The error bars are smaller than the size of the symbols. a) Rescaled mean square distance and (b) probability of contact between monomers n and m = n + sa separated by sa bonds in 2D (black) and 3D (green) linear C600H1202 PE melts. Variation of the shear (xy) component of the gyration tensor, G, with shear rate for the C400 ring (circles) and linear (triangles) PE melts. Plot of (a) the chain alignment angle (black symbols based on the gyration tensor and dark green symbols based on the pressure tensor) and (b) order parameter (largest eigenvalue of the order, S= (3uu−) / 2, where u denotes the unit chain end-to-end vector for the linear polymer or the unit ring diameter vector for the ring polymer) for the C400 ring (circles) and linear (triangles) as a function of the applied shear rate.
Introduction
In addition, the results of recent optical experiments on monolayer Langmuir polymer films support the extended interpenetrated chain conformation over the compact segregated chain conformation of dense 2D monolayers. So, we attempt to address this controversial issue by elucidating the underlying fundamental properties of two-dimensional monolayer melt systems. To fill the missing part of polymer dynamics, we analyze the structural and rheological properties of ring polymer under shear and extensional flows using atomistic non-equilibrium molecular dynamics (NEMD) simulations.
Simulation methodology
Atomistic Molecular Dynamics (MD) simulation
The nearly 2D confined systems used in this study were constructed by placing two simple, rigid, repelling walls that simply do not allow polymer chains to move out of the boundary walls. Each simulation lasted several times longer than the longest relaxation time of the system. Each simulation lasted several times longer than the longest relaxation time of the system.
Coarse-grained Kremer-Grest (KG) simulation
Atomistic Non-equilibrium Molecular Dynamics (NEMD) simulations
The well-known Siepmann–Karaboni–Smit5 atom potential model was used in the simulations, except that the rigid bond was replaced by a flexible bond with a harmonic potential. The LJ intramolecular interaction was set to be active only between atoms separated by more than three bonds along the same chain. Boundary condition Lee–Edwards boundary condition for planar couette flow (PCF) Kraynik–Reinelt boundary condition for planar elongational flow (PEF) Range.
2D Linear and ring polymer
Introduction
Results and discussion…
3(b) compares Pc(sa) of the simulated 2D C600 PE melt with that of the corresponding 3D bulk melt. 1 .3(c), the characteristic correlation length corresponding to the minimum of coss (II) is approximately equal to 6lp, the double of cos =s 0 (I; 3lp) and half of the decorrelation length scale ( III; 12lp. After examining the structural features, we next investigated the dynamic characteristics of the 2D confined systems.
As the chain stiffness increases, the chain configurations of the 2D KG system become more extended and intertwined, similar to the configurations observed in the 2D PE atomic system. The result for the 2D KG system with kθ = 3 agrees quantitatively with that of the 2D atomic system. Interestingly, this overall chain conformation of the 2D ring PE chains qualitatively resembles that of the 2D linear PE counterparts.
2(a) contains the global structural variations of the 2D ring polymer, such as the root mean square radius of gyration as a function of molecular weight. Therefore, many loops are expected to appear along the outline of the ring polymer chain. As the bending constant increases, the chain configurations of the 2D KG ring system become more extended and intertwined.
The result for the 2D KG ring system with kθ = 3 agrees quantitatively with the result of the atomistic 2D ring system. A similar physical picture can be applied to the intramolecular LJ energy results [Fig. Intermolecular part of the pair distribution function, ginter(r), for simulated ring PE melts (left column) and corresponding linear analogues (right column) at different strain rates under (a) PCF and (b) PEF.
Introduction
Results and discussion
According to the Rouse model of the non-entangled ring polymer chain,76,126 the ratio of the mean square radius of gyration between 3D non-entangled linear and ring polymer chains is theoretically calculated as g2 g2. This is expected to be associated with a non-Gaussian shape of the chain in both cases. On the short chain segment length scale, the late departure of the 2D ring polymer chain from the simple rigid rod line implies that it has longer rigid chain segments than the corresponding 3D ring polymer chain.
To evaluate the intrinsic chain stiffness, we analyzed the persistence length of 2D and 3D linear and ring polymer melts using the bond correlation function of the bond vector in Fig. The contact probability characterizing the internal structure of the chain is reported in Fig. 2D surrounding chains cannot penetrate the extended 2D ring polymer chains (or the inner space of the 2D ring polymer) due to the closure structure, resulting in a strong correlation hole effect of the 2D ring polymer melt compared to the 2D linear polymer melt.
