A DSC study of miscibility and phase separation in crystalline polymer blends of phenolphthalein poly(ether ether sulfone) and poly(ethylene oxide)

The miscibility of blends of phenolphthalein poly(ether ether sulfone) (PES-C) and poly(ethylene oxide) (PEO) was established on the basis of the thermal analysis results. Differential scanning calorimetry (DSC) studies showed that the PES-C/PEO blends prepared by casting from N,N-dimethylformamide (DMF) possessed a single, composition-dependent glass transition temperature (T_g), and thus that PES-C and PEO are miscible in the amorphous state at all compositions at lower temperature. At higher temperature, the blends underwent phase separation, and the PES-C/PEO blend system was found to display a lower critical solution temperature (LCST) behavior. The phase separation process in the blends has also been investigated by using DSC. Annealed at high temperatures, the PES-C/PEO blends exhibited significant changes of thermal properties, such as the enthalpy of crystallization and fusion, temperatures of crystallization and melting, depending on blend composition when phase separation occurred. These changes reflect different characteristics of phase structure in the blends, and were taken as probes to determine phase boundary. From both the thermal analysis and optical microscopy, the phase diagram of the blend system was established. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1383–1392, 1997     

Thermosetting polymer blends of unsaturated polyester resin and poly(ethylene oxide). I. Miscibility and thermal properties

The miscibility and thermal properties of polyethylene oxide(PEO)/oligoester resin (OER) blends and PEO/crosslinked polyester (PER) blends were studied by differential scanning calorimetry (DSC). The effect of quenching process on the crystallization behavior of PEO for these two systems were investigated and discussed in details. It has been found that a single, composition dependent glass transition temperature (T_g) was observed for all the blends, indicating that the two systems are miscible in the amorphous state at overall compositions. From the melting point depression of PEO, the interaction parameter χ₁₂ for PEO/OER blends and that for PEO/PER blends were found to be −1.29 and −2.01, respectively. The negative values of χ₁₂ confirmed that both PEO/OER blends and PEO/PER blends are miscible in the molten state. Quenching process has a greater hindrance on the crystallization of PEO/OER blends than on that of PEO/PER blends. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3161–3168, 1997     

Crystallization behavior and toughening mechanism of poly(ethylene oxide) in polyoxymethylene/poly(ethylene oxide) crystalline/crystalline blends

In this study, the unique crystallization behavior of poly(ethylene oxide) (PEO) in polyoxymethylene (POM)/PEO crystalline/crystalline blends was examined in detail. This study was the first to report the typical fractionated crystallization of PEO in POM/PEO blends when PEO is fewer than 30 wt.%. The delayed crystallization temperature of PEO was confirmed at about 5°C to 14°C by using differential scanning calorimetry and perturbation–correlation moving‐window 2D correlation IR spectroscopy. Wide‐angle X‐ray diffraction indicates that no new crystal structures or co‐crystals were generated in POM/PEO. The statistical calculations of scanning electron microscopy photos show that the average diameter of PEO particles is 0.227 µm to 1.235 µm and that the number of small particles is as many as 10⁹ magnitudes per cm³. Theory analysis establishes that the delayed crystallization of PEO is a heterogeneous nucleation process and not a homogeneous nucleation process. A significant toughening effect of PEO to POM was also observed. The impact strength of POM/PEO acquires a maximum of 10.5 kJ/m² when PEO content is 5%. The impact strength of the blend increases by 78.0% compared with pure POM. To improve the toughening effect, the best particle size is established between 0.352 and 0.718 µm, with a PEO particle spacing of 0.351 µm to 0.323 µm. The number of corresponding particles was 0.887 × 10⁹ per cm3 to 3.240 × 10⁹ per cm³. A PEO toughening model for POM was proposed to provide a new and effective way to solve the problem of POM toughening. Copyright © 2014 John Wiley & Sons, Ltd.     

