different concentrations rangingfrom 10% to 30% (Fig. 3; see also Table I). More specif-ically, time constant τs,PCL obtained from PCL, which is akind of polar hydrophobic polymers, shows the trend in thepolarity, that is, polar/hydrophilic gases exhibited lower timeconstants while the hydrophobic gases, such as n-dodecane andODCB yield higher time constants. In contrast to PCL, alkyl-functionalized nanoparticles (C18-STNPs) [4] have long alkylchains, i.e., octadecyl functional groups, therefore, the timeFig. 3. Gas identification using the present viscoelastic model. Plot of τs,PCLand τs,C18-STNPs estimated by the curve fitting using Eq. (4). Each VOCcontains the different concentratoins ranging from 10% to 30%.constant τs,C18-STNPs yields the well-separated clusters betweennon-polar aliphatic and aromatic gases (i.e., n-dodecane andODCB), whereas it shows relatively similar values among thehydrophilic gases (i.e., water and ethanol).Importantly, the amplitude parameters γσsat. obtained fromthe receptor materials for the variety of VOCs clearly showthe linear correlations to those of the concentrations (Fig. 4).This result clearly indicates that the optimized parameters τsand γσsat. obtained from the present model [8] allow us toidentify not only the gas species but also their concentrationswithout the use of the multivariate analyses.V. CONCLUSIONThe analytical model of the nanomechanical sensors coatedwith a viscoelastic material proposed by Wenzel et al. [7]was extended to the multistep injection-purge cycle system[8]. Wenzel’s model includes the stress relaxation behaviorsof the viscoelastic coating film and represents accurate signalresponses. The present model can be used to analyze theabsorption and desorption processes without measuring untilthe signal reaches the steady-state. By measuring a coupleof injection-purge cycles, the accurate values of the coatingparameters can be extracted. Therefore, the optimized param-eters (i.e., τs and σsat.) can be directly used as effective indicesfor the identification of gas species and their concentrations.The parameters obtained from the present model reflect thephysical and chemical parameters of the coating film and thetarget gases. Thus, the present model can be utilized for theanalyses of repeated injection-purge cycles, and the accurateoptimized parameters can also be utilized as effective featuresfor the pattern recognition-based analyses including machinelearning approaches, contributing to the development of thepractical artificial olfaction.ACKNOWLEDGMENTSK.M. acknowledges International Center for Young Scien-tists (ICYS) program, National Institute for Materials Science(NIMS). This work was financially supported by JST CREST(No. JPMJCR1665); a Grant-in-Aid for Scientific ResearchFig. 4. Identification of gas concentrations using the present viscoelasticmodel. Concentration of target analyte from σsat. estimated by the curve fittingusing Eq. (4).(A), MEXT, Japan (No. 18H04168); a Grant-in-Aid for Sci-entific Research (C), MEXT, Japan (No. 20K05345); a Grant-in-Aid for Challenging Research (Pioneering), MEXT, Japan(No. 20K20554); the Public/Private RD Investment StrategicExpansion Program (PRISM), Cabinet Office, Japan; the IzumiScience and Technology Foundation (No. 2020-J-070); Centerfor Functional Sensor & Actuator (CFSN), NIMS; MANA,NIMS; and ICYS, NIMS.REFERENCES[1] K. M. Goeders, J. S. Colton, and L. A. Bottomley, “Microcantilevers:Sensing chemical interactions via mechanical motion,” Chem. Rev. 108,522–542 (2008).[2] K. Minami, K. Shiba, and G. Yoshikawa, “Discrimination of structurallysimilar odorous molecules with various concentrations by using ananomechanical sensor,” Anal. Methods 10, 3720–3726 (2018).[3] K. Minami, G. Imamura, T. Nemoto, K. Shiba, and G. Yoshikawa,”Pattern recognition of solid materials by multiple probe gases,” Mater.Horiz. 6, 580–586 (2019).[4] K. Shiba, R. Tamura, G. Imamura, and G. Yoshikawa, ”Data-drivennanomechanical sensing: specific information extraction from a complexsystem,” Sci. Rep. 7, 3661 (2017).[5] K. Shiba, R. Tamura, T. Sugiyama, Y. Kameyama, K. Koda, E. Sakon, K.Minami, H. T. Ngo, G. Imamura, K. Tsuda, and G. Yoshikawa, “Func-tional nanoparticles-coated nanomechanical sensor arrays for machinelearning-based quantitative odor analysis,” ACS Sens. 3, 1592–1600(2018).[6] H. Xu, K. Kitai, K. Minami, M, Nakatsu, G. Yoshikawa, K. Tsuda,K. Shiba, and R. Tamura, ”Determination of quasi-primary odors byendpoint detection,” Sci. Rep. 11, 12070 (2021).[7] M. J. Wenzel, F. Josse, S. M. Heinrich, E. Yaz, and P. G. Datskos,”Sorption-induced static bending of microcantilevers coated with vis-coelastic material,” J. Appl. Phys. 103, 064913 (2008).[8] K. Minami, K. Shiba, and G. Yoshikawa, ”Sorption-induced static modenanomechanical sensing with viscoelastic receptor layers for multistepinjection-purge cycles,” J. Appl. Phys. 129, 124503 (2021).[9] G. Imamura, K. 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