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Stephen Wu, Yukiko Kondo, Masa-aki Kakimoto, Bin Yang, Hironao Yamada, [Isao Kuwajima](https://orcid.org/0000-0002-5994-3834), [Guillaume Lambard](https://orcid.org/0000-0003-0275-4079), Kenta Hongo, [Yibin Xu](https://orcid.org/0000-0001-8600-8748), Junichiro Shiomi, Christoph Schick, Junko Morikawa, Ryo Yoshida

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[Machine-learning-assisted discovery of polymers with high thermal conductivity using a molecular design algorithm](https://mdr.nims.go.jp/datasets/f2b2dca6-0f86-4212-ab79-a332ce6ae4c3)

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Supplementary InformationMachine-learning-assisted discovery ofpolymers with high thermal conductivityusing a molecular design algorithmStephen Wu, Yukiko Kondo, Masa-aki Kakimoto, Bin Yang, Hironao Yamada, IsaoKuwajima, Guillaume Lambard, Kenta Hongo, Yibin Xu, Junichiro Shiomi, ChristophSchick, Junko Morikawa, Ryo YoshidaThis document provides detailed information on transfer learning models, process of molecule design,and experimental validation, including the polymer synthesis details of the three finally selected candidates.1 Performance of transfer learningAs described in the main text, we produced 1,000 pre-trained neural networks with respect to each of Tg,Tm, and ρ for polymers and CV for monomers. All these models were transferred to those predicting λ usinga randomly chosen 80% of the given 28 samples as training instances and the remaining 20% as testinginstances. The random splitting of data was repeated five times to evaluate the generalization capabilitiesof the transferred models (i.e., Pearson’s correlation and mean absolute error (MAE)), as shown in Fig. S1.Fig. S2 shows the prediction versus observation plot of the best-performing model for the transfer from eachsource property. Overall, the transfer from the monomeric CV to λ reached the best MAE. Therefore, weused this model during the post-screening step of our design process.2 Molecular design processSupplementary Movie S1 shows the dynamic process of modifying the chemical structures with the desiredrange, Tg ∈ {200, 500} and Tm ∈ {300, 600}, starting from 100 initial seeds taken from PoLyInfo. Red circlesrepresent the experimental properties of existing polymers, which were used in the training process, and bluecircles represent the predicted properties of the designed structures that were placed in the top 25 in termsof realized likelihood values at each step of the iteration.3 Selected candidatesTable S1 summarizes the predicted properties of the 24 selected candidates whose chemical structures areshown in Fig. S3.1Mean abs. error (cal/goC) CorrelationTransfer from 
Cv (QM9) to
Cp (PoLyInfo) Mean abs. error (W/mK) CorrelationTransfer from 
Cv (QM9) to
λ (PoLyInfo) Mean abs. error (W/mK) CorrelationMean abs. error (W/mK) CorrelationMean abs. error (W/mK) CorrelationTransfer from 
Tg (PoLyInfo) to
λ (PoLyInfo) Transfer from 
Tm (PoLyInfo) to 
λ (PoLyInfo) Transfer from 
ρ (PoLyInfo) to
λ (PoLyInfo) Mean abs. error (W/mK) CorrelationMean abs. error (W/mK) CorrelationMean abs. error (W/mK) CorrelationTransfer from 
Tg (PoLyInfo) to
λ (PoLyInfo) Transfer from 
Tm (PoLyInfo) to 
λ (PoLyInfo) Transfer from 
ρ (PoLyInfo) to
