Statistical Copolymers Research Articles

Synergistic Polymer Blending Informs Efficient Terpolymer Design and Machine Learning Discerns Performance Trends for pDNA Delivery.

Cationic polymers offer an alternative to viral vectors in nucleic acid delivery. However, the development of polymer vehicles capable of high transfection efficiency and minimal toxicity has remained elusive, and continued exploration of the vast design space is required. Traditional single polymer syntheses with large monomer bases are very time-intensive, limiting the speed at which new formulations are identified. In this work, we present an experimental method for the quick probing of the design space, utilizing a combinatorial set of 90 polymer blends, derived from 6 statistical copolymers, to deliver pDNA. This workflow facilitated rapid screening of polyplex compositions, successfully tailoring polyplex hydrophobicity, particle size, and payload binding affinity. This workflow identified blended polyplexes with high levels of transfection efficiency and cell viability relative to single copolymer controls and commercial JetPEI, indicating synergistic benefits from copolymer blending. Polyplex composition was coupled with biological outputs to guide the synthesis of single terpolymer vehicles, with high-performing polymers P10 and M20, providing superior transfection of HEK293T cells in serum-free and serum-containing media, respectively. Machine learning coupled with SHapley Additive exPlanations (SHAP) was used to identify polymer/polyplex attributes that most impact transfection efficiency, viability, and overall effective efficiency. Subsequent transfections on ARPE-19 and HDFn cells found that P10 and M20 were surpassed in performance by M10, contrasting with results in HEK293T cells. This cell type dependency reinforced the need to evaluate transfection conditions with multiple cell models to potentially identify moieties more beneficial to delivery in certain tissues. Overall, the workflow employed can be used to expedite the exploration of the polymer design space, bypassing extensive synthesis, and to develop improved polymer delivery vehicles more readily for nucleic acid therapies.

Poly(2-Oxazoline) Amphiphilicity Tunes the Excited-State Proton Transfer of Pyrenol-Based Polyphotoacids.

The ability of light to change the properties of light-responsive polymers opens avenues for targeted release of cargo with a high degree of spatial and temporal control. Recently, we established photoacid polymers as light-switchable macromolecular amphiphiles. In these systems, light-induced excited-state proton transfer (ESPT) causes changes in amphilicity. However, as the intermolecular process itself critically depends on the local environment of the photoacid unit within the polymer, the overall amphiphilicity directly influences ESPT. Thus, understanding the impact of the local environment on the photophysics of photoacidic side chains is key to material design. In this contribution we address both thermodynamic and kinetic aspects of ESPT in oxazoline-based amphiphilic polymers with pyrenol-based photoacid side chains. We will compare the effect of polymer design, i. e. statistical and block arrangements, i. e. in poly[(2-ethyl-2-oxazoline)-co-(1-(6/8-hydroxyperene)sulphonylaziridine)] and poly(2-ethyl-2-oxazoline)-block-poly[(2-ethyl-2-oxazoline)-co-(2-(3-(6-hydroxypyrene)sulphonamide)propyl-2-oxazoline), on the intermolecular proton transfer reaction by combining steady-state and time-resolved absorption and emission spectroscopy. ESPT appears more prominent in the statistical copolymer compared to a block copolymer with overall similar pyrenol loading. We hypothesize that the difference is due to different local chain arrangements adopted by the polymers in the two cases.

Kinetic Hydrate Inhibitors─Which is Best, Block or Statistical Copolymers?

Kinetic Hydrate Inhibitors─Which is Best, Block or Statistical Copolymers?

Poly(Sitosterol)-Based Hydrophobic Blocks in Amphiphilic Block Copolymers for the Assembly of Hybrid Vesicles.

