We present detailed results on the effect of chain branching on the topological properties of entangled polymer melts via an advanced connectivity-altering Monte Carlo (MC) algorithm. Eleven representative model linear, short-chain branched (SCB), and long-chain branched (LCB) polyethylene (PE) melts were employed, based on the total chain length and/or the longest linear chain dimension. Directly analyzing the entanglement [or the primitive path (PP)] network of the system via the Z-code, we quantified several important topological measures: (a) the PP contour length Lpp, (b) the number of entanglements Zes per chain, (c) the end-to-end length of an entanglement strand des, (d) the number of carbon atoms per entanglement strand Nes, and (e) the probability distribution for each of these quantities. The results show that the SCB polymer melts have significantly more compact overall chain conformations compared to the linear polymers, exhibiting, relative to the corresponding linear analogues, (a) ∼20% smaller values of 〈Lpp〉 (the statistical average of Lpp), (b) ∼30% smaller values of 〈Zes〉, (c) ∼20% larger values of 〈des〉, and (d) ∼50% larger values of 〈Nes〉. In contrast, despite the intrinsically smaller overall chain dimensions than those of the linear analogues, the LCB (H-shaped and A3AA3 multiarm) PE melts exhibit relatively (a) 7-8% larger values of 〈Lpp〉, (b) 6-11% larger values of 〈Zes〉 for the H-shaped melt and ∼2% smaller values of 〈Zes〉 for the A3AA3 multiarm, (c) 2-5% smaller values of 〈des〉, and (d) 7-11% smaller values of 〈Nes〉. Several interesting features were also found in the results of the probability distribution functions P for each topological measure.
An important objective in polymer science is to manipulate the material properties of polymers by altering their molecular architecture. To this end, understanding of the fundamental role of chain branches along the polymer backbone is crucial. Although the dynamics of linear and long-branched polymers have been thoroughly investigated over the past decades, a comprehensive understanding of branching effects has not yet been obtained, particularly because of a serious lack of knowledge on the role of short-chain branches, the effects of which have mostly been neglected in favor of the standard entropic-based concepts of long polymers. Here we have comprehensively studied the general effect of short-chain branching on the rheological properties of polymeric materials using Brownian dynamics simulations for a series of SCB polymers with systematically varied branch densities and branching architectures along the chain backbone. Our results demonstrate that the short branches, via their fast random motions, give rise to a more compact and less deformed chain structure in response to the applied flow, eventually reducing the shear-thinning behavior in viscosity and the first normal stress coefficient. Most importantly, by altering the distribution of short branches along the backbone, the structural and rheological properties of the SCB system are dramatically changed. We discuss the physical origins and molecular mechanisms underlying these effects and present a detailed interpretation using a molecular-level analysis of individual chain dynamics. This information is valuable, showing us how to systematically tune the material properties by controlling the molecular architecture of branched polymers under various flow conditions.
Based on the novel viewpoint that ring polymers, with their closed-loop molecular geometry, are naturally defined by an intrinsic two-dimensional topological surface, we analyzed the fundamental structural characteristics and dynamic mechanisms of ring polymers under shear flow. We then proposed several representative physical measures that could effectively be used to characterize the overall ring structure and dynamics. To directly quantify the physical properties, an efficient numerical algorithm was further developed to effectively describe various complex curved surfaces represented by flexible ring polymers. Both dilute and melt ring systems were analyzed under shear flow with a wide range of flow strengths using atomistic nonequilibrium molecular dynamics and coarse-grained Brownian dynamics simulations. The general properties of the interchain influence determined from the dilute and melt systems are informative for predicting the structural and dynamical characteristics of semidilute polymer solutions with respect to the polymer concentration. The present analysis can be extended to various ring-type polymers such as branched ring polymers, ring-shaped biological molecules, and two-dimensional polymers.
We present a detailed study of the effects of short branches on the rheological behaviors of H-shaped long-chain branched polymers under shear and uniaxial elongational flows using (single “phantom” chain) bead-spring Brownian dynamics simulations. To clarify the fundamental role of short branches in both flow types, the short branches are distributed either along the chain backbone or along the four dangling long arms of the H-polymer. We observe that the fast random motions of the highly mobile short branches (in association with their very short characteristic relaxation time scales) constantly disturb chain conformation, generally leading to a more compact and less deformed chain structure against the applied flow. Accordingly, the structural and dynamical properties of the short-chain branched (SCB) H-polymers in response to the flow are strongly dependent on the location of the short branches along the chain. For instance, in comparison to the original H-polymer, the H-(SCB_backbone) polymer, where the short branches are allocated along the backbone, exhibits considerably less shear-thinning behavior resulting from the lesser degree of chain alignment and structural deformation of the SCB backbone. In contrast, the H-(SCB_arm) polymer, where the short branches are allocated along the four long arms, displays a higher degree of shear-thinning behavior arising from an effective tensile force (created by the tightly coiled “superbead” character of the arms via fast short-branch dynamics) that stretches out the backbone. Importantly, the fundamental role of the short branches in determining rheological characteristics of the SCB H-polymers remains unchanged, regardless of the flow type and flow strength.
We present a detailed analysis of the interfacial chain structure and dynamics of confined polymer melt systems under shear over a wide range of flow strengths using atomistic nonequilibrium molecular dynamics simulations, paying particular attention to the rheological influence of the closed-loop ring geometry and short-chain branching. We analyzed the interfacial slip, characteristic molecular mechanisms, and deformed chain conformations in response to the applied flow for linear, ring, short-chain branched (SCB) linear, and SCB ring polyethylene melts. The ring topology generally enlarges the interfacial chain dimension along the neutral direction, enhancing the dynamic friction of interfacial chains moving against the wall in the flow direction. This leads to a relatively smaller degree of slip (ds) for the ring-shaped polymers compared with their linear analogues. Furthermore, short-chain branching generally resulted in more compact and less deformed chain structures via the intrinsically fast random motions of the short branches. The short branches tend to be oriented more perpendicular (i.e., aligned in the neutral direction) than parallel to the backbone, which is mostly aligned in the flow direction, thereby enhancing the dynamic wall friction of the moving interfacial chains toward the flow direction. These features afford a relatively lower ds and less variation in ds in the weak-to-intermediate flow regimes. Accordingly, the interfacial SCB ring system displayed the lowest ds among the studied polymer systems throughout these regimes owing to the synergetic effects of ring geometry and short-chain branching. On the contrary, the structural disturbance exerted by the highly mobile short branches promotes the detachment of interfacial chains from the wall at strong flow fields, which results in steeper increasing behavior of the interfacial slip for the SCB polymers in the strong flow regime compared to the pure linear and ring polymers.
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