λ (PoLyInfo) Transfer from Tg (PoLyInfo) to λ (PoLyInfo)Transfer from Tm (PoLyInfo) to λ (PoLyInfo)Transfer from ρ (PoLyInfo) to λ (PoLyInfo)Transfer from CV (QM9) to λ (PoLyInfo)Figure S1: MAE and Pearson’s correlation coefficients of the predicted λ with respect to the 28 observationsthat were calculated by the transferred models from Tg, Tm, ρ, and monomeric CV, respectively.2Prediction (cal/goC) Observation (cal/go C)Transfer from 
Cv (QM9) to
Cp (PoLyInfo) Prediction (W/mK) Observation (W/mK)Transfer from 
Cv (QM9) to
λ (PoLyInfo) Prediction (W/mK) Observation (W/mK)Prediction (W/mK) Observation (W/mK)Prediction (W/mK) Observation (W/mK)Transfer from 
Tg (PoLyInfo) to
λ (PoLyInfo) Transfer from 
Tm (PoLyInfo) to 
λ (PoLyInfo) Transfer from 
ρ (PoLyInfo) to
λ (PoLyInfo) Prediction (W/mK) Observation (W/mK)Prediction (W/mK) Observation (W/mK)Prediction (W/mK) Observation (W/mK)Transfer from 
Tg (PoLyInfo) to
λ (PoLyInfo) Transfer from 
Tm (PoLyInfo) to 
λ (PoLyInfo) Transfer from 
ρ (PoLyInfo) to
λ (PoLyInfo) Transfer from Tg (PoLyInfo) to λ (PoLyInfo)Transfer from Tm (PoLyInfo) to λ (PoLyInfo)Transfer from ρ (PoLyInfo) to λ (PoLyInfo)Transfer from CV (QM9) to λ (PoLyInfo)Figure S2: Prediction and observation plots for the transferred models on λ, whose source models weretrained on different data sets with regard to Tg, Tm, ρ, and monomeric CV, respectively.3Table S1: Predicted property values of the 24 selected candidates.Polymer SA Tg (◦C) Tm (◦C) ρ (g/cm3) λ (W/mK)1 3.41 248.6 465.6 1.331 0.2372 2.55 141.7 408.1 1.220 0.2343 2.61 272.3 440.9 1.290 0.2284 3.70 286.4 403.7 1.308 0.2465 3.78 279.0 309.4 1.260 0.2336 1.46 184.3 333.8 1.278 0.2147 2.52 255.8 275.2 1.264 0.2278 2.56 171.8 328.1 1.212 0.1959 2.91 365.1 487.9 1.325 0.22310 2.43 176.5 398.2 1.209 0.22611 2.76 277.9 513.6 1.259 0.22512 2.41 181.3 417.5 1.218 0.19713 2.17 228.3 426.1 1.288 0.22514 2.23 199.6 439.8 1.224 0.22215 2.58 160.8 374.3 1.196 0.20616 2.82 187.6 520.3 1.256 0.22817 2.88 201.6 459.6 1.282 0.22518 2.33 245.8 399.3 1.273 0.21819 1.70 121.5 321.0 1.260 0.21820 4.33 137.5 346.3 1.274 0.21321 2.37 166.6 353.4 1.266 0.21322 2.21 136.6 230.7 1.188 0.22223 3.15 185.3 421.7 1.281 0.23124 2.81 123.9 351.0 1.251 0.236412345NNOOOONHOOONHO�NHO2OOOOO NHOO3NHNHOO4NHNHOO5NNOOOONHOOONHO�NHO2OOOOO NHOO3NHNHOO4NHNHOO5NNOOOONHOOONHO�NHO2OOOOO NHOO3NHNHOO4NHNHOO5NNOOOONHOOONHO�NHO2OOOOO NHOO3NHNHOO4NHNHOO5NNOOOONHOOONHO�NHO2OOOOO NHOO3NHNHOO4NHNHOO5NHOO6OOONHNHO7O 89OO1�NHOONHNHONHOO6OOONHNHO7O 89OO1�NHOONHNHONHOO6OOONHNHO7O 89OO1�NHOONHNHONHOO6OOONHNHO7O 89OO1�NHOONHNHONHOO6OOONHNHO7O 89OO1�NHOONHNHOOOOO11O 12NHONHOOO13OO14O15OOOO11O 12NHONHOOO13OO14O15OOOO11O 12NHONHOOO13OO14O15OOOO11O 12NHONHOOO13OO14O15OOOO11O 12NHONHOOO13OO14O15OOOO16OOOO17OO18NHNHOONHO1920,�21OO22OOOO16OOOO17OO18NHNHOONHO1920,�21OO22OOOO16OOOO17OO18NHNHOONHO1920,�21OO22OOOO16OOOO17OO18NHNHOONHO1920,�21OO22OOOO16OOOO17OO18NHNHOONHO1920,�21OO22OOOO16OOOO17OO18NHNHOONHO1920,�21OO22OOONH23OOO24OOOO25O26O27OO28OOONH23OOO24OOOO25O26O27OO28OOONH23OOO24OOOO25O26O27OO286789101112131415161718192021222324Figure S3: Chemical structures of the repeat units of the 24 computationally designed polymers.54 Experimental validationThis section summarizes all details of experiments performed in this study. Table S2 summarizes all thematerial properties tested on the three newly synthesized polymers.Table S2: Experimental properties of the three newly synthesized polymers compared with predictions frommachine learning models (α: thermal diffusivity, CP: specific heat