Amphiphilic block copolymer and lipids can be assembled into hybrid vesicles (HVs), which are an alternative to liposomes and polymersomes. Block copolymers that have either poly(sitostryl methacrylate) or statistical copolymers of sitosteryl methacrylate and butyl methacrylate as the hydrophobic part and a poly(carboxyethyl acrylate) hydrophilic segment are synthesized and characterized. These block copolymers assemble into small HVs with soybean L-α-phosphatidylcholine (soyPC), confirmed by electron microscopy and small-angle X-ray scattering. The membrane's hybrid nature is illustrated by fluorescence resonance energy transfer between labeled building blocks. The membrane packing, derived from spectra when using Laurdan as an environmentally sensitive fluorescent probe, is comparable between small HVs and the corresponding liposomes with molecular sitosterol, although the former show indications of transmembrane asymmetry. Giant HVs with homogenous distribution of the block copolymers and soyPC in their membranes are assembled using the electroformation method. The lateral diffusion of both building blocks is slowed down in giant HVs with higher block copolymer content, but their permeability toward (6)-carboxy-X-rhodamine is higher compared to giant vesicles made of soyPC and molecular sitosterol. This fundamental effort contributes to the rapidly expanding understanding of the integration of natural membrane constituents with designed synthetic compounds to form hybrid membranes.

Composition drift in radical copolymerization

Composition drift in radical copolymerization is a topic of practical importance for the synthesis of homogeneous statistical copolymers and gradient copolymers, which generally does not receive much attention in most polymer chemistry textbooks. The aim of this paper is to provide a tutorial on the topic in which we provide some additional theory in a straightforward and accessible manner and show that composition drift can easily be described quantitatively. Furthermore we show how to circumvent composition drift in a semi-batch approach and by using a continuous stirred tank reactor (CSTR).

Effect of tetrahydrofuran on the anionic copolymerization of 4‐trimethylsilylstyrene with isoprene

AbstractThe statistical anionic copolymerization of 4‐trimethylsilylstyrene (TMSS) with isoprene (I) in cyclohexane was investigated using in situ near‐infrared (NIR) spectroscopy in the presence of various amounts of the polar modifier tetrahydrofuran (THF). Polymers with narrow molecular weight distribution of 85–138 kg/mol and dispersities of 1.09–1.22 were obtained. By increasing modifier content, the reactivity ratios can be adjusted over a wide range from rTMSS < rI to rTMSS >> rI. Compared to the system styrene/isoprene (S/I) only a minute amount of modifier (0.5 eq THF relative to lithium) is sufficient to alter the reactivity ratios, resulting in an ideally random copolymerization, which validates the higher reactivity of TMSS compared to styrene. Using these reactivity ratios, molar and volume composition gradients were calculated. Additionally, the glass transition temperature and microstructure of the polyisoprene units were investigated via differential scanning calorimetry and proton nuclear magnetic resonance. The results are encouraging for the use of these materials in high‐end applications like membranes.

Deciphering the Lipid-Random Copolymer Interactions and Encoding Their Properties to Design a Hybrid System.

Lipid/copolymer colloidal systems are deemed hybrid materials with unique properties and functionalities. Their hybrid nature leads to complex interfacial phenomena, which have not been fully encoded yet, navigating their properties. Moving toward in-depth knowledge of such systems, a comprehensive investigation of them is imperative. In the present study, hybrid lipid/copolymer structures were fabricated and examined by a gamut of techniques, including dynamic light scattering, fluorescence spectroscopy, cryogenic transmission electron microscopy, microcalorimetry, and high-resolution ultrasound spectroscopy. The biomaterials that were mixed for this purpose at different ratios were 1,2-dioctadecanoyl-sn-glycero-3-phosphocholine and four different linear, statistical (random) amphiphilic copolymers, consisting of oligo(ethylene glycol) methyl ether methacrylate as the hydrophilic comonomer and lauryl methacrylate as the hydrophobic one. The colloidal dispersions were studied for lipid/copolymer interactions regarding their physicochemical, morphological, and biophysical behavior. Their membrane properties and interactions with serum proteins were also studied. The aforementioned techniques confirmed the hybrid nature of the systems and the location of the copolymer in the structure. More importantly, the random architecture of the copolymers, the hydrophobic-to-hydrophilic balance of the nanoplatforms, and the lipid-to-polymer ratio are highlighted as the main design-influencing factors. Elucidating the lipid/copolymer interactions would contribute to the translation of hybrid nanoparticle performance and, thus, their rational design for multiple applications, including drug delivery.

Encapsulation of Nanoparticles with Statistical Copolymers with Different Surface Charges and Analysis of Their Interactions with Proteins and Cells.

