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[Hayato Maeda](https://orcid.org/0009-0004-1662-8000), [Stephen Wu](https://orcid.org/0000-0002-7847-8106), [Rika Marui](https://orcid.org/0009-0009-2506-1196), Erina Yoshida, Kan Hatakeyama-Sato, Yuta Nabae, Shiori Nakagawa, Meguya Ryu, Ryohei Ishige, Yoh Noguchi, [Yoshihiro Hayashi](https://orcid.org/0000-0002-7650-4083), [Masashi Ishii](https://orcid.org/0000-0003-0357-2832), [Isao Kuwajima](https://orcid.org/0000-0002-5994-3834), Felix Jiang, Xuan Thang Vu, [Sven Ingebrandt](https://orcid.org/0000-0002-0405-2727), Masatoshi Tokita, [Junko Morikawa](https://orcid.org/0000-0002-9530-9478), [Ryo Yoshida](https://orcid.org/0000-0001-8092-0162), Teruaki Hayakawa

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[Discovery of liquid crystalline polymers with high thermal conductivity using machine learning](https://mdr.nims.go.jp/datasets/a7f166ae-ceaf-4618-a87f-03cae6b633f2)

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Discovery of liquid crystalline polymers with high thermal conductivity using machine learningnpj | computationalmaterials ArticlePublished in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Scienceshttps://doi.org/10.1038/s41524-025-01671-wDiscovery of liquid crystalline polymerswith high thermal conductivity usingmachine learningCheck for updatesHayato Maeda 1,10, Stephen Wu 2,3,10, Rika Marui 1, Erina Yoshida1, Kan Hatakeyama-Sato1,Yuta Nabae1, Shiori Nakagawa1, Meguya Ryu1,4, Ryohei Ishige1, Yoh Noguchi2,5, Yoshihiro Hayashi 2,3,Masashi Ishii 6, Isao Kuwajima6, Felix Jiang7, Xuan Thang Vu7, Sven Ingebrandt 7, Masatoshi Tokita1,Junko Morikawa 1,8 , Ryo Yoshida 2,3,6,9 & Teruaki Hayakawa1Next-generation power electronics require efficient heat dissipation management, and moleculardesign guidelines are needed to develop polymers with high thermal conductivity. Polymer materialshave considerably lower thermal conductivity than metals and ceramics due to phonon scattering inthe amorphous region. The spontaneous orientation of the molecular chains of liquid crystallinepolymers could potentially give rise to high thermal conductivity, but the molecular design of suchpolymers remains largely empirical. In this study,wedevelopedamachine learningmodel that predictswith more than 96% accuracy whether liquid crystalline states will form based on the chemicalstructure of the polymer. By exploring the inverse mapping of this model, we identified acomprehensive set of chemical structures for liquid crystalline polyimides. The polymers were thenexperimentally synthesized, and the results confirmed that they form liquid crystalline phases, with allpolymers exhibiting calculated thermal conductivities within the range of 0.722–1.26Wm−1 K−1.Machine learning is revolutionizing materials research by enabling data-driven predictive science. In recent years, machine learning-enabledmolecular design, with the objective of identifying new materials withspecific, desired properties, has made significant strides1,2. The typicalworkflow consists of forward and inverse predictions3. First, a statisticalmodel is built to predict the target properties of a givenmaterial based on itscompositional and structural features. Subsequently, inverse mapping ofthismodel is explored to predictmaterials with the desired properties in thereverse direction. Various machine learning techniques have been activelydeveloped to apply this concept in polymer chemistry, including a widerange of property predictors4–7 and inverse design methods using virtualpolymer generators such as molecular generative artificial intelligence8–10.Notably, proof-of-concept examples include the discovery of amorphouspolymers with high thermal conductivity4, lithium-ion conductingpolymers11,12, gas-separating polymer membranes13, and high-temperaturepolymer dielectrics14. However, few cases of polymers that were initiallypredicted by machine learning and subsequently verified experimentallyhave been reported. In this nascent field, our work advances the proof-of-concept of machine learning-driven polymermaterial design for real-worldapplications through the successful discovery of liquid crystalline polymerswith high thermal conductivity.As the demand for the miniaturization and portability of electronicdevices increases, researchers have focused on the development of light-weight, highly insulating polymers with high thermal conductivity forefficient heat dissipation. However, the thermal conductivity of amorphouspolymers is one to three orders ofmagnitude lower than those ofmetals andceramics15,16, which is a major barrier to their practical application. Ingeneral, polymers without free electrons exhibit low thermal conductivitybecause phonons, the dominant factor in heat transport, tend to scatter inthe amorphous region. To overcome this empirical and theoretical limita-tion, inorganic fillers are commonly added to the polymer matrix17. How-ever, increasing the filler content causes other polymer properties such as1School of Materials and Chemical Technology, Institute of Science Tokyo, Meguro-ku, Tokyo, Japan. 