Lamellar crystal thickness lc of isotactic polybutene-1(it-PB1)have been investigated for crystal-lization in the melt over a wide range of crystallization temperature T from 40°C to 90°C by small angle X-ra...Lamellar crystal thickness lc of isotactic polybutene-1(it-PB1)have been investigated for crystal-lization in the melt over a wide range of crystallization temperature T from 40°C to 90°C by small angle X-ray scattering experiments and density measurements.The crystal thickness lc demonstrates two linear dependences on inverse supercooling and a transition from one dependence to the other has been observed around T=65°C.Each of the two dependences obeys the nucleation theory in the high and low supercooling ranges,respec-tively.Chain folding free energy q determined from the low supercooling range is larger than that determined from the high supercooling range.Possible mechanisms for the transition are discussed taking account of entropy of chain folding directions.展开更多
In this paper,we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation,which is a sixth-order nonlinear damped wave eq...In this paper,we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation,which is a sixth-order nonlinear damped wave equation.The schemes are linear,conserve mass and unconditionally dissipate a pseudo energy.We prove rigorously second-order error estimates in both time and space for the phase field variable in discrete norms.We also present some numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy.展开更多
基金Professor Miyaji of Kyoto University for valuable advice and encouragement.
文摘Lamellar crystal thickness lc of isotactic polybutene-1(it-PB1)have been investigated for crystal-lization in the melt over a wide range of crystallization temperature T from 40°C to 90°C by small angle X-ray scattering experiments and density measurements.The crystal thickness lc demonstrates two linear dependences on inverse supercooling and a transition from one dependence to the other has been observed around T=65°C.Each of the two dependences obeys the nucleation theory in the high and low supercooling ranges,respec-tively.Chain folding free energy q determined from the low supercooling range is larger than that determined from the high supercooling range.Possible mechanisms for the transition are discussed taking account of entropy of chain folding directions.
基金supported by National Natural Science Foundation of China(Grant Nos.11901489 and 11971407)supported by National Science Foundation of USA(Grant No.DMS-1720442)。
文摘In this paper,we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation,which is a sixth-order nonlinear damped wave equation.The schemes are linear,conserve mass and unconditionally dissipate a pseudo energy.We prove rigorously second-order error estimates in both time and space for the phase field variable in discrete norms.We also present some numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy.
