Structural and Dynamical Characteristics of Short-Chain Branched Ring Polymer Melts at Interface under Shear Flow

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.


Introduction
Interfacial polymeric liquids in confined systems exhibit a variety of distinctive properties and phenomena compared to ordinary bulk polymeric liquids, such as solid-like behavior, high viscosity, oscillatory solvation force, and extrusion instability [1][2][3][4][5][6][7][8]. Numerous experimental, computational, and theoretical studies have been conducted for a variety of confined polymeric systems with respect to the wall roughness, degree of wettability, polymer molecular weight, and degree of confinement [9][10][11][12][13][14][15][16][17][18][19]. An important physical behavior that occurs in confined polymer systems is the interfacial slip of polymer chains at the boundary walls, which is considered one of the major physical origins of the melt inter-and intramolecular Lennard-Jones (LJ) interactions, the thermostat, and the flow field (see the Supporting Information of Ref. 39 for the detailed r-RESPA formula) [38,39].
The lattice parameter of the simple cubic wall corresponded to the LJ size parameter of the wall atoms σ w = 1.33 σ CH 2 for all systems [23]. The LJ energy parameter of the wall atoms was set to ε w /k B = 939 K, which is comparable to that of a mica surface (ca. 200-400 mJ/m 2 ) [19]. All of the systems were subjected to steady shear flow over a wide range of shear rates γ mσ 2 /ε ≤ 0.2, where m (=14 g/mol), σ (=3.95 Å), and ε (ε/k B = 46 K where k B is Boltzmann's constant) denote the mass, size, and energy parameter for the CH 2 units, respectively. The longest characteristic relaxation time τ R of the system was as follows: τ R = 20.7 ± 4.5 ns, 2.55 ± 0.4 ns, 35.5 ± 7.2 ns, and 9.4 ± 1.0 ns for the simulated linear, ring, SCB linear, and SCB ring PE melts, respectively. The τ R was estimated from the integral below the stretched exponential curve describing the decay of the time autocorrelation function of the unit chain end-to-end vector for linear polymers and the unit ring diameter vector for ring polymers [29]. To obtain statistically accurate results, the simulation for each system was executed for a sufficiently long time (e.g., more than 5 times the longest relaxation time of the system). Additional details of the potential model and simulation method are described in the Supplementary Materials.

Results and Discussion
Following the previous studies [23][24][25][26], here we analyzed the degree of slip (d s ) for the confined polymeric system defined as d s = 1 − . γ real / . γ ideal = V s /V w , where V s is the total slip velocity occurring at the top and bottom walls and V w is the applied velocity of the moving top wall toward the flow direction in shear flow. Whereas the ideal (nominal) shear rate . γ ideal = V w /H is based on the assumption of the no-slip boundary condition with H being the box dimension in the velocity gradient (y-)direction, the real shear rate . γ real = (V w − V s )/H accounts for a finite slip at the boundary walls. Practically, we evaluated the value of . γ real for the d s of the confined systems as follows: the y-dimension of the simulation box (i.e., H) was divided into several bins with a constant interval, and the streaming velocity in the flow direction for each bin was calculated by averaging the x component of velocity for all atoms belonging to that bin. Then, the final streaming velocity was obtained by applying a fifth-order polynomial fitting to the velocity data measured in each MD step and averaging the resulting velocity profile over a sufficiently long system trajectory (see the Supporting Information of [23] for additional details).
