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[Yusuke Hibi](https://orcid.org/0000-0003-4006-1070), Shiho Uesaka, [Masanobu Naito](https://orcid.org/0000-0001-7198-819X)

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[Thermogravimetry-Synchronized, Reference-Free Quantitative Mass Spectrometry for Accurate Compositional Analysis of Polymer Systems Without Prior Knowledge of Constituents](https://mdr.nims.go.jp/datasets/8a3cc19c-df90-459e-9fd5-c0d7ebedc1bb)

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Thermogravimetry-synchronized, reference-free quantitative mass spectrometry for accurate compositional analysis of polymer systems without prior knowledge of constituentsAnalystPAPERCite this: DOI: 10.1039/d4an00624kReceived 29th April 2024,Accepted 21st June 2024DOI: 10.1039/d4an00624krsc.li/analystThermogravimetry-synchronized, reference-freequantitative mass spectrometry for accuratecompositional analysis of polymer systemswithout prior knowledge of constituents†Yusuke Hibi, * Shiho Uesaka and Masanobu Naito *Compositional analysis (CA)—identification and quantification of the system constituents—is the most fun-damental and decisive approach for investigating the system of interest. Pyrolysis mass spectrometry (MS)with a high resolution of over 10 000 is very effective for chemical identification and is directly applicableto polymer materials regardless of their solubilities. However, it is less helpful for quantification, especiallywhen the references, i.e., pure constituents, are unknown, non-isolable and thus cannot be prepared. Tocompensate for this weakness, herein we propose reference-free quantitative mass spectrometry (RQMS)with enhanced quantification accuracy assisted by synchronized thermogravimetry (TG). The key tosuccess lies in correlating the instantaneous weight loss from TG with the MS signal, enabling the quanti-tative evaluation of the distinct ionization efficiency for each fragment individually. The determinedionization efficiencies allow the conversion of MS signal intensities of pyrolyzed fragments into weightabundances. In a benchmark test using ternary polymer systems, this new framework named TG-RQMSdemonstrates accurate CA within ±1.3 wt% errors without using any prior knowledge or spectra of thereferences. This simple yet accurate and versatile CA method would be an invaluable tool to investigatepolymer materials whose composition is hardly accessible via other analytical methods.IntroductionCompositional analysis (CA) is the most fundamentalapproach for investigating the system of interest.“Composition” usually means chemical composition; however,recent studies showed that the CA framework can access geo-metric/physical information as well, e.g., the monomersequence along the main chain1 and thermal properties,2 viacarefully selecting the system constituents, which furtherenhances the importance of CA. The feasibility of CA via somespectroscopy depends on the availability of the references, i.e.,pure system constituents. When a comprehensive libraryincluding all possible reference spectra is available, CA issimply reduced to spectral deconvolution under the assump-tion of a linear mixing model.3 A representative example iselemental CA using techniques such as electron energy lossspectroscopy (EELS)4 and energy dispersive X-ray (EDX).5 Sincethe number of natural elements is limited to 92, a comprehen-sive library can be prepared and is usually installed by defaulton the instrument. In contrast, such libraries for molecular-level CAs are not feasible to be prepared, since the size of allpossible molecular structures is on the order of 1060.6Therefore, reference spectra must be prepared for each individ-ual case, which is feasible only when all system componentsare known and isolable. In mass spectrometry (MS), thisapproach is well-known as label-free quantitative MS and is fre-quently used in proteomics.7 This strategy was also exploitedin pyrolysis-MS for quantifying microplastics in soil.8 However,material scientists often face situations where the system com-ponents are unknown or non-isolable and thus the referencespectra are not feasible to be prepared. Even in such cases, werecently demonstrated that CA was executable via reference-free quantitative MS (RQMS) based on pyrolysis-MS;1 