Development of a methodology to predict material properties from environmental exposure. II. Structural features

A general scheme is presented in the first part of this series in which degradation‐induced changes in a polymer that are produced by exposure to an aggressive environment are linked to measurable kinetic parameters and molecular weight distribution variations. Although general in nature for all polymers and environments, the data were collected on bisphenol A polycarbonate that was degraded by elevated temperatures. A parameter, τ, the product of a kinetic rate constant, k, and the environmental exposure time, provided a metric that was suitable for superposition methods to reduce the data. τ was directly related to the molecular weight distribution shifting during environmentally induced changes. This article extends the methodology to structure–property correlations such as the relationship of the glass‐transition temperature, rheology, and the tensile strength of polycarbonate after the environmental treatment. Again, in a universal fashion, the τ value (the degree of degradation) was sufficient to model the observed physical property changes with the amount of exposure to the hostile environment. As long as the kinetics of the process of change are amenable to a mathematical model and a quantitative measure of the change in a fundamental polymer parameter is available, this methodology should be applicable to any polymer in any environment. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 802–812, 2002     

Thermomechanical properties and phase structure of epoxy/silica nano‐hybrid materials constructed from a linear silicone oligomer

Epoxy‐grafted silicone oligomer (ESO), which has a linear silicone chain in the backbone moiety, was synthesized from a trifunctional alkoxysilane via a sol–gel reaction. Characterization of ESO was performed with ¹H and ²⁹Si NMR, Fourier transform infrared, and gel permeation chromatography. The number‐average molecular weight of ESO was 3300. By adding the silicone oligomer as the inorganic source in the curing process of the epoxy resin, novel epoxy/silica hybrid materials were prepared. It was observed by transmission electron microscope that fine silica‐rich domains of about 5‐nm diameter were uniformly dispersed in the cured epoxy matrix. Thermomechanical properties of the hybrid materials were also investigated. The storage modulus in the rubbery region and the peak area of the tan δ curve at the glass‐transition region increased and decreased, respectively, with the hybridization of the silica network. The mobility of the epoxy network chains should be considerably suppressed by the hybridization with the silica network. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1631–1639, 2005     

Perfluoropolyether alkyl diesters: Structure effects of the alkyl group on the kinetics of the hydrolysis reactions

A series of perfluoropolyether bis‐carboxylic esters was synthesized and their hydrolytic stability investigated. Their formula is ROOCCF₂O(CF₂CF₂O)_p(CF₂O)_qCF₂COOR, where p/q = 1.07 and p + q = 2.94. The alkyl group, R, varied both in terms of steric hindrance and electron‐withdrawing ability. Kinetic and thermodynamic data were obtained under homogeneous conditions and compared to a fully hydrogenated ester having a closely related structure CH₃(CH₂)₃OOCCH₂O(CH₂CH₂O)_nCH₂COO(CH₂)₃CH₃, where n? = 10.6. Neutral ester hydrolysis (NEH) conditions were selected with methyl ethyl ketone as a solvent and a 3–4:1 water/ester ratio. The course of the reaction was monitored by ¹⁹F NMR or ¹H NMR (when R = CH₃CH₂? ). Results indicated that the hydrolysis of fluorinated esters, with alkyl aliphatic substituents, is governed by steric hindrance of the substituents. Two distinctive kinetic regimes were observed. The first one, at low conversion, was characterized by lower kinetic constants and related to true NEH conditions. The second regime appeared at higher conversion when acidic autocatalysis dictated the reaction behavior. This is the only observed mechanism when esters more sensitive to the hydrolysis are considered. In these cases, polar factors prevail over steric considerations. Finally, all fluorinated esters of the class (I) showed a much higher reactivity than the hydrogenated ester whose hydrolysis took place only in the presence of a strong acidic catalyst. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 4266–4280, 2002     

