Non-contemporaneous variations and H�lder?s principle

Liang, Lizhen; Hai-Chang, Hu; Liu, Shiquan

doi:10.1360/02yw0121

Cited by 30 publications

(42 citation statements)

References 9 publications

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“…The controllable properties based on the octene content, besides excellent processability of EOC, have widen its application areas. The results indicated that by applying the suitable compatibilization, EOC could desirably modify the toughness and the impact resistance of a wide range of thermoplastics such as PP, PET, polyamide 6, and PS . To the best of our knowledge, the role of nanoclay platelets as a compatibilizer for PS/EOC blend systems and how they affect the interfacial interactions between phases and their rheological and mechanical properties, besides their morphology, have not been investigated yet.…”

Section: Introductionmentioning

confidence: 99%

“…The results indicated that by applying the suitable compatibilization, EOC could desirably modify the toughness and the impact resistance of a wide range of thermoplastics such as PP, PET, polyamide 6, and PS. [16][17][18][19][20][21][22] To the best of our knowledge, the role of nanoclay platelets as a compatibilizer for PS/EOC blend systems and how they affect the interfacial interactions between phases and their rheological and mechanical properties, besides their morphology, have not been investigated yet. Therefore, in this contribution, the compatibilization role of montmorillonite nanoclay (Cloisite 20A) at different loadings is investigated for immiscible PS/EOC blends.…”

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confidence: 99%

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Assessment of compatibilization role of nanoclay in immiscible polystyrene/ethylene–octene copolymer blends via wide‐angle X‐ray scattering, microstructure, rheological analyses, and mechanical properties

Kiani

Entezam

Khonakdar

et al. 2019

J of Applied Polymer Sci

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Polystyrene (PS)/ethylene–octene copolymer (EOC) blends with 80/20 wt % composition containing different amounts (0, 1.0, 2.5, 5.0 and 7.5 wt %) of an organically modified nanoclay were prepared by one‐step melt‐mixing method. Also, the EOC‐rich blends with 80 wt % EOC content loaded with 0 and 5.0 wt % of the nanoclay were prepared under the similar processing conditions. Presence of both PS and EOC chains in between clay layers localized at the interface of the blends could be deduced by X‐ray diffraction analysis, which suggested formation possibility of PS‐EOC physical structures at the blend interface. Transmission electron microscopy results confirmed that clay nanoparticles were mainly localized at the interface of the blends and also partly in the PS and EOC components of the systems. The localization of the nanoclay was also described by the linear viscoelastic melt rheological studies. It is also revealed that nanoclay had stronger interactions with PS than EOC. This is reflected in the higher tensile properties in the PS‐rich system. The analysis of morphology of the developed systems by emulsification curve revealed that the optimum amount of nanoclay to modify PS‐rich blend is 2.5 wt %. At this clay loading, the blend exhibited the highest impact resistance. According to the overall results, suitability of nanoclay was confirmed for compatibilization of the PS/EOC blends. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48748.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Assessment of compatibilization role of nanoclay in immiscible polystyrene/ethylene–octene copolymer blends via wide‐angle X‐ray scattering, microstructure, rheological analyses, and mechanical properties

Kiani

Entezam

Khonakdar

et al. 2019

J of Applied Polymer Sci

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“…We know that the beam, plate, shell are the main components of aerospace engineering structures. In numerical simulation, it needs to consider the nearness degree [20] of admissible function. Take the plate as an example: Its controlling equation contains fourth derivative.…”

Section: The Quasi-variational Principle Of the Single Flexible Body mentioning

confidence: 99%

Quasi-variational principles of single flexible body dynamics and their applications

Liang

Liu²,

Zhou

2009

Sci. China Ser. G-Phys. Mech. Astron.

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The reasons for studying single flexible body dynamics are that on one hand, it is the basis of flexible multi-body dynamics. If the theory of the single flexible body dynamics has been deeply studied, the theory of flexible multi-body dynamics will be researched easily. On the other hand, it has its unique and important applications. Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body mechanics. Taking the interceptor as an example, this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body dynamics. Taking the launch of rocket as an example, it has illustrated the features of "one force for two effects" in a single flexible body dynamics. With an example of the extending flexible beam coupled with the spacecraft attitude, it has shown the transition from the single flexible body dynamics to the flexible multi-body dynamics. Finally, a number of related problems are discussed.variational principle, non-conservative system, aerospace dynamics, flexible multi-body dynamics, single flexible body dynamics

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“…Jiang et al . studied the effect of PS and SEBS addition on the mechanical and the thermal properties of POE . They reported that the addition of SEBS copolymer resulted in finer dispersion of PS particles in POE matrix and significantly increased the tensile strength of POE/PS blend.…”

Section: Introductionmentioning

confidence: 99%

Melt rheology and interfacial properties of binary and ternary blends of PS, EOC, and SEBS

Entezam

Poormadadkar

Khonakdar

et al. 2019

J of Applied Polymer Sci

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This works systematically investigates the interfacial properties of the binary and the ternary blends based on polystyrene (PS), ethylene octene copolymer (EOC), and styrene–ethylene–butylene–styrene (SEBS) by analyzing the melt linear rheological behavior of the blends and neat components. Moreover, the relationship between rheology, phase morphology, and mechanical properties of PS/EOC ternary blends with various quantities of SEBS were studied. The surface shear modulus (β) and interfacial tension values obtained by Palierne model indicated that the EOC/SEBS blend has the best interfacial properties, while the lowest interaction was found for PS/EOC blend. Based on the Palierne model and Harkin's spreading coefficients a core–shell type morphology with EOC phase encapsulated by the SEBS shell dispersed in the PS matrix was determined for the ternary blends. Scanning electron microscopy results revealed that both fibrillar and droplet forms of dispersed phase could be developed during the blending of PS and EOC in presence of SEBS. The extent of fibrillar morphology and interfacial interactions in PS/EOC/SEBS ternary blends was dependent on the SEBS content. The improvement of the mechanical properties of PS/EOC blends in the presence of SEBS was evidenced by the tensile and impact resistance experiments. The tensile strength reinforcement was more pronounced for the ternary blends with more fibrillar dispersed phase. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48791.

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Non-contemporaneous variations and H�lder?s principle

Cited by 30 publications

References 9 publications

Assessment of compatibilization role of nanoclay in immiscible polystyrene/ethylene–octene copolymer blends via wide‐angle X‐ray scattering, microstructure, rheological analyses, and mechanical properties

Assessment of compatibilization role of nanoclay in immiscible polystyrene/ethylene–octene copolymer blends via wide‐angle X‐ray scattering, microstructure, rheological analyses, and mechanical properties

Quasi-variational principles of single flexible body dynamics and their applications

Melt rheology and interfacial properties of binary and ternary blends of PS, EOC, and SEBS

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