there,unmeasurable reference spectra were inferred from a spectraldataset of mixtures. This data-driven method inspired by unsu-pervised learning techniques for spectral imaging9,10 iseffective especially when the analyte compositions areunknown but can be somehow modulated by changing experi-mental conditions. Indeed, by inferring reference spectra ofsequence-defined copolymers based on a dataset of random†Electronic supplementary information (ESI) available: Materials and methods,supplementary figures (Fig. S1 and S2) and spectral dataset with sample infor-mation (Data S1–S3). See DOI: https://doi.org/10.1039/d4an00624kData-driven Polymer Design Group, Research Center for Macromolecules andBiomaterials, National Institute for Materials Science (NIMS), 1-2-1, Sengen,Tsukuba, Ibaraki 305-0047, Japan. E-mail: hibi.yusuke@nims.go.jp,naito.masanobu@nims.go.jpThis journal is © The Royal Society of Chemistry 2024 AnalystOpen Access Article. Published on 26 June 2024. Downloaded on 7/21/2024 9:41:35 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineView Journalhttp://rsc.li/analysthttp://orcid.org/0000-0003-4006-1070http://orcid.org/0000-0001-7198-819Xhttps://doi.org/10.1039/d4an00624khttps://doi.org/10.1039/d4an00624khttp://crossmark.crossref.org/dialog/?doi=10.1039/d4an00624k&domain=pdf&date_stamp=2024-07-12http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4an00624khttps://pubs.rsc.org/en/journals/journal/ANcopolymers synthesized from various monomer feed ratios,RQMS solved a long-standing question in polymer science—how to analyze sequence distribution in copolymers.1 With theversatility of pyrolysis-MS, which is directly applicable to anypolymer/composite materials, regardless of their solubilities insolvents, RQMS has great potential to be a decisive characteriz-ation method in polymer science. However, the reported accu-racy in benchmark CA for ternary polymer systems was insuffi-cient with ±5 wt% composition errors, which might cause non-negligible inconsistency between RQMS and conventionalnuclear magnetic resonance (NMR) in sequence distributionanalysis.1 To become a more reliable and quantitative charac-terization method, drastic improvements in accuracy areneeded for RQMS.To this end, herein, we propose thermogravimetry-assistedRQMS (TG-RQMS). The concurrent measurement of TG andMS (TG-MS) was first proposed in the 1960s, originallydesigned to identify the chemical structures of pyrolyzedgases.11 Later, TG-MS was utilized for quantifying small mole-cules such as H2O, CO and CO2, based on the finding that theMS peak intensities and weight losses were identically pro-portional, regardless of their chemical structures.12 However,larger fragments generated from polymer pyrolysis have indivi-dually different ionization efficiencies and also undergovarious ionization fragmentations. Therefore, the proportionalconstants between MS peak intensities and weight losses arepeak-wisely different, obscuring how to quantitatively andcomplementarily analyze TG-MS. Nevertheless, MS peak inten-sities and derivative TG (dTG) (Fig. 1) are at least correlated,even if not proportional, which would allow converting the MSpeak intensities into the weight abundances of pyrolyzed frag-ments. This conversion would put more focus on the frag-ments with lower ionization coefficients during the analysis;they are less dominant in MS spectra but may occupy a rela-tively large fraction by weight, as compared to those withhigher ionization coefficients. To intuitively understand thiskey concept, assume a trace amount of contaminant with amuch higher ionization coefficient as compared to major poly-meric components; then, the observed MS spectra would besignificantly distorted by the contaminant. Nevertheless, itsimportance can be properly assessed through the conversioninto the weight fraction. To this end, the principal contri-bution of this paper is to first provide a quantitative methodfor determining the distinct ionization efficiency of each frag-ment individually. Ionization efficiency for each fragment isherein defined as the ratio of MS peak intensity to weight.Although TG data allow for the capture of instantaneousweight loss, this represents the aggregate weight loss fromFig. 