capacity, ρ: density, λ: thermal conduc-tivity, ηinh: inherent viscosity, TG10: temperature of the weight loss 10%, Xc: crystallinity). Compressedfilm-shaped samples were used in all cases except the X-ray diffraction of polymer 19a. We report valuesfrom prediction (pre), observation (obs), and observation after annealing (anneal). (* DSC failed to measureTg values, and instead, FSC was introduced to determine Tg and Tm. ** Thermal conductivity of annealedpolymer 4 was obtained using the heat capacity and density measured for non-heat-treated samples. # Xcof polymer 19a was measured in powder form).Polymer 4 (pre) 4 (obs) 4 (anneal) 13(pre) 13 (obs) 13 (anneal) 19 (pre) 19a (obs)Tg (◦C) (DSC) 286 N/A* - 228 N/A* - 121 194Tg (◦C) (FSC) 286 221 - 228 226 - 121 191Tm (◦C) (FSC) 404 513 - 426 494 - 321 303α (mm2/s) - 0.168 0.263 - 0.152 0.254 - 0.133CP (at 25–27◦C) - 1.13 - - 1.14 1.10 - 1.19ρ (at 16–20◦C) 1.308 1.373 - 1.288 1.295 1.386 1.260 1.233λ (W/mK) 0.246 0.261 0.408** 0.225 0.224 0.387 0.218 0.195ηinh (dL/g) - 0.193 - - 0.317 - - 0.313TG10 (◦C) - 400 - - >500 - - 361Xc - 0.16 - - 0.30 0.30 - 0.09#4.1 MeasurementsInfrared (IR) absorption spectra of polymers were measured by the KBr tablet method using Fourier trans-form IR spectroscopy (FTIR) on a Perkin Elmer Spectrum One (Massachusetts, USA). The attenuated totalreflection (ATR) IR method was applied to measure the IR reflection spectra of compressed thick samples.Proton (1H) nuclear magnetic resonance (NMR) spectra were recorded using a JEOL ECS-400 (Tokyo,Japan) with dimethyl sulfoxide-d6 (DMSO-d6) as a solvent. The inherent viscosity (ηinh) of polymers wasmeasured at 0.5 g/dL in N ,N -dimethylacetamide(DMAc) or in concentrated sulfonic acid solutions at 30◦Cwith an Ostwald viscometer. Thermal gravimetric analysis (TGA) and differential scanning calorimetry(DSC) were performed using a Perkin Elmer TGA7 and a Perkin Elmer DSC7, respectively, at a heatingrate of 10◦C/min under a nitrogen atmosphere. The specific heat (CP) of polymers was calculated by asimple comparison of the heat flow rates into a sample and a calibration substance (sapphire) by the classi-cal three-step technique in a temperature range of 20–50◦C using DSC. Thermo-mechanical analysis (TMA)was undertaken using a SEIKO (Tokyo, Japan) TMA - SS-6000 to measure thermal expansion at a heatingrate of 5◦C/min under ambient atmospheric conditions. The crystallinity of powder or compressed pelletsamples was determined by a Rigaku (Tokyo, Japan) wide-angle X-ray diffraction (WAXD) Mini Flex 600.The thermal diffusivity of the synthesized polymers was measured by the temperature wave method usingan ai-Phase mobile 1 supplied by ai-Phase Co. Ltd. (Tokyo, Japan). The density was determined byArchimedes’ method using an electronic densimeter SD-200L supplied by Alpha Mirage Co. Ltd. (Tokyo,Japan).Tg of polymer 19a was 194◦C, as measured by differential scanning calorimetry (DSC). In contrast, thecrystallinity of polymers 4 and 13 was 16% and 30%, respectively, as obtained by WAXD of compressedpellet samples. Although Tg of polymer 19a was observed clearly by DSC, no clear Tg value was measuredin the cases of polymers 4 and 13 in compressed pellets using a thermal mechanical analyser (TMA). Thepredicted values of Tg of polymers 4, 13, and 19a were 286◦C, 228◦C, and 122◦C, respectively. As discussed6below, by introducing fast scanning calorimetry (FSC), Tg and