. γ real was then calculated by applying linear regression to the average streaming velocity data along the velocity gradient direction. We also note that the degree of slip is directly related to the standard slip length (L s ) by d −1 s = 1 + L −1 s with L s ≡ L s /H. Figure 1 presents the variation of the degree of slip for the simulated linear C 128 H 258 , ring C 128 H 256 , SCB linear C 178 H 358 , and SCB ring C 178 H 356 PE melts with respect to the applied shear rate over a wide range of flow strengths for the confined systems. The slip behavior of d s for similar linear, ring, and SCB linear PE melts under shear flow was previously investigated in conjunction with the underlying molecular mechanisms [23,25,26]. To help interpret the general behavior of interfacial slip for the SCB ring melts in view of the combined rheological influence of the ring geometry and short-chain branching, here we analyzed the degree of slip and characteristic molecular mechanisms for the SCB ring polymer via direct comparison with those for the corresponding linear, ring, and SCB linear polymers. First, we note in Figure 1 that the pure linear and ring melts exhibit three distinct characteristic d s regimes with respect to the shear rate, i.e., an increasing, decreasing, and increasing behavior of d s in the weak, intermediate, and strong flow regimes, respectively. In contrast, the SCB linear and SCB ring melts display almost constant behavior of d s in the weak-to-intermediate flow regimes, followed by a rapid increase of d s in the strong flow regime. To understand these distinctive slip behaviors of d s for each system, it is essential to examine the fundamental molecular mechanisms of polymer chains at interfaces as a function of the applied shear rate by considering the dynamical influences of the external flow field and polymer-wall interactions [23][24][25][26]. distinctive slip behaviors of s d for each system, it is essential to examine the fundamental molecular mechanisms of polymer chains at interfaces as a function of the applied shear rate by considering the dynamical influences of the external flow field and polymer-wall interactions [23][24][25][26].    In the weak flow regime, the applied shear force induces the interfacial linear chains to undergo z-to-x chain rotation while residing in the xz-plane, and the degree of chain alignment in the flow direction increases as the shear rate increases. This effectively reduces the dynamic friction of polymer chains moving against the wall in the flow direction, thereby increasing the degree of slip [23]. The ring polymer also exhibits a similar in-plane z-to-x rotation, enhancing the interfacial slip. However, in comparison to the linear polymer, the ring polymer has a relatively larger chain dimension in the neutral (z-)direction owing to its intrinsic closed-loop molecular geometry, which promotes the dynamic friction of ring chains against the wall. This leads to a relatively smaller s d value and less pronounced increase in s d for the ring polymer in the weak flow regime in comparison to the linear analogue, as observed in Figure 1.
Looking into the effect of short-chain branching, the SCB linear polymer similarly exhibits z-tox chain rotation, thus reducing the overall interfacial dynamic friction and enhancing the wall slip. However, in contrast to the general alignment of the chain backbone in the flow direction, the short branches tend to be oriented more perpendicular (i.e., aligned in the neutral direction) than parallel to the backbone owing to their bonded and nonbonded intramolecular LJ interactions with the neighboring backbone atoms around the branch points. This orientational tendency of short-chain   In the weak flow regime, the applied shear force induces the interfacial linear chains to undergo z-to-x chain rotation while residing in the xz-plane, and the degree of chain alignment in the flow direction increases as the shear rate increases. This effectively reduces the dynamic friction of polymer chains moving against the wall in the flow direction, thereby increasing the degree of slip [23]. The ring polymer also exhibits a similar in-plane z-to-x rotation, enhancing the interfacial slip. However, in comparison to the linear polymer, the ring polymer has a relatively larger chain dimension in the neutral (z-)direction owing to its intrinsic closed-loop molecular geometry, which promotes the dynamic friction of ring chains against the wall. This leads to a relatively smaller d s value and less pronounced increase in d s for the ring polymer in the weak flow regime in comparison to the linear analogue, as observed in Figure 1.
Looking into the effect of short-chain branching, the SCB linear polymer similarly exhibits z-to-x chain rotation, thus reducing the overall interfacial dynamic friction and enhancing the wall slip. However, in contrast to the general alignment of the chain backbone in the flow direction, the short branches tend to be oriented more perpendicular (i.e., aligned in the neutral direction) than parallel to the backbone owing to their bonded and nonbonded intramolecular LJ interactions with the neighboring backbone atoms around the branch points. This orientational tendency of short-chain branches along the z-direction effectively increases the polymer-wall friction, diminishing the interfacial slip. These two contrasting contributions between the backbone and short branches cancel each other out to result in a nearly constant behavior of d s in the weak flow regime for the SCB linear polymer ( Figure 1). We further note that the short branches have intrinsically fast random Brownian kinetics owing to their very short characteristic relaxation time scale (e.g.,~0.06 ns for C 5 H 12 at T = 450 K and p = 1 atm), and thus their dynamics are practically unaffected by the external flow field [25,27]. Such fast random movements of short branches along the chain backbone constantly disturb the overall chain conformation and tend to diminish the degree of structural deformation of the polymer chains in response to the applied flow. This further facilitates the overall chain dimension of SCB polymers in the neutral direction.