1 TG-TOFMS setup for TG-RQMS. The weight and MS spectra are recorded every second. The synchronous analysis of instantaneous weightloss (dTG) and MS spectra allow the estimation of ionization efficiencies of pyrolyzed fragments for improving the RQMS accuracy.Paper AnalystAnalyst This journal is © The Royal Society of Chemistry 2024Open Access Article. Published on 26 June 2024. Downloaded on 7/21/2024 9:41:35 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4an00624khundreds of peaks that emerge simultaneously in the corres-ponding mass spectra. Consequently, determining ionizationefficiency for each peak by solving the simultaneous equationsbetween TG and MS peaks becomes impractical due to theexcessive number of variables relative to the number ofequations. Therefore, we initially consolidate the peaks intoapproximately ten basis spectra using the unsupervised learn-ing algorithm of soft-orthogonality constrained non-negativematrix factorization with automatic relevance determination(ARD-SO-NMF),9 the linear combination of which best rep-resents the original MS spectra. Subsequently, we determinethe ionization efficiency for each of these basic spectra.Indeed, as described below, this simple strategy significantlyimproves the RQMS accuracy within estimated compositionerrors of ±1.3 wt% in a benchmark test. TG-RQMS also allowsthe quantification of 1000 ppm level of additives.Furthermore, the inferred reference spectra retain the highresolution of over 10 000 at around 100 m/z provided by time-of-flight MS (TOFMS), allowing easy chemical identification aswell. In the following section, we describe detailed experi-mental and mathematical procedures.Experimental sectionTG-TOFMS measurements were conducted at NIMS with a con-nected system of TG-DTA8122 (Rigaku) and JMS-T2000GCAccuTOF (JEOL) with an electron impact (EI) ion source (seethe Methods section in the ESI† for detailed measurementconditions). TG-quadrupole MS measurements were con-ducted at Rigaku with a connected system of TG-DTA8122 andJMS-Q1500GC (JEOL) with an EI ion source. Unless otherwisenoted, the ionization energy was set to 70 eV. For the bench-mark CA test, binary or ternary samples of polyethyl-methacrylate (E; Mw = 515 000), polymethylmethacrylate (M;Mw = 66 700) and polystyrene (S; Mw = 18 100) were prepared asfollows. First, the blended polymers at a certain mixing ratiowere dissolved in 1,4-dioxane (total polymeric concentration,3.3 wt%) and about 30 μL of the solution was dropcast on analuminum pan (polymer sample weight, about 1 mg). Aftersolvent evaporation under vacuum for 12 hours, an aluminumlid was put on the pan on top of which an internal standard of4,4′-di-tert-butylbiphenyl (dtBbph, about 0.5 mg) was placed sothat it would not contact the polymeric sample. Since dtBbphrapidly evaporates at a significantly lower temperature ofaround 150 °C, which is much lower than the polymerdecomposition temperature of over 300 °C, there were twoinstances of weight loss. The first and second weight lossescorresponded to dtBbph weight (Ws) and polymer weight (Wp),respectively (Fig. 1). As a result, precise measurements of exactweights were not necessary during sample preparation. Thedouble-bottom pan was loaded into the combustion chamberof TG and pyrolyzed at elevated temperature from 50 to 600 °Cat a heating rate of 25 °C min−1. The pyrolyzed gases werepassed through a transfer tube kept at 350 °C into the EI ionsource of TOFMS (Fig. 1). The pyrolysis gases generated attemperatures above 350 °C may condense on the transfer tube.However, the interior of the tube is under reduced pressuredue to the MS vacuum chamber, creating conditions less con-ducive to condensation. Furthermore, since pyrolysis finelydivides the polymer into small molecules, the vapor pressureof the pyrolysis gas generated at high temperatures is notnecessarily low. Nonetheless, constant vigilance is required toprevent contamination from the transfer tube and chambers.We have confirmed that the total ion currents of the back-ground mass spectra before and after dataset creation weremore than four orders of magnitude lower than thosemeasured during the experiments, confirming that contami-nation is negligible. The delay time for transporting and spec-tral intensity of MS were corrected using the internal standardas described later. The acquisition intervals of the