2The Institute of Statistical Mathematics, ResearchOrganization of Information and Systems, Tachikawa, Tokyo, Japan. 3The Graduate University for Advanced Studies, SOKENDAI, Tachikawa, Tokyo, Japan.4NationalMetrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan. 5School of Life Sciences, TokyoUniversity of Pharmacy and Life Sciences, Hachioji, Tokyo, Japan. 6National Institute for Materials Science, Tsukuba, Ibaraki, Japan. 7Institute of Materials inElectrical Engineering 1, RWTH Aachen University, Aachen, Germany. 8Research Center for Autonomous Systems Materialogy (ASMat), Institute of InnovativeResearch, Institute of Science Tokyo, Midori-ku, Yokohama, Japan. 9TRIP Headquarters, RIKEN, Wako, Saitama, Japan. 10These authors contributed equally:Hayato Maeda, Stephen Wu. e-mail: morikawa.j.4f50@m.isct.ac.jp; yoshidar@ism.ac.jp; hayakawa@mct.isct.ac.jpnpj Computational Materials |          (2025) 11:205 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01671-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01671-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01671-w&domain=pdfhttp://orcid.org/0009-0004-1662-8000http://orcid.org/0009-0004-1662-8000http://orcid.org/0009-0004-1662-8000http://orcid.org/0009-0004-1662-8000http://orcid.org/0009-0004-1662-8000http://orcid.org/0000-0002-7847-8106http://orcid.org/0000-0002-7847-8106http://orcid.org/0000-0002-7847-8106http://orcid.org/0000-0002-7847-8106http://orcid.org/0000-0002-7847-8106http://orcid.org/0009-0009-2506-1196http://orcid.org/0009-0009-2506-1196http://orcid.org/0009-0009-2506-1196http://orcid.org/0009-0009-2506-1196http://orcid.org/0009-0009-2506-1196http://orcid.org/0000-0002-7650-4083http://orcid.org/0000-0002-7650-4083http://orcid.org/0000-0002-7650-4083http://orcid.org/0000-0002-7650-4083http://orcid.org/0000-0002-7650-4083http://orcid.org/0000-0003-0357-2832http://orcid.org/0000-0003-0357-2832http://orcid.org/0000-0003-0357-2832http://orcid.org/0000-0003-0357-2832http://orcid.org/0000-0003-0357-2832http://orcid.org/0000-0002-0405-2727http://orcid.org/0000-0002-0405-2727http://orcid.org/0000-0002-0405-2727http://orcid.org/0000-0002-0405-2727http://orcid.org/0000-0002-0405-2727http://orcid.org/0000-0002-9530-9478http://orcid.org/0000-0002-9530-9478http://orcid.org/0000-0002-9530-9478http://orcid.org/0000-0002-9530-9478http://orcid.org/0000-0002-9530-9478http://orcid.org/0000-0001-8092-0162http://orcid.org/0000-0001-8092-0162http://orcid.org/0000-0001-8092-0162http://orcid.org/0000-0001-8092-0162http://orcid.org/0000-0001-8092-0162mailto:morikawa.j.4f50@m.isct.ac.jpmailto:yoshidar@ism.ac.jpmailto:hayakawa@mct.isct.ac.jpwww.nature.com/npjcompumatsadhesion, flowability, processability, and insulation to significantlydeteriorate18. Additionally, if the thermal resistance of thematrix polymer ishigh, the thermal conductivity of the composite material reaches a ceiling;therefore, it is imperative to improve the thermal conductivity of thepolymer matrix itself 19. Therefore, attempts have been made to suppressphonon scattering by utilizing liquid crystalline phase formation to inducean ordered alignment of polymer chains20. However, the design of liquidcrystalline polymers remains purely empirical, and relies extensively on trialand error. While some trends have been identified—for example, the ten-dency of phenyl benzoate backbones or certain alkyl spacer chains to pro-mote liquid crystallinity21–26—polymers with complex molecularinteractions, such as charge-transfer interactions in polyimides, oftendeviate from these trends, resulting in numerous exceptions27.In this study, we developed amachine learning algorithm to predict thechemical structure of a polymer-repeating unit capable of forming liquidcrystalline phases. This is an indirect approach that aims to enhance thethermal conductivity by addressing the challenge posed by the lack of acomprehensive dataset on the thermal conductivity of orientedpolymers.Weconstructed a binary classifier using the compositional and structural featuresof the polymer-repeating unit as inputs from a labeled dataset of liquidcrystalline polymers and other polymers that were previously synthesized.The prediction accuracy of the constructedmodel in discriminating whethera polymer exhibits a liquid-crystalline phase exceeded 96%.Using thismodel,weconductedhigh-throughputvirtual screening to search forpolyimides thatform liquid crystalline