Highly Fluorinated Comb‐Shaped Copolymers as Proton Exchange Membranes (PEMs): Improving PEM Properties Through Rational Design

A new class of comb‐shaped polymers for use as a proton conducting membrane is presented. The polymer is designed to combine the beneficial physical, chemical, and structural attributes of fluorinated Nafion‐like materials with higher‐temperature, polyaromatic‐based polymer backbones. The comb‐shaped polymer unites a rigid, polyaromatic, hydrophobic backbone with lengthy hydrophilic polymer side chains; this combination affords direct control over the polymer nanostructure within the membrane and results in distinct microphase separation between the opposing domains. The microphase separation serves to compartmentalize water into the hydrophilic polymer side chain domains, resulting in effective membrane water management and excellent proton conductivities.     

Highly Efficient Microscopic Charge Transport within Crystalline Domains in a Furan‐Flanked Diketopyrrolopyrrole‐Based Conjugated Copolymer

Elucidating the interrelation between the molecular structure and charge transport properties in conjugated polymer thin films is an essential issue in developing the design principle of high‐performance polymer materials for application in organic electronics. In particular, the backbone planarity is suggested to be a key element that governs the transport performance, especially in recently developed donor–acceptor (D–A)‐type copolymers exhibiting high mobility, whereas the direct evaluation of the intrinsic transport performance, usually realized only within the small crystalline domains, is difficult by using conventional macroscopic measurements. Here, it is demonstrated that a D–A type copolymer, PDPPF‐DTT, which consists of furan‐flanked diketopyrrolopyrrole (DPP) and dithienothiophene (DTT) units in the conjugated backbone, exhibits a highly efficient charge transport performance within the crystalline domains with a remarkably low activation energy of less than 8 meV, based on microscopic measurements using field‐induced electron spin resonance spectroscopy. This high transport performance is primarily caused by the high backbone planarity realized by introducing furan‐flanked DPP and fused dithienothiophene units, which is demonstrated from the density functional theory calculations. This result provides a microscopic indication of the effectiveness of the present molecular design to produce a planar backbone and realize highly efficient charge transport performance.     

ε‐Branched Flexible Side Chain Substituted Diketopyrrolopyrrole‐Containing Polymers Designed for High Hole and Electron Mobilities

Based on the integrated consideration and engineering of both conjugated backbones and flexible side chains, solution‐processable polymeric semiconductors consisting of a diketopyrrolopyrrole (DPP) backbone and a finely modulated branching side chain (ε‐branched chain) are reported. The subtle change in the branching point from the backbone alters the π?π stacking and the lamellar distances between polymer backbones, which has a significant influence on the charge‐transport properties and in turn the performances of field‐effect transistors (FETs). In addition to their excellent electron mobilities (up to 2.25 cm² V^?1 s^?1), ultra‐high hole mobilities (up to 12.25 cm² V^?1 s^?1) with an on/off ratio (I_on/I_off) of at least 10⁶ are achieved in the FETs fabricated using the polymers. The developed polymers exhibit extraordinarily high electrical performance with both hole and electron mobilities superior to that of unipolar amorphous silicon.     

Toward the Prediction and Control of Glass Transition Temperature for Donor–Acceptor Polymers

Semiconducting donor–acceptor (D–A) polymers have attracted considerable attention toward the application of organic electronic and optoelectronic devices. However, a rational design rule for making semiconducting polymers with desired thermal and mechanical properties is currently lacking, which greatly limits the development of new polymers for advanced applications. Here, polydiketopyrrolopyrrole (PDPP)‐based D–A polymers with varied alkyl side‐chain lengths and backbone moieties are systematically designed, followed by investigating their thermal and thin film mechanical responses. The experimental results show a reduction in both elastic modulus and glass transition temperature (T_g) with increasing side‐chain length, which is further verified through coarse‐grained molecular dynamics simulations. Informed from experimental results, a mass‐per‐flexible bond model is developed to capture such observation through a linear correlation between T_g and polymer chain flexibility. Using this model, a wide range of backbone T_g over 80 °C and elastic modulus over 400 MPa can be predicted for PDPP‐based polymers. This study highlights the important role of side‐chain structure in influencing the thermomechanical performance of conjugated polymers, and provides an effective strategy to design and predict T_g and elastic modulus of future new D–A polymers.     

