# Fileset

[d4mh01606h.pdf](https://mdr.nims.go.jp/filesets/0d1fddcb-009d-4ec2-8ae1-29e77c950239/download)

## Creator

Bin Xu, Touchy Abeda Sultana, Koki Kitai, Jiang Guo, Toyomitsu Seki, [Ryo Tamura](https://orcid.org/0000-0002-0349-358X), [Koji Tsuda](https://orcid.org/0000-0002-4288-1606), [Junichiro Shiomi](https://orcid.org/0000-0002-3552-4555)

## Rights



## Other metadata

[Experiment-in-loop interactive optimization of polymer composites for “5G-and-beyond” communication technologies](https://mdr.nims.go.jp/datasets/33322e9b-550a-4148-9641-0107dfa2d509)

## Fulltext

Experiment-in-loop interactive optimization of polymer composites for “5G-and-beyond” communication technologiesMaterialsHorizonsrsc.li/materials-horizons COMMUNICATION  Junichiro Shiomi  et al .  Experiment-in-loop interactive optimization of polymer composites for “5G-and-beyond” communication technologies ISSN 2051-6347Volume 12Number 1021 May 2025Pages 3173–35603332 |  Mater. Horiz., 2025, 12, 3332–3340 This journal is © The Royal Society of Chemistry 2025Cite this: Mater. Horiz., 2025,12, 3332Experiment-in-loop interactive optimization ofpolymer composites for ‘‘5G-and-beyond’’communication technologies†Bin Xu,‡ab Touchy Abeda Sultana,‡b Koki Kitai,b Jiang Guo,c Toyomitsu Seki,dRyo Tamura, e Koji Tsuda c and Junichiro Shiomi *ab‘‘Fifth-generation-and-beyond’’ communication technologies havesparked considerable demand for polymer composite materials withlow coefficients of thermal expansion (CTE) and low dielectric loss athigh operation frequencies. However, the complexity of processparameters and the lack of knowledge about fabrication procedureshinder this goal. In this study, state-of-the-art experiment-in-loopBayesian optimization (EiL-BO) was developed to optimize a com-posite of a perfluoroalkoxyalkane matrix with silica fillers. TheGaussian process equipped with an automatic relevance determina-tion kernel that automatically adjusts the scaling parameters ofindividual dimensions effectively enhances EiL-BO’s ability to searchfor candidates in a complex and anisotropic multidimensional space.This addresses the critical challenge of handling problems withhigh-dimensional parameters and is capable of managing eight-dimensional parameters, including filler morphology, surface chemistry,and compounding process parameters. The obtained optimal compositeshows a low CTE of 24.7 ppm K�1 and an extinction coefficient of9.5 � 10�4, outperforming the existing polymeric composite,revealing exceptionally effective and versatile EiL-BO that acceler-ates the development of advanced materials.IntroductionWith the advent of fifth-generation (5G) wireless technology,there is a growing demand for polymer materials as packagingmaterials and device components such as printed circuitboards.1,2 Owing to the utilization of high-frequency micro-/millimeter-wave bands, materials with low dielectric permittiv-ity (e) and loss tangent (tan d) at high frequencies are requiredto facilitate rapid and high-quality signal transmission. How-ever, high heat intensity due to elevating device power may leadto thermal deformation. Since polymers typically exhibit acoefficient of thermal expansion (CTE) that is far higher thanthat of other parts of the device, the difference in the CTE canthus degrade the device and affect its operation. Therefore,polymeric materials with low CTEs are in high demand.Fluororesins, such as perfluoroalkoxyalkane (PFA) and poly-tetrafluoroethylene (PTFE), are among the most promisingcandidates because the C–F bond has an ultralow dipolemoment and electronic susceptibility, which is the key to lowe and tan d. Moreover, the strong electronegativity of fluorine iseffective in reducing ion and electron polarizability, which isa Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo,Bunkyo, Tokyo, 113-8656, Japan. E-mail: shiomi@photon.t.u-tokyo.ac.jpb Institute of Engineering Innovation, The University of Tokyo, 2-11 Yayoi, Bunkyo,Tokyo, 113-8656, Japanc Department of Computational Biology and Medical Sciences, The University ofTokyo, 5-1-5 Kashiwa-no-ha, Kashiwa-shi, Chiba-ken, 277-8561, Japand Technology and Innovation Center, Daikin Industries, Ltd, 1-1, Nishihitotsuya,Settu, Osaka, 566-8585, Japane Center for Basic Research on Materials, National Institute for Materials Science,305-0044 1-1 Namiki, Tsukuba, Ibaraki, 305-0047, Japan† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4mh01606h‡ These authors contributed equally (B. Xu and T. A. Sultana).Received 9th November 2024,Accepted 14th February 2025DOI: 10.1039/d4mh01606hrsc.li/materials-horizonsNew conceptsIn this study, Bayesian optimization using an ARD kernel was employed tofacilitate an interactive experiment-in-loop optimization process for thefabrication of polymer composites for applications in the field of ‘‘5G andbeyond’’ communication technologies. While machine learning approaches,including Bayesian optimization, have proven effective in optimizingmaterial structures and processing parameters in material fabrication, thefabrication of complex composites with anisotropic and high-dimensionalparameter spaces remains challenging. The efficiency of the as-developedoptimization methodology is notable: composite materials with superiorperformance, surpassing that reported in previous studies, were achievedin only few iterations. The resulting materials concurrently exhibit both lowthermal expansion and low dielectric loss at high operational frequencies, upto the GHz range, addressing one of the most critical issues in packagingmaterials for ‘‘5G and beyond’’ communication technologies.This workdemonstrates a proof of concept for an interactive, experiment-in-loopoptimization process equipped with an ARD kernel. The significance ofthis approach in handling high-dimensional and anisotropic candidatespaces was validated, showing promise for accelerating advancements inmaterials science, even when fundamental knowledge and experience arelimited.MaterialsHorizonsCOMMUNICATIONOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article OnlineView Journal  | View