states. In liquid crystalline polyimides, rigidmesogenscomposed of aromatic segments (including conjugated rings and imidegroups) promote molecular alignment, while flexible spacer chains (con-sisting of alkyl or similar groups) enhance themolecular mobility to facilitatethe formation of the liquid crystalline state21. In addition, six polymers wereselected from a narrowed-down library of candidates for experimental ver-ification by the de novo syntheses of their monomers followed by theirpolymerization reactions. As a result, all six polymers were successfullysynthesized, and the resulting polymers spontaneously formed smectic liquidcrystal phases. Moreover, by applying a lock-in photothermal method formeasuring the in-plane thermal diffusivity using arrayed temperature sensorson suspended SiNX membranes, their thermal conductivities were experi-mentally confirmed to reach0.722−1.26Wm−1K−1. These are thefirst liquidcrystalline polymers predicted and discovered via machine learning.ResultsPerformance of the machine learning modelThe machine learning task is formulated as a supervised learning problemaimed to classify the chemical structure of a polymer repeat unit denoted asX into two classes with the binary variable Y 2 f�1; 1g indicating a liquidcrystalline state (Y ¼ 1) or a non-liquid crystalline state (Y ¼ �1) (Fig. 1a).The compositional and structural features of a given repeat unit are encodedinto a 397-dimensional descriptor vector (ϕ Xð Þ 2 R397). Here, only linearhomopolymers without additives were considered for the learning andprediction tasks by focusing on their intrinsic properties and avoiding theinfluence of additives or copolymerization, which can affect liquid crystal-line phase formation. The descriptorwas formed through the concatenationof two different descriptors: a 207-dimensional vector of RDKit descriptorsrepresenting various physical, chemical, and structural features of polymermolecules (https://www.rdkit.org/), and a 190-dimensional quantitativedescriptor that encodes empirical force field parameters derived using ageneral AMBER force field version 2 (GAFF2)28, which is widely used in all-atomclassicalmolecular dynamics simulations29,30. The calculations of thesetwo polymer descriptors were performed using the Python librariesXenonPy5,31 andRadonPy29, which implementwrapper functions for RDKitand the Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS)32, respectively. To properly describe the periodicity of polymerrepeating structures, the descriptor was calculated after linearly linking thehead and tail of the repeating unit 10 times to form a decamer30. Thedescriptor calculation procedure is described in the Supplementary Infor-mation (Section 1.2; pages S2 and S3).Amachine learning classifierY ¼ f ϕ Xð Þ� �defines amapping fromthe vectorized polymer to the binary class label by indicating whetherthe polymer would exhibit a liquid crystalline state. As positiveinstances (P) for the binary classification task, we used a list of 951liquid crystalline polymers compiled from PoLyInfo33, a polymerproperty database that had been manually compiled based on a lit-erature survey. The polymer list was partially labeled with moredetailed annotations representing liquid crystalline states such as thenematic and smectic phases; however, in this study, they were mergedinto a single label (liquid crystal). A total of 3,597 polymers without anyrecord of forming liquid crystalline states were extracted from thedatabase and used as unlabeled instances (U).Fig. 1 | Machine learning process for predicting whether a polymer with adesigned repeating unit exhibits liquid crystalline states. aMachine learningworkflow. b Prediction accuracy (confusion matrix, precision, recall, and F1 scores)for test datasets; standard deviations of the performance metrics obtained from 100independent tests are shown in parentheses.https://doi.org/10.1038/s41524-025-01671-w Articlenpj Computational Materials |          (2025) 11:205 2https://www.rdkit.org/www.nature.com/npjcompumatsNotably, these polymers are not necessarily true negative cases, andtheir liquid crystallinity has not been confirmed. No comprehensive data-base of negative cases has been constructed for liquid crystalline polymers.In machine learning, this problem is known as positive and unlabeled (PU)learning34. In the present study, we applied the classical PU learning algo-rithm proposed by Elkan et al.35 to calibrate the classification probability.However, the effect of the PU learning calibration was insignificant. Theprotocols established for data preparation and PU learning are provided inSupplementary Information (Section 1.3; pages S3 and S4).The binary classifier was modeled as a conventional multilayer per-ceptron neural