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We study self-affine tiles generated by iterated function systems consisting of affine mappings whose linear parts are defined by different matrices. We obtain an interior theorem for these tiles. We prove a tiling theorem by showing that for such a self-affine tile, there always exists a tiling set. We also obtain a more complete interior theorem for reptiles, which are tiles obtained when the matrices in the iterated function system are similarities. Our results extend some of the classical ones by Lagarias and Wang (Adv. Math. 121(1), 21–49 (1996)), where the IFS maps are defined by a single matrix. [ABSTRACT FROM AUTHOR]

For x ∈ [ 0 , 1 ] , the run-length function r n (x) is defined as the length of longest run of 1’s among the first n dyadic digits in the dyadic expansion of x. We study the Hausdorff dimension of the exceptional set in Erdös–Rényi limit theorem. Let φ : N → (0 , ∞) be a monotonically increasing function with lim n → ∞ φ (n) = ∞ and 0 ≤ α ≤ β ≤ ∞ , define E α , β φ = { x ∈ [ 0 , 1 ] : lim inf n → ∞ r n (x) φ (n) = α , lim sup n → ∞ r n (x) φ (n) = β }. We prove that E α , β φ has Hausdorff dimension one if lim n , p → ∞ φ (n + p) - φ (n) p = 0 and that E 0 , ∞ φ is residual in [0,1] when lim inf n → ∞ φ (n) n = 0 . [ABSTRACT FROM AUTHOR]

Highlights: The SiO2 nanofiber membranes and MXene@c-MWCNT6:4 as one unit layer (SMC1) were bonded together with 5 wt% PVA solution. When the structural unit is increased to three layers, the resulting SMC3 has an average electromagnetic interference SET of 55.4 dB and a low thermal conductivity of 0.062 W m−1 K−1. SMCx exhibit stable electromagnetic interference shielding and excellent thermal insulation even in extreme heat and cold environment. A lightweight flexible thermally stable composite is fabricated by combining silica nanofiber membranes (SNM) with MXene@c-MWCNT hybrid film. The flexible SNM with outstanding thermal insulation are prepared from tetraethyl orthosilicate hydrolysis and condensation by electrospinning and high-temperature calcination; the MXene@c-MWCNTx:y films are prepared by vacuum filtration technology. In particular, the SNM and MXene@c-MWCNT6:4 as one unit layer (SMC1) are bonded together with 5 wt% polyvinyl alcohol (PVA) solution, which exhibits low thermal conductivity (0.066 W m−1 K−1) and good electromagnetic interference (EMI) shielding performance (average EMI SET, 37.8 dB). With the increase in functional unit layer, the overall thermal insulation performance of the whole composite film (SMCx) remains stable, and EMI shielding performance is greatly improved, especially for SMC3 with three unit layers, the average EMI SET is as high as 55.4 dB. In addition, the organic combination of rigid SNM and tough MXene@c-MWCNT6:4 makes SMCx exhibit good mechanical tensile strength. Importantly, SMCx exhibit stable EMI shielding and excellent thermal insulation even in extreme heat and cold environment. Therefore, this work provides a novel design idea and important reference value for EMI shielding and thermal insulation components used in extreme environmental protection equipment in the future. [ABSTRACT FROM AUTHOR]

The use of antibacterial biodegradable polymers is of great importance nowadays in medical applications. In this manuscript, poly(butylenes adipate-co-terephthalate)/poly(lactic acid) blend-based antibacterial bionanocomposites were prepared by melt-processing. We use organically modified montmorillonite (MMT) and graphene nanoplatelets (GNP) as antibacterial property enhancers which are both processing platelike structure, while ciprofloxacin hydrochloride (CFX·HCl) was chosen as a biocide. Either MMT or GNP increases the antibacterial properties during the whole study and tunes the release of CFX·HCl from the bionanocomposites. This was proven by agar diffusion tests and antimicrobial release measurements. The morphology of the bionanocomposites was conducted by using scanning and transmission electron microscopies, and evidence of exfoliation was observed. Contact angle and water uptake of the bionanocomposites were studied showing hydrophilic performance and more percentage water uptake. The final effect on mechanical and blood compatibility was also investigated. The results reveal excellent possibility of using MMT- and GNP-modified PLA/PBAT polymer blends to tune antibacterial properties for specific biomedical applications. [ABSTRACT FROM AUTHOR]

