Three-dimensional Spherulitic Growth Research Articles

Non-Isothermal Crystallization Kinetics of Poly(ethylene glycol) and Poly(ethylene glycol)-B-Poly(ε-caprolactone) by Flash DSC Analysis.

The non-isothermal crystallization behaviors of poly (ethylene glycol) (PEG) and poly (ethylene glycol)-b-poly(ε-caprolactone) (PEG-PCL) were investigated through a commercially available chip-calorimeter Flash DSC2+. The non-isothermal crystallization data under different cooling rates were analyzed by the Ozawa model, modified Avrami model, and Mo model. The results of the non-isothermal crystallization showed that the PCL block crystallized first, followed by the crystallization of the PEG block when the cooling rate was 50–200 K/s. However, only the PEG block can crystallize when the cooling rate is 300–600 K/s. The crystallization of PEG-PCL is completely inhibited when the cooling rate is 1000 K/s. The modified Avrami and Ozawa models were found to describe the non-isothermal crystallization processes well. The growth methods of PEG and PEG-PCL are both three-dimensional spherulitic growth. The Mo model shows that the crystallization rate of PEG is greater than that of PEG-PCL.

Morphology and crystallization kinetics of Rubber-modified Nylon 6 Prepared by Anionic In-situ Polymerization

Abstract In this work, we modified nylon 6 with liquid rubber by in-situ polymerization. The infrared analysis suggested that HDI urea diketone is successfully blocked by caprolactam after grafting on hydroxyl of HTPB, and the rubber-modified nylon copolymer is generated by the anionic polymerization. The impact section analysis indicated the rubber-modified nylon 6 resin exhibited an alpha crystal form.With an increase in the rubber content, nylon 6 was more likely to generate stable α crystal. Avrami equation was a good description of the non-isothermal crystallization kinetics of nylon-6 and rubber-modified nylon-6 resin. Moreover, it is found that the initial crystallization temperature of nylon-6 chain segment decreased due to the flexible rubber chain segment. n value of rubber-modified nylon-6 indicated that its growth was the coexistence of two-dimensional discoid and three-dimensional spherulite growth. Finally, the addition of the rubber accelerated the crystallization rate of nylon 6.

Isothermal cold crystallization kinetics and properties of thermoformed poly(lactic acid) composites: effects of talc, calcium carbonate, cassava starch and silane coupling agents

The effects of three different fillers (i.e., talc, calcium carbonate, and cassava starch) and surface functionalization by 3-aminopropyltriethoxysilane (APTES) and vinyltriethoxysilane (VTES) on morphology, thermal and tensile properties of the poly(lactic acid) (PLA) composites were comparatively examined. Dynamic differential scanning calorimetry (DSC) results revealed that the incorporation of filler can facilitate the cold crystallization of PLA, as confirmed by lowered cold crystallization temperature. By fitting DSC data with Avrami model, the highest isothermal cold crystallization rate constant k and the shortest crystallization half time t1/2 were obtained for the PLA/talc composites under isothermal temperature of 100 °C, implying that talc was the most effective nucleating agent for PLA in this study. The average Avrami index n of neat PLA and its composites lay within the same range of 3.0–3.6, which reflected the three-dimensional spherulitic growth of PLA with the mixture of instantaneous nuclei and sporadic nuclei. In comparison with the composite cast films, the thermoformed films had higher degree of crystallinity as well as higher tensile strength and Young’s modulus owing to the chain orientation upon annealing. Furthermore, the addition of silane-treated talc, especially APTES-treated talc, fastened cold crystallization rate and enhanced tensile properties because of the improved interfacial interaction between talc particles and PLA matrix.

Nonisothermal Cold Crystallization Kinetics of Poly(lactic acid)/Bacterial Poly(hydroxyoctanoate) (PHO)/Talc

AbstractThe effects of bacterial poly(hydroxyoctanoate) (PHO) and talc on the nonisothermal cold crystallization behaviours of poly(lactic acid) (PLA) were analysed with differential scanning calorimetry (DSC), and the thermal stability of the samples was observed with thermal gravimetric analysis (TGA). The modified Avrami’s model was used to describe the nonisothermal cold crystallization kinetics of neat PLA and its blends. The activation energies E for nonisothermal cold crystallization were calculated by the isoconversional method of Kissinger-Akahira-Sunose (KAS). The DSC results showed that the PLA/PHO blends were immiscible in the whole studied range, and as the PHO and talc content increased, the crystallization rate of PLA accelerated, and the crystallinity of PLA in the PLA samples increased. The values of the Avrami exponent indicated that the nonisothermal cold crystallization of the neat PLA and its blends exhibited heterogeneous, three-dimensional spherulitic growth. The E values were strongly dependent on PHO and talc. The TGA results showed that the presence of PHO and talc slightly influenced the thermal stability of PLA.