Proton Conductor Confinement Strategy for Polymer Electrolyte Membrane Assists Fuel Cell Operation in Wide-Range Temperature

Acid loss and plasticization of phosphoric acid (PA)-doped polymer electrolyte membranes are critical hampers for its actual application especially during startup/shutdown stages due to the produced water and thermal stress. To conquer these barriers, a proton conductor confinement strategy is introduced, which may trap PA molecules in the side-chain acidophilic microphase and weaken plasticizing effect caused by PA toward the polymer backbone to remain membrane tensile stress. The grafted polyphenylene oxide (PPO) is synthesized as model polymers, both molecular electrostatic potential and molecular dynamics reveal the retention mechanism between PA and side-chain of PPO as well as the aggregation state of PA. Through precisely regulating polymer side-chain structure and defined plasticization quantitative indicator, significant refinements in membrane's conductivity, durability, and single-cell performance are achieved successfully. The designed PPO membranes exhibit ultra-fast and stable proton conducting even at low proton carrier concentrations and under wide-range working temperature between 80 ^oC–180 °C as well as satisfied resistance to harsh accelerated aging test. These insights will shed light on holistic understanding of PA interactions and retention from molecular level, and provide radical approaches toward high-performance PA/PEMs design.     

Printing 2D Conjugated Polymer Monolayers and Their Distinct Electronic Properties

Recently, 2D monolayer films of conjugated polymers have gained increasing attention owing to the preeminence of 2D inorganic films that exhibit unique optoelectronic and mechanical properties compared to their bulk analogs. Despite numerous efforts, crystallization of semiconducting polymers into highly ordered 2D monolayer films still remains challenging. Herein, a dynamic‐template‐assisted meniscus‐guided coating is utilized to fabricate continuous, highly ordered 2D monolayer films of conjugated polymers over a centimeter scale with enhanced backbone π–π stacking. In contrast, monolayer films printed on solid substrates confer upon the 1D fiber networks strong alkyl side‐chain stacking at the expense of backbone packing. From single‐layers to multilayers, the polymer π‐stacks change from edge‐on to bimodal orientation as the film thickness reaches ≈20 nm. Spectroscopic and cyclic voltammetry analysis reveals an abrupt increase in J‐aggregation and absorption coefficient and a decrease in bandgap and highest occupied molecular orbital level until critical thickness, possibly arising from the straightened polymer backbone. This is corroborated by an abrupt increase in hole mobility with film thickness, reaching a maximum of 0.7 cm² V^?1 s^?1 near the critical thickness. Finally, fabrication of chemical sensors incorporating polymer films of various thicknesses is demonstrated, and an ultrahigh sensitivity of the ≈7 nm thick ultrathin film (bilayers) to 1 ppb ammonia is shown.     

Investigations into inward positioned 3,3′-Dihexylditheinylbenzothiadiazole (DTBTh)-Benzodithiophene (BDT) based polymer solar cells by controlling molecular weight and alkyl side chain

In previous studies, PSCs based on polymers with an inward alkyl positioned DTBT unit showed poor power conversion efficiency mainly due to the greatly distorted polymer backbone structure caused by severe steric hindrance between the alkyl groups on the flanking thiophene of DTBT and the BT unit. In this study, PSCs based on polymers with an inward alkyl positioned DTBT unit are markedly improved by controlling the molecular weight and alkyl chain length. Two BDT-DTBTs and one BDT-BT polymers were synthesized by engineering alkylthienyl chains on BDT and by installing these with a short alkyl chain on the inward alkyl positioned DTBT. Extraordinary bathochromic shifts in the absorption maxima at 146 nm for PA and 165 nm for PB were observed going from solution to a solid film state, suggesting great differences in the polymer structures of the two states. Optical and electrochemical measurements were taken, and the HOMO levels of PA, PB, and PC were determined to be −5.76, −5.66, and −5.71 eV, respectively, indicating very low-lying HOMO energy levels. The optimized PSCs based on PA, PB, and PC exhibit power conversion efficiencies (PCEs) of 3.75%, 2.42%, and 2.30%, respectively, with V_oc (0.77–0.86 V), J_sc (6.9–8.7 mA/cm²), and FF (38–52%). We believe that the highest PCE for the PSCs based on PA may be attributed to the high molecular weight and improved processability relative to those of PB and PC. A theoretical study suggests that the polymer backbones of PA and PB are highly distorted between the donor unit and the acceptor unit, by as much as 49°, possibly by the steric hindrance between BT and the inward positioned methyl group on the flanking thiophene. Therefore, the conjugations for the HOMO p-orbitals of PA and PB are highly localized throughout the backbone while the conjugations for the HOMO p-orbitals of PC are well delocalized. The AFM study revealed that DIO additive greatly changed the morphology of the polymer blend from an amorphous state into distinct nanoscale phase separated states, leading to a great improvement in PCEs. The XRD study revealed that all polymers are amorphous.     