In this work, poly(ethylene glycol) (PEG)/boron nitride nanosheets (BNNS) masterbatch was prepared by freeze-drying their ultrasonically homogenized aqueous suspension, followed by melt-mixing with poly(lactic acid) (PLA) to fabricate the nanocomposites. The effect of PEG and BNNS on the crystallization behavior of PLA was investigated. The dynamic mechanical properties, thermal conductivity and thermal stability of the nanocomposites were also evaluated. It was found that, under quiescent conditions, PEG and BNNS had a synergistic effect on accelerating the nonisothermal crystallization of PLA. Unexpectedly, under injection molding conditions, the combination of PEG and BNNS had a negative effect on PLA crystallization. This can be ascribed to the plasticizing effect of PEG, which relaxes the orientation of PLA chains and retards flow-induced crystallization. Dynamic mechanical analysis (DMA) showed that the presence of BNNS enhanced the heat resistance of PLA only when PLA was crystallized, while further incorporation of PEG had a negative effect. Nevertheless, simultaneous use of PEG and BNNS had a synergistic effect on enhancing the thermal conductivity of PLA. [ABSTRACT FROM AUTHOR]

Highlights: Cellulose aerogel with vertically oriented structure was obtained by constructing a vertically aligned SiC nanowires/BN network via the ice template assisted strategy. The thermal conductivity of the composite in the vertical direction reaches 2.21 W m−1 K−1 at a low hybrid filler loading of 16.69 wt%, which was increased 890% compared to pure epoxy. The composite exhibits good electrically insulating with a volume electrical resistivity about 2.35×1011 Ω cm, and displays excellent electromagnetic wave absorption performance. With the innovation of microelectronics technology, the heat dissipation problem inside the device will face a severe test. In this work, cellulose aerogel (CA) with highly enhanced thermal conductivity (TC) in vertical planes was successfully obtained by constructing a vertically aligned silicon carbide nanowires (SiC NWs)/boron nitride (BN) network via the ice template-assisted strategy. The unique network structure of SiC NWs connected to BN ensures that the TC of the composite in the vertical direction reaches 2.21 W m−1 K−1 at a low hybrid filler loading of 16.69 wt%, which was increased by 890% compared to pure epoxy (EP). In addition, relying on unique porous network structure of CA, EP-based composite also showed higher TC than other comparative samples in the horizontal direction. Meanwhile, the composite exhibits good electrically insulating with a volume electrical resistivity about 2.35 × 1011 Ω cm and displays excellent electromagnetic wave absorption performance with a minimum reflection loss of − 21.5 dB and a wide effective absorption bandwidth (< − 10 dB) from 8.8 to 11.6 GHz. Therefore, this work provides a new strategy for manufacturing polymer-based composites with excellent multifunctional performances in microelectronic packaging applications. [ABSTRACT FROM AUTHOR]

Highlights: Ni-MXene/MF foam is synthesized via an electrostatic assembly and dip-coating process. The "micro-capacitor" structure of Ni/MXene and the 3D porous structure of MF endow the foam excellent impedance matching and wave absorption performance. The excellent heat insulation, infrared stealth, and flame-retardant performances are achieved. The development of multifunctional and efficient electromagnetic wave absorbing materials is a challenging research hotspot. Here, the magnetized Ni flower/MXene hybrids are successfully assembled on the surface of melamine foam (MF) through electrostatic self-assembly and dip-coating adsorption process, realizing the integration of microwave absorption, infrared stealth, and flame retardant. Remarkably, the Ni/MXene-MF achieves a minimum reflection loss (RLmin) of − 62.7 dB with a corresponding effective absorption bandwidth (EAB) of 6.24 GHz at 2 mm and an EAB of 6.88 GHz at 1.8 mm. Strong electromagnetic wave absorption is attributed to the three-dimensional magnetic/conductive networks, which provided excellent impedance matching, dielectric loss, magnetic loss, interface polarization, and multiple attenuations. In addition, the Ni/MXene-MF endows low density, excellent heat insulation, infrared stealth, and flame-retardant functions. This work provided a new development strategy for the design of multifunctional and efficient electromagnetic wave absorbing materials. [ABSTRACT FROM AUTHOR]