Crystallization and morphology of poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) blends. II. Morphology and crystallization kinetics by time resolved X‐ray scattering

The development of the morphology in poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) (PVDF/PHB) blends upon isothermal and anisothermal crystallization is investigated by time‐resolved small‐ and wide‐angle X‐ray scattering. The components are completely miscible in the melt but crystallize separately; they crystallize stepwise at different temperatures or sequentially with isothermal or anisothermal conditions, respectively. The PVDF crystallizes undisturbed whereas PHB crystallizes in a confined space that is determined by the existing supermolecular structure of the PVDF. The investigations reveal that composition inhomogeneities may initially develop in the remaining melt or in the amorphous phases of the PVDF upon crystallization of that component. The subsequent crystallization of the PHB depends on these heterogeneities and the supermolecular structure of PVDF (dendritically or globularly spherulitic). PHB may form separate spherulites that start to grow from the melt, or it may develop “interlocking spherulites” that start to grow from inside a PVDF spherulite. Occasionally, a large number of PVDF spherulites may be incorporated into PHB interlocking spherulites. The separate PHB spherulites may intrude into the PVDF spherulites upon further growth, which results in “interpenetrating spherulites.” Interlocking and interpenetrating are realized by the growth of separate lamellar stacks (“fibrils”) of the blend components. There is no interlamellar growth. The growth direction of the PHB fibrils follows that of the existing PVDF fibrils. Depending on the distribution of the PHB molecules on the interlamellar and interfibrillar PVDF regions, the lamellar arrangement of the PVDF may contract or expand upon PHB crystallization and the adjacent fibrils of the two components are linked or clearly separated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 974–985, 2004     

Synthesis and characterization of poly(ethylene oxide)/polylactide/poly(ethylene oxide) triblock copolymer

Poly(ethylene oxide/polylactide/poly(ethylene oxide) (PEO/PL/PEO) triblock copolymers, in which each block is connected by an ester bond, were synthesized by a coupling reaction between PL and PEO. Hydroxyl‐terminated PLs with various molecular weights were synthesized and used as hard segments. Hydroxyl‐terminated PEOs were converted to the corresponding acid halides via their acid group and used as a soft segment. Triblock copolymers were identified by Fourier transform infrared spectroscopy, ¹H NMR, and gel permeation chromatography. Differential scanning calorimetry (DSC) and X‐ray diffractometry of PEO/PL/PEO triblock copolymers suggested that PL and PEO blocks were phase‐separated and that the crystallization behavior of the PL block was markedly affected by the presence of the PEO block. PEO/PL/PEO triblock copolymers with PEO 0.75k had two exothermic peaks (by DSC), and both peaks were related to the crystallization of PL. According to thermogravimetric analysis, PEO/PL/PEO triblock copolymer showed a higher thermal stability than PL or PEO. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2545–2555, 2002     

Phase behavior and crystallization of a poly(ethylene oxide)/cellulose acetate butyrate blend

The phase behavior of a partially miscible blend of poly(ethylene oxide) (PEO) and cellulose acetate butyrate (CAB) and the crystalline microstructure of PEO in the blend were studied with differential scanning calorimetry (DSC), optical microscopy, and synchrotron small‐angle X‐ray scattering (SAXS) methods. PEO/CAB showed a lower critical solution temperature (LCST) of 168 °C at the critical composition of PEO of 60 wt %. All blend compositions showed a single glass‐transition temperature (T_g) when they were prepared at temperatures lower than the LCST. However, with increasing CAB content, T_g of the blend changed abruptly at 70 wt % CAB; that is, a cusp existed. Below 70 wt % CAB, the change in T_g with blend composition was predicted by the Brau–Kovacs equation, whereas this change was predicted by the Fox equation at higher CAB contents. A gradual but small depression of the melting point of PEO in the blend with an increasing amount of CAB suggested that the PEO/CAB blends exhibited a weak intermolecular interaction. From DSC and SAXS experiments, it was found that amorphous CAB was incorporated into the interlamellar region of PEO for blends with less than 20 wt % CAB, whereas it was segregated to exist in the interfibrillar region in PEO for other blends with larger amounts of CAB. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1673–1681, 2002     