Constructing High-Efficiency Orange-Red Thermally Activated Delayed Fluorescence Polymers by Excited State Energy Levels Regulation via Backbone Engineering

Thermally activated delayed fluorescence (TADF) materials have attracted extensive attention because of their 100% theoretical exciton utilization. Solution-processable orange-red TADF polymers are one of indispensable participants. Herein, a series of orange-red TADF polymers with dibenzothiophene (DBT) and carbazole (Cz) units as joint backbones are synthesized. Their performance can be successfully optimized by regulating the connection positions of DBT units through backbone engineering. It is found that the pNAI37 series with DBT units embedded in the polymeric backbones at the 3, 7 sites display a better performance than those connected at the 2, 8 sites. The optimal polymer, pNAI3705, exhibits a better excited state nature, leading to the photoluminescence quantum yield of 60%. Consequently, pNAI3705 based organic light-emitting diodes reach a maximum external quantum efficiency of 20.16%, and maintain 10.61% at 500 cd m⁻², which is in first tier among orange-red polymers. These results unambiguously suggest the potential application of the combined DBT and Cz backbones in TADF polymers. This design strategy may provide a versatile approach for optimizing the properties of TADF polymers through backbone engineering.     

A diketopyrrolopyrrole-based regular terpolymer bearing two different π-extended donor units and its application in solar cells

In this study, to adjust the desired molecular energy levels and bandgap energies of polymers for photovoltaic applications, a regular terpolymer structure was designed. A new regular terpolymer, poly(DPP4T-alt-TBP), containing diketopyrrolopyrrole (DPP), BT, and BP units in the repeating group was successfully synthesized. The DPP-BT monomeric unit in polymer backbone enhanced chain packing and induced a high-lying highest occupied molecular orbital (HOMO) level and the DPP-BP segment induced a deeper HOMO level. The lowest unoccupied molecular orbital (LUMO) level of the terpolymer was also controlled in a similar manner. The HOMO level of the terpolymer was similar to that of poly(DPP-alt-BP), and the energies of the LUMOs were governed by the DPP-BT unit. The polymer chain arrangement of the terpolymer on the substrate was observed to be a mix of face-on and edge-on orientations, which is a different chain arrangement mode to those shown in both poly(DPP-alt-BP) and poly(DPP-alt-BT). A TFT fabricated with poly(DPP4T-alt-TBP) had a charge carrier mobility of 0.59 cm² V⁻¹ s⁻¹ and a moderately high current on/off ratio. Furthermore, a polymer solar cell containing the terpolymer and PC₇₁BM had a power conversion efficiency of 4.54%, which is significantly higher than those of the PCEs of poly(DPP-alt-BP) and poly(DPP-alt-BT)-based solar cells with identical device configurations.     

Impact of Polystyrene Oligomer Side Chains on Naphthalene Diimide–Bithiophene Polymers as n‐Type Semiconductors for Organic Field‐Effect Transistors

A series of naphthalene diimide‐based conjugated polymers are prepared with various molar percentage of low molecular weight polystyrene (PS) oligomer of narrow polydispersity as the side chain. The PS side chains are incorporated through preparation of a macromonomer by chain termination of living anionic polymerization. The effects of the PS side chains amount (0–20 mol%) versus overall sidechain on the electrical properties of the resulting polymers as n‐type polymer semiconductors in field‐effect transistors are investigated. We observe that all the studied polymers show similarly high electron mobility (≈0.2 cm² V^?1 s^?1). Importantly, the polymers with high PS side chain content (20 mol%) show a significantly improved device stability under ambient conditions, when compared to the polymers at lower PS content (0–10 mol%). By comparing this observation to the physical blending of the conjugated polymer with PS, we attribute the improved stability to the covalently attached PS side chains potentially serving as a molecular encapsulating layer around the conjugated polymer backbone, rendering it less susceptible to electron traps such as oxygen and water molecules.     