Tm of all three polymers were successfullyobserved.The compressed pellet thermal conductivities of polymers 4 and 13 were 0.26 W/mK and 0.22 W/mKat room temperature (r.t.), respectively. However, after annealing at 400◦C, these values increased by morethan 50% to 0.41 W/mK and 0.39 W/mK, respectively.4.2 ReagentsTerephthaloyl chloride M1, terephthalic dihydrazide M2,terephthalic acid M3, 1,4-bis(4-aminophenoxy)benzeneM4, m-phenylene diamine M7,3-aminobutanoic acid M8, benzylalcohol M9, triphenylphosphite, pyridine, tri-ethylamine, palladium on carbon (10 w%), and toluene sulfonic acid were sourced from Tokyo Chemical In-dustry. Anhydrous grade solvents, namely, dichloromethane (DMC), ethylacetate, N ,N -dimethylacetamide(DMAc), and N -methylpyrrolidone (NMP), were also purchased from Tokyo Chemical Industry. Tereph-thaloyl chloride was purified by sublimation, and other reagents and solvents were used as received.4.3 Preparation of monomers and polymersPreparation of polymer 4In a flask, 1.94 g (10 mmol) of terephthalic dihydrazide M2 was dissolved in 30 mL of NMP under N2. Next,2.03 g (10 mmol) of terephthaloyl chloride M1 dissolved in 10 mL of NMP was added under cooling by icebath. The solution was stirred overnight at r.t. and then added to 500 mL of methanol. The obtainedpowdery polymer was dried at 100◦C under reduced pressure. The yield of polymer 4 was 2.79 g (86%).This polymer was insoluble in organic solvents. The inherent viscosity was 0.192 dL/g measured at 30◦Cconcentration of 5 g/L in conc. sulfuric acid. Elemental analysis: Cal. C, 59.3%, H, 3.7%, N, 17.3%, Obs.C, 55.6%, H, 3.9%, N, 16.9%. The IR spectrum is shown in Fig. S4a.Preparation of polymer 13In a flask, 0.83 g (5 mmol) of terephthalic acid M3 was dissolved in 8 mL of NMP containing 0.5 g of lithiumchloride under a nitrogen atmosphere (N2). Next, 1.46 g (5 mmol) of 1,4-bis(4-aminophenoxy)-benzene M4,3.10 g (5 mmol) of triphenyl phosphite, 2.5 mL of pyridine, and finally 1 mL of NMP for washing the flaskwere added consecutively. The mixture was stirred for 3 h at 100◦C under a nitrogen atmosphere. Whiteprecipitate was observed during the reaction. After the solution was cooled to r.t., it was added to 350 mLof methanol. The solid polymer was separated by filtration and washed in boiling methanol. The obtainedpowdery polymer was dried at 100◦C under reduced pressure. The yield was 2.05 g (97%), and this polymerwas insoluble in organic solvents. The inherent viscosity measured at 30◦C concentration of 5 g/L in conc.sulfuric acid was 0.317 dL/g. Elemental analysis: Cal. C, 73.9%, H, 4.3%, N, 6.6% Obs. C, 71.9%, H, 4.1%,N, 6.4%. The IR spectrum is shown in Fig. S4b.Preparation of monomer M6Monomer M6, the monomer for polymer 19a, was developed as shown in Fig. S5. Terephthaloyl chloridemono-benzyl ester was prepared in situ from terephthaloyl chloride M1 and an equi-molar amount of benzylalcohol M9. Then, the benzyl ester of p-toluene sulfonic acid salt M10, which was synthesized by ordinaryamino acid esterification starting from 3-aminobutanoic acid M8, was reacted in the solution to obtaindibenzyl ester M11, the precursor of monomer M6.A mixture of 2.70 g (25 mmol) of benzyl alcohol M9 and 3.17 g of triethylamine in 20 mL of DMC wasadded to a 5.075 g (25 mmol) solution of terephthaloyl chloride M1 in 100 mL of DMC at r.t. This mixturewas then refluxed for 2 h under a nitrogen atmosphere. After