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Rational design of all organic polymer dielectrics

Rational design of all organic polymer dielectrics ARTICLE Received 20 May 2014 | Accepted 29 Jul 2014 | Published 17 Sep 2014 DOI: 10.1038/ncomms5845 1,2 1,2 2,3 2,3 4 5 Vinit Sharma , Chenchen Wang , Robert G. Lorenzini , Rui Ma , Qiang Zhu , Daniel W. Sinkovits , 6 4,7,8 5 2,3 2 Ghanshyam Pilania , Artem R. Oganov , Sanat Kumar , Gregory A. Sotzing , Steven A. Boggs 1,2 & Rampi Ramprasad To date, trial and error strategies guided by intuition have dominated the identification of materials suitable for a specific application. We are entering a data-rich, modelling-driven era where such Edisonian approaches are gradually being replaced by rational strategies, which couple predictions from advanced computational screening with targeted experimental synthesis and validation. Here, consistent with this emerging paradigm, we propose a strategy of hierarchical modelling with successive downselection stages to accelerate the identification of polymer dielectrics that have the potential to surpass ‘standard’ materials for a given application. Successful synthesis and testing of some of the most promising identified polymers and the measured attractive dielectric properties (which are in quantitative agreement with predictions) strongly supports the proposed approach to material selection. 1 2 Department of Materials Science and Engineering, University of Connecticut, Storrs, Connecticut 06269, USA. Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA. Department of Chemistry, Institute of Materials Science, University of Connecticut, Storrs, Connecticut 4 5 06226, USA. Department of Geosciences and Center for Materials by Design, Stony Brook University, Stony Brook, New York 11794, USA. Department of Chemical Engineering, Columbia University, New York, New York 10027, USA. Materials Science and Technology Division (MST-8), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. Moscow Institute of Physics and Technology, 9 Institutskiy lane, Moscow 141700, Russia. Northwestern Polytechnical University, Xi’an 710072, China. Correspondence and requests for materials should be addressed to R.R. (email: [email protected]). NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 1 & 2014 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 olymeric dielectric materials are pervasive in modern screening attempted in this work, we identify attractive polymers electronics and electrical systems. They have found based on their dielectric constant and band gap values, both of 1–6 Papplications in the areas of capacitive energy storage , which can be computed with reasonable accuracy using quantum 7–9 10–12 transistors , photovoltaic devices and electrical mechanical computations. As noted earlier, dielectrics for high 13,14 insulation . The selection and design of a polymer depends energy density capacitor applications need to satisfy additional on the requirements specific to the application, which, in the case requirements, including low dielectric loss and high dielectric of dielectric applications, can be stated in terms of a subset of the breakdown strength (thus making the presently adopted screen- following properties: dielectric constant, band gap, dielectric ing criteria necessary but not sufficient conditions). Since the breakdown field, dielectric loss, morphology, glass transition current state-of-the-art does not allow us to determine these temperature, mechanical strength, cost and so on. Although the attributes quantitatively in a high-throughput framework, we use property requirements can be specified with reasonable precision, the band gap as a proxy. Recent work suggests that large values of trial and error strategies (aided by chemical intuition or the intrinsic breakdown strength of a variety of insulators are 26,27 serendipity) have dominated the identification or discovery of correlated with large band gap values . Besides, the band gap suitable candidates that meet such requirements. While and dielectric constant, in and of themselves, are important successful, these strategies suffer from the fact that they are not properties in a variety of applications. generalizable, and discoveries (and, equally importantly, the lack Our step-by-step computational search strategy to arrive at of such prospects) cannot be rigorously assessed. The community promising polymeric dielectrics is depicted schematically in Fig. 1. is thus gradually migrating towards systematic computation- This strategy includes the following successive (and to some extent, 15,16 driven materials (down) selection paradigms . iterative) steps: (1) Combinatorial chemical space exploration using Consider, for instance, the case of polymers for capacitive 1D polymerchainswithfourindependent blocks perrepeatunit; energy storage applications. The on-going electrification of (2) Promising repeat unit (that is, sequence of blocks) identification 17,18 19 land and sea transportation, as well as other military and based on band gap and dielectric constant estimates; (3) 3D 19,20 civilian systems has increased the demand for high energy structure/morphology predictions of polymers composed of the density capacitors. The choice of polymers (over ceramics) in downselected repeat units; (4) Property predictions of the 3D capacitive energy storage applications is motivated by the need systems; and (5) Synthesis of the identified polymers, followed by for ‘graceful failure’ of the dielectric at high fields. Metallized testing and validation. Steps 3–5 are time-intensive. Hence, polymers offer the only scalable capacitor technology that meets candidates identified in Step 2, which are amenable to synthesis, this need. The energy stored in a capacitor is proportional to the are favored in Steps 3–5. Application of this strategy to the design of dielectric constant and the square of the electric field. Thus, organic polymeric dielectrics for high energy density applications materials of interest should display a high dielectric constant and has identified several polymers, some of which (especially those high electrical breakdown field. In addition, low dielectric loss with prior evidence of synthesis success) are listed in Table 1. The and resistance to high field degradation of the polymer itself are top three members of Table 1 have also been synthesized by us, and important requirements as well. The present state-of-the-art in high energy density metalized film capacitors employ biaxially Step 1: Combinatorial chemical space exploration oriented polypropylene (BOPP), which has a small area (B1cm ) breakdown field of about 750 MV m and a dielectric constant Polymer block options: B B B B 4 2 4 2 -CH -, -C H -, -C H S-, of about 2.2. Various attempts to replace BOPP have been based B B 2 6 4 4 2 B B 1 1 3 3 1,21,22 -CO-, -NH-, -O-, -CS- on poly(vinyledene fluoride) (PVDF) and its copolymers , 23–25 polymer nanocomposites and so on. All such potential replacements have suffered from either high loss (PVDF and its Step 2: Promising repeat unit identification copolymers) or low breakdown field (nanofilled polymers). High-throughput density functional theory (DFT), A strategy is needed to identify promising new polymers. Effective medium theory In this contribution, we present a rational design strategy of hierarchical modelling with successive downselection stages to efficiently screen and identify advanced polymer dielectrics for Step 3: Structure/morphology predictions capacitive energy storage applications. Specifically, quantum Evolutionary structure search (based on DFT), Melt-and-quench based search (based on force fields) mechanics-based combinatorial searches of chemical space are used to identify polymer repeat units that could lead to desirable dielectric properties, followed by configurational space searches Step4 : Property predictions using evolutionary and classical molecular dynamics schemes to Dielectric tensor (using perturbation theory), band structure determine the three-dimensional (3D) arrangement of polymers (using hybrid functional), infrared and x-ray spectra (and their properties) built from the desirable repeat units. Successful synthesis and testing of some of the most promising identified polymers and the measured attractive dielectric Step 5 : Synthesis, Testing & Validation properties supports the proposed approach to material selection. Solvent casting of polymer films, infrared and x-ray spectra, dielectic spectroscopy Results Figure 1 | A schematic illustration of our rational polymer dielectric Overview. In essence, we show that a systematic combinatorial design strategy. The strategy involves five consecutive steps: (1) Combinatorial chemical space exploration, using 1D polymer chains search of the polymer chemical and configurational spaces can lead to new polymers with attractive combinations of properties. containing four independent blocks with periodic boundary conditions along the chain axis, (2) Promising repeat unit identification, by screening based By chemical space, we refer to the various building blocks (‘monomers’) in the polymer, while configurational space on band gap and dielectric constant, (3) 3D structure/morphology encompasses the connectivity sequences possible with these predictions of polymers composed of the downselected repeat units, building blocks, the manner in which the resulting chains pack (4) Property predictions of the 3D systems. Finally, (5) Synthesis testing together, and the larger scale morphology. In a first line of and validation. 