Effects of graphene and carbon nanotube fillers on the shear properties of epoxy

The effects of quantity of graphene and carbon nanotube‐based fillers and their pendant functional groups on the shear properties of a thermoset epoxy were investigated. Two novel functionalized graphenes, one with epoxy functionality and the other with an amine, are synthesized for this purpose. Nanocomposites are prepared at concentrations of 0.5, 1, 2, 3, 5, and 10 wt % and the effects of functionalization on the homogeneity of dispersion and the shear mechanical properties are investigated. The properties of the epoxy nanocomposites containing epoxy‐ and amine‐functionalized graphene are compared with those containing graphene oxide, Claisen‐functionalized graphene, neat multiwalled carbon nanotubes (MWNTs), three types of epoxy‐functionalized MWNT (EpCNT), and the unfilled epoxy. One of the EpCNT ( EpCNT3 ) was found to increase the plateau shear storage modulus by 136% (1.67–3.94 MPa) and the corresponding loss modulus by almost 400% at a concentration of 10 wt %. Several other fillers were also found to increase shear properties at certain concentrations. A hybrid system of EpCNT3 and graphite was also studied, which improved the storage modulus by up to 51%. SEM images reveal a correlation between thorough dispersion of the additive and enhancement of shear modulus. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 997–1006     

Synthesis of optically active alicyclic polyimides from a chiral,nonracemic dianhydride

Optically active alicyclic polyimides were prepared for the first time from (?)‐[1S*,5R*,6S*]‐3‐oxabicyclo[3.2.1]octane‐2,4‐dione‐6‐spiro‐3′‐(tetrahydrofuran‐ 2′,5′‐dione) [(?)‐DAn] via polycondensation with diamines and subsequent chemical or thermal imidization. The dianhydride (?)‐DAn was synthesized by an asymmetric Diels–Alder reaction of a chiral itaconic acid derivative as a key step. Colorless or slightly yellow flexible films were obtained for the (?)‐DAn‐derived polyimides {PI[(?)‐DAn]s}. PI[(?)‐DAn]s showed good solubility toward dipolar aprotic solvents and pyridine. For 1,4‐dioxane and chloroform, the optically active polyimides showed slightly better solubility than the corresponding polyimides prepared from rac‐DAn [PI(rac‐DAn)s]. PI[(?)‐DAn]s showed glass‐transition temperatures of 267–268 °C and 10% weight‐loss temperatures of 416–424 °C in nitrogen. These values were almost identical to those of PI(rac‐DAn)s. The circular dichroism spectra of PI[(?)‐DAn]s showed exciton coupling patterns indicating that to some extent these polyimides had a higher order structure in solution. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 4038–4044, 2002     

Synthesis and properties of highly refractive polyimides derived from fluorene‐bridged sulfur‐containing dianhydrides and diamines

Highly refractive and transparent polyimides (PIs) based on fluorene‐bridged and sulfur‐containing monomers have been developed. An aromatic dianhydride, 4,4′‐[p‐thiobis(phenylenesulfanyl)]diphthalic anhydride (3SDEA), was polymerized with several fluorene‐containing diamines, including commercially available 9,9′‐bis(p‐aminophenyl)fluorene (APF), 9,9′‐bis[4‐(p‐aminophenoxy)phenyl]fluorene (OAPF), and newly synthesized 9,9′‐bis[4‐(p‐aminophenyl)sulfanylphenyl]fluorene (ASPF) to afford series A PIs. Meanwhile, series B PIs were obtained from a new dianhydride, 4,4′‐[(9H‐fluorene‐9‐ylidene)bis(p‐phenylsulfanyl)]diphthalic anhydride (FPSP) and two aromatic diamines, ASPF and 4,4′‐thiobis[(p‐phenylenesulfanyl)aniline] (3SDA) via a two‐step polycondensation procedure. The PIs exhibit good thermal stabilities, such as relatively high glass transition temperatures in the range of 220–270 °C and high initial thermal decomposition temperatures (T_10%) exceeding 490 °C. The 9,9′‐disubstituted fluorene moieties endow the PI films with good optical transparency. The optical transmittances of the PI films at 450 nm are all higher than 80% for the thickness of about 10 μm. Furthermore, the highly aromatic fluorene moiety and flexible thioether linkages in the molecular chains of the PIs provide them with high refractive indices of 1.6951–1.7258 and small birefringence of 0.0056–0.0070. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1510–1520, 2008     