Polymers 2020, 12, x FOR PEER REVIEW 5 of 14 branches along the z-direction effectively increases the polymer-wall friction, diminishing the interfacial slip. These two contrasting contributions between the backbone and short branches cancel each other out to result in a nearly constant behavior of ds in the weak flow regime for the SCB linear polymer ( Figure 1). We further note that the short branches have intrinsically fast random Brownian kinetics owing to their very short characteristic relaxation time scale (e.g., ~0.06 ns for C5H12 at T = 450 K and p = 1 atm), and thus their dynamics are practically unaffected by the external flow field [25,27]. Such fast random movements of short branches along the chain backbone constantly disturb the overall chain conformation and tend to diminish the degree of structural deformation of the polymer chains in response to the applied flow. This further facilitates the overall chain dimension of SCB polymers in the neutral direction. By combining the respective influences of the ring topology and short-chain branching on the interfacial dynamics, we can reliably predict the general behavior of ds for the SCB ring polymer. As mentioned above, the ring polymer, owing to its closed-loop topology, has a larger chain dimension in the neutral direction in comparison to the linear analogue. Furthermore, the fast random motions of the highly mobile short branches along the backbone constantly disturb the overall chain conformation, leading to lesser degrees of chain stretch and orientation along the flow direction and also a relatively larger chain dimension along the neutral direction. Thus, both the ring geometry and short-chain branching are expected to diminish the overall chain extension and alignment in the flow direction and increase the chain dimension in the neutral direction, synergistically enhancing the dynamic friction of interfacial chains moving against the wall. We therefore consider that the SCB ring polymer would exhibit significantly lower values of s d in the weak flow regime in comparison to the other (linear, ring, and SCB linear) polymers, which is confirmed by the results shown in Figure  1.
Let us now examine the slip behavior of each polymer system in the intermediate flow regime. Two representative molecular mechanisms were identified for the interfacial linear polymer in this regime [23]: (i) an out-of-plane wagging mechanism (i.e., repetitive motions of the (outer) parts of the By combining the respective influences of the ring topology and short-chain branching on the interfacial dynamics, we can reliably predict the general behavior of d s for the SCB ring polymer. As mentioned above, the ring polymer, owing to its closed-loop topology, has a larger chain dimension in the neutral direction in comparison to the linear analogue. Furthermore, the fast random motions of the highly mobile short branches along the backbone constantly disturb the overall chain conformation, leading to lesser degrees of chain stretch and orientation along the flow direction and also a relatively larger chain dimension along the neutral direction. Thus, both the ring geometry and short-chain branching are expected to diminish the overall chain extension and alignment in the flow direction and increase the chain dimension in the neutral direction, synergistically enhancing the dynamic friction of interfacial chains moving against the wall. We therefore consider that the SCB ring polymer would exhibit significantly lower values of d s in the weak flow regime in comparison to the other (linear, ring, and SCB linear) polymers, which is confirmed by the results shown in Figure 1.
Let us now examine the slip behavior of each polymer system in the intermediate flow regime. Two representative molecular mechanisms were identified for the interfacial linear polymer in this regime [23]: (i) an out-of-plane wagging mechanism (i.e., repetitive motions of the (outer) parts of the interfacial chains between detachment from the wall due to the external flow field and attachment to the wall due to the attractive polymer-wall interaction) and (ii) a disentanglement mechanism between the interfacial chains and nearby surrounding bulk chains via chain alignment and stretch along the flow direction. These two molecular processes effectively mitigate the movement of interfacial chains at the wall in the flow direction, resulting in an overall decreasing tendency of d s for the linear and ring  Figure 1. Notably, interfacial ring polymers, in addition to the loop wagging mechanism, exhibit a loop migration dynamic mechanism where locally created loop segments can propagate along the chain toward the flow direction [26]. Because the loops can be created locally and randomly along the ring chain via thermal Brownian motion, the applied flow field, and intermolecular collisions, the loop wagging and loop migration dynamics may occur at any position of the chain, which is in contrast to the case of the linear polymer for which the out-of-plane wagging mechanism commonly occurs near the chain ends. Furthermore, the loop migration mechanism facilitates the movement of the whole ring chain in the flow direction and thus enhances the polymer slip at the wall. Additionally, the closed-loop topology of ring chains results in relatively fewer entanglement interactions compared to linear chains. These two factors together lead to a smaller decrease in d s for the ring polymer compared to the linear polymer in the intermediate flow regime (see Figure 1).