Issuehttps://orcid.org/0000-0002-0349-358Xhttps://orcid.org/0000-0002-4288-1606https://orcid.org/0000-0002-3552-4555http://crossmark.crossref.org/dialog/?doi=10.1039/d4mh01606h&domain=pdf&date_stamp=2025-03-10https://doi.org/10.1039/d4mh01606hhttps://doi.org/10.1039/d4mh01606hhttps://rsc.li/materials-horizonshttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606hhttps://pubs.rsc.org/en/journals/journal/MHhttps://pubs.rsc.org/en/journals/journal/MH?issueid=MH012010This journal is © The Royal Society of Chemistry 2025 Mater. Horiz., 2025, 12, 3332–3340 |  3333beneficial for low dielectric loss. However, the CTEs of fluoro-resins are relatively high. This issue can be addressed by compo-siting fluororesins with ceramic fillers such as silica,3 TeO2,4perovskite (Ca, Li, and Sm)TiO3,5 and 0.7Ba(Co1/3Nb2/3)O3–0.3Ba(Zn1/3Nb2/3)O3 (BCZN).6In polymer composites, the CTE and dielectric properties arehighly sensitive to various factors. These include the shape andvolume fraction of fillers, their surface chemistry, and processingparameters. Liu et al. performed surface functionalization for asilica filler using methyltriethoxysilane to enhance the compat-ibility between the silica filler and the PTFE matrix. Enhancedcompatibility not only improves the dispersion of the filler but alsopromotes interaction at the interface, which can confine themovement of the PTFE chain and thus reduce the CTE anddielectric loss.3 A similar approach involving surface functionaliza-tion was adopted by Jin et al.,7 Yuan et al.,8 and Wang et al.,6 wherereduction in the CTE and dielectric loss was achieved. Ren et al.studied the effect of the filler shape by comparing spherical andfibrous silica and reduced e and tand using fibrous silica. Theyattributed this to the high aspect ratio, which hindered chainrelaxation.9 Alhaji et al. studied the effect of the size of sphericalsilica fillers and realized that a smaller filler size can effectivelyreduce the CTE but lead to higher e and tand.10 This conclusion issupported by the work of Chen et al., who claimed that dielectric-performance degradation is caused by interfacial polarizationbecause of the higher interface density in the case of the smallerfiller size.11 However, contradictory conclusions were drawn in thetheoretical study conducted by Qin et al.12 and the experimentalstudy conducted by Ibrahim et al.13 In these cases, rather than theinterfacial polarization, the effect that interface limit the orienta-tion and the movement of dipoles and the polymer chain is morepredominant in the interfacial region. The effect decreases the eand tand. The competition between these two effects is affected bythe interfacial structures, which are determined by the fillerdispersion and the interfacial compatibility.14 Overall, owing tothe complexity of the fabrication parameters and the resultingfiller dispersion and interfacial effect, fabricating the desiredpolymer composites with a low CTE and high-frequency dielectricloss is a challenge, and requires time- and labor-intensive tasks.Recently, machine learning-driven optimization has emergedas a valuable tool in materials science. Bayesian optimization(BO), one of the commonly used machine learning methods, hasproven to be useful for various applications, particularly thosecombining high-throughput computational methods for dataacquisition. Ju et al. optimized the thermal conductivity of a Si/Ge superlattice structure and achieved the optimized structure by438 data, only 3.4% of the total candidates.15 In the study byYamawaki et al., BO could identify the top 0.5% structures usingless than half the amount of data required in a random search foroptimizing the thermoelectric figure of merit (FOM) of a holeygraphene nanoribbon structure.16 Okazawa et al. optimized thestructure of binary alloy catalysts for the dissociation of thenitrogen bond using BO and realized a minimal surface energyof B0.2 eV Å�2 within only one iteration, significantly outper-forming the random search strategy.17 Tsuji et al. optimizednanocluster catalysts for efficient ammonia synthesis, where BOsignificantly accelerated the search for the optimal catalyst withintwo or three iterations.18 Takahashi et al. achieved a far higherefficiency in exploring dielectrics with a high dielectric constantusing BO compared with a random search.19 BO has alsobeen utilized in the polymer materials, including machiningprocess optimization,20 porous media analysis,21 and laser materialprocessing.22 These studies demonstrate the effectiveness of BO inexperiments searching for optimal process parameters for polymers.In these studies, a kernel involving simple Gaussian process regres-sion (GPR) with a fixed length scale was proven to be sufficientlyeffective for the BO of an isotropic data space. However, in practicalinvestigations aimed at fabricating ready-to-use materials, the transi-tion from simulation-based optimization to experiment-in-loop opti-mization is critical. Although there has been an increasing numberof studies on experiment-in-loop optimization,23–26 researchers typi-cally avoid complicating the variety of input parameters to reducethe required number of experiments, because the acquisition ofexperimental data is far more costly than simulation data. This hasmotivated the development of high-throughput robot-assistedexperimental approaches specialized for a particular purpose.23–26However, neither manual nor automated experimental-in-loop opti-mization has been realized for polymer compounds because of thelarge dimensions in the material and process parameters and thecomplexity of processes such as compounding and hot pressing,which are difficult to fully automate.To increase the efficiency of BO, recent efforts have focusedon improving the surrogate model. Herbol et al. increased theefficiency of structure optimization for hybrid organic–inorganicperovskites by applying a custom GPR kernel that used the under-lying knowledge of this material system.27 Similar approaches wereadopted by Khatamsaz et al., who used physics-informed GPR tooptimize the design of NiTi shape-memory alloys via a thermaltreatment process.28 Nevertheless, these approaches