Crystallization kinetics of crosslinkable polymer complexes of novolac resin and poly(ethylene oxide)

Results of a study on the isothermal crystallization and thermal behavior of both uncured and hexamine-cured novolac/poly(ethylene oxide) (PEO) complexes are reported. The crystallization behavior of PEO in complexes is strongly influenced by factors such as composition, crystallization temperature, complexation, and crosslinking. The time dependence of the relative degree of crystallinity at high conversion deviated from the Avrami equation. The cured complexes exhibited an obvious two-stage crystallization (primary crystallization and crystal perfection), and this was more evident at higher crystallization temperature and high PEO-content. The addition of a noncrystallizable component into PEO caused a depression of both the overall crystallization rate and the melting temperature. In general, complexation and curing resulted in an increase in the overall crystallization rate. Complexation and curing are beneficial to the nucleation of PEO. Additionally, curing led to changes of the nucleation mechanism. Experimental data on the overall kinetic rate constant K_n were analyzed by means of the nucleation and crystal growth theory. For uncured complexes, the surface free energy of folding, σ_e, increased with increasing novolac content, whereas for cured complexes, σ_e displayed a maximum with the variation of composition. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2726–2736, 1999     

Effect of poly(ethylene oxide) on the structure and properties of poly(vinyl alcohol)

To improve the drawability of poly(vinyl alcohol) (PVA) thermal products, poly(ethylene oxide) (PEO), a special resin with good flexibility, excellent lubricity, and compatibility with many resins, was applied, and the Fourier transform infrared spectroscopy, dynamic mechanical analysis (DMA), differential scanning calorimetry (DSC), and wide‐angle X‐ray diffraction (WXRD) were adopted to study the hydrogen bonds, water states, thermal properties, crystal structure, and nonisothermal crystallization of modified PVA. It was found that PEO formed strong hydrogen bonds with water and PVA, thus weakened the intra‐ and inter‐hydrogen bonds of PVA, changed the aggregation states of PVA chains, and decreased its melting point and crystallinity. Moreover, the interactions among PVA, water, and PEO retarded the water evaporation and made more water remain in the system to plasticize PVA. The existence of PEO also slowed down the melt crystallization process of PVA, however, increased the nucleation points of system, thus made more and smaller spherulites formed. The weakened crystallization capability of PVA and the lubrication of PEO made PVA chains to have more mobility under the outside force and obtain high mechanical properties. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1946–1954, 2010     

Miscibility,crystallization kinetics,and morphology of poly(β‐hydroxybutyrate) and poly(methyl acrylate) blends

The miscibility, spherulite growth kinetics, and morphology of binary blends of poly(β‐hydroxybutyrate) (PHB) and poly(methyl acrylate) (PMA) were studied with differential scanning calorimetry, optical microscopy, and small‐angle X‐ray scattering (SAXS). As the PMA content increases in the blends, the glass‐transition temperature and cold‐crystallization temperature increase, but the melting point decreases. The interaction parameter between PHB and PMA, obtained from an analysis of the equilibrium‐melting‐point depression, is −0.074. The presence of an amorphous PMA component results in a reduction in the rate of spherulite growth of PHB. The radial growth rates of spherulites were analyzed with the Lauritzen–Hoffman model. The spherulites of PHB were volume‐filled, indicating the inclusion of PMA within the spherulites. The long period obtained from SAXS increases with increased PMA content, implying that the amorphous PMA is entrapped in the interlamellar region of PHB during the crystallization process of PHB. All the results presented show that PHB and PMA are miscible in the melt. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1860–1867, 2000     

Crystallization kinetics of poly(ethylene oxide) confined in semicrystalline poly(vinylidene) fluoride