Nylon‐6 nanocomposites,study of the influence of the nanofiller nature on morphology and material properties

In this article we investigated the influence of various nanofilllers' aspect ratio, chemical nature, and organic modification on some selected nylon‐6 properties, such as crystallinity, thermal and mechanical resistance, and fire behavior. Materials were prepared by twin‐screw extrusion and characterized by means of scanning and transmission electron microscopy, X‐ray diffraction, thermogravimetric analysis, tensile tests, and cone calorimeter. Fillers characteristics were found to influence at different extents the material final properties. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1935–1948, 2009     

Reorganization of poly(ethylene terephthalate) structures and conformations to alter properties

The solid‐state morphologies, structures, and chain conformations of poly (ethylene terephthalate) (PET) have been reorganized/altered from those normally produced by solution and melt processing. This has been achieved by two distinct methods: (1) formation of a crystalline inclusion compound (IC) between guest PET and host γ‐cylodextrin (γ‐CD), followed by removal of the host γ‐CD and coalescence of the guest PET (c‐PET) and (2) rapid precipitation of PET from a warm trifluoracetic acid solution into a large excess of rapidly stirred acetone (p‐PET). Our prior observations (FTIR, NMR, DSC, X‐ray) demonstrated that c‐PET processed in this manner has a morphology, structure, and non‐crystalline chain conformations that are quite distinct from those of as‐received PET (asr‐PET). Where possible to compare, here we find that c‐ and p‐PETs behave very similarly, but very distinctly from asr‐PET. The reorganized c‐ and p‐PETs were found to be repeatedly rapidly crystallizable from the melt with a high level of crystallinity, and in their non‐crystalline regions to have tightly packed chains predominantly adopting highly extended kink conformations, which evidence no glass‐transition behavior. What is most unusual and somewhat puzzling is that their contrasting structures, morphologies, conformations, and thermal responses were observed to be independent of melt annealing, and persisted even after holding both samples above T_m for extended periods (hours). p‐PET, which can be produced in larger quantities than c‐PET, was utilized to measure additional macroscopic properties, such as melt viscosities, densities, and the stress‐strain and thermal shrinkage of melt‐pressed films, for comparison to those of asr‐PET. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 735–746, 2007     

Prediction of paper permanence by accelerated aging I. Kinetic analysis of the aging process

The validity of accelerated aging tests to predict and rank papers on their permanence has been under question, preventing the development of performance-based standards for permanent paper. We conducted a general kinetic analysis to investigate the aging process of paper. A general kinetic model is proposed to describe the depolymerization of cellulose. Experimentally it was shown that in the case of aging, cellulose degradation follows classic first-order kinetics as a special case of our general kinetic model. The Arrhenius equation was critically re-examined for the case of a multiple reaction system. It was shown analytically that the Arrhenius equation is still applicable when certain conditions are met. This was convincingly supported by experimental results. We also analysed the dependence of the degradation rate on the moisture content and hydrogen ion concentration. By conducting systematic experiments on these two factors, a general and quantitative relationship was established to explain the contribution of each factor and their interactions. Finally, based on this kinetic analysis, the effects of storage conditions on the life expectancy of paper were estimated.     