Influence of clay surfactants polarity on the crystallization and rheological behavior of nanocomposites of PDLLA

The effect of clay hydrophobicity on the cold crystallization and rheological properties of nanocomposites of poly(D,L-lactic acid) (PDLLA) was investigated. Crystallization was evaluated by DSC for isothermal and non-isothermal conditions. The clay modified with a hydrophilic surfactant acts as a nucleating agent, while the clay modified with a hydrophobic surfactant acts in an opposite way. The Avrami and Ozawa parameters showed a three-dimensional spherulitic growth for all samples and the activation energy increased for the hydrophobic clay and decrease for the hydrophilic one. The equilibrium melting point for the PDLLA was found at 161oC, being slightly altered as function of the surfactant polarity. The rheological behavior was investigated in terms of Isothermal Flow-Induced Crystallization and Structural Recovery. The hydrophobic clay showed to reduce the mobility of chains and retard the chain relaxation, which is attributed to the formation of a network, while the hydrophilic clay increased the chain mobility.

Combined effect of nucleating agent and plasticizer on the crystallization behaviour of polylactide

Different plasticized and nucleated polylactide (PLA) systems were prepared and characterized. Two PLA with different l-lactic acid contents (96 and 99.5%) were plasticized with dioctyl adipate (DOA) and nucleated by talc, ethylene bis(stearamide) (EBS), or d-lactic acid-based PLA (PDLA). Crystallization behaviour was studied by differential scanning calorimetry (DSC), wide-angle X-ray diffraction (WAXD), and polarized optical microscopy (POM). The combination of plasticizer and nucleating agent was proved to be a very effective approach to improve crystallization velocity of different PLA matrices. Within the studied crystallization temperature range, faster crystallization rates were achieved at lower temperatures. WAXS results indicated the coexistence of α and α′ crystals in all studied systems, except those which showed very low crystallization degrees. Avrami exponent remained constant at around n ≈ 3 for all systems, suggesting equivalent three-dimensional spherulitic growth behaviour regardless crystallization temperature, nucleating agent, and the stereochemistry of the matrix used. Usually, injection-moulding process, where molten polymer is under high pressure, is used for PLA polymer processing. To analyze the effect of pressure on the crystallization process, pressure volume temperature (PVT) measurements were carried out on the systems that showed the fastest crystallization process under atmospheric pressure by DSC. Results showed that the crystallization process was considerably accelerated under pressure.

Nonisothermal crystallization behavior and molecular dynamics of poly(lactic acid) plasticized with jojoba oil

Poly(lactic acid) (PLA) containing different contents of jojoba oil (3 and 7 mass%; namely PLA-3JO and PLA-7JO), as natural plasticizer, was prepared via melt compounding. The nonisothermal crystallization behavior of PLA in the presence of jojoba oil was investigated from the glassy state. The obtained results revealed that the rate of crystallization and degree of crystallinity increased with increasing the content of jojoba. The nonisothermal crystallization kinetics was analyzed by the Avrami–Jeziorny model. Avrami exponent (n) of the PLA, PLA-3JO and PLA-7JO was found to be 4.08, 3.28 and 3.09, respectively, suggesting that the nonisothermal cold crystallizations of the plasticized PLA follow a heterogeneous nucleation and three-dimensional spherulitic growth, as occurring in the neat PLA. Furthermore, the activation energy of nonisothermal crystallization process (ΔE a) was calculated as a function of blend composition based on the Kissinger equation. It was found that the ΔE a of PLA insignificantly changed in the presence of jojoba oil. The dielectric properties of totally amorphous and crystallized plasticized PLA were also investigated for the α-relaxation process as a function of the temperature and frequency. The α-relaxation process was analyzed with Havriliak–Negami and Vogel–Fulcher–Tammann models, and fitting parameters with their evolution were discussed.