2 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. Guidance based on amenability to synthesis NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 ARTICLE appear attractive based on the measured dielectric properties. In total) and the band gap for the 267 polymers, including the what follows, we describe the details of our search strategy in a step- prototypical system, polyethylene (when all four blocks are set to by-step manner. -CH -), which has the largest band gap and the smallest dielectric constant of all systems studied. As can be seen from Fig. 2a, the upper bound of the electronic part of the dielectric constant Combinatorial chemical space exploration. The first level of versus the band gap data displays a near perfect inverse screening involves the 1D catenation of repeat units into a dependence. This imposes a theoretical limit on the achievable polymer chain. In the present search, repeat units were con- electronic part of the dielectric constant, a limit that can be structed using four building blocks in the repeat unit with each understood by regarding this property as related to a sum over block drawn from the following pool of possibilities: -CH -, electronic transitions from occupied to unoccupied states .On -C H -, -C H S-, -NH-, -CO-, -O-, -CS-, as depicted in Fig. 1. 6 4 4 2 the other hand, the ionic part of the dielectric constant, which is These blocks were chosen because they are common in polymer determined by the infrared (IR)-active zone centre phonon modes backbones, including polyethylene, polyesters, polyamides, poly- (that is, the modes that display a time-varying dipole ethers and polyureas. After the elimination of obviously unstable 31,32 moment) , is not correlated with the band gap, as seen from combinations of these building blocks (such as systems contain- Fig. 2b. The ionic dielectric constant can thus be exploited to ing contiguous -CO- or -O- blocks) and accounting for transla- increase the total dielectric constant without compromising the tional and inversion symmetry, we were left with 267 unique band gap. repeat units (c.f. Supplementary Table 1). Density functional Figure 2c, which shows the variation of the total dielectric theory (DFT) computations were performed to determine the constant with the band gap, is a ‘map’ of the achievable optimal 1D structure of each of these systems, followed by combination of these properties within the chemical space the estimation of the electronic and ionic contributions to the explored. Capacitive energy storage and some electronics dielectric constant by a combination of density functional 28,29 applications, for example, gate insulations, could draw from the perturbation theory (DFPT) and effective medium theory . large dielectric constant and moderate band gap region of this The latter approach is critical as it allows us to estimate the plot. As illustrated in Fig. 2c, downselection, starting from the set dielectric constant of a macroscopic polymer based just on its 1D of 267 polymers with four-block repeat units, proceeded by 28,29 structure, as explained previously . considering the polymers with total dielectric constant 4B4eV and band gap 4B3 eV. Polymers that survive this initial Promising repeat unit identification. Figure 2 portrays the screening step are predominantly composed of at least one of relationship between the dielectric constant (electronic, ionic and the polar units, namely -NH-, -CO- and -O-, and at least one of the aromatic rings, namely -C H - and -C H S-. -NH-, -CO- and 6 4 6 2 -O- tend to enhance the ionic part of the dielectric constant, while Table 1 | Promising polymer repeat units identified at Step 2 the aromatic groups boost the electronic part. A selected of the screening process. assortment of these promising polymers (especially those with prior evidence of synthesis success) are listed in Table 1 in System repeat unit Polymer class decreasing order of total dielectric constant. Interestingly, none of NH-CO-NH-C H Polyurea 6 4 these specific polymers have been considered in the past for CO-NH-CO-C H Polyimide 6 4 dielectric applications, although a few other polymers in the NH-CS-NH-C H Polythiourea 6 4 general classes listed in Table 1 (for example, polythiourea ) have NH-C H -C H -C H Polyamine 6 4 6 4 6 4 CO-C H -CO-O Polyester, polyanhydride been shown to hold promise for dielectric applications. 6 4 C H -C H -C H -O Polyether 6 4 6 4 6 4 CH -C H -C H -O Polyether 2 6 4 6 4 CH -CO-C H -O Polyether, polyketone 2 6 4 Structure/morphology prediction. We now consider only the CH -C H -CO-O Polyester 2 6 6 top three downselected cases of Table 1, namely, [-NH-CO-NH- CH -NH-CO-NH Polyurea C H -] , [-CO-NH-CO-C H -] and [-NH-CS-NH-C H -] . 6 4 n 6 4 n 6 4 n CH -NH-CS-NH Polythiourea The 3D structure of these three polymers was determined CH -C H -CH -O Polyether 2 6 4 2 using two complementary approaches: (1) a version of the The screening was based on the estimated dielectric properties of the polymers and their Universal Structure Predictor: Evolutionary Xtallography amenability to synthesis (past synthesis efforts, when available, are cited). The top three 33–37 (USPEX) method specially modified to handle repeat units polymers were taken all the way to Step 5 (synthesis and testing). rather than atoms as the building blocks, and (2) a classical ab c 0.1 Polyethylene Electronic Ionic Total 1 1 0.01 12 3 45 67 8 12 3 45678 12 3 45678 Band gap (eV) Band gap (eV) Band gap (eV) Figure 2 | The dielectric constant versus band gap relationship of 1D polymers. Computed (a) electronic, (b) ionic and (c) total dielectric constant (along the polymer chain axis) as a function of the band gap. The associated errors in the dielectric constant computed using density functional perturbation theory for single chains, and subsequently estimated using effective medium theory for a bulk environment are also shown. The highlighted region corresponds to the most ‘promising repeat units’ composed of at least one of -NH-, -CO- and -O-, and at least one of -C H - and –C H S- blocks. 6 4 6 2 Band gap was computed using the HSE06 electronic exchange-correlation functional. NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 3 & 2014 Macmillan Publishers Limited. All rights reserved. Dielectric constant Dielectric constant Dielectric constant ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 O O H H H ab c N N N O S n n 15 15 15 Biherringbone E = 3.5 eV,  = 5.7,  = 4.0 g t e 10 10 10 Parallel Herringbone-diagonal Parallel-diagonal E = 3.5 eV,  = 5.2,  = 4.1 E = 2.9 eV,  = 5.3,  = 4.3 g t e g t e E = 4.2 ev,  = 4.5,  = 3.1 g t e Alternating-diagonal 5 5 5 E = 3.7 eV,  = 5.2,  = 4.1 g t e Alternating-diagonal Alternating-parallel Parallel-diagonal E = 4.1 eV,  = 4.3,  = 3.2 0 0 g t e E = 3.0 eV,  = 6.0,  = 4.2 g t e E = 4.0 eV,  = 5.7,  = 4.0 g t e Figure 3 | Predicted properties and structures of the identified promising polymers. The repeat units of the three identified polymers are (a) [-NH-CO-NH-C H -] (b) [-CO-NH-CO-C H -] and (c) [-NH-CS-NH-C H -]. The crystal structures of [-NH-CO-NH-C H -] are predicted by 6 4 6 4 6 4 6 4 evolutionary structure search (using DFT) and melt-and-quench (using force-field (FF)) schemes, while in other two polymers only evolutionary structure search (using DFT) method has been used. The zero of the energy scale corresponds to the most stable structures. For each predicted structure, the calculated values of the band gap (E ), total (E ) and electronic (E ) part of dielectric constants are also listed. g t e ab c Biherringbone Biherringbone Parallel-diagonal Expt. 6 Alternating-diagonal Herringbone-diagonal Herringbone -diagonal 5 Herringbone-diagonal Biherringbone Alternating-diagonal Alternating -diagonal Parallel-diagonal Parallel- –1 diagonal Expt. –2 Expt. Expt. –3 10 20 30 40 50 60 70 500 1,000 1,500 2,000 2,500 10 100 1k –1 2 (degree) Wavenumber (cm ) Frequency (Hz) Figure 4 | Experimental and predicted data for the polymer with repeat unit [-NH-CO-NH-C H -]. (a) X-ray diffraction data (b) IR spectra, 6 4 and (c) dielectric spectra (top panel) and loss factor (bottom panel). Expt, experimental. molecular dynamics based melt-and-quench approach. the orientational average ranging from 4 to 6, double that of The former used DFT energetics (here used with 4 repeat units polyethylene or polypropylene. The electronic part of the per unit cell) and hence provide ground state (0 K) results, while dielectric constant for all polymers ranges from 3 to 4, placing the latter used a newly generated force field and hence could treat these with polymers that display the highest known refractive much larger systems containing thousands of repeat units per indices . Assuming that the predicted ground state structures 36,37 unit cell at nonzero temperatures. Both the modified USPEX remain stable at elevated temperatures close to room and the melt-and-quench schemes lead to several low energy temperatures (a reasonable assumption based on the discussion configurations, which were equivalent within the expected above), the predicted band gaps and dielectric constants are uncertainties of the force-field and DFT energy predictions. expected to be valid at those elevated temperatures as well. In This is reassuring as it