# Fileset

[AIP_humidity_SI.pdf](https://mdr.nims.go.jp/filesets/fa177dff-d5ac-4985-9a6f-e8966ca01047/download)

## Creator

[Meng-Qun Feng](https://orcid.org/0000-0002-3185-7555), [Kosuke Minami](https://orcid.org/0000-0003-4145-1118), [Yingcheng Zhou](https://orcid.org/0000-0002-6999-4897), [Genki Yoshikawa](https://orcid.org/0000-0002-9136-8964)

## Rights

©2025 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Analytical modeling and decoupling of humidity effects in nanomechanical sensing based on sorption kinetics and viscoelastic stress relaxation](https://mdr.nims.go.jp/datasets/78086aa9-f01b-4c3b-b6f4-90e0516a3776)

## Fulltext

Supplemental MaterialforAnalytical modeling and decoupling of humidity effects in nanomechanicalsensing based on sorption kinetics and viscoelastic stress relaxationMeng-Qun Feng,1, 2 Kosuke Minami,1, 3, ∗ Yingcheng Zhou,1, 2 and Genki Yoshikawa1, 2, †1Research Center for Macromolecules and Biomaterials,National Institute for Materials Science (NIMS),1-1 Namiki, Tsukuba, Ibaraki 305-0044 Japan2Materials Science and Engineering, Graduate School of Pure and Applied Science,University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 Japan3International Center for Young Scientists (ICYS),National Institute for Materials Science (NIMS),1-1 Namiki, Tsukuba, Ibaraki 305-0044 Japan(Dated: April 28, 2025)∗ Author to whom correspondence should be addressed; MINAMI.Kosuke@nims.go.jp† Author to whom correspondence should be addressed; YOSHIKAWA.Genki@nims.go.jpS1S I. SUPPLEMENTARY FIGURESFIG. S1. Numerical calculations of the signal responses for a single injection using derived model in eq 7.Offset responses σ(t)−σw to analytes with different τs with varied humidity differences ∆σw = 2, 1, 0, –1,–2, and –3. Colors indicate the different τs: blue, τs = 5 [s]; sky blue, τs = 10 [s]; green, τs = 20 [s]; yellow,τs = 30 [s]; red, τs = 60 [s].S2FIG. S2. Numerical calculations of the signal responses for multistep injection-purge cycles using derivedmodel in eq 7. Offset responses σ(t)˘σw to analytes with different s with varied humidity differences ∆σw.Colors indicate the different τs: blue, τs = 5 [s]; sky blue, τs = 10 [s]; green, τs = 20 [s]; yellow, τs = 30 [s];red, τs = 60 [s].S3FIG. S3. Numerical calculations of the signal responses for multistep injection-purge cycles using derivedmodel in eq 7. Model responses to highly humidified analytes, i.e., fixed σw +∆σw = 6, under varied initialhumidity Cw ∝ σw with different τs. Colors indicate the different τs: blue, τs = 5 [s]; sky blue, τs = 10 [s];green, τs = 20 [s]; yellow, τs = 30 [s]; red, τs = 60 [s].S4FIG. S4. Responses to pure BTEX at the different concentrations. The output signals are shown as solidlines, while the predicted responses based on the extracted fitting parameters are represented by dashedlines. (a) benzene, (b) toluene, (c) ethylbenzene, and (d) m-xylene. Analyte concentrations are indicated bycolors: 5%, blue; 10%, orange; and 15%, green.S5FIG. S5. Responses to BETX at different concentrations under ∆Cw = 20%RH; the initial humidity levelCw from left to right are Cw = 0, 20, and 40%RH. Analyte concentrations are indicated by colors: 5%, blue;10%, orange; and 15%, green, with predicted responses based on the extracted fitting parameters shown asdashed lines.S6FIG. S6. Responses to BETX at different concentrations under ∆Cw = 30%RH; the initial humidity levelCw from left to right are Cw = 0, 20, and 40%RH. Analyte concentrations are indicated by colors: 5%, blue;10%, orange; and 15%, green, with predicted responses based on the extracted fitting parameters shown asdashed lines.S7FIG. S7. Responses to BETX at different concentrations under ∆Cw = 40%RH; the initial humidity levelCw from left to right are Cw = 0, 20, and 40%RH. Analyte concentrations are indicated by colors: 5%, blue;10%, orange; and 15%, green, with predicted responses based on the extracted fitting parameters shown asdashed lines.S8FIG. S8. Responses to toluene under positive and negative humidity changes (∆Cw = ±20%RH). a,b) Theresponses to toluene vapor at Cg = 5% under positive (red; ∆Cw = 20%RH) and negative humidity changes(blue; ∆Cw = –20%RH). c,d) Subtracted signals. Gray, pure toluene; red dashed lines, ∆Cw = 20%RH; bluedashed lines, ∆Cw =−20%RH. e,f) Magnified responses from 20 to 40 s. g,h) Subtracted signals. See alsoFig. S11 for comparison between the pure signal and subtracted responses.S9FIG. S9. Responses to toluene under positive and negative humidity changes (∆Cw = ±20%RH). a,b) Theresponses to toluene vapor at Cg = 10% under positive (red; ∆Cw = 20%RH) and negative humidity changes(blue; ∆Cw = –20%RH). c,d) Subtracted signals. Gray, pure toluene; red dashed lines, ∆Cw = 20%RH; bluedashed lines, ∆Cw =−20%RH. e,f) Magnified responses from 20 to 40 s. g,h) Subtracted signals. See alsoFig. S11 for comparison between the pure signal and subtracted responses.S10FIG. S10. Responses to toluene under positive and negative humidity changes (∆Cw = ±20%RH). a,b) Theresponses to toluene vapor at Cg = 15% under positive (red; ∆Cw = 20%RH) and negative humidity changes(blue; ∆Cw = –20%RH). c,d) Subtracted signals. Gray, pure toluene; red dashed lines, ∆Cw = 20%RH; bluedashed lines, ∆Cw =−20%RH. e,f) Magnified responses from 20 to 40 s. g,h) Subtracted signals. See alsoFig. S11 for comparison between the pure signal and subtracted responses.S11FIG. S11. Comparison of subtracted responses obtained from positive (∆Cw = 20%RH; red dashed lines)and negative humidity differences (∆Cw = −20%RH; blue dashed lines) to the responses to pure toluenevapors (gray lines). Ci = 5% (a), 10% (b), and 15% (c).S12