network. A total of 85% of the entire dataset was randomlyselected and used as the training set, while the remaining 15%was used as atest set for evaluating the model performance. A randomly selected 85% ofthe training dataset was applied for training, and the remainder was utilizedfor the validation set. The hyperparameters of the classificationmodel wereoptimized using the black box optimization software Optuna36, whichadjusted the number and width of the hidden layers to minimize the vali-dation F1 score with this random split (see details in SupplementaryInformation (Section 1.2; page S2 and S3)). To assess the variation in theperformance metrics, we independently repeated the training and testingprocess 100 times using different random data splits.According to Fig. 1b, the average classification accuracy exceeds 96%.The mean values of recall and precision are 0.92 and 0.90, respectively,suggesting that the trade-off between the false and true positive rates is wellbalanced. Although the data are not shown herein, we confirmed that othermachine learning algorithms, such as ensemble learning, achieve com-parative predictive performance.Virtual screening of liquid crystalline polyimidesUsing the PU learning-calibrated classifier, we conducted an exhaustivesearch for polymers that undergo liquid crystallization. The search spacewas limited to polyimides, which are usually synthesized via the poly-condensation of tetracarboxylic dianhydride and diamine monomers. Tocreate a virtual library, we decomposed the template structure of polyimidesinto five building blocks labeled A-E in Fig. 2a. According to this decom-position, the acid dianhydride and diamine are composed of symmetricmolecules. Fragmentsmatching the structural patternof eachbuildingblockwere searched among a set of highly available compounds in the smallmolecule database ZINC37. Considering these combinations, 115,536 virtualpolyimideswere computationally generated. In polyimides, the rigid chains,which consist of conjugated aromatic rings bonded to imide groups, pro-mote molecular orientation to instill mesogenic behavior. In contrast, theflexible spacer groups tend to form an amorphous structure that canstrongly absorb impact energy. Because the rigid and flexible componentsare arranged symmetrically, the self-assembled higher-order structures arealso expected to exhibit structural equivalence (symmetry) and periodicityin the plane of the main chain. Thus, a virtual library was constructedfollowing this design and synthesis strategy.By applying a median liquid crystal transition probability of unity and astandard deviation of less than 0.2 as thresholds, approximately 91% of thecandidatepolymerswerefilteredout, resulting in10,825polyimidespredictedtoexhibit liquid crystallinity. Figure 2b shows a two-dimensional (2D) repre-sentation of the selected candidates using the uniformmanifold approximationand projection (UMAP) algorithm38, in which the chemical structure of eachrepeat unit was encoded into the descriptor following the procedure utilizedduring the construction of the predictive models. We applied hierarchicaldensity-based spatial clustering of applications with noise (known asHDBSCAN)39,40 to theprojectedpolymers,which suggested thepresence of 391different clusters. Subsequently,weselectedcandidates suitable for experimentalsynthesis by examining representatives from the 391 clusters and those withclosely related structures. Specifically, the repeating unit of a representativepolyimide candidate from each cluster was reviewed by a polymer synthesisexpert to assess the synthesizabilityof eachdianhydride anddiaminemonomer,as well as the availability of the necessary ingredients. As a consequence, sixpolyimides (Fig. 3) were selected from several promising clusters and success-fully synthesized;X-raystructural analysisof thesepolyimidebulkfilmsrevealedthe formation of smectic liquid crystalline phases (Supplementary Information,Section 3.5 (pages S40–S41)). Further details of the selection procedure areprovided in the Supplementary Information (Section 1.5; pages S4–S6).Analysis of higher-order structures in spin-coated filmsThe higher-order structures within the spin-coated thin films wereanalyzed by conducting Grazing Incidence Wide-Angle X-ray Diffrac-tion (GIWAXD) measurements. In this study, the in-plane thermaldiffusivity of polyimide films—fabricated via spin coating followed bythermal imidization—was measured using SiNX devices. The small sizeof these devices meant that conducting GIWAXD directly on the poly-imide films formed on them was challenging. Therefore, similar filmswere replicated on silicon wafers under identical spin-coating conditionsto facilitate GIWAXD measurements. To quantify the molecularFig. 