Polymer blends based on poly(vinylidene fluoride) (PVDF) and poly(ethylene oxide) (PEO) have been prepared to analyze the crystallization kinetics of poly(ethylene oxide) confined in semicrystalline PVDF with different ratios of both polymers. Both blend components were dissolved in a common solvent, dimethyl formamide. Blend films were obtained by casting from the solution at 70 °C. Thus, PVDF crystals are formed by crystallization from the solution while PEO (which is in the liquid state during the whole process) is confined between PVDF crystallites. The kinetics of crystallization of the confined PEO phase was studied by isothermal and nonisothermal experiments. Fitting of Avrami model to the experimental DSC traces allows a quantitative comparison of the influence of the PVDF/PEO ratio in the blend on the crystallization behavior. The effect of melting and further recrystallization of the PVDF matrix on PEO confinement is also studied. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 588–597     

Studies of photooxidative degradation of poly(vinyl chloride)/poly(ethylene oxide) blends

The photooxidative degradation of blends (in a full range of compositions) of amorphous poly(vinyl chloride) (PVC) with semicrystalline poly(ethylene oxide) (PEO) in the form of thin films is investigated using absorption spectroscopy (UV–visible and Fourier transform infrared) and atomic force microscopy (AFM). The amount of insoluble gel formed as a result of photocrosslinking is estimated gravimetrically. It is found that the PVC/PEO blendsí susceptibility to photooxidative degradation differs from that pure of the components and depends on the blend composition and morphology. Photoreactions such as degradation and oxidation are accelerated whereas dehydrochlorination is retarded in blends. The photocrosslinking efficiency in PVC/PEO blends is higher than in PVC; moreover, PEO is also involved in this process. AFM images showing the lamellar structure of semicrystalline PEO in the blend lead to the conclusion that the presence of PVC does not disturb the crystallization process of PEO. The changes induced by UV irradiation allow the observation of more of the distinct PEO crystallites. This is probably caused by recrystallization of short, more mobile chains in degraded PEO or by partial removal of the less stable amorphous phase from the film surface. These results confirm previous information on the miscibility of PVC with PEO. The mechanism of the interactions between the components and the blend photodegradation are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 585–602, 2004     

Poly(hydroxyether of phenolphthalein) and its blends with poly(ethylene oxide)

Poly(hydroxyether of phenolphthalein) (PPH) was synthesized through the polycondensation of phenolphthalein with epichlorohydrin. It was characterized by Fourier transform infrared (FTIR) spectroscopy, NMR spectroscopy, and differential scanning calorimetry (DSC). The miscibility of the blends of PPH with poly(ethylene oxide) (PEO) was established on the basis of the thermal analysis results. DSC showed that the PPH/PEO blends prepared via casting from N,N‐dimethylformamide possessed single, composition‐dependent glass‐transition temperatures. Therefore, the blends were miscible in the amorphous state for all compositions. FTIR studies indicated that there were competitive hydrogen‐bonding interactions with the addition of PEO to the system, which were involved with OH…O?C〈, ? OH…? OH, and ? OH vs ether oxygen atoms of PEO hydrogen bonding, that is both intramolecular and intermolecular, between PPH and PEO). Some of the hydroxyl stretching vibration bands significantly shifted to higher frequencies, whereas others shifted to lower frequencies, and this suggested the formation of hydrogen bonds between the pendant hydroxyls of PPH and ether oxygen atoms of PEO, which were stronger than the intramolecular hydrogen bonding between hydroxyls and carbonyls of PPH. The FTIR spectra in the range of carbonyl stretching vibrations showed that the hydroxyl‐associated carbonyl groups were partially set free because of the presence of the competitive hydrogen‐bonding interactions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 466–475, 2003     

Conformational changes of poly(ethylene oxide) in poly(ethylene oxide)/poly(methyl methacrylate) blends by supercritical carbon dioxide