Encapsulation with polymers is a well-known strategy to stabilize and functionalize nanomaterials and tune their physicochemical properties. Amphiphilic copolymers are promising in this context, but their structural diversity and complexity also make understanding and predicting their behavior challenging. This is particularly the case in complex media which are relevant for intended applications in medicine and nanobiotechnology. Here, we studied the encapsulation of gold nanoparticles and quantum dots with amphiphilic copolymers differing in their charge and molecular structure. Protein adsorption to the nanoconjugates was studied with fluorescence correlation spectroscopy, and their surface activity was studied with dynamic interfacial tensiometry. Encapsulation of the nanoparticles without affecting their characteristic properties was possible with all tested polymers and provided good stabilization. However, the interaction with proteins and cells significantly depended on structural details. We identified statistical copolymers providing strongly reduced protein adsorption and low unspecific cellular uptake. Interestingly, different zwitterionic amphiphilic copolymers showed substantial differences in their resulting bio-repulsive properties. Among the polymers tested herein, statistical copolymers with sulfobetaine and phosphatidylcholine sidechains performed better than copolymers with carboxylic acid- and dimethylamino-terminated sidechains.

Four-Component Statistical Copolymers by RAFT Polymerization.

This manuscript serves as the starting point for in-depth research of multicomponent, statistical, methacrylate-based copolymers that potentially mimic the behavior of proteins in aqueous solutions. These synthetic macromolecules are composed of specially chosen comonomers: methacrylic acid (MAA), oligoethylene glycol methyl ether methacrylate (OEGMA475), 2-(dimethylamino)ethyl methacrylate (DMAEMA) and benzyl methacrylate (BzMA). Monomer choice was based on factors such as the chemical nature of pendant functional groups, the polyelectrolyte/polyampholyte and amphiphilic character and the overall hydrophobic-hydrophilic balance (HLB) of the obtained quaterpolymers. Their synthesis was achieved via a one-pot reversible addition fragmentation chain transfer (RAFT) polymerization in two distinct compositions and molecular architectures, linear and hyperbranched, respectively, in order to explore the effects of macromolecular topology. The resulting statistical quaterpolymers were characterized via 1H-NMR and ATR-FTIR spectroscopies. Their behavior in aqueous solutions was studied by dynamic (DLS) and electrophoretic light scattering (ELS) and fluorescence spectroscopy (FS), producing vital information concerning their self-assembly and the structure of the formed aggregates. The physicochemical studies were extended by tuning parameters such as the solution pH and ionic strength. Finally, the quaterpolymer behavior in FBS/PBS solutions was investigated to test their colloid stability and biocompatibility in an in vivo-mimicking, biological fluid environment.

Block and Statistical Copolymers of Methacrylate Monomers with Dimethylamino and Diisopropylamino Groups on the Side Chains: Synthesis, Chemical Modification and Self-Assembly in Aqueous Media.

The synthesis of amphiphilic diblock and statistical (random) copolymers of poly(dimethylamino ethyl methacrylate) and poly((2-(diisopropylamino) ethyl methacrylate) using the reversible addition-fragmentation chain transfer polymerization technique (RAFT polymerization) is reported. The precursor copolymers were chemically modified to create derivative copolymers of polyelectrolyte and polyampholyte nature with novel solution properties. Moreover, their molecular and physicochemical characteristics, as well as their self-assembly in aqueous media as a function of molecular architecture and composition, are investigated by using size exclusion chromatography, spectroscopic characterization techniques and light scattering techniques. Furthermore, the behavior and properties of the obtained micelles and aggregates were studied, depending on the pH, temperature and ionic strength of the aqueous solutions. The response of the systems to changes in these parameters shows interesting behavior and new properties that are useful for their utilization as nanocarriers of pharmaceutical compounds.

Selective and Controlled Grafting from PVDF-Based Materials by Oxygen-Tolerant Green-Light-Mediated ATRP.

