The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behav...The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behavior of dispersed long chains.Using molecular dynamics simulations based on the Kremer-Grest model,we systematically explore the N_(S)-dependence of static conformations,equilibrium dynamics,and nonlinear shear responses in unentangled long-chain/short-chain polymer blends.Our results demonstrate a decoupling between the static and dynamic sensitivity to N_(S):while the static chain size,R_g,follows Flory theory with slight swelling at small N_(S) due to incomplete excluded volume screening,the diffusion coefficient,D,and the relaxation time,τ_(0),exhibit a strong,non-monotonic N_(S)-dependence,transitioning from monomeric friction dominance at small N_(S) to collective segmental rearrangement at large N_(S).Additionally,we observe partial decoupling between the viscous and normal stress responses:while the zero-shear viscosity,η,is strongly N_(S)-dependent,the first and second normal stress coefficients,Ψ_(1) and Ψ_(2),collapse onto universal curves when scaled by the dimensionless shear rate,γτ_(0),suggesting a common mechanism of orientation and stretching.Under shear,long chains compress in the vorticity direction λ_(z)~Wi^(-0.2),which reduces collision frequency and contributes to shear thinning,while the scaling of weaker orientation resistance m_(G)~Wi^(0.35)reflects hydrodynamic screening by the short-chain matrix.These findings highlight the limitations of single-chain models and emphasize the necessity of considering N_(S)-dependent matrix dynamics and flow-induced structural changes in understanding the rheology of unentangled polymer blends.展开更多
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financially supported by the National Natural Science Foundation of China(Nos.22341304,22303100 and 12205270)the National Key R&D Program of China(Nos.2023YFA1008800 and 2020YFA0713601)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDC0180303)。
文摘The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behavior of dispersed long chains.Using molecular dynamics simulations based on the Kremer-Grest model,we systematically explore the N_(S)-dependence of static conformations,equilibrium dynamics,and nonlinear shear responses in unentangled long-chain/short-chain polymer blends.Our results demonstrate a decoupling between the static and dynamic sensitivity to N_(S):while the static chain size,R_g,follows Flory theory with slight swelling at small N_(S) due to incomplete excluded volume screening,the diffusion coefficient,D,and the relaxation time,τ_(0),exhibit a strong,non-monotonic N_(S)-dependence,transitioning from monomeric friction dominance at small N_(S) to collective segmental rearrangement at large N_(S).Additionally,we observe partial decoupling between the viscous and normal stress responses:while the zero-shear viscosity,η,is strongly N_(S)-dependent,the first and second normal stress coefficients,Ψ_(1) and Ψ_(2),collapse onto universal curves when scaled by the dimensionless shear rate,γτ_(0),suggesting a common mechanism of orientation and stretching.Under shear,long chains compress in the vorticity direction λ_(z)~Wi^(-0.2),which reduces collision frequency and contributes to shear thinning,while the scaling of weaker orientation resistance m_(G)~Wi^(0.35)reflects hydrodynamic screening by the short-chain matrix.These findings highlight the limitations of single-chain models and emphasize the necessity of considering N_(S)-dependent matrix dynamics and flow-induced structural changes in understanding the rheology of unentangled polymer blends.
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.