In this work, biodegradable poly(lactic acid) (PLA)/Ti3C2Tx MXene nanocomposites were prepared through melt compounding. The roles of MXene in nonisothermal melt and cold crystallization of PLA were explored. The morphology, structure and crystallization behavior were studied using polarized optical microscopy, wide-angle X-ray diffraction and differential scanning calorimetry. For nonisothermal melt crystallization, the presence of MXene increases the crystallinity and shortens the half-crystallization time but does not change the crystallization peak temperature of PLA. For nonisothermal crystallization from the glassy state, the incorporation of MXene decreases the cold crystallization peak temperature and reduces the crystallinity marginally but does not affect the half-crystallization time of PLA. The crystallization kinetics analysis based on the Avrami equation shows that, for both the melt and cold crystallization, the crystallization mechanism is unchanged irrespective of the addition of MXene. The investigation would be useful for understanding the correlation between processing and properties of PLA/MXene nanocomposites. [ABSTRACT FROM AUTHOR]

Poly(l-lactic acid) (PLLA) is a biodegradable and biocompatible polyester with great promise to be used in biomedical fields. Blending with poly(ethylene oxide) (PEO) can further improve the biocompatibility of PLLA. In this work, the effect of miscible blending of PEO on the crystal structure of PLLA was investigated. For neat PLLA, α′- and α-crystals are formed at crystallization temperature Tc < 110 °C and Tc ≥ 110 °C, respectively. With increasing PEO content, the difference of lattice spacing between α′- and α-crystals is gradually reduced. As PEO reaches 10 wt%, there is no apparent evidence of the presence of α′-crystal in the investigated Tc ranges. The blending effect of PEO on the crystal polymorphism of PLLA can be ascribed to the declined equilibrium melting point and lowered glass transition temperature. [ABSTRACT FROM AUTHOR]

Highlights: Flexible Ag microparticle/MXene-based energy-harvesting films were fabricated via simple spraying and hot-pressing. Optimal film shows high conductivity and effective electro/photo-thermal abilities. It can be easy assembled single-electrode TENG and the output voltage is enhanced by assembled two triboelectrification layers.Ultra-thin flexible films have attracted wide attention because of their excellent ductility and potential versatility. In particular, the energy-harvesting films (EHFs) have become a research hotspot because of the indispensability of power source in various devices. However, the design and fabrication of such films that can capture or transform different types of energy from environments for multiple usages remains a challenge. Herein, the multifunctional flexible EHFs with effective electro-/photo-thermal abilities are proposed by successive spraying Ag microparticles and MXene suspension between on waterborne polyurethane films, supplemented by a hot-pressing. The optimal coherent film exhibits a high electrical conductivity (1.17×104 S m−1), excellent Joule heating performance (121.3 °C) at 2 V, and outstanding photo-thermal performance (66.2 °C within 70 s under 100 mW cm−1). In addition, the EHFs-based single-electrode triboelectric nanogenerators (TENG) give short-circuit transferred charge of 38.9 nC, open circuit voltage of 114.7 V, and short circuit current of 0.82 μA. More interestingly, the output voltage of TENG can be further increased via constructing the double triboelectrification layers. The comprehensive ability for harvesting various energies of the EHFs promises their potential to satisfy the corresponding requirements. [ABSTRACT FROM AUTHOR]