2 | Virtual screening of liquid crystalline polyimides. a The rigid and flexiblechains of polyimides were divided into five building blocks, and the correspondingfragment set for each block was extracted from the Zinc database. By combining thesefragments, 115,536 virtual polyimides were computationally generated. b Thechemical structures of the virtual polymers are visualized using the UMAP projection(in gray). The 10,825 candidates predicted to exhibit liquid crystallinity were clusteredinto 391 groups based onmolecular similarity and visualized in different colors. Fromthese clusters, six polyimides were selected and successfully synthesized.https://doi.org/10.1038/s41524-025-01671-w Articlenpj Computational Materials |          (2025) 11:205 3www.nature.com/npjcompumatsorientation within the spin-coated films, the uniaxial orientational orderparameter S ¼ 3 cos2ϕ� �� 1� �=2 was calculated using the azimuthaldistribution of the diffraction intensity at 2θ � 20�. This calculationmethod follows the approach described by Ishige et al.41.ThemeasuredGIWAXDprofiles show that the diffraction is somewhatconcentrated on the meridional axis, indicating preferential in-plane orien-tation ofmesogens in the thinfilms (Fig. 4a–f). The S values calculated for thefilms ranged from�0:33 to�0:45 (see the rightmost column of Table 1).Mesogens of which themolecular orientation is such that the long axisis oriented perfectly parallel to the substrate surface would display a 2DGIWAXD profile with the diffraction concentrated on the meridional lineparallel to thefilmnormal, yielding an S value of�0:5. The range of S valuesobtained in our work suggests that the alignment of the mesogens is notentirely parallel to the substrate surface. The in-planemolecular orientationdevelops during the imidizationprocess,where apolyimidefilmfixedonto asilicon wafer undergoes contraction. GIWAXD profiles measured imme-diately after spin coating and solvent removal, i.e., before the imidizationprocess, showed azimuthally spread diffraction, indicating a lack of pre-ferential molecular orientation (see Fig. S57 in the Supplementary Infor-mation, Section 3.5 (page 44)).Moreover, SAXS and WAXD analyses of the bulk samples suggestedthat PIC1-1, 1-2, and 2-1 exhibited a smectic B-like phase, whereas PIC3-1and 3-2 demonstrated a smectic E-like phase. PIC2-2, similar to PIC3-1 and3-2, formed a close-packed arrangement between neighboring molecules(Fig. S54). In thin films, however, the intensity vs. q profiles shown in Fig. 4gindicated that the peak shape around q � 15 nm�1 for PIC2-2, 3-1, and 3-2differed from those observed in bulk analyses. This discrepancy suggests thatin thinfilms, themolecular alignmentover longdistancesmaybe insufficientto produce the diffraction patterns characteristic of a smectic E-like phase.According to the S values listed in Table 1, no significant differences inthe degree of in-plane orientation were observed between the PIC1-1 andPIC1-2 samples, nor between the PIC3-1 and PIC3-2 samples. However, adifferent trend was observed for the PIC2 series, where PIC2-1 exhibited ahigher degree of in-plane orientation compared to PIC2-2. Additionally, thePIC3 series displayed a lower degree of in-plane orientation than both thePIC1 and PIC2 series. These findings suggest that differences in the struc-tureof themesogen significantly affect theS values,whereas variations in thespacer length do not have a substantial impact.The presence of a methylene group at the center of the mesogen in thePIC2 series influences the higher-order structure and S values. The results ofsubsequent analyses of the bulk samples presented in Fig. S57 reveal thedistinct higher-order structural characteristics of the PIC2 samples as com-pared with the other samples. This suggests that the methylene group of themesogen in the PIC2 series plays a critical role in determining the degree ofmolecular orientation and structural evolution during thermal imidization.Evaluation of thermophysical propertiesThe in-plane thermal conductivity (λ) and phase transition temperatures ofthe synthesized liquid crystalline polyimides were investigated. The results,including the in-plane thermal diffusivity (α), specific heat capacities (Cp),densities (ρ), and λ (calculated using α, Cp, ρ), as well as the phase transitiontemperatures, are summarized in Table 1. Measurement of the thermalconductivity and diffusivity of microscopically ordered liquid crystallinepolymer thin films requires unique setups and equipment with high preci-sion and fine spatial resolution. Several techniques, such as a thermal bridgemethod42, atomic force microscopy cantilever-assisted measurements43, andtime-domain thermoreflectance44, have been employed for measuring themicroscale thermal