In contrast, both the SCB linear and SCB ring polymers exhibit nearly constant behavior for d s with respect to the shear rate throughout the weak and intermediate flow regimes. As mentioned previously, the highly mobile short branches make the overall chain structure more compact and less deformed (with highly curvy backbone structures) against the applied flow [25]. This structural feature entails smaller entanglement interactions between chains and less variation in the degree of entanglement with respect to the flow strength, ultimately weakening the degree of the out-of-plane wagging and disentanglement mechanisms and consequently affording the apparent constant behavior of d s for the SCB polymers.
In the strong flow regime, the external flow field is sufficiently strong to overcome the attractive polymer-wall interactions and cause intensive dynamical collisions between interfacial chains and the wall. This leads the interfacial chains to frequently detach from the wall and undergo irregular (chaotic) chain rotation and tumbling dynamics. This dynamic feature underlies a rapid increase in the degree of slip in this flow regime for all of the polymer systems ( Figure 1).
It is interesting to note that whereas the tumbling dynamics occurs exclusively with the chain ends for the linear polymer, it can occur with any local loop(s) along the chain in the case of the ring polymer. This fact leads to two distinct types of tumbling mechanism: end-loop tumbling and center-loop tumbling [32]. The end-loop tumbling mechanism is induced by the local loops situated near the ends (outermost parts) of the stretched ring backbone along the flow direction, which is essentially similar to the typical end-over-end tumbling mechanism of the linear polymer. In contrast, the center-loop tumbling mechanism is driven by the loops located in the middle of the stretched ring backbone. Therefore, whereas end-loop tumbling practically occurs in the shear or flow-gradient (xy-)plane, the center-loop mechanism exhibits a diagonal chain rotation lying through both the xyand yz-planes. These dynamic mechanisms were observed for both pure ring and SCB ring polymers at the interface under strong flow fields (specific quantification of the individual loop-tumbling mechanisms will be presented later).
Another interesting feature is that the interfacial SCB linear polymer exhibits not only the hairpin-like end-over-end tumbling behavior (similar to the linear polymer) but also additional distinct mechanisms such as head-roll and tail-roll tumbling dynamics, which is essentially caused by the short branches forming the compact head or tail parts along the chain backbone during the tumbling event [25]. However, such rolling mechanisms were rarely observed in the case of the SCB ring polymer studied here. This is attributed to the relatively larger chain dimension along the neutral direction for the SCB ring polymer compared to the corresponding SCB linear polymer in addition to the rather double-stranded stretched ring conformations at strong flow fields, both of which may have effectively impeded the whole chain rolling along the flow direction (additionally, the C 128 backbone length of the present C 178 H 356 SCB ring PE might not be sufficiently long to facilitate chain rolling). It is also important that the short branches promote the interfacial chain detachment from the wall by constantly disturbing the chain conformation via their fast random motions. This leads to a steeper increasing Polymers 2020, 12, 3068 7 of 13 behavior of d s in the strong flow regime for both SCB linear and ring polymers in comparison to the corresponding pure linear and ring polymers. Figure 3 displays the steady-state streaming velocity profiles in the flow direction along the velocity gradient direction for the four polymer systems at an intermediate flow strength. In general, the nonlinearity of the velocity profile for a polymeric material is associated with the degree of interfacial slip. As noted earlier, . γ real was calculated by applying linear regression to the streaming velocity data along the y-direction. Clearly, the pure linear and ring polymers exhibit a noticeable deviation from the ideal velocity profile (i.e., assuming the no-slip boundary condition) due to finite slip at the walls. Interestingly, the corresponding SCB linear and ring systems at the same shear rate display velocity profiles rather close to the ideal one (d s ≈ 0), indicating apparently small interfacial slip. This behavior results from the enhanced polymer-wall friction due to the highly mobile short branches. Furthermore, owing to the additional wall friction caused by its closed-loop geometry, the SCB ring polymer exhibits even smaller interfacial slip than the SCB linear polymer.