typicallyrequire an in-depth understanding of the underlying mechanisms,which are not applicable to the fabrication of polymer compositesfor 5G. Automatic relevance determination (ARD) kernel is analternative approach that can automatically adjust the ‘‘weights’’ ofindividual input dimensions to accurately capture and balance theunique influence of each input feature on the objective.29,30 TheARD kernel may be a valuable tool for optimizing the fabricationprocess for the proposed polymer-based composite with a lowCTE, e, and tand.In this study, we employed experiment-in-loop BO for fabri-cating a PFA polymer/silica composite via a compoundingprocess. We used five types of silica fillers, which differed inshape, size, surface functionalization, and volume fraction. Inaddition to the compounding process parameters, an eight-dimensional parameter space was defined as the input para-meter. To manage this high-dimensional space, the weights ofthe individual dimensions are automatically adjusted using anARD kernel. The application of the ARD kernel increases theefficiency of BO, by quickly targeting the parameters for fabri-cating composites. The obtained optimal composite shows a lowCTE of 24.7 ppm K�1 and an extinction coefficient of 9.5� 10�4,superior to polymers for 5G wireless technology reported inprevious studies. We also systematically examined the structuralCommunication Materials HorizonsOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606h3334 |  Mater. Horiz., 2025, 12, 3332–3340 This journal is © The Royal Society of Chemistry 2025improvement during the BO process and found that the topo-logical structure is crucial for achieving a low CTE. We found athree-phase composite consisting of voids, fillers, and a matrix,with a specific distribution, shape, and volume fraction, whichcan lead to the relaxation of inward bending deformation by thecollective movement of the silica filler and PFA may be respon-sible for the strongly suppressed thermal expansion.Results and discussionFabrication of PFA/silica compositesTo realize a high CTE and low dielectric loss, we composed aPFA resin (HS-230, Daikin) with silica fillers of various shapes,sizes, and surface functionalization via a compounding process(filler details are presented in Table S1, ESI†). A dual-screw cycling-type compounding machine (MC15HT, Xplore Instruments) wasused, which allowed flexible control of the compounding time androtation speed. The compounding temperature was fixed at 380 1C,which was higher than the melting point of PFA at 310 1C. Theprocess temperature was fixed according to a pre-experiment,which revealed that the CTE decreased with the increase incompounding temperature and saturated above 370 1C (Fig. S1,ESI†). Following the compounding process, we used a hot-pressmachine to mold the sample from the filament shape into a thinfilm at 360 1C. The hot-pressing temperature was selected toachieve an appropriate thickness for subsequent measurements.The film was then cut to a specific size and assessed throughdielectric measurements and thermomechanical analysis to obtainthe CTE, e, and tand values.Evaluation of the PFA compositeThe dielectric properties including e and tan d were measuredby a cavity resonator method at a frequency of 10 GHz. Themeasurement was conducted using a Microstrip Line DielectricResonator System (AET Japan), which ensures high precision inhigh-frequency dielectric property characterization. The systemoperates in the transverse electric (TE) mode, where the electricfield is primarily transverse to the propagation direction,minimizing conductor losses and enhancing the measurementaccuracy. This method provides high sensitivity to dielectricproperties, making it particularly suitable for characterizinglow-loss polymer composites.The coefficient of thermal expansion (CTE) was measuredusing a NETZSCH TMA 402 thermomechanical analyzer in anitrogen (N2) atmosphere. The measurement was conductedover a temperature range of 20 1C to 150 1C, with both heatingand cooling rates set at 5 K min�1. The CTE was determinedfrom the cooling curve by calculating the average expansionrate, i.e., the total change in length divided by the total tem-perature change.Bayesian optimizationTo efficiently optimize the experimental parameters for thefabrication of the PFA/silica composite, we employed BO withan ARD kernel GPR model using the PHYSBO package.31 Thecommon kernel setting for the GPR model is the radius basisfunction (RBF), which is also called the squared exponentialkernel. The RBF kernel between two points x0 and x in the inputspace is defined as follows:k x; x0ð Þ ¼ s2 expx� x0k k22l2� �; (1)where s is the variance parameter, which controls the overallvariability, l is the length-scale parameter, which controls howfast the correlation for two points decays with distance, andxi � x0i�� ��2 is the Euclidean distance between the two points. Forthe ARD kernel, the RBF kernel is modified to allow anindependent length scale for each input dimension as follows:kARD xi; x0i� �¼ s2 exp �12XDi¼lxi � x0i�� ��2l2i !; (2)where D represents the number of dimensions in the inputspace, xi and x0i represent the ith-dimension input, and li is thelength-scale parameter for the ith-dimension input.32 The ARDkernel automatically adjusts the relevance of individual dimen-sions of distinct physical factors, which was proved to be moreeffective than the RBF kernel in handling tasks with complexitiesas high as eight dimensions.10 In the ARD kernel, li was adjustedby maximizing the marginal log-likelihood (MLE) of the Gaussianprocess mode. For this process, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, which efficiently estimates the inverseHessian approximation by storing only the most recent gradientinformation, was used. Notably, in the PHYSBO package, all thesehyperparameters were adjusted automatically.A schematic of the BO-driven experimental loop is shown inFig. 