Structure and properties for transparent polypropylene containing sorbitol‐based clarifier

Relation between structure and properties is studied for polypropylene (PP) containing 1,3:2,4‐di‐benzylidene sorbitol (DBS) that forms network structure composed of nanofibrils in a molten PP. It is found that the aggregation state of DBS, which can be controlled by the applied flow field and thermal history, affects the spherulite texture of PP and thus the transparency. When injection‐molded products, in which the nanofibrils of DBS orient to the flow direction, are reprocessed at 180 °C, that is, lower temperature than the melting point of DBS, the obtained material shows high level of transparency, although it has been believed that sorbitol‐derivatives have to be melted and dissolved into the molten PP at high temperature, for example, 240 °C. Further, it is found that the particle flow occurs in the blend at 180 °C. The applied shear force generates the particles, that is, flow units, by the fragmentation of the network structure. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 41–47, 2008     

Synthesis and properties of aromatic polyamides based on a benzonorbornane bis(ether carboxylic acid)

A set of new aromatic polyamides containing ether and benzonorbornane units were synthesized by the direct phosphorylation polycondensation of 3,6‐bis(4‐carboxyphenoxy)benzonorbornane with various aromatic diamines. The polymers were produced in high yields and moderate to high inherent viscosities (0.64–1.70 dL/g). The polyamides derived from rigid diamines such as p‐phenylenediamine and benzidine were semicrystalline and insoluble in organic solvents. The other polyamides were amorphous and organosoluble and afforded flexible and tough films via solution casting. These films exhibited good mechanical properties, with tensile strengths of 95–101 MPa, elongations at break of 13–25%, and initial moduli of 1.97–2.33 GPa. The amorphous polyamides showed glass‐transition temperatures between 176 and 212 °C (by differential scanning calorimetry) and softening temperatures between 194 and 213 °C (by thermomechanical analysis). Most of the polymers did not show significant weight loss before 450 °C in nitrogen or in air. Some properties of these polyamides were also compared with those of homologous counterparts without the pendent norbornane groups. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 947–957, 2002     

Phosphinated phenols from acid‐fragmentation of bisphenols and their unsymmetrical diamine derivatives for copolyimides

Four novel diamines (9–12) were prepared by a two‐step procedure from phosphinated phenols (1–4) that were prepared from acid‐fragmentation of four bisphenols, including bisphenol A, 4,4′‐isopropylidenebis(2,6‐dimethylphenol), cis(4‐hydroxyphenyl)cyclohexane, and 9,9′‐bis(4‐hydroxyphenyl)fluorene, followed by nucleophilic addition of 9,10‐dihydro‐oxa‐10‐phosphaphenanthrene‐10‐oxide (DOPO). Copolyimides based on (9–12) /4,4′‐diaminodiphenyl ether (ODA)/dianhydride were prepared. The structure‐property relationship on the copolyimides was discussed. Due to the structural similarity, (9) /ODA‐based copolyimides were compared with (10) /ODA‐based copolyimides, while (11) /ODA‐based copolyimides were compared with (12) /ODA‐based copolyimides. The dimethyl substitutents cause (10) /ODA‐based copolyimides to display higher T_g, modulus, dimensional stability, contact angle, and better solubility than (9) /ODA‐based copolyimides. (12) /ODA‐based copolyimides that exhibit fluorene moieties display higher T_g and thermal stability, but a lower contact angle and poorer solubility than (11) /ODA‐based copolyimides that exhibit cyclohexane moieties. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 390–400     

Fluoropolyethers end‐capped by polar functional groups. III. Kinetics of the reactions of hydroxy‐terminated fluoropolyethers and model fluorinated alcohols with cyclohexyl isocyanate catalyzed by organotin compounds

The kinetics of the dibutyltin dilaurate (DBTDL)‐catalyzed urethane formation reactions of cyclohexyl isocyanate (CHI) with model monofunctional fluorinated alcohols and fluoropolyether diol Z‐DOL H‐1000 of various molecular weights (100–1084 g mol^?1) in different solvents were studied. IR spectroscopy and chemical titration methods were used for measuring the rate of the total NCO disappearance at 30–60 °C. The effects of the reagents and DBTDL catalyst concentrations, the solvent and hydroxyl‐containing compound nature, and the temperature on the reaction rate and mechanism were investigated. Depending on the initial reagent concentration and solvent, the reactions could be well described by zero‐order, first‐order, second‐order, or more complex equations. The reaction mechanism, including the formation of intermediate ternary or binary complexes of reagents with the tin catalyst, could vary with the concentration and solvent and even during the reaction. The results were treated with a rate expression analogous to those used for enzymatic reactions. Under the explored conditions, the rate of the uncatalyzed reaction of fluorinated alcohols with CHI was negligible. Moreover, there was no allophanate formation, nor were there other side reactions, catalysis by urethane in the absence of DBTDL, or a synergetic effect in the presence of the tin catalyst. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3771–3795, 2002     