Polymers 2020, 12, x FOR PEER REVIEW 7 of 14 rolling). It is also important that the short branches promote the interfacial chain detachment from the wall by constantly disturbing the chain conformation via their fast random motions. This leads to a steeper increasing behavior of s d in the strong flow regime for both SCB linear and ring polymers in comparison to the corresponding pure linear and ring polymers. Figure 3 displays the steady-state streaming velocity profiles in the flow direction along the velocity gradient direction for the four polymer systems at an intermediate flow strength. In general, the nonlinearity of the velocity profile for a polymeric material is associated with the degree of interfacial slip. As noted earlier,  rea l was calculated by applying linear regression to the streaming velocity data along the y-direction. Clearly, the pure linear and ring polymers exhibit a noticeable deviation from the ideal velocity profile (i.e., assuming the no-slip boundary condition) due to finite slip at the walls. Interestingly, the corresponding SCB linear and ring systems at the same shear rate display velocity profiles rather close to the ideal one ( s d ≈ 0), indicating apparently small interfacial slip. This behavior results from the enhanced polymer-wall friction due to the highly mobile short branches. Furthermore, owing to the additional wall friction caused by its closed-loop geometry, the SCB ring polymer exhibits even smaller interfacial slip than the SCB linear polymer. To further understand the interfacial characteristics in conjunction with the dynamic mechanisms, we analyzed the structural properties of the interfacial chains with centers of mass located within a distance of 2.5 from the wall. Figure 4 presents the xx-, yy-, and zz-components of the gyration tensor G of the interfacial chains for each system as a function of the applied flow strength. It should be noted that to examine the influence of short-chain branching on the overall chain structure, only the chain backbone (excluding the short branches) was included in the calculation of G for the SCB polymers. To further understand the interfacial characteristics in conjunction with the dynamic mechanisms, we analyzed the structural properties of the interfacial chains with centers of mass located within a distance of 2.5 σ from the wall. Figure 4 presents the xx-, yy-, and zz-components of the gyration tensor G of the interfacial chains for each system as a function of the applied flow strength. It should be noted that to examine the influence of short-chain branching on the overall chain structure, only the chain backbone (excluding the short branches) was included in the calculation of G for the SCB polymers.
First, as the shear rate increases in the weak flow regime, the linear polymer exhibits an increasing behavior of G xx (which approaches a plateau value) and a decreasing behavior of both G zz and G yy . This is directly related to the z-to-x rotation mechanism of the interfacial chains with their decreased y dimension via chain alignment and stretch in the flow direction. Upon further increasing the flow strength to the intermediate flow regime, G xx shows almost constant behavior while both G zz and G yy continue to decrease until reaching a minimum value. These features can be understood by considering the aforementioned out-of-plane wagging and disentanglement mechanisms of the interfacial chains in the intermediate flow regime. Both mechanisms lead to significant suppression of the rotation and tumbling dynamics for the interfacial chains moving away from the wall. In the strong flow regime, as the shear rate increases, G xx appears to rapidly decrease, whereas both G yy and G zz display a gradual increase. This is directly associated with the irregular rotation and tumbling dynamic mechanism of the interfacial chains via their strong dynamical collisions with the wall, which facilitates the detachment of the interfacial chains from the wall and their frequent movement toward the bulk region. Overall similar behavior is exhibited by the ring polymer, which, however, owing to its intrinsic closed-loop molecular geometry, shows somewhat smaller variation in each component (G xx , G yy , and G zz ) with respect to the flow strength compared to the linear polymer. It is also noted that the ring topology gives rise to an increase in G zz and a decrease in G yy .