1. In the first round of BO, we conducted six experimentsand used the datasets to train a GPR model, aiming to predictthe mean of the target yield m(x) and the standard deviation s(x),where x represents the input parameters. These experimentswere conducted using randomly selected experimental para-meters, which included the material parameters determinedby the materials added to the compounding machine and theprocess parameters for compounding, such as the compound-ing time and rotation speed. The definitions of each dimensionand the range of the input parameters are listed in Table 1. Weallowed the mixing of different filler shapes owing to thesynergistic effect observed in previous studies, where a mixtureof fillers with varying shapes and sizes significantly improvedboth the CTE and dielectric properties.33,34 Although the under-lying mechanism has not been well established, this strategywas helpful for achieving the desired properties. Moreover, thissetting allowed us to determine the optimal filler type.Furthermore, since the 5G-and-beyond wireless technologyrequires a low CTE and low dielectric loss simultaneously, wedefined a figure of merit (FOM) as the target function, asfollows:FOM = (emax � e)/erange � (d � dmin)/drange, (3)where e represents the CTE, and d represents the dielectricextinction coefficient, which is given byffiffiep� tan d. The subscriptsMaterials Horizons CommunicationOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606hThis journal is © The Royal Society of Chemistry 2025 Mater. Horiz., 2025, 12, 3332–3340 |  3335max, min, and range represent the maximum, minimum, andrange of either e or d. Herein, emax represents the highest CTEachievable in the composite, which corresponds to the CTE of purePFA. dmin refers to the lowest achievable dielectric extinctioncoefficient, which is the extinction coefficient of pure silica. Bothparameters were obtained through experimental measurements.The FOM formulation was designed to ensure balanced optimiza-tion of CTEs and extinction coefficients by normalizing bothterms. This prevents the BO process from disproportionatelyprioritizing one parameter over the other due to differences intheir absolute variation ranges. This FOM describes the normal-ized variation rate of the CTE and the extinction coefficient; alarger FOM corresponds to a lower CTE and extinction coefficient.After the GPR was trained with the initial datasets, theacquisition functions based on the trained GPR model canoutput several new data points corresponding to the experi-mental parameters that are likely to yield a high FOM and thecorresponding x via the expected improvement (EI), as follows:EI(x) = (m(x) � FOMcurrent_max)f(z) + s(x)f(z), (4)z ¼ mðxÞ � FOMcurrentmaxsðxÞ ; (5)We then conducted experiments following the sets of para-meters of the top five candidates predicted by the EI functionand repeated the procedure for 11 rounds. All hyperparametersand scaling parameters of the individual dimensions wereautomatically adjusted in each round.BO process analysisFig. 2(a) illustrates the results of the BO process, showing arapid increase in the FOM, which peaked in the fourth round,as indicated by the gray spots. We also compared the predictedvalues and variances of the FOM before each round to assessthe divergence between the experimental results and the GPRmodel prediction, which helps us to evaluate the impact of theBO process and verify its effect. The predicted values varysimilarly to the experimental results, peaking in the fourthround, and the variance decreased as the predicted valuesincreased. During the third and fourth rounds, the predictedvalues closely matched the experimental results with a smallvariance, demonstrating the effectiveness of the ARD-GPRsurrogate model in capturing the relationship between inputparameters and target material properties. This consistencysuggests that the BO process effectively guided the optimizationtowards high-FOM candidates. After reaching the maximumFOM in the fourth round, predictions with a larger variancewere observed, indicating that the BO process exploited thesearch space with higher uncertainty. Conversely, predictionswith smaller variances aim to further explore the maximumFOM in search regions with lower uncertainty, as the model wastrained with a more densely distributed dataset. The selectionFig. 1 Schematic of the experiment-in-loop BO process for the fabrica-tion of the ‘‘5G-and-beyond’’ PFA composite with low dielectric loss andthermal expansion. An experiment involving (a) compounding and hotpressing was conducted for the fabrication of (b) the PFA/silica composite,followed by (c) performance evaluation of the FOM based on measure-ments of the CTE and dielectric properties. (d) Collected experimental datawere then fed to (e) the ARD kernel to train the model to suggestexperimental parameters of candidates in the next iteration.Table 1 Definitions of descriptors for the input parametersProcessparametersPlate fillercondition Spherical filler condition Filament filler condition Filler weightsaTime(min)Rotation(rpm)SurfacetreatmentSurfacetreatment DiameterSurfacetreatment DiameterWeight ofplatefiller (g)Weight ofsphericalfiller (g)Weight offilamentfiller (g)5 50 With (1) With Small (2.2 mm) With Small (0.7–2.1 mm) 0 0 07 100 Without (0) Without Large (20 mm) Without Large (7.5 mm) 1 1 19 150 2 2 2200 3 3 3250 Small diameter and without surface function (0) 4 4 4Small diameter and with surface function (1) 5 5 5Large diameter and without surface function (2) 6 6 6Large diameter and with surface function (3) 7 7 7a Maximum 7 g in total.Communication Materials HorizonsOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606h3336 |  Mater. Horiz., 2025, 12, 3332–3340 This journal is © The Royal Society of Chemistry 2025between exploration and exploitation is automatically deter-mined by auto-adjusted hyperparameters in PHYSBO.To further analyze the prediction accuracy of the surrogatemodel throughout the BO process, a series of parity plots weremade (Fig. S5, ESI†). The results indicated that the coefficientof determination (R2) reached its highest value (B0.73) arounditeration 4, aligning well with the optimization peak observedin Fig. 2(a). However, after iteration 6, R2 declines, indicatingan increase in prediction variance. This can be attributed