Shear band formation and mode II fracture of polymeric glasses

Mode I and II fracture studies were performed from quasistatic to low velocity impact rates on polymethyl methacrylate (PMMA) and polycarbonate (PC). Mode II tests used an angled double‐edge notched specimen loaded in compression. The shear banding response of PMMA is shown to be highly sensitive to rate, with diffuse shear bands forming at low rates and sharp distinct shear bands forming at high rates. As the rate increases, shear deformation becomes more localized to the point where Mode II fracture occurs. PC is much less rate dependent and stable shear band propagation is observed over the range of rates studied with lesser amounts of localization. A new theory is formulated relating orientation in a shear band to intrinsic material properties obtained from true‐stress true‐strain tests. In a qualitative sense the theory predicts the high rate sensitivity of PMMA. A kinematic limit for orientation within a shear band is also derived based on entanglement network parameters. Mode II fracture in PMMA is shown to occur at this kinematic limit. For the case of PC, the maximum impact rates were not high enough to reach the kinematic limit. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Thermal and mechanical properties of a dendritic hydroxyl‐functional hyperbranched polymer and tetrafunctional epoxy resin blends

Blends of a tetrafunctional epoxy resin, tetraglycidyl‐4,4′‐diaminodiphenylmethane (TGDDM), and a hydroxyl‐functionalized hyperbranched polymer (HBP), aliphatic hyperbranched polyester Boltorn H40, were prepared using 3,3′‐diaminodiphenyl sulfone (DDS) as curing agent. The phase behavior and morphology of the DDS‐cured epoxy/HBP blends with HBP content up to 30 phr were investigated by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and scanning electron microscopy (SEM). The phase behavior and morphology of the DDS‐cured epoxy/HBP blends were observed to be dependent on the blend composition. Blends with HBP content from 10 to 30 phr, show a particulate morphology where discrete HBP‐rich particles are dispersed in the continuous cured epoxy‐rich matrix. The cured blends with 15 and 20 phr exhibit a bimodal particle size distribution whereas the cured blend with 30 phr HBP demonstrates a monomodal particle size distribution. Mechanical measurements show that at a concentration range of 0–30 phr addition, the HBP is able to almost double the fracture toughness of the unmodified TGDDM epoxy resin. FTIR displays the formation of hydrogen bonding between the epoxy network and the HBP modifier. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 417–424, 2010     

Impact of average free‐volume element size on transport in stereoisomers of polynorbornene. II. Impact of temperature on solubility

This article evaluates the influence of temperature on the sorption of gases in two isomers of polynorbornene. The subject polymers were stereoisomers with nearly identical bulk density and total free volume. Because of differences in the mobility of the polymer backbone, the isomers packed differently resulting in differences in the average free‐volume element size within the matrix. The influence of these differences on free‐volume element size was characterized by the heat of sorption of gases in the matrix. The most pronounced differences were observed in the isosteric heats of sorption of condensable carbon dioxide and methane in the polymer isomers. This analysis suggests that the relative space available for sorption into free‐volume elements is higher in the methyl II isomer relative to methyl III. These conclusions support the physical characterizations reported in Part I of this series suggesting that the methyl II isomer has larger average free‐volume elements but fewer of them than the methyl III isomer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1939–1946, 2003     

Lamellar cluster structure formation resulting from interchain interaction in a novel aromatic polyimide based on PMDA monomer