Electron–Hole Recombination in Uniaxially Aligned Semiconducting Polymers

A promising, general strategy for improving performance of optoelectronic devices based on conjugated polymer semiconductors is to make better use of the fast intrachain transport along the covalently bonded polymer backbone. Little is known, however, about how the recombination rate between electrons and holes would be affected in device structures in which current flow is primarily along the polymer chain. Here a light‐emitting field effect transistor (LFET) structure with a uniaxially aligned semiconducting polymer is used to show that the width and shape of the recombination zone depend strongly on polymer alignment. For alignment of the polymer parallel to the current the emission zone is 5–10 times wider than for perpendicular alignment. 2D drift‐diffusion modeling is used to show that such significant widening of the recombination zone in the case of parallel alignment implies that the recombination rate constant is more than 100 times lower than expected for standard Langevin recombination. On the basis of Monte Carlo modeling it is proposed that such unexpected weak recombination is a result of the significant mobility anisotropy of the aligned polymer. These results provide new fundamental insight into the recombination physics of polymer semiconductors.     

Systematic Investigation of Side‐Chain Branching Position Effect on Electron Carrier Mobility in Conjugated Polymers

Recently, polymer field‐effect transistors have gone through rapid development. Nevertheless, charge transport mechanism and structure‐property relationship are less understood. Here we use strong electron‐deficient benzodifurandione‐based poly(p‐phenylene vinylene) ( BDPPV ) as polymer backbone and develop six BDPPV ‐based polymers ( BDPPV‐C1 to C6 ) with various side‐chain branching positions to systematically study the side‐chain effect on device performance. All the polymers exhibited ambient‐stable n‐type transporting behaviors with the highest electron mobility of up to 1.40 cm² V^?1 s^?1. The film morphologies and microstructures of all the six polymers were systematically investigated. Our results demonstrate that the interchain π–π stacking distance decreases as moving the branching position away from polymer backbones, and an unprecedentedly close π–π stacking distance down to 3.38 Å is obtained for BDPPV‐C4 to C6 . Nonetheless, closer π–π stacking distance does not always correlate with higher electron mobility. Polymer crystallinity, thin film disorder, and polymer packing conformation, which all influenced by side‐chain branching position, are proved to show significant influence on device performance. Our study not only reveals that π–π stacking distance is not the decisive factor on carrier mobility in conjugated polymers but also demonstrates that side‐chain branching position engineering is a powerful strategy to modulate and balance these factors in conjugated polymers.     

Electronic Structure of Self‐Assembled Monolayers on Au(111) Surfaces: The Impact of Backbone Polarizability

Modifying metal electrodes with self‐assembled monolayers (SAMs) has promising applications in organic and molecular electronics. The two key electronic parameters are the modification of the electrode work function because of SAM adsorption and the alignment of the SAM conducting states relative to the metal Fermi level. Through a comprehensive density‐functional‐theory study on a series of organic thiols self‐assembled on Au(111), relationships between the electronic structure of the individual molecules (especially the backbone polarizability and its response to donor/acceptor substitutions) and the properties of the corresponding SAMs are described. The molecular backbone is found to significantly impacts the level alignment; for molecules with small ionization potentials, even Fermi‐level pinning is observed. Nevertheless, independent of the backbone, polar head‐group substitutions have no effect on the level alignment. For the work‐function modification, the larger molecular dipole moments achieved when attaching donor/acceptor substituents to more polarizable backbones are largely compensated by increased depolarization in the SAMs. The main impact of the backbone on the work‐function modification thus arises from its influence on the molecular orientation on the surface. This study provides a solid theoretical basis for the fundamental understanding of SAMs and significantly advances the understanding of structure–property relationships needed for the future development of functional organic interfaces.     