The effects of supercritical carbon dioxide (SC CO₂) fluids on the morphology and/or conformation of poly(ethylene oxide) (PEO) in PEO/poly(methyl methacrylate) (PMMA) blends were investigated by means of differential scanning calorimetry (DSC), wide‐angle X‐ray diffraction (WAXD), and Fourier transform infrared (FTIR). According to DSC data for a given blend, the melting enthalpy and, therefore, degree of crystallinity of PEO were increased, whereas the melting temperature of PEO was decreased, with SC CO₂ treatment. The enhancement of PEO crystallization with SC CO₂ treatment, as demonstrated by DSC data, was supported by WAXD data. According to FTIR quantitative analyses, before SC CO₂ treatments, the conformation of PEO was transformed from helix to trans planar zigzag via blending with PMMA. This helix‐to‐trans transformation of PEO increased proportionally with increasing PMMA content, with around 0.7% helix‐to‐trans transformation per 1% PMMA incorporation into the blend. For a given blend upon SC CO₂ treatments, the conformation of PEO was transformed from trans to helix. This trans‐to‐helix transformation of PEO decreased with increasing PMMA contents in the blends because of the presence of interactions between the two polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2479–2489, 2004     

聚氧乙烯／聚酚氧共混体系的结晶行为及相容性研究

对聚氧化乙烯/聚酚氧(PEO/PH)共混体系的研究表明,随共混体系中非晶组份PH含量的增加,Avrami指数n值由2.0～2.3变为1.5～2.0,体系的结晶由盘状生长转化为纤维状生长;成核方式由方式Ⅰ转化为方式Ⅱ.PEO/PH共混体系的平衡熔点随PH含量的增加而降低,相互作用能量密度B=-1.46cal/mol,说明体系是互容的。     

Morphology of poly(ethylene oxide)/poly(vinyl acetate) blends

The morphology of poly(ethylene oxide)/poly(vinyl acetate) (PEO/PVAc) blends was examined using small angle X-ray scattering (SAXS) and optical microscopy. The morphological and structural parameters of the blends are dependent on both composition and crystallization conditions. Optical microscopy revealed that blend samples prepared by solution casting crystallized with volume-filling crystals up to a composition of 30/70 wt% PEO/PVAc; at higher PVAc content there was no evidence of crystallization in the temperature range studied. Pure PEO always crystallized with a spherulite-hedrite morphology. The formation of spherulites was relatively favoured at lower crystallization temperatures and by addition of PVAc to PEO. Small angle X-ray intensity profiles were analyzed using a recently developed methodology and it was found that, for a given crystallization temperature, the amorphous and interphase thicknesses increased with increasing PVAc content but that the average crystalline thickness was independent of composition. The morphological and structural properties of the PEO/PVAc blends were attributed to the presence of non-crystallizable material in both the interlamellar and interfibrillar regions.     

Nonisothermal crystallization and melting behavior of poly(β‐hydroxybutyrate)–Poly(vinyl‐acetate) blends

Nonisothermal crystallization and melting behavior of poly(β‐hydroxybutyrate) (PHB)–poly(vinyl acetate) (PVAc) blends from the melt were investigated by differential scanning calorimetry using various cooling rates. The results show that crystallization of PHB from the melt in the PHB–PVAc blends depends greatly upon cooling rates and blend compositions. For a given composition, the crystallization process begins at higher temperatures when slower scanning rates are used. At a given cooling rate, the presence of PVAc reduces the overall PHB crystallization rate. The Avrami analysis modified by Jeziorny and a new method were used to describe the nonisothermal crystallization process of PHB–PVAc blends very well. The double‐melting phenomenon is found to be caused by crystallization during heating in DSC. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 443–450, 1999     

Miscibility and spherulite growth kinetics in the poly(ethylene oxide)/poly(benzyl methacrylate) system

This study for the first time discovered miscibility in the binary blend of semicrystalline poly(ethylene oxide) (PEO) with amorphous poly(benzyl methacrylate) (PBzMA). Differential scanning calorimetry, optical and scanning electron microscopy, and infrared spectroscopy were performed to characterize and demonstrate miscibility in the PEO/PBzMA system. The glass‐transition behavior and Fourier transform infrared results suggest that the intermolecular interactions between the pairs were likely nonspecific and at best comparable to those among the same constituent component. The melting‐point depression study yielded χ = −0.1, indicating a relatively low interaction strength. It is concluded that the phase behavior of the blend was miscibility with nonspecific interactions, mostly a matched polar–polar intermolecular attraction. PEO spherulitic crystallization in the blend is discussed to support the miscibility behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 562–572, 2000     