indicates that the ground state structures situations when amorphous polymeric phases are expected in predicted by DFT are expected to be stable at higher temperatures reality (aided by competing energetics or favourable kinetics), as well. Figure 3 shows the energetic ordering of a few low energy some deviations in the dielectric constant with respect to those structures for each of the three polymers considered at this stage. predicted here is to be expected. Nevertheless, as dielectric Simulated X-ray diffraction (XRD) and infrared (IR) spectra behaviour is generally dominated by local chemistry and bonding, based on the predicted low energy structures for all three the deviations are expected to be small (see discussion below polymers are presented in Figs 4–6, and discussed and compared pertaining to the [-CO-NH-CO-C H -] and [-NH-CS-NH- 6 4 n with measurements below. C H -] polymers). The predicted values of the total (E ) and 6 4 n t electronic (E ) parts of dielectric constants for all three polymers considered are listed in Fig. 3. As can be seen, the fidelity of the Property predictions. The computed band gap values of all the predictions of Step 2 persist at Step 4 of our process (insofar as identified low energy structures are listed in Fig. 3. As can be seen, the band gap and dielectric constant values are concerned). except in the case of [-NH-CS-NH-C H -] , the band gap (E ) 6 4 n g values are over 3.5 eV for all identified structures. Computed electronic band structure and density of states are shown in Validation through synthesis and testing. Synthesis of the Supplementary Information (c.f. Supplementary Figure 1). The [-NH-CO-NH-C H -] , [-CO-NH-CO-C H -] and [-NH-CS- 6 4 n 6 4 n dielectric constants were determined using DFPT, with results for NH-C H -] polymers proceeded via adaptation of previous 6 4 n 4 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. Energy (meV per atom) Intensity (a.u.) Transmittance Loss (tan ) Dielectric constant NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 ARTICLE ab c Parallel- Parallel-diagonal 5 Parallel-diagonal diagonal Expt. Alternating-diagonal Alternating-diagonal Alternating- 3 diagonal –1 Expt. –2 Expt. Expt. –3 10 100 1k 10 20 30 40 50 60 70 500 1,000 1,500 2,000 2,500 –1 2 (degree) Wavenumber (cm ) Frequency (Hz) Figure 5 | Experimental and predicted data for the polymer with repeat unit [-CO-NH-CO-C H -]. (a) X-ray diffraction data (b) IR spectra, 6 4 and (c) dielectric spectra (top panel) and loss factor (bottom panel). Expt, experimental. ab c Parallel Parallel Expt. Alternating-parallel Alternating-parallel 5 Parallel Alternating- parallel –1 Expt. –2 Expt. Expt. –3 10 20 30 40 50 60 70 500 1,000 1,500 2,000 2,500 10 100 1k –1 2 (degree) Wavenumber (cm ) Frequency (Hz) Figure 6 | Experimental and predicted data for the polymer with repeat unit [-NH-CS-NH-C H -]. (a) X-ray diffraction data (b) IR spectra, 6 4 and (c) dielectric spectra (top panel) and loss factor (bottom panel). Expt, experimental. efforts . Measurements were performed on pressed pellets of the (over all directions) total dielectric constant values for all four synthesized polymers. The measured band gap values of the three predicted [-NH-CO-NH-C H -] crystal structures. Once again, 6 4 n polymers are 3.9 eV, 4.0 eV and 3.1 eV, respectively, in good the agreement between measurement and predictions is excellent. agreement with the predictions listed in Fig. 3. The predicted XRD spectra of the [-CO-NH-CO-C H -] , and 6 4 n Considering [-NH-CO-NH-C H -] first (Fig. 4a), a character- [-NH-CS-NH-C H -] polymers (Figs 5a and 6a) do not match 6 4 n 6 4 n istic double peak in the XRD spectra at 2yE20 can be seen for well with the measured spectra, which display broad peaks. This all the predicted structures except the ‘biherringbone’ case, in line indicates that the synthesized and cast [-CO-NH-CO-C H -] 6 4 n with the measurements, with the agreement being best for the and [-NH-CS-NH-C H -] polymers are in semicrystalline or 6 4 n ‘parallel-diagonal’ case. The correspondence between the amorphous form. On the other hand, the measured and measured IR spectrum (Fig. 4b) and that of the four predicted calculated IR spectra (Figs 5b and 6b) are in good agreement structures is uniformly good. This is not surprising as the IR for both [-CO-NH-CO-C H -] and [-NH-CS-NH-C H -] for 6 4 n 6 4 n peaks are dominated by intra-chain ‘bonded’ interactions. Such the same reasons identified above in the discussion of the interactions are roughly the same for all four predicted structures, [-NH-CO-NH-C H -] polymer. The measured dielectric con- 6 4 n which differ largely only in the manner in which the individual stant of [-CO-NH-CO-C H -] is in the range of 4.2–4.8 and that 6 4 n chains are packed. Based on these findings, we conclude that the of [-NH-CS-NH-C H -] is in the 5.7–6.7 range, both in good 6 4 n [-NH-CO-NH-C H -] polymer is dominated by regions of agreement with predictions (shown in Figs 5c and 6c, and in 6 4 n ‘parallel-diagonal’ structure, although smaller portions of the Fig. 3), despite the fact that the predictions are made for the other three structures cannot be ruled out at or close to room crystalline varieties of these polymers. Both polymers display temperatures. dielectric loss larger than that of the [-NH-CO-NH-C H -] . 6 4 n Figure 4c portrays the dielectric spectrum for the synthesized [-NH-CO-NH-C H -] polyurea system. Across a wide frequency 6 4 n range, the dielectric constant is in the 5.4–5.8 range, and the Discussion dielectric loss at 1 kHz is in the range of 1%, an acceptable value We have outlined a rational procedure for systematically for some applications. Figure 4c also shows the computed average exploring polymer chemical spaces and identifying potentially NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 5 & 2014 Macmillan Publishers Limited. All rights reserved. Intensity (a.u.) Intensity (a.u.) Transmittance Transmittance Loss (tan ) Dielectric constant Loss (tan ) Dielectric constant ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 useful dielectrics based on the dielectric constant and band Structure prediction using evolutionary algorithm. A specifically designed 36,37 33–35,37 constrained evolutionary algorithm , embodied in the USPEX code was gap as initial screening criteria. This procedure is computationally used to predict polymeric crystal structures starting from the single polymeric driven (with ample guidance from chemical intuition and chains discussed above (using first-principles quantum mechanical computations synthesis considerations) and uses a combination of quantum for the total ground state energy of the crystals). This newly developed method mechanical calculations, force-field simulations and structure uses a specification of well-defined molecular repeat units rather than individual atoms as the starting point . The diversity of the population of structures is and property prediction schemes in a hierarchical manner. enhanced by using space-group symmetry combined with random cell parameters, A class of organic polymers involving seven distinct building 36,37 and random positions and orientations of the molecular units . During the blocks was screened using this approach and several promising evolutionary optimization, structures with different sequence and packing of these polymers were identified. A common feature of these down- repeat units are generated and relaxed. We performed multiple runs of evolutionary search with two and four repeat units. The total energies were selected polymers is the occurrence of at least one of the polar obtained with the PBE exchange-correlation functionals using the dispersion units, -NH-, -CO- and -O-, and at least one of the aromatic correction prescribed by the vdW-TS approach . In all cases considered here, the rings, -C H - and -C H S-. Three of the most promising cases 6 4 6 2 energetic orderings are invariant with respect to the choice of different exchange- were synthesized and tested. The favourable agreement correlation functionals. between the measured and predicted (structural, electronic and dielectric) properties of all three polymers, and the low Structure prediction using the melt-and-quench scheme. The simulations dielectric loss of one of these (namely, [-NH-CO-NH-C H -] ) 54 6 4 n were performed using the LAMMPS molecular dynamics package and the provides validation and hope for such a rational computationally OPLS-2005 force field . The polymer [-NH-CO-NH-C H -]n requires a torsion 6 4 potential for N-C-N-CA (where CA is an aromatic carbon) which is not present in driven approach for materials discovery. Indeed, processable the force field. This potential was calculated using the molecule CO-(NH-C H ) 6 4 2 variants of the polymers identified here are presently being via fitting to the difference in energy, between using the force field and using further evaluated. Hartree–Fock 6-31G*, minimized under constraint of the two torsions of this type While the present development is certainly a significant in a series of calculations to sweep out the full range of motion. To make the torsion potential fit all configurations satisfactorily, it was necessary to modify advance over empiricism, consistent with the emerging paradigm 15,16 the atomic partial charges. These were set to match Mulliken charges scaled down of computation-driven materials (down)selection , it is only by a factor of 1.86, and the charges of H and CA bonded to N were adjusted to an initial attempt that should be extended by including other ensure a good fit. critical properties in the screening process. Such properties Two kinds of simulations were performed, which differed in whether the polymers were terminated with an end group within the periodic cell or whether include dielectric loss, dielectric breakdown strength, mechanical they were covalently bonded to the other end of the polymer via the periodic behaviour, glass transition temperature and charge carrier wrapping. The first set consisted of 18mer chains terminating in phenyl rings. mobility. The current state-of-the-art limits our ability to A single chain was quenched into a straight conformation corresponding to the predict these properties rapidly and with high fidelity. It is minimization of all bonds, angles and torsions. The single chain was replicated in a 6 6 rectangular array. The system was heated at 1 K ps , and the structure was hoped that recent advances in data-driven and first-principles observed to change between 800 and 860 K. The 860 K configuration was selected methodologies will allow us overcome these limitations with for cooling at various rates. At the cooling rate of  10 K ps , a ‘parallel’ crystal 16,40 time . While the present effort has focussed primarily on was produced with a ‘herringbone’ defect, but cooling at 1ps produced a high energy density capacitor dielectrics, polymers for other perfect ‘parallel’ crystal. After further study, this melt-and-quench process was applications (for example, organic semiconductors or organic repeated starting with a perfect ‘parallel-diagonal’ crystal. During heating at 1Kps , this crystal underwent two transitions between 710 and 810 K before photovoltaics) can be identified in a systematic manner using an showing signs of melting at 850 K. The 820 K configuration cooled at either 1or extended version of the present strategy by considering other 0.1 K ps yielded a ‘biherringbone’ crystal. relevant screening criteria and many types of blocks. The second set of simulations consisted of a 4 4 array of 4mer chains connected to themselves through the periodic boundary, making them effectively infinite. Owing to the periodic restriction, nematic order remains at very high temperatures (1,000 K). Crystals were obtained by cooling from this high- Methods temperature state. The initial configuration of the crystals before heating is thus First-principles computations. The quantum mechanical computations were immaterial. Usually, the ‘herringbone’ configuration was obtained, in both fast performed using DFT as implemented in the Vienna ab initio software 1  1 ( 10 K ps ) and slow quenches ( 0.05 K ps ), but two cases resulted in 41,42 package . The generalized gradient approximation functional, parametrized by 1  1 ‘biherringbone’ configurations ( 10 K ps ,  0.2 K ps ). ‘Parallel’ crystals Perdew, Burke and Ernzerhof (PBE) to treat the electronic exchange-correlation were never obtained after cooling if the system had been heated 4900 K. interaction, the projector augmented wave potentials and plane-wave basis functions up to a kinetic energy cutoff of 500 eV, were employed. The supercells were relaxed using a conjugate gradient algorithm until the forces on all atoms Synthesis and characterization details. For the synthesis of the first two poly- were o0.02 eV Å . As the PBE functional is known to underestimate band gaps mers, namely, [-NH-CO-NH-C H -] and [-CO-NH-CO-C H -], a flame-dried, 6 4 6 4 of insulators, the Heyd Scuseria Ernzerhof HSE06 functional was used to argon-flushed 125 ml round bottom flask equipped with a reflux condenser, obtain corrected band gap values for all systems considered. gas inlet, magnetic stirbarand 50-ml dry dimethylsulphoxide were used. In the The 1D systems considered in Step 1 were composed of all-trans infinitely polyurea case [-NH-CO-NH-C H -], equimolar amounts of p-phenylene diiso- 6 4 long isolated chains containing four independent building units in a supercell cyanate and p-phenylenediamine were used, while for the polyimide [-CO-NH- geometry (with periodic boundary conditions along the axial direction). In a CO-C H -], equimolar amounts of terephthalamide and terephthaloyl chloride 6 4 combinatorial and exhaustive manner, each block in the polymer backbone was were used (35 mmol). The mixtures were heated at 350 K for 8 h under pre-purified allowed to be one of the following units: -CH -, -NH-, -C(¼ O)-, -C H - argon, after which they were poured into dry tetrahydrofuran. The white solid 2 6 4 (benzene), -C H S- (thiophene), -C(¼ S)- or -O-, which are commonly seen in precipitates were filtered and washed copiously in fresh tetrahydrofuran, followed 4 2 29,46,47 polymer backbones . The scheme results in 267 symmetry unique cases. by drying in vacuo. The yields for the polyurea and polyimide were nearly A Monkhorst–Pack k-point mesh of 1 1 k (with kc 450) was used to quantitative. produce converged results for a supercell of length c (Å) along the chain The following synthesis route was adopted for the [-NH-CS-NH-C H -] 6 4 direction (that is, the z direction). The stress component along the z direction was polymer. To a dry 100 ml three-neck flask, 0.9614 g (5 mmol) of p-phenylene required to be o1.0 10 GPa. The dielectric permittivity of the isolated diisothiocyanate and 10 ml dry dimethylsulfoxide were added under nitrogen with 48,49 polymer chains placed in a large supercell was first computed within the DFPT stirring, followed by the addition of 0.5407 g (10 mmol) of p-phenylenediamine. formalism, which includes contributions from the polymer as well as from the The reaction was carried out at room temperature. After 6 h, a white powder surrounding vacuum region of the supercell. Next, treating the supercell as a crashed out of the solution. The mixture was poured into 150 ml of methanol, vacuum-polymer composite, effective medium theory was used to estimate the filtered and washed with methanol several times, and dried in vacuo. A white solid dielectric constant of just the polymer chains using methods described was obtained at 89% yield (1.337 g). 28,29 recently . XRD patterns were obtained on a Bruker D5005 X-ray diffractometer equipped In the case of polymer crystals (discussed below), van der Waals interactions with a 2.2 kW copper X-ray tube. The dielectric spectra were obtained on an were taken into account using the vdW-TS functional . Phonon dispersion curves IMASS time domain dielectric spectrometer. Measurements were taken by were calculated using the supercell approach with the finite displacement method sandwiching a pressed pellet of material between silicone rubber guarded 52 53 as implemented in the PHONOPY code , while FullProf suite was used to electrodes. Pellets were prepared in a hydraulic press with a 1 inch circular pellet simulate the XRD patterns. mould. IR spectra were obtained on a Nicolet Magna-IR 560 spectrometer using 6 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. 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The intrinsic electrical breakdown strength of insulators from first principles. Appl. Phys. Lett. 101, 132906 (2012). 28. Pilania, G. et al. New Group 4 chemical motifs for polymeric dielectrics with Acknowledgements high energy density. J. Chem. Inf. Model. 53, 879–886 (2013). This paper is based on the work supported by a Multidisciplinary University Research 29. Wang, C. C., Pilania, G. & Ramprasad, R. Dielectric properties of carbon-, Initiative (MURI) grant (N00014-10-1-0944) from the Office of Naval Research (ONR). silicon-, and germanium-based polymers: a first-principles study. Phys. Rev. B Computational support was provided by the Extreme Science and Engineering Discovery 87, 035103 (2013). Environment (XSEDE) and the National Energy Research Scientific Computing Center 30. Brothers, E. N., Scuseria, G. E. & Kudin, K. N. Longitudinal polarizability of (NERSC). A.R.O. thanks the National Science Foundation (grants EAR-1114313, carbon nanotubes. J. Phys. Chem. B 110, 12860–12864 (2006). DMR-1231586), DARPA (Grants No. W31P4Q1310005, and No. W31P4Q1210008), NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 7 & 2014 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 grant of the Government of the Russian Federation (No. 14.A12.31.0003) and CRDF shaped the manuscript. All authors discussed the results and commented on the Global (UKE2-7034-KV-11). Ms JoAnne Ronzello and Dr Yang Cao are gratefully manuscript. acknowledged for assistance with electrical characterization of the polymer samples. Dr Kenny Lipkowitz, Dr Paul Armistead and Ms Patricia Irwin are acknowledged for Additional information support, discussions and general guidance. Supplementary Information accompanies this paper at http://www.nature.com/ naturecommunications Author contributions Competing financial interests: The authors declare no competing financial interests. R.R. designed and supervised the study. The high-throughput computations and combinatorial screening were performed by C.W. and G.P. (guided by R.R.). Structure Reprints and permission information is available online at http://npg.nature.com/ prediction using the evolutionary structure search scheme was performed by V.S. reprintsandpermissions/ and Q.Z. (guided by A.R.O.) and using the melt-and-quench approach by D.W.S. (guided by S.K.). Synthesis, characterization and testing of the polymers were performed by How to cite this article: Sharma, V. et al. Rational design of all organic polymer R.G.L. and R.M. (guided by G.A.S. and S.A.B.). R.R., V.S., S.K. and S.A.B. wrote and dielectrics. Nat. Commun. 5:4845 doi: 10.1038/ncomms5845 (2014). 8 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. 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Rational design of all organic polymer dielectrics