conductivity of polymers. In this study, the thermo-physical properties were evaluated by a microscale temperature wave ana-lysis method (μ-TWA) using a device consisting of a line-shaped or spiral-shaped temperature sensor array on a 2D silicon nitride (SiNx) membranewith a thickness of 50 or 150 nm45 and ultrafast scanning calorimetry(FSC)46. The method employing the array-type sensors (μ-TWA) enabledrapid measurements of the in-plane thermal diffusivity of the alignedpolyimide nanofilms to obtain thermal diffusivity distributions at differentpositions. The thermal conductivities of liquid crystalline polymers wereobatind by measured thermal diffusivities, densities and specific heat capa-cities according to the following equation λ ¼ αρCp. Detailed descriptions ofthe measurement techniques and the corresponding results are provided inthe Supplementary Information (Sections 3.3 and 3.4; pages S36–S39).Using this method, the in-plane thermal conductivity of the newlysynthesized liquid crystalline aromatic polyimide nanofilm (PIC2-1) pre-pared via spin coatingwas computed from themeasured thermal diffusivity,which reached 1.26Wm−1 K−1. This value was significantly higher thanthose of commercial polyimides in their nearly amorphous states47 and ofpreviously reported non-crosslinked liquid crystalline polyimides48. ThePICX-2 samples exhibited higher thermal conductivities compared to thePICX-1 samples. This result aligns with previous studies showing thatincreased molecular rigidity promotes thermal conductivity49. The PICX-2samples, with their shorter alkyl spacer chains, have more rigid molecularFig. 3 | Chemical structures of the six polyimidesselected for synthesis through virtual screeningand their corresponding monomers. The poly-imides were derived from combinations of threetypes of dianhydrides (TAC1, TAC2, TAC3) andtwo types of diamines (DAC1, DAC2).PIC2-2PIC1-2PIC2-1PIC1-1PIC3-2PIC3-1Polyimides Selected for SynthesisTAC3TAC1TAC2Tetracarboxylic DianhydridesDAC1DAC2Diamineshttps://doi.org/10.1038/s41524-025-01671-w Articlenpj Computational Materials |          (2025) 11:205 4www.nature.com/npjcompumatsstructures than the PICX-1 samples, which likely contributes totheir superior thermal conductivities. Furthermore, among the PICX-2samples, those with S values closer to�0:5, indicative of a higher degree ofin-plane molecular orientation, exhibited higher thermal conductivities.Specifically, PIC1-2 demonstrated the highest thermal conductivity,whereas the thermal conductivity of PIC3-2, which had the largest Svalue, was the lowest. These findings clearly indicate that themolecular chain orientation exerts a significant effect on the thermal con-ductivity. Figure 5 illustrates the relationship between the structural char-acteristics of the molecule (chain rigidity), degree of in-plane molecularorientation (evaluated on the basis of the order parameter S), and thermalconductivity.The FSC measurements revealed first-order phase transitions at tem-peratures higher than 350 °C in the course of an ultra-fast temperature scan(10,000 K/s using FSC) during the heating and cooling processes. Theseobservations were made possible by the extremely short residence times athigh temperatures, which significantly suppressed the thermal decom-position of aromatic polyimides. To the best of our knowledge, this is thefirst study in which a liquid crystal transition at temperatures above 350 °Chas been actually observed as a transient transitionwith an enthalpy change.DiscussionThis study demonstrates thatmachine learning can predict the formation ofliquid crystalline phases for various polymers based on their chemicalFig. 4 | GIWAXD profiles of the spin-coatedpolyimide films on silicon wafers. a PIC1-1 PI,b PIC1-2 PI, c PIC2-1 PI, d PIC2-2 PI, e PIC3-1 PI,f PIC3-2 PI, and g Intensity vs. q profiles. The filmswere prepared under the same spin coating condi-tions as the samples fabricated for μ-TWA to ensureconsistency in the film thickness and morphology.PIC1-2 PIPIC2-2 PIPIC3-2 PIPIC1-1 PIPIC2-1 PIPIC3-1 PIGIWAXD Intensity vs. q Profilesabcdefghttps://doi.org/10.1038/s41524-025-01671-w Articlenpj Computational Materials |          (2025) 11:205 5www.nature.com/npjcompumatsstructures. The trained predictor achieved an accuracy of over 96% withinthe chemical space of the tested polymer sets. Six polyimides were suc-cessfully synthesized according to the molecular design predicted viamachine learning. They formed higher-order structures with smectic liquidcrystalline phases. These are the first liquid crystalline polymers predictedand discovered by machine learning in the history of polymer materialsresearch. In this proof-of-concept study, we aimed to suppress phononscattering and enhance the thermal conductivity