Poly(ether ether ketone) (PEEK) is a high-performance thermoplastics with outstanding mechanical properties and thermal resistance (serving temperature up to 250 °C). Although many studies have been performed on the stress–strain behavior and related modeling, less attention has been paid on the structural and orientational evolution of PEEK during tensile deformation. In this work, the orientational and structural evolution during tensile deformation at a wide range of temperatures from 30 to 170 °C was probed ex situ by wide-angle X-ray diffraction and differential scanning calorimetry. The enthalpy of cold crystallization of PEEK as a function of strain, which reflects the content of amorphous fraction and the disorder degree of crystals, presents an interesting dependence on tensile temperature. The evolution of orientation with strain is strongly dependent on the tensile temperature. Oriented PEEK presents much improved modulus and tensile strength compared to that of undrawn PEEK. This finding demonstrated that pre-stretching especially at temperatures above Tg is an effective way to improve the mechanical property of PEEK. [ABSTRACT FROM AUTHOR]

Poly(lactic acid) (PLA)/poly(ethylene oxide) (PEO) blends nucleated by a self-assembly nucleating agent, N,N′,N″-tricyclohexyl-1,3,5-benzenetricarboxylamide (BTCA), were prepared by melt blending. The crystallization behavior and mechanical properties of the materials were investigated by differential scanning calorimetry, polarized optical microscopy, wide-angle X-ray diffraction, dynamic mechanical analyzer and tensile testing. It was found that PEO had a synergistic effect together with BTCA on promoting PLA crystallization, besides its toughening effect on the material. Moreover, BTCA revealed prominent reinforcement effect on both neat PLA and PLA/PEO blends in the glass transition region and above, indicating the improvement on the heat resistance of the materials. [ABSTRACT FROM AUTHOR]

The crystallization behavior of partially melted poly(ether ether ketone) (PEEK) was investigated by differential scanning calorimetry. The influence of pre-crystallization conditions was studied in details. After partial melting, the maximum peak shifts to higher temperature by 8.4-11.8 °C during subsequent cooling, indicating that self-nucleation remarkably enhanced the overall crystallization rate of PEEK. An interesting finding is that the self-nucleation temperature domain of PEEK is way outside the melting curve, and its magnitude is greatly large (28-35 °C). Moreover, samples that were pre-crystallized nonisothermally or from the glassy state exhibit a larger self-nucleation effect, and a larger self-nucleation temperature domain. The isothermal crystallization data were analyzed by the Avrami model. The Avrami exponent is found to be remarkably different for melts with and without self-nucleation effects, indicating that self-nucleation changes the crystallization mechanism of PEEK. [ABSTRACT FROM AUTHOR]

Liquid-sensing behaviors of carbon black (CB)/polyamide 6 (PA6)/high-density polyethylene (HDPE) composite containing conductive electrospun fibrous network were investigated by detecting electrical resistance variations toward different solvents. The material exhibited a good sensing selectivity, which could be predicted by Flory-Huggins interaction parameter χ . In immersion-drying runs (IDRs), the composite showed a large liquid-sensing responsivity but poor reproducibility toward 'good solvent' xylene. After long-term immersion treatment in xylene, the metastable conductive pathways became stabilized, and a better reproducibility was finally achieved. Absorption/desorption equilibrium state of the composite in 'moderate' or 'poor' solvents was reached more easily than that in good solvent. Additionally, more rapid response, higher sensing responsivity, and better reproducibility of the composite in 'moderate solvent' cyclohexane were observed at a higher environment temperature. These results indicated that liquid-sensing behaviors of conductive polymer composites could be tailored by tuning the microstructure or utilizing the pretreatment. [ABSTRACT FROM AUTHOR]

Polymer processing generally plays a crucial role in determining the development of microstructure in the fabricated product. In this paper, isotactic polypropylene (iPP) containing 0.1 wt% β-nucleating agent was extruded via a slit die and immediately melt-stretched upon various stretching rates (SR) at the die exit. The microstructure of β-nucleated iPP samples was investigated using two-dimensional wide-angle X-ray diffraction and small-angle X-ray scatterings (2D-WAXD/SAXS) measurements. It is observed that, no matter what SR is, lamellar branching of β-form crystal is formed in melt-stretched samples, which is scarcely reported in open literatures. A method is proposed to calculate the crystallinity of daughter lamellae in β-crystal ( X). It is found that X decreases with increasing SR, indicating that lamellar branching of β-form crystal is restrained by higher SR. Such case should be attributed to the denser-oriented structures (e.g., shish) induced by higher SR, leaving a confined space between adjacent-oriented structures for the growth of daughter lamellae. [ABSTRACT FROM AUTHOR]