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ARTICLE Received 20 May 2014 | Accepted 29 Jul 2014 | Published 17 Sep 2014 DOI: 10.1038/ncomms5845 1,2 1,2 2,3 2,3 4 5 Vinit Sharma , Chenchen Wang , Robert G. Lorenzini , Rui Ma , Qiang Zhu , Daniel W. Sinkovits , 6 4,7,8 5 2,3 2 Ghanshyam Pilania , Artem R. Oganov , Sanat Kumar , Gregory A. Sotzing , Steven A. Boggs 1,2 & Rampi Ramprasad To date, trial and error strategies guided by intuition have dominated the identification of materials suitable for a specific application. We are entering a data-rich, modelling-driven era where such Edisonian approaches are gradually being replaced by rational strategies, which couple predictions from advanced computational screening with targeted experimental synthesis and validation. Here, consistent with this emerging paradigm, we propose a strategy of hierarchical modelling with successive downselection stages to accelerate the identification of polymer dielectrics that have the potential to surpass ‘standard’ materials for a given application. Successful synthesis and testing of some of the most promising identified polymers and the measured attractive dielectric properties (which are in quantitative agreement with predictions) strongly supports the proposed approach to material selection. 1 2 Department of Materials Science and Engineering, University of Connecticut, Storrs, Connecticut 06269, USA. Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA. Department of Chemistry, Institute of Materials Science, University of Connecticut, Storrs, Connecticut 4 5 06226, USA. Department of Geosciences and Center for Materials by Design, Stony Brook University, Stony Brook, New York 11794, USA. Department of Chemical Engineering, Columbia University, New York, New York 10027, USA. Materials Science and Technology Division (MST-8), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. Moscow Institute of Physics and Technology, 9 Institutskiy lane, Moscow 141700, Russia. Northwestern Polytechnical University, Xi’an 710072, China. Correspondence and requests for materials should be addressed to R.R. (email: [email protected]). NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 1 & 2014 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 olymeric dielectric materials are pervasive in modern screening attempted in this work, we identify attractive polymers electronics and electrical systems. They have found based on their dielectric constant and band gap values, both of 1–6 Papplications in the areas of capacitive energy storage , which can be computed with reasonable accuracy using quantum 7–9 10–12 transistors , photovoltaic devices and electrical mechanical computations. As noted earlier, dielectrics for high 13,14 insulation . The selection and design of a polymer depends energy density capacitor applications need to satisfy additional on the requirements specific to the application, which, in the case requirements, including low dielectric loss and high dielectric of dielectric applications, can be stated in terms of a subset of the breakdown strength (thus making the presently adopted screen- following properties: dielectric constant, band gap, dielectric ing criteria necessary but not sufficient conditions). Since the breakdown field, dielectric loss, morphology, glass transition current state-of-the-art does not allow us to determine these temperature, mechanical strength, cost and so on. Although the attributes quantitatively in a high-throughput framework, we use property requirements can be specified with reasonable precision, the band gap as a proxy. Recent work suggests that large values of trial and error strategies (aided by chemical intuition or the intrinsic breakdown strength of a variety of insulators are 26,27 serendipity) have dominated the identification or discovery of correlated with large band gap values . Besides, the band gap suitable candidates that meet such requirements. While and dielectric constant, in and of themselves, are important successful, these strategies suffer from the fact that they are not properties in a variety of applications. generalizable, and discoveries (and, equally importantly, the lack Our step-by-step computational search strategy to arrive at of such prospects) cannot be rigorously assessed. The community promising polymeric dielectrics is depicted schematically in Fig. 1. is thus gradually migrating towards systematic computation- This strategy includes the following successive (and to some extent, 15,16 driven materials (down) selection paradigms . iterative) steps: (1) Combinatorial chemical space exploration using Consider, for instance, the case of polymers for capacitive 1D polymerchainswithfourindependent blocks perrepeatunit; energy storage applications. The on-going electrification of (2) Promising repeat unit (that is, sequence of blocks) identification 17,18 19 land and sea transportation, as well as other military and based on band gap and dielectric constant estimates; (3) 3D 19,20 civilian systems has increased the demand for high energy structure/morphology predictions of polymers composed of the density capacitors. The choice of polymers (over ceramics) in downselected repeat units; (4) Property predictions of the 3D capacitive energy storage applications is motivated by the need systems; and (5) Synthesis of the identified polymers, followed by for ‘graceful failure’ of the dielectric at high fields. Metallized testing and validation. Steps 3–5 are time-intensive. Hence, polymers offer the only scalable capacitor technology that meets candidates identified in Step 2, which are amenable to synthesis, this need. The energy stored in a capacitor is proportional to the are favored in Steps 3–5. Application of this strategy to the design of dielectric constant and the square of the electric field. Thus, organic polymeric dielectrics for high energy density applications materials of interest should display a high dielectric constant and has identified several polymers, some of which (especially those high electrical breakdown field. In addition, low dielectric loss with prior evidence of synthesis success) are listed in Table 1. The and resistance to high field degradation of the polymer itself are top three members of Table 1 have also been synthesized by us, and important requirements as well. The present state-of-the-art in high energy density metalized film capacitors employ biaxially Step 1: Combinatorial chemical space exploration oriented polypropylene (BOPP), which has a small area (B1cm ) breakdown field of about 750 MV m and a dielectric constant Polymer block options: B B B B 4 2 4 2 -CH -, -C H -, -C H S-, of about 2.2. Various attempts to replace BOPP have been based B B 2 6 4 4 2 B B 1 1 3 3 1,21,22 -CO-, -NH-, -O-, -CS- on poly(vinyledene fluoride) (PVDF) and its copolymers , 23–25 polymer nanocomposites and so on. All such potential replacements have suffered from either high loss (PVDF and its Step 2: Promising repeat unit identification copolymers) or low breakdown field (nanofilled polymers). High-throughput density functional theory (DFT), A strategy is needed to identify promising new polymers. Effective medium theory In this contribution, we present a rational design strategy of hierarchical modelling with successive downselection stages to efficiently screen and identify advanced polymer dielectrics for Step 3: Structure/morphology predictions capacitive energy storage applications. Specifically, quantum Evolutionary structure search (based on DFT), Melt-and-quench based search (based on force fields) mechanics-based combinatorial searches of chemical space are used to identify polymer repeat units that could lead to desirable dielectric properties, followed by configurational space searches Step4 : Property predictions using evolutionary and classical molecular dynamics schemes to Dielectric tensor (using perturbation theory), band structure determine the three-dimensional (3D) arrangement of polymers (using hybrid functional), infrared and x-ray spectra (and their properties) built from the desirable repeat units. Successful synthesis and testing of some of the most promising identified polymers and the measured attractive dielectric Step 5 : Synthesis, Testing & Validation properties supports the proposed approach to material selection. Solvent casting of polymer films, infrared and x-ray spectra, dielectic spectroscopy Results Figure 1 | A schematic illustration of our rational polymer dielectric Overview. In essence, we show that a systematic combinatorial design strategy. The strategy involves five consecutive steps: (1) Combinatorial chemical space exploration, using 1D polymer chains search of the polymer chemical and configurational spaces can lead to new polymers with attractive combinations of properties. containing four independent blocks with periodic boundary conditions along the chain axis, (2) Promising repeat unit identification, by screening based By chemical space, we refer to the various building blocks (‘monomers’) in the polymer, while configurational space on band gap and dielectric constant, (3) 3D structure/morphology encompasses the connectivity sequences possible with these predictions of polymers composed of the downselected repeat units, building blocks, the manner in which the resulting chains pack (4) Property predictions of the 3D systems. Finally, (5) Synthesis testing together, and the larger scale morphology. In a first line of and validation. 