Study of Non-Isothermal Crystallization of Polydioxanone and Analysis of Morphological Changes Occurring during Heating and Cooling Processes.

Non-isothermal crystallization kinetics of polydioxanone (PDO), a polymer with well-established applications as bioabsorbable monofilar suture, was investigated by Avrami, Mo, and isoconversional methodologies. Results showed Avrami exponents appearing in a relatively narrow range (i.e., between 3.76 and 2.77), which suggested a three-dimensional spherulitic growth and instantaneous nucleation at high cooling rates. The nucleation mechanism changed to sporadic at low rates, with both crystallization processes being detected in the differential scanning calorimetry (DSC) cooling traces. Formation of crystals was hindered as the material crystallized because of a decrease in the motion of molecular chains. Two secondary nucleation constants were derived from calorimetric data by applying the methodology proposed by Vyazovkin and Sbirrazzuoli through the estimation of effective activation energies. In fact, typical non-isothermal crystallization analysis based on the determination of crystal growth by optical microscopy allowed secondary nucleation constants of 3.07 × 105 K2 and 1.42 × 105 K2 to be estimated. Microstructure of sutures was characterized by a stacking of lamellae perpendicularly oriented to the fiber axis and the presence of interlamellar and interfibrillar amorphous regions. The latter became enhanced during heating treatments due to loss of partial chain orientation and decrease of electronic density. Degradation under various pH media revealed different macroscopic morphologies and even a distinct evolution of lamellar microstructure during subsequent heating treatments.

Primary and Secondary Crystallization Kinetic Analysis of Poly(Hexamethylene Succinate)

Isothermal crystallization kinetics of poly(hexamethylene succinate) (PHS) were investigated by using differential scanning calorimetry (DSC). Primary and secondary crystallization behaviors were described satisfactorily by a modified Avrami model. The obtained results suggest that primary crystallization under isothermal conditions involves three-dimensional spherulite growth with athermal nucleation, and secondary crystallization displays approximate one-dimensional crystal growth.

Polymer crystallization dynamics investigated by synchronous scanning spectrum.

There is a cosine function between the reflected light intensity of a solid surface and its refractive index. And the mean squared fluctuation of refractive index is related to fluctuation of density and concentration. So some internal structures changes of materials can be reflected by changes in reflected light. Based on this theory, the synchronous scanning spectrum (SSS) technique was successfully applied to monitor melting and nonisothermal melt-crystallization of poly(ε-caprolactone) (PCL) film on a copper substrate. SSS can be implemented on a spectrofluorimeter by simultaneously scanning the excitation and emission monochromators (i. e, Δλ = λex-λem = 0 nm). In SSS of PCL films, two dominant peaks correlated to the light source spectrum of the spectrofluorimeter (at 467 and 473 nm) were used to characterize the macromolecular structure evolution during the melting and nonisothermal melt-crystallization processes. Detailed thermodynamic and crystallization kinetics parameters obtained by SSS method. The Avrami exponent n obtained by SSS method is in the range of 2.8-3.2 with an average of 3.13, illustrating a heterogeneous nucleation process followed by a three-dimensional spherulitic crystal growth mechanism. The crystallization activation energy is -158.2 kJ · mol(-1). These results are in agreement with values determined from differential scanning calorimetry (DSC) method. It indicates that SSS technique is a simple, effective in situ method for measuring the dynamic melting and crystallization process of polymers. Moreover, the SSS method is a universal spectroscopic technique based on a spectrofluorimeter for monitoring both luminescent and non-luminous solid polymers.

Isothermal Cold Crystallization and Melting Behaviors of Poly(lactic acid)/Epoxy Vinyl Polyhedral Oligomeric Silsesquioxanes Nanocomposites

Poly(l-lactic acid) (PLA)/epoxy vinyl polyhedral oligomeric silsesquioxane (EP-POSS) nanocomposites were prepared via melt blending. The isothermal cold crystallization and melting behavors of pure PLA and its nanocomposites were investigated using differential scanning calorimetry (DSC). The crystal growth model of PLA was a mixture of two-dimensional discotic growth and three-dimensional spherulite growth, as evidenced by the values of the Avrami exponent ranging from 2.15 to 2.66. The crystallization rate displayed a great dependence on the EP-POSS loading level and crystallization temperature, and a transition from regime II to regime III was observed around 115°C. The values of fold surface free energy were calculated from the nucleation parameter which was determined by the Hoffman-Lauritzen equation. Polarizing microscope images (POM) indicated that EP-POSS promoted the nucleation of PLA.