A carbon black (CB)/polypropylene (PP)/ultrahigh-molecular-weight polyethylene (UHMWPE) composite with a segregated structure was fabricated by using binary polymer granules as matrices. In preparation, an ethanol-assisted dispersion method was employed to disperse CB particles on the surface of the two polymer granules. The segregated conductive network was then constructed by hot compaction based on the volume exclusion effect of the polymer matrices. The conductive composite shows an ultralow percolation threshold of 0.34 vol.%. In temperature-resistivity test, a double positive temperature coefficient (PTC) effect was observed. In addition, the negative temperature coefficient (NTC) effect was eliminated significantly. These interesting temperature-resistivity behaviors were ascribed to the introduction of the binary polymer matrices and the mobility limitation of CB particles located at the PP/UHMWPE interface. These characteristics were probed by in situ morphology observation in heating process. The present paper provides a novel route for preparing conductive composites with an ultralow percolation threshold, a wider PTC region, and a zero NTC effect. [ABSTRACT FROM AUTHOR]

The strain-sensing behaviors of carbon black (CB)/polypropylene (PP) and carbon nanotubes (CNTs)/PP conductive composites prepared by the vacuum-assisted hot compression were studied and compared. When ten extension-retraction cycles were applied, it was found for CB/PP, the value of the maximum responsivity (Δ R/ R, Δ R-the instantaneous variation of the resistance during the test, R-the original resistance) decreased gradually with increasing the cycle number, but it began to rise from the seventh cycle. The value of the min Δ R/ R increased during the whole test. While for CNTs/PP, both the values of the max and min Δ R/ R decreased rapidly. It is suggested that the different behaviors mainly depend on the distinction in the dimension of the conductive fillers and the preparation technique. [ABSTRACT FROM AUTHOR]

In this paper, injection-molded isotactic polypropylene (iPP) microparts and macroparts were respectively fabricated by the molds with different thickness under the same processing conditions. Comparative study on microstructure and mechanical property was carried out by means of scanning electron microscopy (SEM), two-dimensional wide-angle X-ray diffraction (2D-WAXD), two-dimensional small-angle X-ray scattering (2D-SAXS), differential scanning calorimetry (DSC) and tensile test. SEM images reveal that the two parts show distinctly different hierarchical structure. An obvious ‘skin–core’ structure is present for the macroparts, while a wide distribution of shish-kebab structure develops in both shear and core layer for microparts, exhibiting a specific ‘core-free’ morphology. 2D-WAXD, 2D-SAXS and DSC results show that microparts have higher orientation degree and crystallinity as compared to macroparts, which are responsible for the remarkably high tensile strength and modulus. Our work provides a good example for better understanding processing structure–property relationship of iPP through tuning their internal microstructure. [ABSTRACT FROM AUTHOR]

Carbon black (CB)/poly (lactic acid) (PLA) conductive biopolymer composite were fabricated by casting. A low percolation value (1.25 vol%) is achieved due to the formation of a two-dimensional conductive network in the composite. Vapor sensing behaviors of the CB/PLA conductive composite were studied. A high chemical selectivity with respect to different organic vapors and a good reproducibility to two typical solvents, ethyl acetate and ethanol, during exposure-drying runs have been demonstrated. The variations of the sensing behaviors during exposure-drying processes were associated with the evolvement of CB conductive networks. The results indicate that the Flory-Huggins interactions parameter x12, related to the solubility parameter (thermodynamic factor), molar volume (kinetic factor) and the measurement temperature, affects the vapor sensing behaviors of CB/PLA composite significantly. These results suggest CB/PLA conductive biopolymer composite can be applied as a nice vapor sensor candidate. [ABSTRACT FROM AUTHOR]