to theshift from exploitation to exploration, the uneven distributionof data points leading to reduced model accuracy in unexploredregions, and the increasing complexity of the objective func-tion. These findings highlight the limitations of the surrogatemodel in later iterations, suggesting potential improvements inBO strategies.Further analysis of the scaling parameters of the ARD kernelduring BO (Fig. 2(b)) revealed the most critical dimensions fordetermining the FOM across the BO rounds. Herein, smallerscaling parameters indicate the dimensions that are moreimportant for determining the output value. As the optimiza-tion progressed, these parameters initially fluctuated signifi-cantly. Here, we focused on the fourth round, in which the BOprediction value peaked with a small variance. We found thatthe top three critical dimensions were the weight of the platefiller, the condition (size/surface chemistry) of the plate filler,and the weight of the filament filler. These scaling parametersprovide valuable insights into the most critical parameters fordesigning polymer composites with low CTE and dielectriclosses. Notably, they can be either positive or negative for theFOM. As discussed later, the sample with high FOM (sample #D)usually consists of a large amount of filament fillers, whereas thelower-FOM filler samples (sample #A) consist of more platefillers without surface functionalization. The insights from thescaling parameters align with the analysis of the sample para-meters, indicating the effect of the ARD kernel in capturing thecritical dimensions. Herein, although the scaling parameterseventually stabilized as more datasets were used in the BOprocess, they were less valuable because a large number ofpredictions after the fourth round exhibit large variance.Performance of PFA/silica compositesFig. 2(c) and (d) illustrate the variation in CTE, e, and tan d duringthe BO. As the optimization progresses, the CTE decreases,reaching a minimum after four rounds of BO. The CTE alignswell with the FOM, which also reaches its optimal value in thefourth round. In comparison, tan d decreases more rapidly. Afterjust one round of BO, it reaches 5.75� 10�4, which is close to theminimum value (5.47 � 10�4) among all the acquired data. Afterthe first iteration, tan d remains relatively constant, with only afew data points exhibiting relatively high values. In contrast, edoes not exhibit a clear trend in the BO process, fluctuatingslightly around an average of 2.44, with a standard deviationwithin 6% and a maximum fluctuation of only 18% (Fig. S2,ESI†). This makes the extinction coefficient follow the trend oftan d, rapidly reduced by in the first iteration by approximately400% and remain relatively constant within a standard deviationof 60% for the remainder of the BO process. The reduction in theCTE is relatively slow; the CTE is minimized in the fourth round,which indicates the required number of rounds for maximizingthe FOM.After the fourth round of BO, a PFA/silica composite (sample#D) with excellent properties was fabricated, featuring a CTE of24.76 ppm K�1, e of 2.56, and tan d of 6 � 10�4 (extinctioncoefficient of 9.5 � 10�4). This sample consists only of filamentfillers, with no surface functionalization and small diameters(details of the sample #D parameters are provided in Table 2).In contrast, the low-FOM samples typically include spherical andplate fillers (the parameters and performance of all samples arepresented in Table S2, ESI†). Moreover, the rotation speed andtime are less important in determining the FOM (samples #Dand #E). As stated above, these results are consistent withthe conclusions drawn from the scaling parameters of the ARDkernel.Fig. 3(a) and (b) present the comparisons of the CTE/dielectricextinction coefficient and FOM of the present study with those ofprevious studies, whose FOM values were calculated based oneqn (3). The CTE of 24.76 ppm K�1 is almost the lowest, exceptfor the silica/PTFE and silica/PEEK composite fabricated by Jianget al.33 and Xue et al.,35 respectively, while their extinctioncoefficients are more than one order of magnitude higher thanthose in the present study. Despite showing a slightly higher CTEFig. 2 Evolution of the properties of the PFA/silica composite fabricatedduring the BO process. (a) Evolution of the prediction/variance in the BOprocess and the experimental results. (b) Evolution of the ARD scalingparameters of individual dimensions during the BO process. (c) CTE, (d) eand tan d variations during BO. The dots indicate the value at eachiteration, and the lines represent the present best value during BO.Materials Horizons CommunicationOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606hThis journal is © The Royal Society of Chemistry 2025 Mater. Horiz., 2025, 12, 3332–3340 |  3337than the composites reported by Jiang et al. and Xue et al., thecomposite fabricated in this study shows a better performanceoverall considering a combination of both CTE and extinctioncoefficient values, which achieved a record-high FOM of 0.782,surpassing not only the fluor resin/silica composite but alsocomposites with other components such as polystyrene (PS)/silica,34 polyetheretherketone (PEEK)/silica,35 and epoxy resin/boron nitride nanotube (BNNT).36 Details regarding the compo-nent of these samples and their CTE, dielectric properties arepresented in Table S3 (ESI†). The highly efficient process for thefabrication of the practical PFA composite with excellent perfor-mance highlights the superiority of combining the ARD kernelwith experiment-in-loop optimization.Chemical components and structure of PFA/silica compositesWe systematically investigated the chemical components andstructure of the PFA composite to gain insights into the enhancedperformance, particularly focusing on the CTE, which is primarilyoptimized during the BO process. We analyzed five representativesamples, labeled #A to #E selected from the BO process. Thefabrication parameters and properties are presented in Table 2.According to the effective medium theory (EMT),39–41 the CTE ofcomposite materials is determined by the CTE