MS spectraand weight losses were one second. The raw profile spectrawere converted to centroid spectra using msAxel (JEOL) with±2 mDa tolerance. The RQMS analysis were conducted usingthe same algorithm presented in the previous reports (see theoriginal developments9,10 and our implementation1), exceptthat the spectral fragment abundances (FA) were converted tothe weight-base fragment abundances (wFA) using a dTG curveas described later.Results and discussionMS intensity normalizationPrior to analysis with (TG-)RQMS, the signal intensity of theMS spectra was normalized for each sample using the peakintensity of the internal standard (Is; see Fig. 1). Given that thesignal intensity of MS in TG-MS can significantly vary from dayto day based on the equipment’s condition, this normalizationis crucial for maintaining long-term dataset stability and fortransferring the dataset to different equipment. To see the nor-malization effect, PS samples with various weights weremeasured. As shown in Fig. 2, the linearity of the MS intensi-ties and sample amounts of PS were insufficient before thenormalization; however, multiplication by the factor of Ws/Iswell established the linearity, suggesting the feasibility ofquantitative analysis. The linearity was maintained even whendifferent MS setups at different institutes were used (red:measured at NIMS with TG-TOFMS; blue: measured at Rigakuwith TG-quadrupole MS). This strongly suggested long-termdataset stability and data-sharing feasibility in contrast to thereported RQMS based on environment-specific direct analysisin real-time MS (DART-MS) under open air.13 Since we are onlyinterested in weight fractions, not the absolute abundances,hereafter the MS intensity was further divided by the sampleweight Wp. The delay of MS spectra from TG caused by gastransportation (typically 10–20 seconds) was corrected usingthe standard peaks of dTG and TIC curves so that they wouldmatch on the time axis. After the intensity normalization anddelay corrections, 840 MS spectra acquired at 250–600 °C(8–22 min), corresponding to the polymer decompositionstage, were extracted and integrated into NT spectra (typicallyAnalyst PaperThis journal is © The Royal Society of Chemistry 2024 AnalystOpen Access Article. Published on 26 June 2024. Downloaded on 7/21/2024 9:41:35 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4an00624kNT = 10). The spectral dataset composed of NTN spectra (N: thenumber of mixed samples) was then subjected to (TG-) RQMSanalysis to output the inferred reference spectra and their frac-tion in each sample.Benchmark CA for ternary polymer systemsThe purpose of this benchmark CA test is to verify the accuracyof (TG-) RQMS. We therefore prepared a ternary polymersystem with known compositions so that RQMS accuracy canbe evaluated by the difference between the inferred and knownground-truth compositions. During the composition inference,neither the known compositions of any mixture samples northe reference spectra of the pure constituents were used. Thislimitation can create the same situation as CA of unknownpolymer systems where only mixture spectra with unknowncompositions are given. In this paper, we do not conduct CAon really unknown polymer systems, since the inferred compo-sition cannot be readily verified. Such a practical applicationof RQMS, which is beyond the scope of this paper, can befound in sequence distribution analysis.1 It should be notedthat in such a practical situation, the number of system con-stituents is not necessarily limited to three and CAs forsystems with five, nine, and 13 constituents were demonstratedin the previous report.1 However, since it has been shown thatincreasing the number of constituents does not increase thedifficulty of the problem,7 only ternary and quaternary systemswere used for the verification of RQMS accuracy in this paper.Leaving the mathematical discussion for later, we firstdescribe the results of benchmark CA for a ternary system ofpolyethylmethacrylate (E), polymethylmethacrylate (M) andpolystyrene (S). The used dataset consisted of 32 samples ofbinary or ternary mixtures, none of which exceeded 80 wt%composition for any component (therefore, reference-free).The fractions estimated by the previously reported RQMSwithout utilizing TG curves significantly