2 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. Guidance based on amenability to synthesis NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 ARTICLE appear attractive based on the measured dielectric properties. In total) and the band gap for the 267 polymers, including the what follows, we describe the details of our search strategy in a step- prototypical system, polyethylene (when all four blocks are set to by-step manner. -CH -), which has the largest band gap and the smallest dielectric constant of all systems studied. As can be seen from Fig. 2a, the upper bound of the electronic part of the dielectric constant Combinatorial chemical space exploration. The first level of versus the band gap data displays a near perfect inverse screening involves the 1D catenation of repeat units into a dependence. This imposes a theoretical limit on the achievable polymer chain. In the present search, repeat units were con- electronic part of the dielectric constant, a limit that can be structed using four building blocks in the repeat unit with each understood by regarding this property as related to a sum over block drawn from the following pool of possibilities: -CH -, electronic transitions from occupied to unoccupied states .On -C H -, -C H S-, -NH-, -CO-, -O-, -CS-, as depicted in Fig. 1. 6 4 4 2 the other hand, the ionic part of the dielectric constant, which is These blocks were chosen because they are common in polymer determined by the infrared (IR)-active zone centre phonon modes backbones, including polyethylene, polyesters, polyamides, poly- (that is, the modes that display a time-varying dipole ethers and polyureas. After the elimination of obviously unstable 31,32 moment) , is not correlated with the band gap, as seen from combinations of these building blocks (such as systems contain- Fig. 2b. The ionic dielectric constant can thus be exploited to ing contiguous -CO- or -O- blocks) and accounting for transla- increase the total dielectric constant without compromising the tional and inversion symmetry, we were left with 267 unique band gap. repeat units (c.f. Supplementary Table 1). Density functional Figure 2c, which shows the variation of the total dielectric theory (DFT) computations were performed to determine the constant with the band gap, is a ‘map’ of the achievable optimal 1D structure of each of these systems, followed by combination of these properties within the chemical space the estimation of the electronic and ionic contributions to the explored. Capacitive energy storage and some electronics dielectric constant by a combination of density functional 28,29 applications, for example, gate insulations, could draw from the perturbation theory (DFPT) and effective medium theory . large dielectric constant and moderate band gap region of this The latter approach is critical as it allows us to estimate the plot. As illustrated in Fig. 2c, downselection, starting from the set dielectric constant of a macroscopic polymer based just on its 1D of 267 polymers with four-block repeat units, proceeded by 28,29 structure, as explained previously . considering the polymers with total dielectric constant 4B4eV and band gap 4B3 eV. Polymers that survive this initial Promising repeat unit identification. Figure 2 portrays the screening step are predominantly composed of at least one of relationship between the dielectric constant (electronic, ionic and the polar units, namely -NH-, -CO- and -O-, and at least one of the aromatic rings, namely -C H - and -C H S-. -NH-, -CO- and 6 4 6 2 -O- tend to enhance the ionic part of the dielectric constant, while Table 1 | Promising polymer repeat units identified at Step 2 the aromatic groups boost the electronic part. A selected of the screening process. assortment of these promising polymers (especially those with prior evidence of synthesis success) are listed in Table 1 in System repeat unit Polymer class decreasing order of total dielectric constant. Interestingly, none of NH-CO-NH-C H Polyurea 6 4 these specific polymers have been considered in the past for CO-NH-CO-C H Polyimide 6 4 dielectric applications, although a few other polymers in the NH-CS-NH-C H Polythiourea 6 4 general classes listed in Table 1 (for example, polythiourea ) have NH-C H -C H -C H Polyamine 6 4 6 4 6 4 CO-C H -CO-O Polyester, polyanhydride been shown to hold promise for dielectric applications. 6 4 C H -C H -C H -O Polyether 6 4 6 4 6 4 CH -C H -C H -O Polyether 2 6 4 6 4 CH -CO-C H -O Polyether, polyketone 2 6 4 Structure/morphology prediction. We now consider only the CH -C H -CO-O Polyester 2 6 6 top three downselected cases of Table 1, namely, [-NH-CO-NH- CH -NH-CO-NH Polyurea C H -] , [-CO-NH-CO-C H -] and [-NH-CS-NH-C H -] . 6 4 n 6 4 n 6 4 n CH -NH-CS-NH Polythiourea The 3D structure of these three polymers was determined CH -C H -CH -O Polyether 2 6 4 2 using two complementary approaches: (1) a version of the The screening was based on the estimated dielectric properties of the polymers and their Universal Structure Predictor: Evolutionary Xtallography amenability to synthesis (past synthesis efforts, when available, are cited). The top three 33–37 (USPEX) method specially modified to handle repeat units polymers were taken all the way to Step 5 (synthesis and testing). rather than atoms as the building blocks, and (2) a classical ab c 0.1 Polyethylene Electronic Ionic Total 1 1 0.01 12 3 45 67 8 12 3 45678 12 3 45678 Band gap (eV) Band gap (eV) Band gap (eV) Figure 2 | The dielectric constant versus band gap relationship of 1D polymers. Computed (a) electronic, (b) ionic and (c) total dielectric constant (along the polymer chain axis) as a function of the band gap. The associated errors in the dielectric constant computed using density functional perturbation theory for single chains, and subsequently estimated using effective medium theory for a bulk environment are also shown. The highlighted region corresponds to the most ‘promising repeat units’ composed of at least one of -NH-, -CO- and -O-, and at least one of -C H - and –C H S- blocks. 6 4 6 2 Band gap was computed using the HSE06 electronic exchange-correlation functional. NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 3 & 2014 Macmillan Publishers Limited. All rights reserved. Dielectric constant Dielectric constant Dielectric constant ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 O O H H H ab c N N N O S n n 15 15 15 Biherringbone E = 3.5 eV,  = 5.7,  = 4.0 g t e 10 10 10 Parallel Herringbone-diagonal Parallel-diagonal E = 3.5 eV,  = 5.2,  = 4.1 E = 2.9 eV,  = 5.3,  = 4.3 g t e g t e E = 4.2 ev,  = 4.5,  = 3.1 g t e Alternating-diagonal 5 5 5 E = 3.7 eV,  = 5.2,  = 4.1 g t e Alternating-diagonal Alternating-parallel Parallel-diagonal E = 4.1 eV,  = 4.3,  = 3.2 0 0 g t e E = 3.0 eV,  = 6.0,  = 4.2 g t e E = 4.0 eV,  = 5.7,  = 4.0 g t e Figure 3 | Predicted properties and structures of the identified promising polymers. The repeat units of the three identified polymers are (a) [-NH-CO-NH-C H -] (b) [-CO-NH-CO-C H -] and (c) [-NH-CS-NH-C H -]. The crystal structures of [-NH-CO-NH-C H -] are predicted by 6 4 6 4 6 4 6 4 evolutionary structure search (using DFT) and melt-and-quench (using force-field (FF)) schemes, while in other two polymers only evolutionary structure search (using DFT) method has been used. The zero of the energy scale corresponds to the most stable structures. For each predicted structure, the calculated values of the band gap (E ), total (E ) and electronic (E ) part of dielectric constants are also listed. g t e ab c Biherringbone Biherringbone Parallel-diagonal Expt. 6 Alternating-diagonal Herringbone-diagonal Herringbone -diagonal 5 Herringbone-diagonal Biherringbone Alternating-diagonal Alternating -diagonal Parallel-diagonal Parallel- –1 diagonal Expt. –2 Expt. Expt. –3 10 20 30 40 50 60 70 500 1,000 1,500 2,000 2,500 10 100 1k –1 2 (degree) Wavenumber (cm ) Frequency (Hz) Figure 4 | Experimental and predicted data for the polymer with repeat unit [-NH-CO-NH-C H -]. (a) X-ray diffraction data (b) IR spectra, 6 4 and (c) dielectric spectra (top panel) and loss factor (bottom panel). Expt, experimental. molecular dynamics based melt-and-quench approach. the orientational average ranging from 4 to 6, double that of The former used DFT energetics (here used with 4 repeat units polyethylene or polypropylene. The electronic part of the per unit cell) and hence provide ground state (0 K) results, while dielectric constant for all polymers ranges from 3 to 4, placing the latter used a newly generated force field and hence could treat these with polymers that display the highest known refractive much larger systems containing thousands of repeat units per indices . Assuming that the predicted ground state structures 36,37 unit cell at nonzero temperatures. Both the modified USPEX remain stable at elevated temperatures close to room and the melt-and-quench