of the polymers byincreasing the molecular orientation order through liquid crystalline phaseformation.As anticipated, the thermal conductivity of the synthesized liquidcrystalline polyimides exceeded 1.2Wm−1 K−1, which is significantly higherthan those of commercial polyimides in their nearly amorphous states.Currently, fundamental methodology is not available for computa-tionally predicting the likelihoodof liquid crystalline phase formation in anygiven polymer, and the molecular design of these materials remains highlyempirical. The proposed method offers potential as a powerful tool forfacilitating the study of not only liquid crystalline polyimides but also otherliquid crystalline polymers; however, several challenges persist. The repor-ted predictive accuracy is an estimate based on a limited set of polymers,whichnecessitates the determinationof the true generalizationperformanceoutside the current data distribution. Additionally, this study focused onbinary classification to predict whether a polymer would exhibit liquidcrystalline behavior, yet the prediction of specific phase types, such asnematic, smectic, and crystalline phases, should also be addressed to enablethe synthesis of polymers with targeted liquid crystalline phases. Anothermatter is the predictability of phase transition temperatures. Furthermore,predicting the physical properties of liquid crystalline polymers representsanother important challenge. Constructing a comprehensive database andestablishing a methodological basis for data-driven liquid crystalline poly-mer chemistry are desirable goals for future studies.MethodsSynthesis of predicted polyimidesDetailed reaction conditions and nuclear molecular resonance (NMR) andFourier-transform infrared (FT-IR) spectra of the resulting compounds areprovided in the Supplementary Information (Sections 2.1–2.5; pagesS6–S34). Examples of the synthesis procedures are provided in Fig. 6.Synthesis of tetracarboxylic dianhydrides. The three types oftetracarboxylic dianhydrides (TAC1-3) were synthesized through a three-Table 1 | Experimental properties of the six synthesized polyimidesSample TLCh(°C) Tm (°C) TLCc(°C) TC (°C) α (×10−7 m2 s−1) d (nm) Cp (Jg−1 K−1)ρ (g cm−3) λ (W m−1 K−1) SPIC1-1 391/399 459/457 314/305 403/393 5.74 ± 0.01 600 1.18 1.32 0.894 ± 0.003 −0.45PIC1-2 424/- 478/459 334/326 445/424 7.93 ± 0.08 500 1.16 1.37 1.26 ± 0.013 −0.44PIC2-1 402/- 474/477 273/259 360/352 5.77 ± 0.04 470 1.2 1.31 0.904 ± 0.007 −0.40PIC2-2 - 460/463 298/332 356/454 6.88 ± 0.17 260 1.13 1.36 1.06 ± 0.026 −0.35PIC3-1 - 464/492 325/321 411/411 4.71 ± 0.05 540 1.16 1.32 0.722 ± 0.008 −0.33PIC3-2 - 456/420 -/349 374/372 6.35 ± 0.36 270 1.13 1.38 0.990 ± 0.056 −0.33TLC, Tm, and Tc valuesmeasured via FSCat scan rates of 5000 and 10,000 K/s during heating and cooling; thermal diffusivities αmeasured by μ-TWA; thickness valuesdmeasured by the step profilometer(Alpha-Step IQ); specific heat capacitiesCp determined via differential scanning calorimetry; densities ρmeasured by the density gradient tubemethod; and thermal conductivities λ calculated from the α,Cp, and density values. The uniaxial orientational order parameter S was calculated from the GIWAXD results.Fig. 5 | Relationship between rigidity of the molecular chain, in-plane molecular orientation, and in-plane thermal conductivity (λ).https://doi.org/10.1038/s41524-025-01671-w Articlenpj Computational Materials |          (2025) 11:205 6www.nature.com/npjcompumatsstep process using different aromatic diamines as starting materials. In thefirst step, the aromatic diamines reacted with 4-methoxybenzoic acidchloride to form amides, using N-methyl-2-pyrrolidone (NMP) as thesolvent and pyridine as the base. The resultant compounds were purifiedvia recrystallization from dimethylformamide. The second step involved ademethylation reaction using thiophenol, following the method developedby Chakraborti et al.50. The demethylated products were purified throughreprecipitation in methanol. In the third step, the hydroxyl-terminatedcompounds were esterified with trimellitic anhydride chloride, followed byrecrystallization using γ-butyrolactone.Synthesis of diamines. The two diamines were synthesized fromdibromoalkanes in a two-step process. Thefirst step involvedWilliamsonether synthesis with 4-nitrophenol, followed by reduction of the nitrogroups to amino groups via hydrogenation using a Pd/C catalyst. Theresulting compounds were purified by recrystallization in ethanol forsubsequent polymerization.Preparation of polyimide samples. The three tetracarboxylic dia-nhydrides and two diamines were polymerized in NMP to prepare sixpoly(amic acid) solutions. Portions of these solutions were drop-castonto glass plates and thermally imidized for wide-angle X-ray analyses.Additional samples were prepared for FSC measurements. Theremaining solutions were reprecipitated, dried, and redissolved forfurther analysis. For thermal diffusivity measurements, a 10 wt.