deviated from theground-truth (Fig. 3A). This could be attributable to the sharedsubstructure of methacrylic backbones of E and M, whichcaused significant peak-overlapping among the constituents.Indeed, the reference spectra of E and M (Fig. 3D) were verysimilar. Despite this inherent difficulty of polymer CA, con-current TG analysis drastically improved the situation, evenwhen the different constituents generated multiple identicalfragments (Fig. 3B; analyzed by TG-RQMS; also see the numeri-cal data in Table S1†). The root-mean-squared error (RMSE) forestimated fractions was reduced from 0.043 to 0.013 (from±4.3 wt% error down to ±1.3 wt% error; see how to calculatethe error in the “Revisiting RQMS” section). This improvementwas attributable to the conversion of MS signal intensities ofpyrolyzed fragments into weight abundances via TG data,which placed more emphasis on the fragments with lowerionization. It should be noted that various pyrolyzed fragmentswith different ionization efficiencies are simultaneously gener-ated, distorting the proportional relationship between MSsignal intensities (TIC) and instantaneous weight loss (dTG).Nevertheless, by introducing the concept of “inverse ionizationefficiency” inherent to each fragment, TIC and dTG can bequantitatively correlated as discussed later. The concurrentanalysis of TG also allowed the quantification of trace additives(Fig. 3C). These high purity samples (M fraction > 0.99) werenot used for leaning the reference spectra but just projectedonto the learned space spanned by the inferred references,suggesting an accurate inference. Also, the inferred referencespectra showed good consistency with the observed referencespectra (Fig. 3D). Since the inferred reference spectra preservedthe high resolution (over 10 000 at around 100 m/z), the identi-fication of polymeric species was easily executable based onthe monomeric mass. To validate the transferability of thedataset from TOFMS to ubiquitous quadrupole MS, the refer-ence spectra inferred from the TOFMS dataset were roundedinto integer spectra, which were used for deconvoluting theinteger spectrum acquired by quadrupole MS at Rigaku, out-putting the accurate fraction (Fig. 3C). This ensured datasettransferability between different instruments and institutes.To emphasize its distinct advantages over other analyticalmethods, we conducted a TG-RQMS analysis on a quaternarysystem of E/M/R/S, where a random copolymer (R) of methylmethacrylate and styrene with a 1 : 1 monomer compositionwas introduced into the aforementioned ternary system ofE/M/S. Quantifying random copolymers within homopolymerblends is an essential technique for ensuring the quality of,for example, polymer alloys and recycled materials.14 However,it poses a significant challenge in NMR, where the peaks ofeach component tend to overlap almost completely. Toaddress this, we created a new dataset consisting of 58samples of mixtures in the quaternary system of E/M/R/S. It isnoteworthy that the dataset size explosion has been mitigatedFig. 2 MS intensity normalization using internal standards. The circlesand triangles represent the raw and normalized intensities,respectively. The red datapoints represent measurements acquired atNIMS using TG-TOFMS, and the blue datapoints represent measure-ments acquired at Rigaku using TG-quadrupole MS. The dotted linerepresents the best fit line.Paper AnalystAnalyst This journal is © The Royal Society of Chemistry 2024Open Access Article. Published on 26 June 2024. Downloaded on 7/21/2024 9:41:35 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4an00624kcompared to the ternary system of E/M/S. The experimentaland algorithm parameters were largely consistent with thoseof the ternary system (see Table S3†); however, to achieve rela-tively softer ionization, the ionization energy was adjusted to20 eV. The CA result is depicted in Fig. 4, which shows the gapbetween the inferred and ground-truth fractions of the qua-ternary polymers. The RMSE was 0.029 (±2.9 wt% inferenceerror), which was surprisingly accurate considering theinclusion of random copolymers along with the homopoly-mers (also see the numerical reports in Table S2†). The uniqueability of TG-RQMS to accurately estimate compositionswithout references, even in mixtures containing