Rheological Behavior for Polymer Melts and Concentrated Solutions——Part Ⅶ: A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts

Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between and shear rate (), and topologically constrained dimension number and a were derived. Linear viscoelastic parameters and and topologically constrained dimension number and as a function of the primary molecular weight, molecular weight between entanglements and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters G and topologically constrained dimension number a and and molecular weight and from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.

Quantitative simulation and verification of upgrade law of sustainable development in Beijing-Tianjin-Hebei urban agglomeration

The natural formation and development of urban agglomerations is a process in which core cities continue to unite their neighboring cities to enhance sustainability for their own sustainable development.The upgrade mechanism of sustainable development urban agglomeration is a nonlinear composite upgrade curve that is a function of time,increasing with the number of cities.In this paper,the sustainable upgrade function curve,upgrade rate,and upgrade speed of urban agglomerations were solved using a geometrical derivation,and the index system for measuring the upgrade capability of sustainable development of urban agglomerations was established.The dynamic change in economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of a Beijing-Tianjin-Hebei urban agglomeration from 2000 to 2015 was measured by technique for order preference by similarity to an ideal solution and a grey correlation method,and a comprehensive,intercity unite strength model and a unite threshold calculation method for urban agglomerations were established.The research shows that the economic sustainable upgrade capability,social sustainable upgrade capability,environmental sustainable upgrade capability,and comprehensive sustainable upgrade capability of the Beijing-Tianjin-Hebei urban agglomeration all show a wave-like rising trend.The average annual upgrade speeds during 2000-2015 are,respectively,2.4%.1.67%,1.1%,and 1.74%,with the intercity comprehensive unite strength of urban agglomerations maintaining a general increase;but there is a limit to the joint threshold.From 2000 to 2015,as the core city of the Beijing-Tianjin-Hebei urban agglomeration,Beijing,to enhance its sustainable upgrade capability,jointly developed with Tianjin,Langfang,and Baoding before 2000,Tangshan in 2002,Cangzhou in 2009,Zhangjiakou and Shijiazhuang in 2012,and Chengde in 2014.By 2015,the comprehensive unite strength between Beijing and four cities(Handan,Qinhuangdao,Hengshui,and Xingtai) was still lower than the unite threshold of 6.14.These four cities are relatively far from Beijing,and offer no substantial contribution to the sustainable upgrade capability of Beijing.Through multiple fittings of the upgrade curve using the long-term sequence index of the comprehensive sustainable upgrade capability of Beijing(the core city of the Beijing-Tianjin-Hebei urban agglomeration) from 2000 to 2015,it was found that the simulated curve of the comprehensive sustainable upgrade function of the agglomeration was very similar to the curve of the comprehensive sustainable upgrade capability,which indicates that the simulation results are satisfactory.The future comprehensive sustainable upgrade capability of the agglomeration can be analyzed and predicted by the comprehensive sustainable upgrade function model.This study provides quantitative decision-supporting evidence for promoting the coordinated development of the Beijing-TianjinHebei urban agglomeration and provides theoretical guidance and algorithms for determining the number of cities joined with the sustainable development of national urban agglomerations.