where i r and c r denote the position vectors of atom i and the chain center-of-mass with α, β = x, y, z) for the interfacial chains whose center-of-mass is located within a distance of 2.5 from the wall for the (a) C128H258 linear (black triangles) and C178H358 SCB linear (orange triangles) and (b) C128H256 ring (black circles) and C178H356 SCB ring (orange circles) systems as a function of the applied shear rate. To allow comparison with the pure ring and linear systems, only the chain backbone, excluding the short branches, was considered in the calculation of G for the SCB systems. The symbols and vertical lines have the same meaning as in Figure 1. The error bars are smaller than the size of the symbols unless otherwise indicated.
First, as the shear rate increases in the weak flow regime, the linear polymer exhibits an increasing behavior of xx G (which approaches a plateau value) and a decreasing behavior of both zz G and yy G . This is directly related to the z-to-x rotation mechanism of the interfacial chains with where r i and r c denote the position vectors of atom i and the chain center-of-mass with α, β = x, y, z) for the interfacial chains whose center-of-mass is located within a distance of 2.5 σ from the wall for the (a) C 128 H 258 linear (black triangles) and C 178 H 358 SCB linear (orange triangles) and (b) C 128 H 256 ring (black circles) and C 178 H 356 SCB ring (orange circles) systems as a function of the applied shear rate.
To allow comparison with the pure ring and linear systems, only the chain backbone, excluding the short branches, was considered in the calculation of G for the SCB systems. The symbols and vertical lines have the same meaning as in Figure 1. The error bars are smaller than the size of the symbols unless otherwise indicated.
In contrast, the SCB linear and ring polymers exhibit increasing behavior of G xx and decreasing behavior of G yy and G zz throughout the weak-to-intermediate flow regimes, with all components remaining almost constant in the strong flow regime. Furthermore, the SCB polymers display a significant reduction in G xx and increase in G yy and G zz in comparison to the corresponding pure linear and ring polymers. This feature is directly associated with the fact that the structural disturbance by the fast random motions of the short branches results in highly curvy backbone structures and lesser degrees of chain stretch and alignment to the flow direction for the SCB polymers.
It can be summarized that (i) the closed-loop ring geometry tends to reduce both G xx and G yy and promote G zz and (ii) short-chain branching tends to reduce G xx and promote both G yy and G zz .
To investigate the distinctive structural characteristics of the interfacial SCB ring polymer, we conducted the Brightness analysis to categorize the mesoscale chain structures into several representative configurational classes (namely, stretched, coil, dumbbell, kink, half-dumbbell, and fold) on the basis of the monomer distribution along the chain [40,41]. For this analysis, we devised a new scheme that provides detailed structural information for interfacial ring-shaped polymer chains. Specifically, (i) we first identify the longest dimension (R x,max ) of the ring backbone in the flow direction, (ii) we then divide the ring backbone into two linear parts separated by the cutting line of R x,max , and (iii) we finally perform the Brightness analysis for each part separately and categorize the respective molecular configurations into the six representative classes, as depicted in Figure 5a.
behavior of yy G and zz G throughout the weak-to-intermediate flow regimes, with all components remaining almost constant in the strong flow regime. Furthermore, the SCB polymers display a significant reduction in Gxx and increase in Gyy and Gzz in comparison to the corresponding pure linear and ring polymers. This feature is directly associated with the fact that the structural disturbance by the fast random motions of the short branches results in highly curvy backbone structures and lesser degrees of chain stretch and alignment to the flow direction for the SCB polymers. It can be summarized that (i) the closed-loop ring geometry tends to reduce both xx G and yy G and promote zz G and (ii) short-chain branching tends to reduce xx G and promote both yy G and zz G .