random copo-lymers and polymers with slightly different side chains, under-scored its utility.Revisiting RQMSWe first briefly review the previously reported RQMS algor-ithm1 without synchronous analysis of TG, which output theinferred composition, as shown in Fig. 3A. In this section, aMS spectrum is represented by a D-dimensional row vector pre-serving the non-negative signal intensities in D-channels. Apyrolysis-MS spectrum with NT temperature bands is a two-dimensional spectrum represented by a (NT,D)-matrix.However, for simplicity, for a while, we assume a one-dimen-sional spectrum by summing up the NT-spectra along thetemperature axis. A spectral dataset X composed of N-samplesis then represented by a non-negative (NT,D)-matrix X [ RþN�Dstoring the nth sample spectrum at the nth row (Xn:). Themission of RQMS is the simultaneous identification ofK-reference spectra P [ RþK�D (K ≪ N) and their fraction ineach of the N-samples C [ RþN�K . In this paper, we do notconsider chemical reactions/interactions between the com-ponents—see Fig. S1† for how the final CA accuracy isadversely affected when the constituent polymers are reactive/interactive with each other. Under the linear mixing assump-tion, any observed spectrum Xn: would be represented by alinear combination of the K-reference spectra with individuallydifferent mixing fractions, i.e.,Xn: �PKk¼1CnkPk:; s:t:PKk¼1Cnk ¼ 1; ðn ¼ 1; . . . ;NÞ ð1Þwhere Cnk is the weight fraction of the kth component in thenth sample. Since Cn: represents the fraction of the nthsample, it should satisfy the sum-to-one condition. This canFig. 3 Benchmark CA test for ternary polymer films. (A) RQMS-estimated composition and (B) TG-RQMS–estimated composition for the reference-free system (the maximum faction was 80 wt%). Red stars and blue dots represent the ground-truth and inferred compositions, with parings indi-cated by orange arrows. Green dots represent high purity samples or samples measured by quadrupole MS, which were not used for inferring thereference spectra, but just projected on the learned simplex. (C) A log-scale plot along the M–S edge of (B). (D) Reference spectra inferred byTG-RQMS. The overlapped black dotted curves represent the observed spectra.Analyst PaperThis journal is © The Royal Society of Chemistry 2024 AnalystOpen Access Article. Published on 26 June 2024. Downloaded on 7/21/2024 9:41:35 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4an00624kbe simply written as X ≈ CP in a matrix form called non-nega-tive matrix factorization (NMF),15 which is a mathematical rep-resentation of CA. We want to find the most suitable C and Pbest representing the observed spectra X. The long history ofNMF developments tackling difficult questions,16 e.g., how tofind a better solution9 and how to ensure its uniqueness,10can be found in the references. Besides such mathematicaldiscussions, we herein focus on only one practical issuespecific to pyrolysis-MS; the direct factorization of X into thereference spectra P and their fraction C would not be success-ful, since pyrolysis-MS does not observe polymers themselves,but measures their thermally and/or ionically decomposedfragments. We therefore proposed two-step NMFs formulatedas X ≈ AS ≈ (CB)S.1 First, the observed spectra X would be fac-torized into M-fragment spectra S [ RþM�D and their abun-dances in each of the N-samples A [ RþN�M (fragment abun-dances, FA). Subsequently, A would be factorized into FA of theK-pure constituents B [ RþK�M and their fractions in each ofthe N-samples C [ RþN�K . From these definitions, P = BSapparently holds, deriving C and P via X ≈ C(BS) = CP. Toincorporate TG data into RQMS, in the following section weconsider the temperature axis; therefore, the first NMF wasconducted on X̃ [ RþNTN�D rather than X [ RþN�D, output-ting spectrum-wise FA Ã [ RþNTN�M . The (TG-) RQMS accuracywas evaluated by the root mean squared error (RMSE) of Cfrom the ground-truth fraction C̄ only known in the bench-mark CA test, i.e., RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1NXKkXNnðC � C̄Þkn2s.Incorporation of TG curves into RQMSHere, we describe the key contribution of this paper, i.e., TG-syn-chronized RQMS for more accurate compositional analysis(Fig. 3B). After the first NMF X̃ ≈ ãS, we have FAs for each of theNTN-spectra (ã), which are mixing coefficients of the L2-normal-ized fragment spectra (S). The abundances are, however, stronglybiased by their individually different ionization efficiencies and,therefore, do not directly indicate their weight fractions in theanalyte. To convert the spectral FA into weight-base FA (wFA), weexploited TG curves which should hold:ãi:z ¼ wiði ¼ 1;…;NTNÞ ð2Þwhere z [ RþM represents the inverse ionization coefficients ofM-fragments and wi is the sample weight change during the ithtemperature band. The vector w ≡ (w1,…,wNT)T can be calculatedas −ΔTG from TG; therefore, eqn (2) mathematically connectsTG and MS. The unknown z can be easily obtained by solvingeqn (2) via non-negative least-squares algorithms,3 allowing theconversion of the spectral FA ã into wFA: ã(w) = ãZ, where Z =diag(z). Since the temperature distribution of wFA is not helpfulfor CA, Ã wð Þ[ RþNTN�M was converted into A wð Þ [ RþN�M viasample-wise integration along the temperature axis and sub-sequently input into the second NMF, i.e., A(w) ≈ CB, using thereported algorithm (see the original development10 and ourimplementation1). The modified part of the entire algorithm isillustrated in Fig. S2.† This simple update drastically improvedthe CA accuracy for the benchmark test as presented in Fig. 3.ConclusionThis paper first demonstrated how to incorporate TG curvesinto quantitative MS analysis. The update toward TG-RQMSwas trivial: just converting spectral fragment abundances intoweight-base fragment abundances via synchronized TG data.Nevertheless, this TG reinforcement drastically improved theanalytical performances: decreasing the compositional esti-mation errors from ±4.3 wt% down to ±1.3 wt% and allowingthe contaminant quantification on order of 1000 ppm. Thistechnique, capable of detecting extremely small impuritieswith high precision, is expected to be essential for applicationssuch as monitoring the leaching of weathering agents presentin practical polymer materials at very low levels and for qualitycontrol in recycled materials. TG-RQMS is performed underthe linear mixing assumption, yet even for a non-linear mixingsystem with reactive components, “good enough” CA accuracywas demonstrated (Fig. S1†). To achieve more accurate CA forstrongly interacted systems, a non-linear CA framework expli-citly considering interactions/reactions between componentsshould be developed, which could be achievable based on a bi-linear mixing model17—extended version of the linear mixingmodel. Overall, TG-RQMS allows accurate CA without usingany prior knowledge about the system, which would solvelong-standing questions in polymer science, e.g., how toanalyze sequence distribution.Fig. 4 Fractions of E/M/R/S quaternary polymers inferred by theTG-RQMS algorithm without using any reference spectra. Blue dots andred stars represent the inferred and ground-truth fractions, respectively,with orange lines indicating the gaps. The RMSE of the entire datasetwas 0.029.Paper AnalystAnalyst This journal is © The Royal Society of Chemistry 2024Open Access Article. Published on 26 June 2024. Downloaded on 7/21/2024 9:41:35 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d4an00624kAuthor contributionsY. H. conceived the research, conducted the experiments,developed the software, analyzed the data, and wrote themanuscript. S. U. helped with the experiments. Y. H. andM. N. supervised the research.Conflicts of interestY. H. and M. N. are owners of patent applications onTG-RQMS.AcknowledgementsThis work was supported by JSPS KAKENHI Grant NumberJP24K08520 (to Y. H.) and the Core Research for EvolutionalScience and Technology Program of the Japan Science andTechnology Agency under Grant JPMJCR19J3 (to M. N.). Theauthors thank Yoshinobu Hosoi (Rigaku Corporation) for hishelp with TG-quadrupole MS measurements.References1 Y. Hibi, S. Uesaka and M. Naito, A Data-Driven SequencerThat Unveils Latent “Codons” in Synthetic Copolymers,Chem. Sci., 2023, 14, 5619–5626.2 Y. Hibi, Y. Tsuyuki, S. Ishii, E. Ide and M. Naito, DecodingThermal Properties in Polymer-Inorganic Heat Dissipators:A Data-Driven Approach Using Pyrolysis MassSpectrometry, Sci. Technol. Adv. Mater., 2024, 25(1), DOI:10.1080/14686996.2024.2362125.3 D. C. Heinz and C.-I. 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