Crystallization behavior of poly(ethylene terephthalate)/pyrrolidinium ionic liquid

Composites of poly(ethylene terephthalate) (PET) with ionic liquid (IL) as matrix were prepared by in situ polycondensation. XRD and DSC were performed to probe crystal structures and determine the crystallization kinetics during crystallization. ILs could serve as nucleating agents in accelerating the crystallization of PET. However, the ability of ILs to induce crystallization is different with variation of IL content. Avrami analysis revealed that the Avrami exponent, n > 2, testifies to the existence of three-dimensional spherulitic growth. The kinetic equations (the modified Avrami equation and the combined Avrami and Ozawa equation) are employed to analyze the non-isothermal process. The modified Avrami equation could adequately describe the primary non-isothermal crystallization of PET/IL. The approach of combining the Avrami and Ozawa equations provides a fairly satisfactory description of the non-isothermal crystallization of PET/IL. © 2013 Society of Chemical Industry

Isothermal and nonisothermal crystallization kinetics of poly(ϵ‐caprolactone)

AbstractWith increasing environmental awareness, evaluating the potential of biopolymers as a substitute for traditional materials has been of great interest. Crystallization kinetics provides fundamental knowledge required for evaluation, playing vital role in determining the final properties of the product. In this study, the isothermal and nonisothermal crystallization kinetics of poly(ϵ‐caprolactone) (PCL) were investigated with the help of various models. The Avrami model best described the isothermal crystallization kinetics, suggesting three‐dimensional spherulitic growth, which was in agreement with the morphology studies; whereas the Liu model fit well under nonisothermal crystallization conditions. The failure of the Kissinger model to determine the activation energy was overcome with the Friedman model. The kinetic crystallizability determined by the Ziabacki model indicated a higher crystallization ability of PCL at lower cooling rates. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

In Situ Synchrotron X-ray Scattering Study on Isotactic Polypropylene Crystallization under the Coexistence of Shear Flow and Carbon Nanotubes

The crystallization of isotactic polypropylene (iPP) under the coexistence of shear flow and carbon nanotubes (CNTs) was investigated by means of in situ synchrotron X-ray scattering techniques, i.e. wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS). Compared to sheared pure iPP, the combined effect of shear flow and CNTs endowed iPP crystals with weak degree of orientation at the early stage of crystallization but high degree of orientation in the later period. This was because the initial orientation of molecular chains induced by shear was suppressed as a result of the increased viscoelasticity of iPP melt in the presence of CNTs, but subsequently oriented molecular chains were stabilized by CNT surface absorption. The crystallization kinetics of sheared CNTs/iPP nanocomposites was synergistically promoted, where the crystallization rate was increased about 40 times in comparison to that of quiescently crystallized pure iPP. The Avrami exponent of CNTs/iPP nanocomposites and sheared iPP was around 2, indicating two-dimensional lamellar growth. The Avrami exponent of sheared CNTs/iPP nanocomposites surprisingly appeared to be 2.52, suggestive of mixed two-dimensional lamellar growth and three-dimensional sphrulitic growth geometries. Moreover, β-crystals were absent in sheared CNTs/iPP nanocomposites in contrast to the normal observation that α-row nuclei induced by shear generated β-crystals. The synergistic crystallization rate, the mixed crystal growth geometry as well as the absence of β-crystals in sheared CNTs/iPP nanocomposites were in close relation with intense interaction between shear flow and CNTs, which gave rise to extra nuclei in sheared CNTs/iPP melt. Apart from heterogeneous nucleating sites originated from CNTs and homogeneous nucleating sites (row-nuclei) initiated by shear, extra nuclei were taken into account to contribute to the further accelerated crystallization kinetics. The extra nuclei became active growth points of branching sites on the two-dimensional lamellae to generate three-dimensional spherulitic growth, thus leading to mixed crystal growth geometry of sheared CNTs/iPP nanocomposites. Besides, extra nuclei as well as α-nuclei derived from CNTs remarkably encouraged the formation of α-crystals, responsible for inexistence of β-crystals in sheared CNTs/iPP nanocomposites.