Halogen Bonding versus Hydrogen Bonding in Driving Self‐Assembly and Performance of Light‐Responsive Supramolecular Polymers

Halogen bonding is arguably the least exploited among the many non‐covalent interactions used in dictating molecular self‐assembly. However, its directionality renders it unique compared to ubiquitous hydrogen bonding. Here, the role of this directionality in controlling the performance of light‐responsive supramolecular polymers is highlighted. In particular, it is shown that light‐induced surface patterning, a unique phenomenon occurring in azobenzene‐containing polymers, is more efficient in halogen‐bonded polymer–azobenzene complexes than in the analogous hydrogen‐bonded complexes. A systematic study is performed on a series of azo dyes containing different halogen or hydrogen bonding donor moieties, complexed to poly(4‐vinylpyridine) backbone. Through single‐atom substitution of the bond‐donor, control of both the strength and the nature of the noncovalent interaction between the azobenzene units and the polymer backbone is achieved. Importantly, such substitution does not significantly alter the electronic properties of the azobenzene units, hence providing us with unique tools in studying the structure–performance relationships in the light‐induced surface deformation process. The results represent the first demonstration of light‐responsive halogen‐bonded polymer systems and also highlight the remarkable potential of halogen bonding in fundamental studies of photoresponsive azobenzene‐containing polymers.     

On the Impact of Linear Siloxanated Side Chains on the Molecular Self-Assembling and Charge Transport Properties of Conjugated Polymers

Herein reported is the impact of the functionalization of four different semiconducting polymer structures by a linear siloxane-terminated side-chains. The latter is tetrasiloxane (Si₄) or trisiloxane (Si₃) chains, substituted at their extremity to a pentylene linker. The polymer structure is based on 5,6-difluorobenzothiadiazole comonomer (PF2), a diketopyrrolopyrrole unit (PDPP-TT), a naphtalediimide unit (PNDI-T₂), and a poly[bis(thiophen-2-yl)thieno[3,2,b]thiophene (PBTTT). The properties of these siloxane-functionalized polymers are scrutinized and compared with the ones of their alkyl-substituted polymer analogues. The impact of the alkyl-to-siloxane chain substitution clearly depends on the molecular section of the side chains. When a branched 2-octyldodecyl chain (C₂₀) is replaced by a Si₄ chain of same molecular section, the greatest impact is the strong increase of the π-stacking overlap of the polymer backbones. This effect leads to a significative enhancement of the charge mobility values of the polymers. As in-plane and out-of-plane mobility are increased simultaneously, this π-overlap enhancement effect happens to be preponderant over the polymer orientation variations. When a linear tetradecyl chain (C₁₄) is replaced by a linear Si₃ chain of twice larger molecular section, the polymer structure is profoundly affected. While PBTTT-C₁₄ is crystalline and purely edge-on, PBTTT-Si₃ is mesomorphic and shows a mixed face-on/edge-on orientation.     

Thermo‐Mechanical Responses of Liquid‐Crystal Networks with a Splayed Molecular Organization

Films of liquid‐crystal networks with a splayed molecular alignment over their cross‐section display a well‐controlled deformation as a function of temperature. The deformation can be explained in terms of differences in thermal expansion depending on the average molecular orientation of the mesogenic centers of the monomeric units. The thermal expansion of the anisotropic polymers has been characterized as a function of their molecular structure and the polymerization conditions. As a reference, films with an in‐plane 90° twist have also been studied and compared with the splayed, out‐of‐plane molecular rotation. The twisted films show a complex macroscopic deformation owing to the formation of saddle‐like geometries, whereas the deformation of the splayed structured is smooth and well controlled. The deformation behavior is anticipated to be of relevance for polymer‐based microelectromechanical system (MEMS) technology.     

Taming Charge Transport in Semiconducting Polymers with Branched Alkyl Side Chains

The solid‐state packing and polymer orientation relative to the substrate are key properties to control in order to achieve high charge carrier mobilities in organic field effect transistors (OFET). Intuitively, shorter side chains are expected to yield higher charge carrier mobilities because of a denser solid state packing motif and a higher ratio of charge transport moieties. However our findings suggest that the polymer chain orientation plays a crucial role in high‐performing diketopyrrolopyrrole‐based polymers. By synthesizing a series of DPP‐based polymers with different branched alkyl side chain lengths, it is shown that the polymer orientation depends on the branched alkyl chain lengths and that the highest carrier mobilities are obtained only if the polymer adopts a mixed face‐on/edge‐on orientation, which allows the formation of 3D carrier channels in an otherwise edge‐on‐oriented polymer chain network. Time‐of‐flight measurements performed on the various polymer films support this hypothesis by showing higher out‐of‐plane carrier mobilities for the partially face‐on‐oriented polymers. Additionally, a favorable morphology is mimicked by blending a face‐on polymer into an exclusively edge‐on oriented polymer, resulting in higher charge carrier mobilities and opening up a new avenue for the fabrication of high performing OFET devices.     