To investigate the distinctive structural characteristics of the interfacial SCB ring polymer, we conducted the Brightness analysis to categorize the mesoscale chain structures into several representative configurational classes (namely, stretched, coil, dumbbell, kink, half-dumbbell, and fold) on the basis of the monomer distribution along the chain [40,41]. For this analysis, we devised a new scheme that provides detailed structural information for interfacial ring-shaped polymer chains. Specifically, (i) we first identify the longest dimension ( x,max R ) of the ring backbone in the flow direction, (ii) we then divide the ring backbone into two linear parts separated by the cutting line of     It can be seen that the pure ring system exhibits mostly the "stretched-stretched" configuration for the two parts, indicating well-aligned and extended double-stranded ring conformations. In contrast, the SCB ring system displays fairly large proportions of the "fold-stretched" and "kink-stretched" configurations, in addition to the predominant "stretched-stretched" configuration. These structural features are closely associated with the overall curvy extended chain conformations of the interfacial SCB ring chains caused by the disturbance exerted by the highly mobile short branches along the ring backbone. The Brightness results can be seen to be consistent with the results for the gyration tensor G shown in Figure 4. As mentioned earlier, the ring polymer exhibits two types of tumbling dynamics at high flow fields: end-loop and center-loop tumbling (Figure 6a). Both mechanisms are induced by the local loop(s) randomly created along the closed ring backbone via thermal Brownian motion, the applied flow field, and intermolecular collisions between chains [32]. Here we further quantified the proportion of each tumbling mechanism for the interfacial ring and SCB ring polymers as a function of the shear rate (Figure 6b). We first noticed that the center-loop tumbling is generally more dominant than the end-loop tumbling for both pure ring and SCB ring polymers. This can be understood by considering that, whereas the center-loop tumbling can be induced by any local loop along the stretched ring backbone, the end-loop tumbling is induced only by local loops located near the ends of the stretched ring backbone. Notably, the proportion of center-loop tumbling appears to be smaller for the SCB ring polymer than for the pure ring polymer. This is attributed to the relatively larger z-dimension of the interfacial SCB ring chains compared to the interfacial ring chains due to the short branches in the former (Figure 4). mobile short branches along the ring backbone. The Brightness results can be seen to be consistent with the results for the gyration tensor G shown in Figure 4.
As mentioned earlier, the ring polymer exhibits two types of tumbling dynamics at high flow fields: end-loop and center-loop tumbling (Figure 6a). Both mechanisms are induced by the local loop(s) randomly created along the closed ring backbone via thermal Brownian motion, the applied flow field, and intermolecular collisions between chains [32]. Here we further quantified the proportion of each tumbling mechanism for the interfacial ring and SCB ring polymers as a function of the shear rate (Figure 6b). We first noticed that the center-loop tumbling is generally more dominant than the end-loop tumbling for both pure ring and SCB ring polymers. This can be understood by considering that, whereas the center-loop tumbling can be induced by any local loop along the stretched ring backbone, the end-loop tumbling is induced only by local loops located near the ends of the stretched ring backbone. Notably, the proportion of center-loop tumbling appears to be smaller for the SCB ring polymer than for the pure ring polymer. This is attributed to the relatively larger z-dimension of the interfacial SCB ring chains compared to the interfacial ring chains due to the short branches in the former (Figure 4).

Conclusions
In this study, we performed a comprehensive analysis of the interfacial structural and dynamical behavior of confined polymer melt systems possessing various molecular architectures (linear, ring, SCB linear, and SCB ring) under shear flow using atomistic NEMD simulations. We placed a particular focus on the combined rheological influence of the closed-loop ring geometry and shortchain branching on the general structure and dynamics of the interfacial chains. In doing so, we examined the degree of interfacial slip, the underlying characteristic molecular mechanisms, and the detailed chain conformations for interfacial chains with respect to their molecular architectures.
In general, the interfacial linear and ring polymers exhibit three distinct characteristic regimes for the degree of slip ( s d ) with respect to the applied shear rate: an increasing, decreasing, and

Conclusions
In this study, we performed a comprehensive analysis of the interfacial structural and dynamical behavior of confined polymer melt systems possessing various molecular architectures (linear, ring, SCB linear, and SCB ring) under shear flow using atomistic NEMD simulations. We placed a particular focus on the combined rheological influence of the closed-loop ring geometry and short-chain branching on the general structure and dynamics of the interfacial chains. In doing so, we examined the degree of interfacial slip, the underlying characteristic molecular mechanisms, and the detailed chain conformations for interfacial chains with respect to their molecular architectures.