Poly(vinylidene fluoride) (PVDF) shows excellent chemical and thermal resistance and displays high dielectric strength and unique piezoelectricity, which are enabling for applications in membranes, electric insulators, sensors, or power generators. However, its low polarity and lack of functional groups limit wider applications. While inert, PVDF has been modified by grafting polymer chains by atom transfer radical polymerization (ATRP), albeit via an unclear mechanism, given the strong C-F bonds. Herein, we applied eosin Y and green-light-mediated ATRP to modify PVDF-based materials. The method gave nearly quantitative (meth)acrylate monomer conversions within 2 h without deoxygenation and without the formation of unattached homopolymers, as confirmed by control experiments and DOSY NMR measurements. The gamma distribution model that accounts for broadly dispersed polymers in DOSY experiments was essential and serves as a powerful tool for the analysis of PVDF. The NMR analysis of poly(methyl acrylate) graft chain-ends on PVDF-CTFE (statistical copolymer with chlorotrifluoroethylene) was carried out successfully for the first time and showed up to 23 grafts per PVDF-CTFE chain. The grafting density was tunable depending on the solvent composition and light intensity during the grafting. The initiation proceeded either from the C-Cl sites of PVDF-CTFE or via unsaturations in the PVDF backbones. The dehydrofluorinated PVDF was 20 times more active than saturated PVDF during the grafting. The method was successfully applied to modify PVDF, PVDF-HFP, and Viton A401C. The obtained PVDF-CTFE-g-PnBMA materials were investigated in more detail. They featured slightly lower crystallinity than PVDF-CTFE (12-18 vs 24.3%) and had greatly improved mechanical performance: Young's moduli of up to 488 MPa, ductility of 316%, and toughness of 46 × 106 J/m3.

Design of sec-Benzyl Vinyl Ethers toward the Synthesis of Alternating Copolymers Composed of Vinyl Alcohol and Vinyl Ether Units.

In this work, we designed benzyl vinyl ethers carrying alkyl substituents at the benzyl position (i.e., sec-BnVEs) as bulky, reactive, and transformable monomers to realize the alternating cationic copolymerization with an alkyl vinyl ether (VE). In particular, the isopropyl substitution caused not only the bulkiness to suppress the successive propagation but also an enhancement of the vinyl group reactivity to promote crossover propagation with a less bulky VE comonomer. The isopropyl-substituted BnVE (iPr-BnVE) underwent living cationic alternating copolymerization with n-butyl VE (nBVE), and the alternating propagation was strongly suggested by the reactivity ratios. The subsequent deprotection of the sec-benzyl pendant afforded the vinyl alcohol (VA)-nBVE alternating copolymer, and the corresponding statistical copolymer was also synthesized by using the nonsubstituted monomer (BnVE) instead of iPr-BnVE. The alternating copolymer exhibited a higher glass transition temperature, which likely stems from the uniform and efficient hydrogen-bonding formation due to the periodic sequence.

Lamellar Microphase Separation and Phase Transition of Hydrogen-Bonding/Crystalline Statistical Copolymers: Amide Functionalization at the Interface.

Microphase separation of random copolymers, as well as that of high χ-low N block copolymers, is promising to construct sub-10-nm structures into materials. Herein, we designed statistical copolymers consisting of 2-hydroxyethyl acrylate (HEA) and N-octadecylacrylamide (ODAAm) to produce crystallization and hydrogen bond-assisted lamellar structure materials. The copolymers not only formed a crystalline lamellar structure with 3-4 nm domain spacing but also maintained an amorphous lamellar structure via phase transition above the melting temperature up to approximately 100 °C. The key is to introduce hydrogen-bonding amide junctions between the octadecyl groups and the polymer backbones, by which the polymer chains are physically fixed at the interface of lamellar structures even above the melting temperature. The stabilization of the lamellar structure by the amide units is also supported by the fact that the lamellar structure of all-acrylate random copolymers bearing hydroxyethyl and crystalline octadecyl groups is disordered above the melting temperature. By spin-coating on a silicon substrate, the HEA/ODAAm copolymer formed a multilayered lamellar thin film consisting of a hydrophilic hydroxyethyl/main chain phase and a hydrophobic octadecyl phase. The structure and order-disorder transition were analyzed by neutron reflectivity.