The aggregation structure of a novel polyimide ( PIM ‐ 6 ) with six methylene flexible spacing groups in biphenyl side chain synthesized by the traditional two‐step imidisation process was investigated by polarized light microscope (PLM), small angle X‐ray scattering (SAXS), wide angle X‐ray scattering (WAXS), and molecular simulation approach. The agreement between the experimental data and simulation result reveals that due to the predominant interchain interaction, each three backbones stack together to form a distinct lamellar cluster with side chains packed inside dispersedly. The thickness of the lamellar cluster is about 16.0 A°, corresponding to a strong peak at 5.5° in SAXS pattern. As the backbone is not perfectly parallel to each other in each lamellar cluster, the distance between each backbone ranges from 5.8 to 8.8 A° possibly relating to the weak peak at 9.8° in WAXS pattern. Meanwhile, no birefringence or apparent phase texture has been observed by PLM indicating an amorphous nature in this film. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Poly(butylene terephthalate‐co‐5‐tert‐butyl isophthalate) copolyesters: Synthesis,characterization, and properties

A series of poly(butylene terephthalate) copolyesters containing 5‐tert‐butyl isophthalate units up to 50 mol %, as well as the homopolyester entirely made of these units, were prepared by polycondensation from a melt. The microstructure of the copolymers was determined by NMR to be random for the whole range of compositions. The effect exerted by the 5‐tert‐butyl isophthalate units on thermal, tensile, and gas transport properties was evaluated. Both the melting temperature (T_m) and crystallinity were found to decrease steadily with copolymerization, whereas the glass‐transition temperature (T_g) increased and the polyesters became more brittle. Permeability and solubility slightly increased with the content in substituted isophthalic units, whereas the diffusion coefficient remained practically constant. For the homopolyester poly(5‐tert‐butyl isophthalate), all these properties were found to deviate significantly from the general trend displayed by copolyesters, suggesting that a different structure in the solid state is likely adopted in this case. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 92–100, 2005     

Mechanical properties of gradient copolymers of styrene and n‐butyl acrylate

The mechanical properties of linear and V‐shaped compositional gradient copolymer of styrene and n‐butyl acrylate with composition of around 55 wt % styrene were investigated by comparing with their block copolymer counterparts. Compared with their block copolymer counterparts, the gradient copolymers showed lower elastic modulus, much larger elongation at break, and similar ultimate tensile strength at room temperature. This performance could be ascribed to that the local moduli continuously change from the hardest nanodomains to the softest nanodomains in the gradient copolymer, which alleviates the stress concentration during tensile test. Compared with the V‐shaped gradient (VG) copolymer, the linear gradient copolymer showed much higher elastic modulus but lower elongation at break. The mechanical properties of the gradient copolymers were more sensitive to the change in temperature from 9 °C to 75 °C. With recovery temperature increased from 10 °C to 60 °C, the strain recovery of VG copolymer would change steadily from 40% to 99%. However, the elastic recovery of linear and triblock copolymer was poor even at 60 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 860–868     

Effect of solvent–matrix interactions on structures and mechanical properties of micelle‐crosslinked gels

Previous studies on hydrogels crosslinked by acrylated PEO₉₉–PPO₆₅–PEO₉₉ triblock copolymer (F127DA) micelles demonstrate outstanding strength and toughness, which is attributed to the efficient energy dissipation through the hydrophobic association in the micelles. The current study further focuses on how the solvent property affects the structures and the mechanical properties of F127DA micelle crosslinked polyacrylamide gels. Binary solvents comprised of dimethyl sulfoxide (DMSO) and water are used to adjust the polymer/solvent interactions, which consequently tune the conformations of the polymer chains in the network. The presence of DMSO significantly decreases the strength but increased the stretchability of the gels, whereas the overall tensile toughness remained unchanged. In situ small‐angle X‐ray scattering measurements reveal the deformation of micelles along with the stretching direction. A structure evolution mechanism upon solvent change is proposed, according to the experimental observations, to explain influence of solvent quality on the mechanical properties of the micelle‐crosslinked gels. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 473–483