and the mechan-ical properties (Young’s modulus and shear modulus) of indivi-dual components of the composite, including the polymermatrix, fillers, and voids. The properties of the filler and thematrix are affected by their chemical properties. The silica filler isstable during the compounding process because of its highmelting point and mechanical strength. Consequently, the CTEand mechanical properties remain unchanged, and were consid-ered identical for all the samples.However, because the compounding temperature is higherthan the melting point of PFA, chemical properties such as theconcentration of the amorphous component in PFA are assumedto differ under different compounding parameters. In this study,we focused on the amorphous degree of PFA, as a high amor-phous degree typically leads to a high CTE42 and low mechanicalstrength,43 yielding a high CTE of the composite. We investi-gated the PFA matrix using X-ray diffraction (XRD) analysis.Fig. 4(a) shows the XRD patterns of samples #A–#E. The broadpeak at 2y = 171 corresponds to the amorphous component (Ia),and the sharp peak at 2y = 181 signifies the crystal component (Ic).Therefore, we can evaluate the amorphous degree by Ia/(Ia + Ic).As displayed in Fig. 4(b), the samples with a lower CTE exhibit ahigher amorphous degree. This trend is opposite to the aforemen-tioned trend that a higher amorphous degree typically leads to ahigher CTE; therefore, it is unlikely that the strongly suppressedCTE is caused by the change in the amorphous degree of the PFAmatrix.Because the volume fraction of voids and fillers can influ-ence the effective CTE of the composite according to the EMT,we investigated the concentration of voids by measuring theTable 2 Fabrication parameters and properties of Sample #A–#ESampleno.Sample properties Fabrication parametersCTE(ppm K�1) e tan sExtinctioncoefficient FOMTime(min)Rotation(rpm)Plate fillerconditionSphericalfillerconditionFilamentfillerconditionWeight ofthe platefiller (g)Weight ofthe sphericalfiller (g)Weight ofthe filamentfiller (g)#A 121.3 2.26 5.64 � 10�3 8.46 � 10�3 �0.802 5 50 1 0 3 5 0 1#B 122.3 2.25 5.75 � 10�4 8.62 � 10�4 0.141 5 250 1 2 0 0 7 0#C 49.9 2.43 8.27 � 10�4 1.28 � 10�3 0.572 5 250 0 2 0 0 1 6#D 24.8 2.56 5.97 � 10�4 9.50 � 10�4 0.782 7 50 0 0 0 0 0 7#E 28.5 2.50 6.42 � 10�4 1.01 � 10�3 0.750 5 100 0 0 0 0 0 7Fig. 3 Excellent performance compared with previous studies. Comparison of the (a) CTE, dielectric extinction coefficient, and (b) FOM of the PFA/silicacomposite with those of previously reported polymer composites;3–8,10,11,34–38 different colors indicate materials with different chemical components(green: fluor resin/silica composite; orange: fluorresin/other filler composite; purple: composite of other polymers). The red star/column corresponds tothe PFA/silica composite in the present study.Communication Materials HorizonsOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606h3338 |  Mater. Horiz., 2025, 12, 3332–3340 This journal is © The Royal Society of Chemistry 2025density of the composite using Archimedes’ method and calcu-lated the practical volume fractions of the individual compo-nents. The densities of the samples #A–#E are presented inTable S4 (ESI†) and are lower than the theoretical density of a100% dense composite due to the presence of voids. Therefore,we can consider the sample as a three-phase composite consist-ing of voids, silica fillers, and a PFA matrix. Fig. S3 (ESI†) showsthe EMT calculation of the CTE for a three-phase compositealong with the theoretical CTE values for samples #A–#E (seeESI† for details). According to the EMT calculation, althoughboth voids and fillers can result in a lower CTE, the CTE is lesssensitive to voids because their elastic and shear moduli arenegligibly small. However, in the actual experiments, as indi-cated by Fig. 4(d), although the changes in the volume fraction ofvoids are within a limited range of 7.5–14.2% for samples #A–#E,the CTE varies by up to 97.5 ppm K�1, which significantlyincreased the FOM, from –0.802 to 0.782 (Fig. 4(c)). Moreover,although the EMT predicts a reduction in the CTE with anincrease in the filler volume fraction, the experimental resultsdo not exhibit such a reduction. In fact, there is no clearcorrelation between the CTE and the volume fraction of thefiller, as shown in the inset of Fig. 4(d).This suggests that the low CTE achieved here may arise from amore complex mechanism than the simple weighted average ofthe CTE. One possible mechanism is the topology effect proposedby Sigmund et al., where a three-phase composite consisting of amatrix, fillers, and voids can substantially reduce the CTE, evento a negative value, under specific topological conditions.44,45 Insuch a structure, the difference in CTE between the filler and thematrix leads to anisotropic expansion upon heating, potentiallycausing internal bending deformation and macroscopic shrink-age. Voids are critical for providing the necessary physical spacefor internal movement or deformation upon heating, whichrelaxes the thermal expansion within the composite and signifi-cantly reduces its CTE. In this context, apart from the specifictopological design of the composite, a higher porosity, largerinterface area, and larger difference in the CTE between the fillerand the matrix are likely to enhance the topological effect,reducing the CTE. This conclusion aligns with the trendsobserved in the present study, where samples #D and #E, whichhave higher porosity and larger interfacial area owing to the highsurface-to-volume ratio of the filament fillers, exhibit a low CTE.Although drawing a conclusion on how the structural varia-tions affect the CTE is a challenge without systematically varyingthe topological design to investigate the impact on the CTE, wecan gain valuable insights into the character of the topology inachieving a low CTE by analyzing the specific structures of thecomposites. Scanning electron microscopy (SEM) was used toanalyze the microscopic topologies of the fillers and voids.Fig. 4(e)–(h) present the cross-sectional SEM images of repre-sentative samples #A, #B, #C, and #E (additional SEM images ofother samples at both high and low magnifications are shown inFig. S4, ESI†). In sample #A, which contains both filament andplate fillers, these components are uniformly dispersed andexhibit minimal voids, which corresponds to its low porosity. Incontrast, sample #B exhibits large voids, primarily between thefiller and the PFA matrix. In sample #C, which features a mixof spherical and filament fillers, vacancies were observed nearFig. 