schemes lead to several low energy temperatures (a reasonable assumption based on the discussion configurations, which were equivalent within the expected above), the predicted band gaps and dielectric constants are uncertainties of the force-field and DFT energy predictions. expected to be valid at those elevated temperatures as well. In This is reassuring as it indicates that the ground state structures situations when amorphous polymeric phases are expected in predicted by DFT are expected to be stable at higher temperatures reality (aided by competing energetics or favourable kinetics), as well. Figure 3 shows the energetic ordering of a few low energy some deviations in the dielectric constant with respect to those structures for each of the three polymers considered at this stage. predicted here is to be expected. Nevertheless, as dielectric Simulated X-ray diffraction (XRD) and infrared (IR) spectra behaviour is generally dominated by local chemistry and bonding, based on the predicted low energy structures for all three the deviations are expected to be small (see discussion below polymers are presented in Figs 4–6, and discussed and compared pertaining to the [-CO-NH-CO-C H -] and [-NH-CS-NH- 6 4 n with measurements below. C H -] polymers). The predicted values of the total (E ) and 6 4 n t electronic (E ) parts of dielectric constants for all three polymers considered are listed in Fig. 3. As can be seen, the fidelity of the Property predictions. The computed band gap values of all the predictions of Step 2 persist at Step 4 of our process (insofar as identified low energy structures are listed in Fig. 3. As can be seen, the band gap and dielectric constant values are concerned). except in the case of [-NH-CS-NH-C H -] , the band gap (E ) 6 4 n g values are over 3.5 eV for all identified structures. Computed electronic band structure and density of states are shown in Validation through synthesis and testing. Synthesis of the Supplementary Information (c.f. Supplementary Figure 1). The [-NH-CO-NH-C H -] , [-CO-NH-CO-C H -] and [-NH-CS- 6 4 n 6 4 n dielectric constants were determined using DFPT, with results for NH-C H -] polymers proceeded via adaptation of previous 6 4 n 4 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. Energy (meV per atom) Intensity (a.u.) Transmittance Loss (tan ) Dielectric constant NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 ARTICLE ab c Parallel- Parallel-diagonal 5 Parallel-diagonal diagonal Expt. Alternating-diagonal Alternating-diagonal Alternating- 3 diagonal –1 Expt. –2 Expt. Expt. –3 10 100 1k 10 20 30 40 50 60 70 500 1,000 1,500 2,000 2,500 –1 2 (degree) Wavenumber (cm ) Frequency (Hz) Figure 5 | Experimental and predicted data for the polymer with repeat unit [-CO-NH-CO-C H -]. (a) X-ray diffraction data (b) IR spectra, 6 4 and (c) dielectric spectra (top panel) and loss factor (bottom panel). Expt, experimental. ab c Parallel Parallel Expt. Alternating-parallel Alternating-parallel 5 Parallel Alternating- parallel –1 Expt. –2 Expt. Expt. –3 10 20 30 40 50 60 70 500 1,000 1,500 2,000 2,500 10 100 1k –1 2 (degree) Wavenumber (cm ) Frequency (Hz) Figure 6 | Experimental and predicted data for the polymer with repeat unit [-NH-CS-NH-C H -]. (a) X-ray diffraction data (b) IR spectra, 6 4 and (c) dielectric spectra (top panel) and loss factor (bottom panel). Expt, experimental. efforts . Measurements were performed on pressed pellets of the (over all directions) total dielectric constant values for all four synthesized polymers. The measured band gap values of the three predicted [-NH-CO-NH-C H -] crystal structures. Once again, 6 4 n polymers are 3.9 eV, 4.0 eV and 3.1 eV, respectively, in good the agreement between measurement and predictions is excellent. agreement with the predictions listed in Fig. 3. The predicted XRD spectra of the [-CO-NH-CO-C H -] , and 6 4 n Considering [-NH-CO-NH-C H -] first (Fig. 4a), a character- [-NH-CS-NH-C H -] polymers (Figs 5a and 6a) do not match 6 4 n 6 4 n istic double peak in the XRD spectra at 2yE20 can be seen for well with the measured spectra, which display broad peaks. This all the predicted structures except the ‘biherringbone’ case, in line indicates that the synthesized and cast [-CO-NH-CO-C H -] 6 4 n with the measurements, with the agreement being best for the and [-NH-CS-NH-C H -] polymers are in semicrystalline or 6 4 n ‘parallel-diagonal’ case. The correspondence between the amorphous form. On the other hand, the measured and measured IR spectrum (Fig. 4b) and that of the four predicted calculated IR spectra (Figs 5b and 6b) are in good agreement structures is uniformly good. This is not surprising as the IR for both [-CO-NH-CO-C H -] and [-NH-CS-NH-C H -] for 6 4 n 6 4 n peaks are dominated by intra-chain ‘bonded’ interactions. Such the same reasons identified above in the discussion of the interactions are roughly the same for all four predicted structures, [-NH-CO-NH-C H -] polymer. The measured dielectric con- 6 4 n which differ largely only in the manner in which the individual stant of [-CO-NH-CO-C H -] is in the range of 4.2–4.8 and that 6 4 n chains are packed. Based on these findings, we conclude that the of [-NH-CS-NH-C H -] is in the 5.7–6.7 range, both in good 6 4 n [-NH-CO-NH-C H -] polymer is dominated by regions of agreement with predictions (shown in Figs 5c and 6c, and in 6 4 n ‘parallel-diagonal’ structure, although smaller portions of the Fig. 3), despite the fact that the predictions are made for the other three structures cannot be ruled out at or close to room crystalline varieties of these polymers. Both polymers display temperatures. dielectric loss larger than that of the [-NH-CO-NH-C H -] . 6 4 n Figure 4c portrays the dielectric spectrum for the synthesized [-NH-CO-NH-C H -] polyurea system. Across a wide frequency 6 4 n range, the dielectric constant is in the 5.4–5.8 range, and the Discussion dielectric loss at 1 kHz is in the range of 1%, an acceptable value We have outlined a rational procedure for systematically for some applications. Figure 4c also shows the computed average exploring polymer chemical spaces and identifying potentially NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 5 & 2014 Macmillan Publishers Limited. All rights reserved. Intensity (a.u.) Intensity (a.u.) Transmittance Transmittance Loss (tan ) Dielectric constant Loss (tan ) Dielectric constant ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 useful dielectrics based on the dielectric constant and band Structure prediction using evolutionary algorithm. A specifically designed 36,37 33–35,37 constrained evolutionary algorithm , embodied in the USPEX code was gap as initial screening criteria. This procedure is computationally used to predict polymeric crystal structures starting from the single polymeric driven (with ample guidance from chemical intuition and chains discussed above (using first-principles quantum mechanical computations synthesis considerations) and uses a combination of quantum for the total ground state energy of the crystals). This newly developed method mechanical calculations, force-field simulations and structure uses a specification of well-defined molecular repeat units rather than individual atoms as the starting point . The diversity of the population of structures is and property prediction schemes in a hierarchical manner. enhanced by using space-group symmetry combined with random cell parameters, A class of organic polymers involving seven distinct building 36,37 and random positions and orientations of the molecular units . During the blocks was screened using this approach and several promising evolutionary optimization, structures with different sequence and packing of these polymers were identified. A common feature of these down- repeat units are generated and relaxed. We performed multiple runs of evolutionary search with two and four repeat units. The total energies were selected polymers is the occurrence of at least one of the polar obtained with the PBE exchange-correlation functionals using the dispersion units, -NH-, -CO- and -O-, and at least one of the aromatic correction prescribed by the vdW-TS approach . In all cases considered here, the rings, -C H - and -C H S-. Three of the most promising cases 6 4 6 2 energetic orderings are invariant with respect to the choice of different exchange- were synthesized and tested. The favourable agreement correlation functionals. between the measured and predicted (structural, electronic and dielectric) properties of all three polymers, and the low Structure prediction using the melt-and-quench scheme. The simulations dielectric loss of one of these (namely, [-NH-CO-NH-C H -] ) 54 6 4 n were performed using the LAMMPS molecular dynamics package and the provides validation and hope for such a rational computationally OPLS-2005 force field . The polymer [-NH-CO-NH-C H -]n requires a torsion 6 4 potential for N-C-N-CA (where CA is an aromatic carbon) which is not present in driven approach for materials discovery. Indeed, processable the force field. This potential was calculated using the molecule CO-(NH-C H ) 6 4 2 variants of the polymers identified here are presently being via fitting to the difference in energy, between using the force field and using further evaluated. Hartree–Fock 6-31G*, minimized under constraint of the two torsions of this type While the present development is certainly a significant