%solution of redissolved poly(amic acid) was spin-coated onto the sensordevice and silicon wafer (2 cm × 2 cm) for GIWAXD measurements,followed by thermal imidization. Inherent viscosities were measuredusing anOstwald viscometer after dissolving 0.5 g/dL of each poly(amicacid) in NMP.Analysis of higher-order structures in spin-coated filmsThe molecular orientation and higher-order structures of polyimidefilms were analyzed by conducting GIWAXD measurements(Bruker D8 DISCOVER instrument equipped with a VANTEC-500detector and CuKα radiation). The incident angle was consistently setto 0.25°.Measurement of thermophysical propertiesDetailed procedures for the measurement of the polymer properties areprovided in the Supplementary Information (Sections 3.2–3.4; pagesS36–S39).Data availabilityAll data needed to evaluate the conclusions in the paper are present in thepaper and/or the Supplementary Information. 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Chem. 67, 6406–6414 (2002).https://doi.org/10.1038/s41524-025-01671-w Articlenpj Computational Materials |          (2025) 11:205 8https://doi.org/10.1007/3-540-49814-1_3https://doi.org/10.1007/3-540-49814-1_3https://doi.org/10.1007/3-540-49814-1_3https://doi.org/10.1201/9781315272801https://doi.org/10.1201/9781315272801https://doi.org/10.1017/CBO9780511616044https://doi.org/10.1017/CBO9780511616044https://doi.org/10.1142/5309https://doi.org/10.1142/5309https://doi.org/10.1142/5309https://doi.org/10.1007/3-540-12818-2_8https://doi.org/10.1007/3-540-12818-2_8https://doi.org/10.1007/3-540-12994-4_1https://doi.org/10.1007/3-540-12994-4_1https://doi.org/10.1007/3-540-12994-4_1https://doi.org/10.1145/1401890.1401920https://doi.org/10.1145/1401890.1401920https://doi.org/10.1145/1401890.1401920www.nature.com/npjcompumatsAcknowledgementsThe synchrotron radiation experiments were performed at the BL40B2beamline of SPring-8 with the approval of the Japan Synchrotron RadiationResearch Institute (JASRI) (Proposal No. 2022B1131), with support fromDr.Noboru Ohta (JASRI) and Prof. Tomoyasu Hirai (Osaka Institute of Tech-nology). This work was supported by the Japan Science and TechnologyAgency (JST) under theCRESTprogram(GrantNumberJPMJCR19I3) (J.M.,T.H., R.Y., M.T., R.M.). Additionally, we acknowledge the Japan Society forthe Promotion of Science (JSPS) for their support through the KAKENHIprogram (Grant Number 21K04828) (Y.N.) and the Ministry of Education,Culture, Sports, Science and Technology for “Program for PromotingResearches on the Supercomputer Fugaku” (project ID: hp210264) (R.Y.).HM and RM were supported by JST SPRING (Grant No. JPMJSP2106).Author contributionsConceptualization: R.Y., J.M., T.H.; Data Curation: H.M., S.W., J.M.; FormalAnalysis: H.M., S.W., J.M.; Funding Acquisition: Y.N. (Yuta Nabae), R.Y.,J.M.; Investigation: H.M., S.W., R.M., E.Y., S.N., Y.N. (Yoh Noguchi), J.M.;Methodology: M.R., R.I., F.J., X.T.V., S.I., M.T., J.M., R.Y., T.H.; Resources:M.I., I.K.; Software: S.W., Y.N. (Yoh Noguchi), Y.H.; Supervision: R.Y., J.M.,T.H.; Visualization: H.M., S.W., S.N., J.M.; Writing: H.M., S.W., J.M., R.Y.;Writing—review & editing: H.M., S.W., K.H., Y.N. (Yuta Nabae), R.Y.,J.M., T.H.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41524-025-01671-w.Correspondence and requests for materials should be addressed toJunko Morikawa, Ryo Yoshida or Teruaki Hayakawa.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as longas you give appropriate credit to the original author(s) and the source,provide a link to the Creative Commons licence, and indicate if changeswere made. 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To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025https://doi.org/10.1038/s41524-025-01671-w Articlenpj Computational Materials |          (2025) 11:205 9https://doi.org/10.1038/s41524-025-01671-whttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/npjcompumats Discovery of liquid crystalline polymers with high thermal conductivity using machine learning Results Performance of the machine learning model Virtual screening of liquid crystalline polyimides Analysis of higher-order structures in spin-coated films Evaluation of thermophysical properties Discussion Methods Synthesis of predicted polyimides Synthesis of tetracarboxylic dianhydrides Synthesis of diamines Preparation of polyimide samples Analysis of higher-order structures in spin-coated films Measurement of thermophysical properties Data availability References Acknowledgements Author contributions Competing interests Additional information