Enhancing Field‐Effect Mobility of Conjugated Polymers Through Rational Design of Branched Side Chains

The design of polymer semiconductors possessing effective π–π intermolecular interactions coupled with good solution processability remains a challenge. Structure‐property relationships associated with side chain structure, π–π intermolecular interactions, polymer solubility, and charge carrier transport are reported for a donor–acceptor(1)‐donor–acceptor(2) polymer: 5‐Decylheptadecyl (5‐DH), 2‐tetradecyl (2‐DT), and linear n‐octadecyl (OD) chains are substituted onto a polymer backbone consisting of terthiophene units (T) between two different electron acceptors, benzothiadiazole (B), and diketopyrrolopyrrole (D), pTBTD, to afford pTBTD‐5DH, pTBTD‐2DT, and pTBTD‐OD, respectively. In the 5‐DH side chain, the branching position is remote from the polymer backbone, whereas it is proximal in 2‐DT. This study demonstrates that incorporation of branched side chains where the branching position is remote from the polymer backbone merges the advantages of improved solubility from branched units with effective π–π intermolecular interactions normally associated with linear chains on conjugated polymers. pTBTD‐5DH exhibits superior qualities with respect to the degree of polymerization, solution processability, π–π interchain stacking, and charge carrier transport relative to the other analogs. pTBTD‐5DH exhibits a field‐effect hole mobility of up to 2.95 cm² V^–1 s^–1, a factor of 3–7 times that achieved with pBDT6‐DT and pBDT6‐OD.     

Electrochemically Nanostructured Polyvinylferrocene/Polypyrrole Hybrids with Synergy for Energy Storage

Unconjugated redox polymers, such as polyvinylferrocene (PVF), have rarely been used for energy storage due to their low intrinsic conductivity. Conducting polymers with conjugated backbones, though conductive, may suffer from insufficient exposure to the electrolyte due to the often formed nonporous structures. The present work overcomes this limitation via simultaneous electropolymerization of pyrrole and electroprecipitation of PVF on electrode surfaces. This synthesis method relies on the π–π stacking interactions between the aromatic pyrrole monomers and the metallocene moieties of PVF. This fabrication process results in a highly porous polymer film, which enhances the ion accessibility to polypyrrole (PPy). PPy serves as a “molecular wire,” improving the electronic conductivity of the hybrid and the utilization efficiency of ferrocene. The PVF/PPy hybrid exhibited a specific capacitance of 514.1 F g^?1 _, which significantly exceeds those of PPy (27.3 F g^?1) and PVF (79.0 F g^?1), respectively. This approach offers an alternative to nanocarbon materials for improving the electronic conductivity of polymer hybrids, and suggests a new strategy for fabricating nanostructured polymer hybrids. This strategy can potentially be applied to various polymers with π‐conjugated backbones and redox polymers with metallocene moieties for applications such as energy storage, sensing, and catalysis.     

Effect of side chains on phenanthrene based D-A type copolymers for polymer solar cells

A series of low band gap conjugated copolymers containing 9,10-modified phenanthrene and diketopyrrolopyrrole (DPP) units were synthesized as electron donor materials for bulk heterojunction organic solar cells. These donor-acceptor type PDPP copolymers have varying solubilizing groups on their identical conjugated backbones. The optical bandgap of PDPP copolymers is about 1.6 eV which corresponds to the long wavelength region of the solar spectrum. Through the incorporation of phenanthrene units into the conjugated backbone instead of commonly used thiophene derivatives, a higher open-circuit voltage of about 0.8 V could be achieved, as a result of their deeper HOMO level. Of all the devices, the P4:PC₆₁BM BHJ system showed the best performance with a V_oc of 0.79 V, a J_sc of 5.97 mA cm⁻², a fill factor of 0.62 and a power conversion efficiency of 2.73% due to superior nanoscale phase separation between the electron donor and electron acceptor materials than in the other polymers arising from short-branched solubilizing groups on the phenanthrene side of its conjugated backbone.