4 Amorphous component analysis and microstructure characterization of the PFA/silica composite. (a) XRD results for samples #A–#E. The XRDpeaks of amorphous and crystal components are fitted by the Gaussian function and are indicated by the shadowed areas. (b) Amorphous degreesobtained from XRD and the corresponding CTEs (red) for samples #A–#E. (c) FOM and (d) CTE of samples #A–#E with respect to porosity; the dashedcurve is for visual guidance; the inset in (d) shows the CTE under different volume fractions of fillers. SEM images of (e) sample #A, (f) sample #B,(g) sample #C, and (h) sample #E (scale bar = 10 mm). XCT results for (i) sample #A and (j) sample #E and the derived (k) length distribution and(l) orientation of filament silica fillers. The curves represent a Gaussian fit of the histogram.Materials Horizons CommunicationOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606hThis journal is © The Royal Society of Chemistry 2025 Mater. Horiz., 2025, 12, 3332–3340 |  3339both the spherical and filament fillers, and the vacancies nearthe spherical fillers are larger. Samples #D and #E, characterizedby the highest porosity, exhibit small voids close to the filamentfiller, with sizes ranging from tens to hundreds of nanometers.These SEM observations indicate that the void topology differsamong samples and is related to the type of filler used. Inaddition, low-CTE samples typically consist of filament fillers,which not only affect the topology and volume fraction of thevoids but also results in the characterized topology of fillers.To further characterize the topology of the fillers, we inves-tigated samples #A and #E using X-ray computed tomography(XCT) (nano3DX, Rigaku). To achieve sufficient contrast in thedata with a high silica volume fraction, we used a voxel size of0.66 mm, which is smaller than the thickness of the plate filler.As a result, only the filament filler in sample #A could beanalyzed. Fig. 4(i) and (j) show the filament fillers in samples #Aand #E, respectively. The filament in sample #A was shorter(51.5 mm) than that in sample #E (58.6 mm), as shown inFig. 4(k). Moreover, the filament fillers are aligned along theplane of the film, with better alignment in sample #E than insample #A, indicating that the fillers form a continuous net-work in the in-plane direction (Fig. 4(l)). This characteristic ofthe filler topology is similar to the optimal structure thatexhibited a negative CTE in the previous study,45 where thecontinuous phase of the filler was characterized.With the above-mentioned analysis of these representativesamples, correlating the fabrication process, microstructuraltopology, and the resulting CTE, we can summarize key insightsfor optimizing the PFA composite. For instance, increasing thefilament filler content enhances the porosity, facilitating thermalexpansion relaxation, while filament alignment, influenced byrotation speed, may contribute to anisotropic structural effects.Additionally, untreated fibers tend to form interconnected net-works, which effectively suppress CTE. However, it should benoted that while our analysis provides valuable insights into futuresample design, the BO approach does not systematically vary eachparameter, and the process inherently involves some degree ofbias. Therefore, certain interactions may not be fully decoupled,and the conclusions are primarily applicable to local optimization.ConclusionsWe employed an ARD-GPR kernel in experiment-in-loop BO tooptimize the multidimensional experimental parameters forthe compounding process of PFA/silica composites, targeting alow CTE, e, and tan d for applications in the 5G-and-beyondtelecommunications. Exceptional results were achieved, includ-ing a CTE of 24.7 ppm K�1 and an extinction coefficient of9.5 � 10�4. The main feature of the optimal sample is the largeamount of small-diameter filament fillers. With the inauguralmachine learning-driven experimental endeavour in fabricatingpolymer composites with low CTE, e, and tan d, our outcomessurpassed those of previous studies that relied on conventionalempirical approaches. Moreover, the predicted values/variancesagree well with the experimental results. Before reaching themaximum FOM in the fourth round of the BO, the experimentalresults closely follow the predictions, with the variance decreasingand exhibiting minimum values at the data point with maximumFOM. This indicates that the maximum FOM achieved experimen-tally was derived from the BO and not obtained by chance. Moreover,the most critical dimensions, as reflected by the scaling parametersof the ARD kernel, align with the analysis of the characteristics ofsamples with either a high or a low FOM. This consistency verifiesthe effectiveness of the ARD-GPR surrogate model for acceleratingthe BO process with multiple anisotropic dimensions.Further analysis of the chemical components and structuresof several representative samples revealed that the microstruc-tural topologies of the composite, particularly the voids andfillers, are highly correlated with the resulting low CTE. Weattribute the significant reduction in the CTE to the topologicaleffect, which is typically functional in composites with specifi-cally designed topologies. In such structures, a mismatch in theCTE between the filler and the matrix can lead to unevenheating, causing bending and shrinkage. These effects can bemitigated by the spaces provided by the voids, leading to a CTEfar lower than that predicted via EMT.The fabricated polymer composite with ultralow CTE, e, andtan d values is expected to influence the 5G-and-beyond applica-tions by providing a generic and lossless transmission