As in the previous study of a 2D linear polymer between an atomistic and a KG system, the overall PDF profile of an atomistic 2D ring system is well represented by that of a 2D KG ring system with kθ = 3. In contrast, gcm(r) is a 2D KG ring system with kθ > 0 increases slightly at small distances due to the interpenetrated chain configuration. The overall behavior of the gcm(r) coarse-grained KG ring chain with k =3 is consistent with that of an atomistic 2D ring chain.
As with previous study of 2D linear polymer between atomistic and KG system, the overall behavior of structural and dynamic properties of the atomistic 2D system is well represented by the 2D KG system with kθ = 3.
NEMD for 3D bulk ring polymer
Introduction
To investigate the rheological behavior of ring molecules under liquid conditions, several coarse-grained nonequilibrium molecular (NEMD) simulations have recently been performed for ring polymers in solution undergoing shear flow. These studies reported quantitative differences in the rheological properties (such as viscosity and normal stress coefficients) of ring polymers compared to those of the linear analogues and another dynamic mechanism (in addition to normal tumbling motion, as in linear polymers), viz. tank-treading dynamics.113 As shown by Baig and Harmandaris,134 because coarse-grained NEMD simulations can result in quantitatively (even qualitatively) significant discrepancies in the structural and dynamic properties compared to corresponding atomistic NEMD simulations at medium-to-high flow rates, in this work we performed direct atomistic NEMD simulations, which enabled us to perform a comprehensive, quantitative analysis of the linear up to the highly nonlinear rheological properties of ring polymer melts. In an attempt to secure some complete rheological information for ring polymers, we investigated the structural and rheological responses exhibited by short (C78H156) and long (C400H800) ring polyethylene (PE) melts under both shear [planar Couette flow (PCF)] and elongation [plane elongational flow (PEF)].
All results for these ring systems are directly compared to the results of the corresponding linear systems.
Results and discussion
The dotted lines refer to the results of the PE melts of the C78 ring and the solid lines to those of the linear analogues. In the low to intermediate flow regime, where the effect of spatial correlation is dominant, Gxy increases rapidly with increasing shear rate for both ring and linear systems. 5(a) shows the variation of the chain orientation angle with respect to the flow direction as a function of the imposed shear rate.
In general, for both the rotation and the stress tensor, the values of the ring fusion are larger than those of the linear system. 5(b) shows the order parameter of the C400 ring and linear melts as a function of flow strength. First, at low strain rates, both the annulus and the linear melt exhibit a constant viscosity value, regardless of the imposed flow strength and flow type, which.
Variation of the hydrostatic pressure (without the long-range correction) of the simulated systems with the imposed strain rate under PCF and PEF. This is apparently due to a relatively higher value of the energy (repulsive intermolecular structure) at equilibrium in the case of ring fusions. Similar to the results for the intermolecular LJ energy, the ring melts exhibit an apparently larger overall variation of the intramolecular LJ energy than the linear counterparts.
10 presents the results of ginter(r) of the ring and linear melts at three different strain rates under PCF and PEF. 11 presents the variation of the bond-torsion energy and the bond-torsion distribution of the simulated ring and linear systems with the applied flow fields (it would be informative to associate this information with the results of the overall chain structure, the inter- and intramolecular LJ energy, and the hydrostatic pressure of the systems). 11(a) that the torsional energy of ring melting at equilibrium is somewhat greater than that of the linear analogues.
Conclusions
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Microscopic structure, conformation, and dynamics of ring and linear poly(ethylene oxide) melts from detailed atomistic molecular dynamics simulations: chain length dependence and direct comparison with experimental data. Interfacial molecular structure and dynamics of confined ring polymer melts under shear flow. Shear rheology of unentangled and marginally entangled ring polymer melts from large-scale nonequilibrium molecular dynamics simulations. Molecular dynamics study on the structure and relaxation of short-chain branched ring polymer melts.
Flow effects on melt structure and entanglement network of linear polymers: Results from a nonequilibrium molecular dynamics simulation study of a polyethylene melt in steady shear. A molecular dynamics study of the strain-optical behavior of a linear short-chain polyethylene melt under shear. Polymer melts under uniaxial extensional flow: stress-optical behavior from experiments and nonequilibrium molecular dynamics computer simulations.
Rheological and structural studies of linear polyethylene melts under planar extensional flow using nonequilibrium molecular dynamics simulations.