Synthesis and characterization of statistical and block copolymers of n‐hexyl isocyanate and 2‐chloroethyl isocyanate via coordination polymerization

AbstractStatistical and block copolymers of n‐hexyl isocyanate (HIC) and 2‐chloroethyl isocyanate (ClEtIC) were synthesized via cοοrdination polymerization employing the half‐titanocene complex [(η5‐C5H5)((S)‐2‐Bu‐O)TiCl2] as initiator. The complex, bearing a chiral substituent, led to optically active products, as confirmed by circular dichroism measurements. The molecular characterization of all products was carried out by NMR and IR spectroscopy and size exclusion chromatography (SEC), while their thermal stability was investigated through differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and differential thermogravimetry (DTG). The reactivity ratios of the two monomers were determined using various graphical methods, as well as the COPOINT program, according to the terminal copolymerization model. Structural parameters, such as the dyad monomer sequences and the mean sequence lengths were calculated as well. In addition, the kinetics of the thermal degradation of the statistical copolymers was studied, and the activation energies of the thermal degradation were calculated employing the Kissinger, Ozawa–Flynn–Wall (OFW), and Kissinger–Akahira–Sunose (KAS) methods. The block copolymers were synthesized by sequential addition of monomers starting from the polymerization of HIC. Well‐defined products were obtained in a controlled way as revealed by SEC, IR, and NMR measurements.

Dual reconfigurable network from a semi-crystalline functional polyolefin

A statistical copolymer p(E-co-GMA) of ethylene and glycidyle methacrylate (4.5 wt%) is considered as a starting point towards semicrystalline networks with exchangeable links. Application of the binomial law to size exclusion chromatographic data suggests that chains deprived of reactive comonomers would represent less than 6 wt% of the total, allowing to expect the formation of high gel-content networks. Experimentally, up to 98 wt% gel is obtained upon modification with 3,3′-dithiopropionic acid (DTPA). The crosslinking reaction can be performed in the molten state through a 2-steps procedure: 1°) x mol. of a commercial grade p(E-co-GMA), y mol. of DTPA and z mol. of triazabicyclodecene (TBD) are sheared in a twin-screw compounder at 115 °C, a temperature right above the melting point of the polymer precursor, without triggerring the epoxy-acid addition; 2°) the thermolatent reactive blend thereby obtained is then crosslinked at 170 °C. Samples with x = 1, y = 1 to 4 and z = 0 to 0.8 were thus prepared and evaluated. The presence of TBD accelerates disulfide exchange reaction, possibly by involvement of the thiolate anion whereas it decelerates the epoxy-acid addition. The final networks present several characteristic properties of vitrimers such as insolubility in xylene above the melting point, thermo-activated stress relaxation and creep. Particular shape memory regimes, related to the semicrystalline vitrimer character and the high insoluble fraction are demonstrated. Eventually, production scale-up using continuous reactive extrusion is evaluated.

Amphiphilic block copolymers of poly(N-vinyl pyrrolidone) and poly(isobornyl methacrylate). Synthesis, characterization and micellization behaviour in selective solvents

Block copolymers of N-vinyl pyrrolidone (NVP) and isobornyl methacrylate (IBMA), PIBMA-b-PNVP, were prepared employing the RAFT polymerization technique. IBMA was polymerized first followed by the polymerization of NVP in the presence of a suitable fluoroalcohol to accelerate the crossover reaction. The copolymers were characterized by Size Exclusion Chromatography (SEC) and NMR spectroscopy. The thermal stability of these copolymers was studied via Thermogravimetric Analysis (TGA) and Differential Thermogravimetry (DTG), showing unique characteristics compared to the respective PIBMA and PNVP homopolymers. The micellization behavior was studied in THF, which is a selective solvent for the PIBMA blocks. The corresponding statistical copolymers, PNVP-stat-PIBMA were also examined to elucidate the effect of the macromolecular architecture on the micellar properties. Furthermore, the self-assembly behavior in aqueous solutions was studied for the PIBMA-b-PNVP block copolymers. Water is a selective solvent for the PNVP blocks. Static (SLS) and dynamic light scattering (DLS) were employed to study the micellar assemblies. The encapsulation of the hydrophobic compound curcumin within the micellar core of the micellar structures in aqueous solutions was investigated by UV–Vis spectroscopy and DLS measurements.