Dielectric relaxation study of atactic poly(epichlorohydrin)/poly(3-hydroxybutyrate) blends

Binary blends of atactic poly(epichlorohydrin) (aPECH) and poly(3-hydroxybutyrate) (PHB) were investigated as a function of blend composition and crystallization conditions by dielectric relaxation spectroscopy. The quenched samples were found to be miscible in the whole composition range by detecting only one glass transition relaxation, for each composition, which could be closely described by the Gorden-Taylor equation. The cold-crystallized blends displayed two glass transition relaxations at all blend ratios indicating the coexisting of two amorphous populations: a pure aPECH phase dispersed mainly in the interfibrillar zones and a mixed amorphous phase held between crystal lamellae. The interlamellar trapping of aPECH was small and decreases with increasing the overall PHB content in the blend. At high crystallization temperatures the aPECH molecules was found to reside mainly in the interfibrillar regions due to its high mobility relative to the crystal growth rate of PHB. Our results suggest that because the intersegmental interaction in aPECH/PHB blends is weak, the mobility of the amorphous component at a given crystallization temperature decides diluent segregation.     

Micro‐phase‐separation behavior of amphiphilic polyurethanes involving poly(ethylene oxide) and poly(tetramethylene oxide)

The temperature dependence of thermal, morphological, and rheological properties of amphiphilic polyurethanes was examined with differential scanning calorimetry (DSC), wide‐angle X‐ray scattering (WAXS), small‐angle X‐ray scattering (SAXS), rheological measurements, and Fourier transform infrared spectroscopy. Multiblock (MPU) and triblock (TPU) polyurethanes were synthesized with two crystallizable segments—poly(ethylene oxide) (PEO) as a hydrophilic block and poly(tetramethylene oxide) (PTMO) as a hydrophobic block. DSC and WAXS measurements demonstrated that the microphase of MPUs in the solid state is dominantly affected by the PEO crystalline phase. However, high‐order peaks were not observed in the SAXS measurements because the crystallization of the PEO segments in MPUs was retarded by poor sequence regularity. The microphase in the melt state was induced by the hydrogen bonding between the N? H group of hexamethylene diisocyanate linkers and the ether oxygen of PEO or PTMO blocks. As the temperature increased, the smaller micro‐phase‐separated domains were merged into the larger domains, and the liquidlike ordering was eventually disrupted because of the weakening hydrogen bonding. However, the fully homogeneous state of an MPU with a molar ratio of 5/5 PEO/PTMO (MPU55) was not confirmed even at much higher temperatures with both SAXS and rheological measurements. However, the SAXS patterns of TPU showed weak but broad second‐order peaks below the melting temperature of the PEO block. Compared with MPU55, the ordering of the TPU crystalline lamellar stacks was enhanced because of the high sequence regularity and the low hydrogen‐bonding density. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2365–2374, 2003     

FTIR Investigation of ion-dipole interaction in styrene ionomer/poly(ethylene oxide) blends

Fourier-transform infrared (FTIR) spectroscopy was used to examine specific interactions contributing to the partial miscibility in blends of styrene-sodium methacrylate copolymer (S-NaMA) and poly(ethylene oxide) (PEO). From the shifts of carboxylatelon and ether group stretching bands, an important specific interaction was found involving ion-dipole bonding between the ionic group in styrene ionomer and the ether group in PEO. The asymmetric stretching vibration frequency of the carboxylate ion group increases as the fractional amount of PEO in the blend is increased, while the symmetric stretching frequency is decreased. The transition value of the fraction of PEO, above which both vibration frequencies of the carboxylate ion mentioned above remained almost unchanged, increases as the concentration of ionic groups in ionomer is increased. The ether group stretching band shifts to higher frequencies as the PEO content in the ionomer/PEO blend is increased. From the differential scanning calorimetry (DSC) and FTIR studies, we find that the iondipole interaction is the important mechanism that determines the miscibility of S-NaMA/PEO blends. © 1994 John Wiley & Sons, Inc.