Preparation and crystallization behavior of polylactide nanocomposites reinforced with POSS-modified montmorillonite

We herein report the preparation and crystallization behavior of polylactide (PLA) nanocomposites reinforced with polyhedral oligomeric silsesquioxane-modified montmorillonite (POSS-MMT), which is prepared by exchanging sodium cations of pristine sodium montmorillonite (Na-MMT) with protonated aminopropylisobutyl polyhedral oligomeric silsesquioxane (POSS-NH3+). PLA nanocomposites with 1–10 wt% POSS-MMT contents are manufactured via melt-compounding, and their structures and melt-crystallization behavior are investigated. It is characterized that POSS-MMT nanoparticles in the nanocomposites have an exfoliated structure of MMT silicates with POSS-NH3+ and partial POSS-NH2 crystals. DSC cooling thermograms suggest that the overall melt-crystallization rates of the nanocomposite with only 3 wt% POSS-MMT are remarkably enhanced in comparison with the neat PLA. From the isothermal crystallization analysis based on the Avrami model, the overall melt-crystallization of PLA/POSS-MMT nanocomposites is found to be dominated by the heterogeneous nucleation and three-dimensional spherulite growth. Isothermal melt-crystallization experiments using a polarized optical microscope show that the spherulite nucleation density of PLA/POSS-MMT nanocomposites is much higher than that of the neat PLA, whereas the spherulite growth rates of all the nanocomposites are almost identical with the rate of the neat PLA. It is concluded that the highly enhanced melt-crystallization rates of PLA/POSS-MMT nanocomposites stem from the dominant nucleation effect of POSS-MMT nanoparticles for PLA crystals.

Non-isothermal crystallization kinetics of isotactic polypropylene nucleated with nucleating agent bicyclic [2,2,1] heptane di-carboxylate

AbstractBicyclic [2,2,1] heptane di-carboxylate (commercial product name: HPN- 68) is a novel nucleating agent with high nucleation efficiency for isotactic polypropylene (iPP). In this paper, the non-isothermal crystallization kinetics of virgin iPP and iPP nucleated with HPN-68 were investigated by means of a differential scanning calorimeter (DSC).The Caze method was used to analyze the non-isothermal crystallization kinetics. The results show that addition of HPN-68 can increase the crystallization peak temperature (Tp) of iPP greatly under the same cooling rate. Under non-isothermal conditions, the addition of HPN-68 changes the spherulite growth pattern of iPP. For virgin iPP, the growth pattern is mainly spontaneous nucleation followed by three-dimensional spherulite growth, while for iPP nucleated with HPN-68, the growth pattern is mainly heterogeneous nucleation followed by three-dimensional spherulite growth.

Non-isothermal crystallization kinetics of partially miscible ethylene-vinyl acetate copolymer/low density polyethylene blends

The non-isothermal crystallization kinetics of ethylene-vinyl acetate copolymer (EVA, 14 wt% vinyl acetate content), low density polyethylene (LDPE) and their binary blends with different blending ratio were investigated via differential scanning calorimetry. Jeziorny theory and Mo’s method were utilized in evaluating the crystallization behavior of both neat materials successfully. In the primary crystallization stage both EVA and LDPE had three-dimensional spherulitic growth mechanism. Apparently the crystallization rate of LDPE was faster than that of EVA at a low cooling rate. Increase in cooling rate limited the spherulites’ growth, which narrowed their rate difference. Influences from blending on the crystallization kinetics of each component in EVA/LDPE mixture were evaluated by Kissinger’s activation energy (ΔE) and Khanna’s crystallization rate coefficient (CRC). Inter-molecular interaction in the melt increased the ΔE of both EVA and LDPE components at the beginning of cooling. During the primary crystallization stage of LDPE, dilution effect from EVA facilitated the crystal growth in LDPE. Co-crystallization between EVA component and the secondary crystallization stage of LDPE component also increased the CRC of EVA. In blend of EVA/LDPE = 7/3, LDPE obtained the maximal CRC value of 174.2 h–1. Results obtained from various approaches accorded well with each other, which insured the rationality of conclusion.