the mixture was cooled to r.t., 9.14 g ofbenzylester M10 and 6.33 g of triethylamine in 50 mL of DMC was added, and the mixture was stirred atr.t. for 3 h. The resulting reaction mixture was washed with water. DMC was evaporated under reduced71020304050605001000150020002500300035004000T / % Wave number / cm-1332516321542300012743040506070805001000150020002500300035004000T / %Wave number cm-132831214149216451532a bFigure S4: (a) FTIR spectrum for polymer 4. (b) FTIR spectrum for polymer 13.pressure after the solution was dried by anhydrous MgSO4. Compound M11 was obtained by silica gelcolumn chromatography using ethyl acetate as an eluent. The yield was 4.70 g (44%).Next, 4.32 g (10 mmol) of M11 and 1.06 g (1 mmol) of palladium on carbon (10 w%) was mixed with 50mL of ethyl acetate. The flask atmosphere was replaced by hydrogen, and the solution was stirred for 2 days.After the gas in the flask was replaced by nitrogen, 100 mL of 1 M aqueous solution of sodium hydroxidewas added to the reaction mixture. The black-coloured catalyst was removed by filtration, and the filtratewas acidified using 1 M hydrochloric acid. Monomer M6 was obtained as precipitate. The yield was 753 mg(30%). The IR spectrum is shown in Fig. S6a and the NMR spectrum in Fig. S6b.Preparation of polymer 19aPolyamide 19a was prepared from 502 mg (2 mmol) of monomer M6 and 216 mg (2 mmol) of 1,3-phenylenediamineM7 using the same polymerization method as for polyamide 13. Polymerization proceeded in clear solution.The resulting isolated polyamide 19a was soluble in polar solvents, such as NMP and DMAc. The inherentviscosity measured at 30◦C concentration of 5 g/L in DMAc was 0.313 dL/g. Elemental analysis: Cal. C,66.9%, H, 5.3%, N, 13.0% Obs. C, 65.0%, H, 5.6%, N, 12.3%. The IR spectrum and 1H NMR spectrum areshown in Fig. S7a and b, respectively.8+N(CH2CH3)3N(CH2CH3)3,NHOOO OHHOOHClClOOClOOOH3C SO3OONH3NHOOO OOH2 , Pd/CM1 M9M11M10M6H3C SO3HOHONH2 +OHH3C SO3OONH3M8M9M10Figure S5: Synthetic route of monomer M6.9a bFigure S6: (a) FTIR spectrum for monomer M6. (b) 1H NMR spectrum for monomer M6.a bFigure S7: (a) FTIR spectrum for polymer 19a. (b) 1H NMR spectrum for polymer 19a.104.4 Characterization of polymersThermal analysisThe thermal properties of synthesized polymers 4, 13, and 19a were evaluated by DSC, TGA, TMA, and FSC.The specific heat capacities CP of the polymers are shown in Fig. S8a. The glass transition temperature(Tg) of polymer 19a is approximately 194◦C. Polymers 4 and 13 exhibited neither glass transition norcrystallization in the range of conditions of DSC. The TGA and TMA curves for polymers 4 and 13 areshown in Fig. S8b and c, respectively. The temperature at which 10% weight loss of polymer 13 occurred ishigher than 500◦C, indicating high thermal stability. Based on an ultra-fast temperature scan (30,000 K/susing FSC), the glass transition temperature Tg and melting temperature Tm are presented in Fig. S9. Thepredicted versus observed values of Tg and Tm for the synthetic polymers are displayed in Fig. S10.a b cFigure S8: (a) DSC curves for polymers at a heating rate of 10◦C/min under a nitrogen atmosphere, (b)TGA curves for polymers at a heating rate of 10◦C/min under a nitrogen atmosphere, and (c) TMA curvesfor polymers at a heating rate of 5◦C/min under ambient atmospheric conditions.a b cFigure S9: Fast scan DSC curves at a heating/cooling rate of 30,000 K/s under a nitrogen