In order to further investigate shear-induced interfacial crystallization of polymer-based composites, an improved fiber-pulling device was designed and built. Its peculiar characteristic is that a force transducer is assembled to in situ monitor the variation of interfacial shear stress between the polymer matrix and pulling fiber. Thus, the relationship between interfacial shear stress and the subsequent crystalline morphology can be quantitatively established. In the preliminary study via this device, isotactic polypropylene (iPP)/glass fiber composite was adopted as a model system. The results indicate that interfacial crystallization kinetics is promoted by the presence of interfacial shear stress. Furthermore, there are two thresholds of interfacial shear stress for interfacial crystalline morphology. To be specific, one (0.017 MPa) is for the induction of iPP nucleation, above which α-form iPP crystals are obviously encouraged during the subsequent isothermal crystallization; the other is for the generation of β-form iPP crystals (0.042 MPa), above which β-form crystals are favored to be triggered in the transcrystalline region. [ABSTRACT FROM AUTHOR]

The crystallization in isotactic polypropylene (iPP) melt inclusions, encapsulated by transcrystallinity and spherulites, was investigated by polarized light microscope. Generally, owing to the proceeding of crystallization in melt inclusions, a negative pressure will be built up. Up to a critical value, the negative pressure is released by the formation of cavitation in melt. Unexpectedly, β-crystals with different morphologies emerge at different locations in the melt inclusions. For low molecular weight iPP, only smaller β-crystals around bubbles are discernable. Turn to higher molecular weight iPP, apart from the smaller β-crystals, fan-shaped ones can be developed under suitable conditions (e.g., lower than 131 °C) at the growth front of spherulites and transcrystallinity. Considering the characteristics of molecular weight and morphology, it is proposed that β-crystals are induced by different mechanisms. That is, smaller β-crystals are resulted from the stress caused by the appearance of bubbles while the fan-shaped ones are derived due to the temperature gradient during the release of negative pressure. [ABSTRACT FROM AUTHOR]

Polyamide 66 (PA 66) nanofiber bundles were first electrospun and then introduced into isotactic polypropylene (iPP) melts to prepare nanofiber bundle/iPP composites. To reveal the influences of matrix molecular weight ( M) on the transcrystalline layer, three kinds of iPP with different M were adopted. Polarized optical microscope was employed to investigate the transcrystallinity. In the presence of PA 66 nanofiber bundle, the heterogeneous nucleation distinctly happened in iPP melts. Moreover, the higher the iPP M, the denser the nuclei. Both a decrease in matrix M and an increase in isothermal crystallization temperature led to an increase in the induction time. The maximum temperature at which the transcrystalline layer can be optically observed increased with the increase of M. The growth rate of transcrystallinity decreased with the increasing M and crystallization temperature. Moreover, selective melting of the transcrystalline layers confirmed that it was merely composed of α form crystal for all composites. [ABSTRACT FROM AUTHOR]

It is well known that water-assisted injection molding (WAIM) process can be fulfilled based on the melt filling stage of conventional injection molding (CIM) process. However, due to the different physical fields involved during WAIM and CIM processes, WAIM part should exhibit unique morphological features compared with the CIM one. In this study, isotactic polypropylene (iPP) parts were prepared by WAIM and CIM, respectively, and their comparative study on morphology were therefore carried out by means of polarized optical microscopy (POM) and two-dimensional (2D) wide-angle X-ray diffraction (WAXD). POM observations illustrated that the WAIM part exhibits a 'skin-core-water channel' structure, while the CIM part shows a typical 'skin-core' structure. 2D-WAXD results showed obvious arclike reflections in each position along thickness direction of the WAIM part, indicating a pronounced molecular orientation. Furthermore, a parent-daughter model (or branched shish-kebab structure) appears at 0 and 100 μm for both the parts, and the fraction of daughter lamellae for WAIM part is lower than that of CIM part. As for the 1D-WAXD curves, it is noticed that there is a very tiny (300) reflection of β-form in the CIM part, while it is invisible in all positions of the WAIM part. In addition, the crystallinity and crystalline size L of CIM part are found to be higher than that of WAIM part. Those results demonstrate that water penetration and rapid cooling rate have a significant effect on the morphological features of WAIM part. [ABSTRACT FROM AUTHOR]