in a series of calculations to sweep out the full range of motion. To make the torsion potential fit all configurations satisfactorily, it was necessary to modify advance over empiricism, consistent with the emerging paradigm 15,16 the atomic partial charges. These were set to match Mulliken charges scaled down of computation-driven materials (down)selection , it is only by a factor of 1.86, and the charges of H and CA bonded to N were adjusted to an initial attempt that should be extended by including other ensure a good fit. critical properties in the screening process. Such properties Two kinds of simulations were performed, which differed in whether the polymers were terminated with an end group within the periodic cell or whether include dielectric loss, dielectric breakdown strength, mechanical they were covalently bonded to the other end of the polymer via the periodic behaviour, glass transition temperature and charge carrier wrapping. The first set consisted of 18mer chains terminating in phenyl rings. mobility. The current state-of-the-art limits our ability to A single chain was quenched into a straight conformation corresponding to the predict these properties rapidly and with high fidelity. It is minimization of all bonds, angles and torsions. The single chain was replicated in a 6 6 rectangular array. The system was heated at 1 K ps , and the structure was hoped that recent advances in data-driven and first-principles observed to change between 800 and 860 K. The 860 K configuration was selected methodologies will allow us overcome these limitations with for cooling at various rates. At the cooling rate of  10 K ps , a ‘parallel’ crystal 16,40 time . While the present effort has focussed primarily on was produced with a ‘herringbone’ defect, but cooling at 1ps produced a high energy density capacitor dielectrics, polymers for other perfect ‘parallel’ crystal. After further study, this melt-and-quench process was applications (for example, organic semiconductors or organic repeated starting with a perfect ‘parallel-diagonal’ crystal. During heating at 1Kps , this crystal underwent two transitions between 710 and 810 K before photovoltaics) can be identified in a systematic manner using an showing signs of melting at 850 K. The 820 K configuration cooled at either 1or extended version of the present strategy by considering other 0.1 K ps yielded a ‘biherringbone’ crystal. relevant screening criteria and many types of blocks. The second set of simulations consisted of a 4 4 array of 4mer chains connected to themselves through the periodic boundary, making them effectively infinite. Owing to the periodic restriction, nematic order remains at very high temperatures (1,000 K). Crystals were obtained by cooling from this high- Methods temperature state. The initial configuration of the crystals before heating is thus First-principles computations. The quantum mechanical computations were immaterial. Usually, the ‘herringbone’ configuration was obtained, in both fast performed using DFT as implemented in the Vienna ab initio software 1  1 ( 10 K ps ) and slow quenches ( 0.05 K ps ), but two cases resulted in 41,42 package . The generalized gradient approximation functional, parametrized by 1  1 ‘biherringbone’ configurations ( 10 K ps ,  0.2 K ps ). ‘Parallel’ crystals Perdew, Burke and Ernzerhof (PBE) to treat the electronic exchange-correlation were never obtained after cooling if the system had been heated 4900 K. interaction, the projector augmented wave potentials and plane-wave basis functions up to a kinetic energy cutoff of 500 eV, were employed. The supercells were relaxed using a conjugate gradient algorithm until the forces on all atoms Synthesis and characterization details. For the synthesis of the first two poly- were o0.02 eV Å . As the PBE functional is known to underestimate band gaps mers, namely, [-NH-CO-NH-C H -] and [-CO-NH-CO-C H -], a flame-dried, 6 4 6 4 of insulators, the Heyd Scuseria Ernzerhof HSE06 functional was used to argon-flushed 125 ml round bottom flask equipped with a reflux condenser, obtain corrected band gap values for all systems considered. gas inlet, magnetic stirbarand 50-ml dry dimethylsulphoxide were used. In the The 1D systems considered in Step 1 were composed of all-trans infinitely polyurea case [-NH-CO-NH-C H -], equimolar amounts of p-phenylene diiso- 6 4 long isolated chains containing four independent building units in a supercell cyanate and p-phenylenediamine were used, while for the polyimide [-CO-NH- geometry (with periodic boundary conditions along the axial direction). In a CO-C H -], equimolar amounts of terephthalamide and terephthaloyl chloride 6 4 combinatorial and exhaustive manner, each block in the polymer backbone was were used (35 mmol). The mixtures were heated at 350 K for 8 h under pre-purified allowed to be one of the following units: -CH -, -NH-, -C(¼ O)-, -C H - argon, after which they were poured into dry tetrahydrofuran. The white solid 2 6 4 (benzene), -C H S- (thiophene), -C(¼ S)- or -O-, which are commonly seen in precipitates were filtered and washed copiously in fresh tetrahydrofuran, followed 4 2 29,46,47 polymer backbones . The scheme results in 267 symmetry unique cases. by drying in vacuo. The yields for the polyurea and polyimide were nearly A Monkhorst–Pack k-point mesh of 1 1 k (with kc 450) was used to quantitative. produce converged results for a supercell of length c (Å) along the chain The following synthesis route was adopted for the [-NH-CS-NH-C H -] 6 4 direction (that is, the z direction). The stress component along the z direction was polymer. To a dry 100 ml three-neck flask, 0.9614 g (5 mmol) of p-phenylene required to be o1.0 10 GPa. The dielectric permittivity of the isolated diisothiocyanate and 10 ml dry dimethylsulfoxide were added under nitrogen with 48,49 polymer chains placed in a large supercell was first computed within the DFPT stirring, followed by the addition of 0.5407 g (10 mmol) of p-phenylenediamine. formalism, which includes contributions from the polymer as well as from the The reaction was carried out at room temperature. After 6 h, a white powder surrounding vacuum region of the supercell. Next, treating the supercell as a crashed out of the solution. The mixture was poured into 150 ml of methanol, vacuum-polymer composite, effective medium theory was used to estimate the filtered and washed with methanol several times, and dried in vacuo. A white solid dielectric constant of just the polymer chains using methods described was obtained at 89% yield (1.337 g). 28,29 recently . XRD patterns were obtained on a Bruker D5005 X-ray diffractometer equipped In the case of polymer crystals (discussed below), van der Waals interactions with a 2.2 kW copper X-ray tube. The dielectric spectra were obtained on an were taken into account using the vdW-TS functional . Phonon dispersion curves IMASS time domain dielectric spectrometer. Measurements were taken by were calculated using the supercell approach with the finite displacement method sandwiching a pressed pellet of material between silicone rubber guarded 52 53 as implemented in the PHONOPY code , while FullProf suite was used to electrodes. Pellets were prepared in a hydraulic press with a 1 inch circular pellet simulate the XRD patterns. mould. IR spectra were obtained on a Nicolet Magna-IR 560 spectrometer using 6 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. 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B 110, 12860–12864 (2006). DMR-1231586), DARPA (Grants No. W31P4Q1310005, and No. W31P4Q1210008), NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications 7 & 2014 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5845 grant of the Government of the Russian Federation (No. 14.A12.31.0003) and CRDF shaped the manuscript. All authors discussed the results and commented on the Global (UKE2-7034-KV-11). Ms JoAnne Ronzello and Dr Yang Cao are gratefully manuscript. acknowledged for assistance with electrical characterization of the polymer samples. Dr Kenny Lipkowitz, Dr Paul Armistead and Ms Patricia Irwin are acknowledged for Additional information support, discussions and general guidance. Supplementary Information accompanies this paper at http://www.nature.com/ naturecommunications Author contributions Competing financial interests: The authors declare no competing financial interests. R.R. designed and supervised the study. The high-throughput computations and combinatorial screening were performed by C.W. and G.P. (guided by R.R.). Structure Reprints and permission information is available online at http://npg.nature.com/ prediction using the evolutionary structure search scheme was performed by V.S. reprintsandpermissions/ and Q.Z. (guided by A.R.O.) and using the melt-and-quench approach by D.W.S. (guided by S.K.). Synthesis, characterization and testing of the polymers were performed by How to cite this article: Sharma, V. et al. Rational design of all organic polymer R.G.L. and R.M. (guided by G.A.S. and S.A.B.). R.R., V.S., S.K. and S.A.B. wrote and dielectrics. Nat. Commun. 5:4845 doi: 10.1038/ncomms5845 (2014). 8 NATURE COMMUNICATIONS | 5:4845 | DOI: 10.1038/ncomms5845 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved.

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Nature Communications – Springer Journals

Published: Sep 17, 2014

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