atmosphere for(a) polymer 4, (b) polymer 13, and (c) polymer 19a.11Figure S10: Correlation coefficients of predicted Tg and Tm compared to measured values determined by fastscanning calorimetry for the chemically synthesized polymers 4, 13, and 19a.X-ray diffractionIn X-ray diffraction studies, polymer 19a was semi-amorphous, while polymers 4 and 13 were crystalline.X-ray diffraction patterns are shown in Fig. S11a–c, revealing crystallinities of 15.9%, 30.4%, and 9.3%for polymers 4, 13, and 19a, respectively. In addition, the crystallinity of polymer 4 was enhanced afterannealing at 370◦C for 10 min. The X-ray diffraction patterns of polymers 4 and 13 after annealing areshown in Fig. S11d and e. The crystallinity of polymer 4 increased to 45.1%, whereas no change wasobserved for polymer 13. This result is attributed to a crystal structural change (amide band disappearance)in polymer 4 resulting from a high-temperature chemical reaction observed in the FTIR spectrum in Fig.S12. The estimated reaction is shown [1] in Fig. S12c.Temperature wave analysisThermal diffusivity was measured using temperature wave analysis. The phase difference between the inputand output signals was measured as a function of the angular frequency of the input temperature wave, asshown in Fig. S13, for polymers 4, 13, and 19a. the changes before and after heat treatment of polymers 13and 4 are shown together. In the experimental conditions of “thermal thick”, the thermal diffusivity can bederived directly from the slope of the plot if the distance or sample thickness is known.By introducing FSC [2], the Tg and Tm values of the aromatic polyamides were successfully observed forthe first time, as shown in Fig. S9. Typically, these temperatures have not been observed because of thethermal degradation that occurred under conventional DSC. By using the scan rate of 30,000 K/s, Tm valueshigher than 400◦C could be observed, and in parallel, cold crystallization phenomena could be observed inthe case of polymer 13.12a b cd eFigure S11: X-ray diffraction patterns of polymers using compressed pellets or powder: (a) polymer 4, (b)polymer 13, (c) polymer 19a. X-ray diffraction patterns of (d) polymer 4 after annealing at 400◦C for 10min, and (e) polymer 13 after annealing at 370◦C for 10 min.13a bcFigure S12: (a) Comparison of the FTIR spectrum of polymer 4 before and after annealing at 370◦C. (b)Comparison of the ATR FTIR spectrum of polymer 13 before and after annealing at 420◦C. (c) Estimatedreaction of polymer 4 during annealing at 370◦C.a bFigure S13: (a) Phase differences of (a) polymer 4 (thickness d = 165.2 µm, 301.2 µm (annealed at 370◦C)),polymer 19a (d = 146.6 µm), and (b) polymer 13 (thickness d = 180.9 µm, 315.4 µm (annealed at 420◦C))plotted as a function of the square root of the angular frequency of the temperature wave.14References[1] Bhausaheb V Tawade, Nitin G Valsange, and Prakash P Wadgaonkar. Synthesis and characterizationof polyhydrazides and poly(1,3,4-oxadiazole)s containing multiple arylene ether linkages and pendentpentadecyl chains. High Performance Polymers, 29(7):836–848, 2017. doi: 10.1177/0954008316660368.URL https://doi.org/10.1177/0954008316660368.[2] Y.L. Gao, E. Zhuravlev, C.D. Zou, B. Yang, Q.J. Zhai, and C. Schick. Calorimetric measurements ofundercooling in single micron sized snagcu particles in a wide range of cooling rates. ThermochimicaActa, 482(1):1–7, 2009.15