Cysteine-binding adjuvant enhances survival and promotes immune function in a murine model of acute myeloid leukemia

AbstractTherapeutic vaccination has long been a promising avenue for cancer immunotherapy but is often limited by tumor heterogeneity. The genetic and molecular diversity between patients often results in variation in the antigens present on cancer cell surfaces. As a result, recent research has focused on personalized cancer vaccines. Although promising, this strategy suffers from time-consuming production, high cost, inaccessibility, and targeting of a limited number of tumor antigens. Instead, we explore an antigen-agnostic polymeric in situ cancer vaccination platform for treating blood malignancies, in our model here with acute myeloid leukemia (AML). Rather than immunizing against specific antigens or targeting adjuvant to specific cell-surface markers, this platform leverages a characteristic metabolic and enzymatic dysregulation in cancer cells that produces an excess of free cysteine thiols on their surfaces. These thiols increase in abundance after treatment with cytotoxic agents such as cytarabine, the current standard of care in AML. The resulting free thiols can undergo efficient disulfide exchange with pyridyl disulfide (PDS) moieties on our construct and allow for in situ covalent attachment to cancer cell surfaces and debris. PDS-functionalized monomers are incorporated into a statistical copolymer with pendant mannose groups and TLR7 agonists to target covalently linked antigen and adjuvant to antigen-presenting cells in the liver and spleen after IV administration. There, the compound initiates an anticancer immune response, including T-cell activation and antibody generation, ultimately prolonging survival in cancer-bearing mice.

Statistical Copolymerization‐Induced Self‐Assembly (stat‐PISA) for Colloidal Hydrogels

AbstractDespite recent advances in colloidal hydrogels, designing general and robust strategies that enable the controlled fabrication of colloidal hydrogels with strong mechanical properties still proves challenging. Herein, the statistical copolymerization‐induced self‐assembly (stat‐PISA) of monomers with hydrogen bonding ability is developed as a general strategy for colloidal hydrogels with high stretchability, anti‐swelling, and self‐healing abilities. This concept is first verified by the statistical dispersion copolymerization of acrylic acid and diacetone acrylamide, yielding statistical copolymer colloidal particles that further coalesced into a 3D colloidal network due to the hydrogen bonding interactions and hydrophobic microdomains on the colloidal surface. Both the microstructure and the mechanical properties of the colloidal hydrogels can be readily regulated by varying the stat‐PISA formulation. Besides, the colloidal hydrogel is developed as a selective dye adsorbent, with excellent selectivity for positively charged dyes. Due to its anti‐swelling property, the colloidal hydrogel is evaluated as a flexible strain sensor for motion detection underwater. The broad feasibility of this strategy is demonstrated by three additional stat‐PISA formulations, which all yielded colloidal hydrogels with good mechanical properties. This strategy is anticipated to inspire the design of colloidal hydrogels with robust mechanics and tailor‐made functionality, and broaden the potential applications of colloidal hydrogels.

Synthesis of Statistical Multiblock Copolymers through Chain Shuttling Copolymerization with a Thermomechanical Switch Behavior

Synthesis of Statistical Multiblock Copolymers through Chain Shuttling Copolymerization with a Thermomechanical Switch Behavior

A library of thermoresponsive diblock and statistical copolymers: Unravelling the effect of molar mass

In the past decades, thermoresponsive polymers have emerged as smart sensing units and promising candidates for a variety of biomedical applications, including targeted drug delivery and tissue engineering. Designing a well-defined thermoresponsive polymer that is versatile for applications requires a systematic study of its properties against its polymeric parameters (i.e., molar mass, composition, and architecture). In terms of the effect of molar mass (MM), previous studies mainly focused on thermoresponsive homopolymers, while the thermoresponsive behaviour of diblock copolymers remained less explored. In this study, we have successfully synthesised 14 different copolymers based on the ionic and thermoresponsive 2-(dimethylamino)ethyl methacrylate (DMAEMA) and methyl methacrylate (MMA) and 14 different copolymers based on the non-ionic and thermoresponsive oligo(ethylene glycol) methyl ether methacrylate with average Mn 300 g mol−1 (OEGMA300) and MMA, in both diblock and statistical forms. Their molar masses were varied from 3000 g mol−1 up to 43 000 g mol−1, and their thermoresponsive and self-assembly behaviours in aqueous solutions were carefully characterised. Intriguingly, DMAEMA-based copolymers demonstrated an increase in cloud point temperature (Tcp) with MM in diblock structures, but a decrease in statistical structures. Conversely, OEGMA300-based copolymers initially exhibit an increase in Tcp as the MM increases, particularly at lower MMs, and then reach a plateau with only slight changes at higher MMs, irrespective of their architecture. This investigation not only explores the impact of MM on these thermoresponsive polymers but also contributes to the future design and application of these comonomers, owing to their wide versatility and established research interest in the biomedical field.