Isothermal Crystallization Behaviors of Isotactic Polypropylene Nucleated with Nucleating Agent Bicyclic [2,2,1] heptane di-carboxylate

Bicyclic [2,2,1] heptane di-carboxylate (commercial product name: HPN-68) is a novel nucleating agent with high nucleation efficiency for α-iPP. In this article, differential scanning calorimetry (DSC) was adopted to investigate the isothermal crystallization kinetics of isotactic polypropylene (iPP) nucleated with HPN-68. The Avrami equation well described the isothermal crystallization kinetics of iPP nucleated with HPN-68. The results showed that addition of HPN-68 could shorten half crystallization time (t1/2) and increase the crystallization rate of iPP significantly. The Avrami exponents of both virgin iPP and iPP nucleated with HPN-68 were close to 3.0, which indicated that the addition of nucleating agent HPN-68 didn't change the crystallization growth patterns of iPP under isothermal conditions and the crystal growth was heterogeneously nucleated three-dimensional spherulitic growth. In addition, incorporation of nucleating agent HPN-68 obviously decreased the crystallization activation energy ΔE of iPP, from 368 kJ/mol for virgin iPP to 306 kJ/mol.

Isothermal crystallization of poly(glycolic acid-alt-6-hydroxyhexanoic acid) studied by DSC and real time synchrotron SAXS/WAXD

The thermal properties and the isothermal hot crystallization behavior of a new regular polyester constituted of glycolic acid and 6-hydroxyhexanoic acid units were studied by differential scanning calorimetry (DSC). The morphological development during isothermal crystallization was also investigated using simultaneous small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD) techniques with synchrotron radiation. A crystalline–amorphous two-phase lamellar system was assumed and interpreted using correlation functions.Kinetic parameters deduced from the Avrami analysis indicated a three-dimensional spherulitic growth from heterogeneous nuclei, whereas optical micrographs revealed the formation of small spherulites with a negative birefringence and a fibrillar texture. The Lauritzen and Hoffman analysis of crystallization regimes was performed taking into account the kinetic constants of the overall crystallization process deduced from DSC and also the reciprocal crystallization halftimes evaluated by means of DSC, SAXS and WAXD experiments. Data were consistent with a single crystallization regime and yielded similar values for the transport activation energy and the nucleation constant in all cases.The evolution of long period and lamellar thickness was evaluated during crystallization. Changes with both crystallization time and crystallization temperature were significant.

Thermal stability, crystallization, structure and morphology of syndiotactic 1,2-polybutadiene/organoclay nanocomposite

Syndiotactic 1,2-polybutadiene/organoclay nanocomposites were prepared and characterized by thermogravimetry analysis (TGA), X-ray diffraction (XRD), polarized optical microscopy (POM), and differential scanning calorimetry (DSC), respectively. The XRD shows that exfoliated nanocomposites are formed dominantly at lower clay concentrations (less than 2%), at higher clay contents intercalated nanocomposites dominate. At the same time, the XRD indicates that the crystal structures of sPB formed in the sPB/organoclay nanocomposites do not vary, only the relative intensity of the peaks corresponding to (0 1 0) and (2 0 0)/(1 1 0) crystal planes, respectively, varies. The DSC and POM indicate that organoclay layers can improve cooling crystallization temperature, crystallization rate and reducing the spherulite sizes of sPB. TGA shows that under argon flow the nanocomposites exhibit slight decrease of thermal stability, while under oxygen flow the resistance of oxidation and thermal stability of sPB/organoclay nanocomposites were significantly improved relative to pristine sPB. The primary and secondary crystallization for pristine sPB and sPB/organoclay (2%) nanocomposites were analyzed and compared based on different approaches. The nanocomposites exhibit smaller Avrami exponent and larger crystallization rate constant, with respect to pristine sPB. Primary crystallization under isothermal conditions displays both athermal nucleation and three-dimensional spherulite growth and under nonisothermal processes the mechanism of primary crystallization becomes very complex. Secondary crystallization shows a lower-dimensional crystal growth geometry for both isothermal and nonisothermal conditions. The activation energy of crystallization of sPB and sPB/organoclay nanocomposites under isothermal and nonisothermal conditions were also calculated based on different approaches.