Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory.For open chains,although they generally obe...Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory.For open chains,although they generally obey ideal scaling in chain dimensions,local structure exhibits nonideal behavior due to the incomplete excluded volume(EV)screening,the reduced mean square internal distance(MSID)can be well described by Wittmer'theory for linear chains and the resulting chain swelling is architecture dependent,i.e.,the more branches a bit stronger swelling.For rings,unlike open chains they are compact in term of global sizes.Due to EV effect and nonconcatenated constraints their local structure exhibits a quite different non-Gaussian behavior from open chains,i.e.,reduced MSID curves do not collapse to a single master curve and fail to converge to a chain-length-independent constant,which makes the direct application of Wittmer's theory to rings quite questionable.Deviation from ideality is further evidenced by limited applicability of Rouse prediction to mode amplitude and relaxation time at high modes as well as the non-constant and mode-dependent scaled Rouse mode amplitudes,while the latter is architecture-dependent and even molecular weight dependent for rings.The chain relaxation time is architecture-dependent,but the same scaling dependence on chain dimensions does hold for all studied architectures.Despite mode orthogonality at static state,the role of cross-correlation in orientation relaxation increases with time and the time-dependent coupling parameter rises faster for rings than open chains even at short time scales it is lower for rings.展开更多
There are many different classifications of entanglement for multipartite quantum systems,one of which is based on the number of the unentangled particles.In this paper,we mainly study the quantum states containing at...There are many different classifications of entanglement for multipartite quantum systems,one of which is based on the number of the unentangled particles.In this paper,we mainly study the quantum states containing at most k−1 unentangled particles and provide several entanglement criteria based on the different forms of inequalities,which can both identify quantum states containing at most k−1 unentangled particles.We show that these criteria are more effective for some states by concrete examples.展开更多
基金supported by the National Natural Science Foundation of China(Nos.21790343,21574142,21174154)the National Key Research and Development Program of China(No.2016YFB1100800).
文摘Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory.For open chains,although they generally obey ideal scaling in chain dimensions,local structure exhibits nonideal behavior due to the incomplete excluded volume(EV)screening,the reduced mean square internal distance(MSID)can be well described by Wittmer'theory for linear chains and the resulting chain swelling is architecture dependent,i.e.,the more branches a bit stronger swelling.For rings,unlike open chains they are compact in term of global sizes.Due to EV effect and nonconcatenated constraints their local structure exhibits a quite different non-Gaussian behavior from open chains,i.e.,reduced MSID curves do not collapse to a single master curve and fail to converge to a chain-length-independent constant,which makes the direct application of Wittmer's theory to rings quite questionable.Deviation from ideality is further evidenced by limited applicability of Rouse prediction to mode amplitude and relaxation time at high modes as well as the non-constant and mode-dependent scaled Rouse mode amplitudes,while the latter is architecture-dependent and even molecular weight dependent for rings.The chain relaxation time is architecture-dependent,but the same scaling dependence on chain dimensions does hold for all studied architectures.Despite mode orthogonality at static state,the role of cross-correlation in orientation relaxation increases with time and the time-dependent coupling parameter rises faster for rings than open chains even at short time scales it is lower for rings.
基金supported by the National Natural Science Foundation of China(Grant Nos.12071110,11701135 and 11947073)Hebei Natural Science Foundation of China(Grant Nos.A2020205014,A2018205125,and A2017403025)+1 种基金Science and Technology Project of Hebei Education Department,China(Grant Nos.ZD2020167 and ZD2021066)the Foundation of Hebei GEO University(Grant No.BQ201615)。
文摘There are many different classifications of entanglement for multipartite quantum systems,one of which is based on the number of the unentangled particles.In this paper,we mainly study the quantum states containing at most k−1 unentangled particles and provide several entanglement criteria based on the different forms of inequalities,which can both identify quantum states containing at most k−1 unentangled particles.We show that these criteria are more effective for some states by concrete examples.