electronicbase material. Furthermore, the demonstrated material infor-matics methodology employing the ARD kernel in experiment-in-loop BO with multiple anisotropic dimensions showcased auseful approach for accelerating the development of compositematerials for practical applications in various fields.Author contributionsJ. S. conceived and supervised the research; B. X. and T. A. S.performed the sample fabrication; B. X., T. A. S., and T. S.performed the sample characterization and analysis; B. X.performed machine learning and model analysis with the helpof K. K., J. G., R. M., and T. K.; B. X. and J. S. wrote themanuscript with input from all the authors.Data availabilityAll data generated or analyzed during this study are included in thispublished article. Additional raw data supporting the figures areavailable from the corresponding author upon reasonable request.Conflicts of interestThe authors declare no competing interests.AcknowledgementsThe authors acknowledge Takayuki Yamada for the discussionson the thermal expansion of composite materials. The XCTmeasurements were supported by the Tokushima PrefecturalIndustrial Technology Center.Communication Materials HorizonsOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606h3340 |  Mater. Horiz., 2025, 12, 3332–3340 This journal is © The Royal Society of Chemistry 2025References1 R. Li, X. Yang, J. Li, Y. Shen, L. Zhang, R. Lu, C. Wang, X. Zheng,H. Chen and T. Zhang, Mater. Today Phys., 2022, 22, 100594.2 N. Saba and M. Jawaid, J. Ind. Eng. Chem., 2018, 67, 1–11.3 F. Liu, Y. Jin, J. Li, W. Jiang and W. Zhao, Compos. Sci.Technol., 2023, 241, 110142.4 G. Subodh, M. Joseph, P. Mohanan and M. T. Sebastian,J. Am. Ceram. Soc., 2007, 90, 3507–3511.5 L. Zheng, J. Zhou, J. Shen, W. Chen, Y. Qi, S. Shen and S. Li,J. Mater. Sci.: Mater. Electron., 2017, 28, 11665–11670.6 H. Wang, F. Zhou, J. Guo, H. Yang, J. Tong and Q. Zhang,Ceram. Int., 2020, 46, 7531–7540.7 W. Jin, A. Li, Y. Li, Y. Yu, J. Shen, J. Zhou and W. Chen,Ceram. Int., 2022, 48, 28512–28518.8 Y. Yuan, H. Lin, D. Yu, Y. Yin and B. Tang, J. Mater. Sci.:Mater. Electron., 2017, 28, 8810–8817.9 L. Ren, K. Pashayi, H. R. Fard, S. P. Kotha, T. Borca-Tasciucand R. Ozisik, Composites, Part B, 2014, 58, 228–234.10 I. A. Alhaji, Z. Abbas, M. H. Mohd Zaid and A. M. Khamis,Polymers, 2021, 13, 2449.11 Y.-C. Chen, H.-C. Lin and Y.-D. Lee, J. Polym. Res., 2003, 10,247–258.12 H. Qin, K. Liu, M. Tian, J. Mi and L. Zhang, Polymer, 2022,256, 125199.13 I. A. M. Ibrahim, A. A. F. Zikry, M. A. Sharaf, J. E. Mark,K. Jacob, I. M. Jasiuk and R. Tannenbaumn, IOP Conf. Ser.:Mater. Sci. Eng., 2012, 40, 012011.14 L. Wang, J. Yang, W. Cheng, J. Zou and D. Zhao, Front.Mater., 2021, 8, 1–16.15 S. Ju, T. Shiga, L. Feng, Z. Hou, K. Tsuda and J. Shiomi, Phys.Rev. X, 2017, 7, 021024.16 M. Yamawaki, M. Ohnishi, S. Ju and J. Shiomi, Sci. Adv.,2018, 4, 1–8.17 K. Okazawa, Y. Tsuji, K. Kurino, M. Yoshida, Y. Amamotoand K. Yoshizawa, ACS Omega, 2022, 7, 45403–45408.18 Y. Tsuji, Y. Yoshioka, K. Okazawa and K. Yoshizawa, ACSOmega, 2023, 8, 30335–30348.19 A. Takahashi, K. Terayama, Y. Kumagai, R. Tamura and F. Oba,Sci. Technol. Adv. Mater.: Methods, 2023, 3(1), 2261834.20 H. Sun, S.-Q. Zhao, F.-Y. Peng, R. Yan and X.-W. Tang, Adv.Manuf., 2024, DOI: 10.1007/s40436-024-00520-1.21 M. Delpisheh, B. Ebrahimpour, A. Fattahi, M. Siavashi,H. Mir, H. Mashhadimoslem, M. A. Abdol, M. Ghorbani,J. Shokri, D. Niblett, K. Khosravi, S. Rahimi, S. M. Alirahmi,H. Yu, A. Elkamel, V. Niasar and M. Mamlouk, J. Mater.Chem. A, 2024, 12, 20717–20782.22 J. J. Patil, C. T.-C. Wan, S. Gong, Y.-M. Chiang, F. R. Brushettand J. C. Grossman, ACS Nano, 2023, 17, 4999–5013.23 M. Saeidi-Javash, K. Wang, M. Zeng, T. Luo, A. W. Dowlingand Y. Zhang, Energy Environ. Sci., 2022, 15, 5093–5104.24 R. Tamura, T. Osada, K. Minagawa, T. Kohata, M. Hirosawa,K. Tsuda and K. Kawagishi, Mater. Des., 2021, 198,109290.25 Z. Hou, Y. Takagiwa, Y. Shinohara, Y. Xu and K. Tsuda, ACSAppl. Mater. Interfaces, 2019, 11, 11545–11554.26 K. Homma, Y. Liu, M. Sumita, R. Tamura, N. Fushimi,J. Iwata, K. Tsuda and C. Kaneta, J. Phys. Chem. C, 2020,124, 12865–12870.27 H. C. Herbol, W. Hu, P. Frazier, P. Clancy and M. Poloczek,npj Comput. Mater., 2018, 4, 51.28 D. Khatamsaz, R. Neuberger, A. M. Roy, S. H. Zadeh, R. Otisand R. Arróyave, npj Comput. Mater., 2023, 9, 1–11.29 C. E. Rasmussen, Gaussian Processes in Machine Learning,in Advanced Lectures on Machine Learning, ed. O. Bousquet,U. von Luxburg and G. Rätsch, Springer Berlin Heidelberg,Berlin, Heidelberg, 2004, pp. 63–71.30 T. Paananen, J. Piironen, M. R. Andersen and A. Vehtari, npjComput. Mater., 2017, 7, 188.31 Y. Motoyama, R. Tamura, K. Yoshimi, K. Terayama, T. Uenoand K. Tsuda, Comput. Phys. Commun., 2022, 278, 108405.32 T. Paananen, J. Piironen, M. R. Andersen and A. Vehtari,AISTATS 2019 - 22nd Int. Conf. Artif. Intell. Stat., 2020, 89,1743–1752.33 Z. Jiang and Y. Yuan, Mater. Res. Express, 2018, 5, 066306.34 T. S. Sasikala, B. P. Nair, C. Pavithran and M. T. Sebastian,Langmuir, 2012, 28, 9742–9747.35 P. J. Xue, S. L. Liu and J. J. Bian, J. Adv. Dielectr., 2021, 11, 1–8.36 X. Huang, C. Zhi, P. Jiang, D. Golberg, Y. Bando andT. Tanaka, Adv. Funct. Mater., 2013, 23, 1824–1831.37 Y. Li, J. Zhou, J. Shen, Q. Li, Y. Qi and W. Chen, J. Mater. Sci.:Mater. Electron., 2022, 33, 10096–10103.38 Y.-C. Chen, H.-C. Lin and Y.-D. Lee, J. Polym. Res., 2004, 11,1–7.39 Z. Hashin, J. Mech. Phys. Solids, 1991, 39, 745–762.40 B. W. Rosen and Z. Hashin, Int. J. Eng. Sci., 1970, 8, 157–173.41 J. D. Eshelby, Proc. R. Soc. London, Ser. A, 1957, 241, 376–396.42 S. X. Lu, P. Cebe and M. Capel, Polymer, 1996, 37, 2999–3009.43 L. Chevalier, C. Linhone and G. Regnier, Plast., RubberCompos., 1999, 28, 393–400.44 O. Sigmund and S. Torquato, J. Mech. Phys. Solids, 1997, 45,1037–1067.45 O. Sigmund and S. Torquato, Appl. Phys. Lett., 1996, 69,3203–3205.Materials Horizons CommunicationOpen Access Article. Published on 21 February 2025. Downloaded on 5/22/2025 1:55:50 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttps://doi.org/10.1007/s40436-024-00520-1http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4mh01606h