In general, the interfacial linear and ring polymers exhibit three distinct characteristic regimes for the degree of slip (d s ) with respect to the applied shear rate: an increasing, decreasing, and increasing behavior of d s in the weak, intermediate, and strong flow regimes, respectively. In contrast, the interfacial SCB linear and SCB ring polymers display almost constant behavior of d s throughout the weak and intermediate flow regimes followed by rapidly increasing behavior of d s in the strong flow regime.
To elucidate the interfacial slip behavior, it is very informative to analyze the fundamental molecular mechanisms with respect to the three representative (weak, intermediate, and strong) flow regimes. In the weak flow regime, all of the interfacial polymers (linear, ring, SCB linear, and SCB ring) undergo z-to-x chain rotation from the neutral direction to the flow direction, which effectively reduces the dynamic wall friction against chain movement along the flow direction. However, in comparison with its linear analogue, the ring polymer possesses a relatively longer chain dimension in the neutral direction owing to its intrinsic closed-loop geometry, which enhances the dynamic friction of the interfacial ring chains moving against the wall in the flow direction. In the case of the interfacial SCB polymers, whereas the main chain backbone becomes gradually aligned to the flow direction with increasing flow strength (thus decreasing the dynamic wall friction), the short branches tend to be oriented more perpendicular (i.e., aligned in the neutral direction) than parallel to the backbone (thus increasing the dynamic wall friction) in conjunction with their intrinsically fast random motions that are practically unaffected by the imposed flow fields. These two contrasting factors cancel each other out to result in almost constant d s in the weak flow regime for the interfacial SCB polymers. Furthermore, owing to its relatively larger chain dimension in the neutral direction associated with the ring topology, the SCB ring polymer exhibits the lowest degree of slip among all of the polymers.
The basic molecular mechanisms in the intermediate flow regime are out-of-plane chain wagging (i.e., repetitive motions between chain detachment from and chain attachment to the wall) and disentanglement of the interfacial chains from the surrounding bulk chains. The interfacial ring chains exhibit distinct dynamics referred to as loop migration (i.e., the local loops propagate along the chain backbone toward the flow direction) as well as the loop wagging mechanism. In comparison, the SCB polymers exhibit overall weaker out-of-plane wagging and disentanglement mechanisms owing to their more compact and less deformed (highly curvy) chain structures caused by the fast random movement of short branches along the backbone. Again, the interfacial SCB ring polymer displays the lowest value of d s throughout the weak and intermediate flow regimes as a consequence of the synergetic effects of the ring topology and short-chain branching.
In the strong flow regime, the flow field is sufficiently intense to overcome the attractive polymer-wall interactions and induce frequent interfacial chain detachment from the wall and irregular (chaotic) chain rotation and tumbling dynamics via strong dynamical collisions between the interfacial chains and the wall. This induces a rapid increase in the interfacial slip in this flow regime for all of the polymer systems, irrespective of the molecular architecture. In addition, owing to the enhanced interfacial chain detachment from the wall via the constant structural disturbance exerted by the highly mobile short branches, the SCB polymers exhibit even steeper increasing d s behavior in the strong flow regime in comparison to the corresponding pure linear and ring polymers.
Another interesting feature is that the interfacial SCB linear chains exhibit not only hairpin-like tumbling behavior but also two types of rolling dynamics (head-roll and tail-roll tumbling mechanisms) that are essentially induced by the short branches. However, such rolling dynamics were rather absent from the SCB ring system studied here. This is attributed to the difficulties in chain rolling for the stretched double-stranded rings with a relatively large chain dimension along the neutral direction.
It is also notable that the ring-shaped polymers essentially exhibit two types of loop tumbling mechanisms (end-loop and center-loop tumbling) at strong flow fields. The end-loop and center-loop tumbling mechanisms are induced by local loops situated near the ends and in the middle of the stretched ring backbone along the flow direction, respectively. As such, while the end-loop tumbling occurs mostly in the xy-plane, the center-loop tumbling occurs diagonally through both the xyand yz-planes. It is found that the interfacial SCB ring polymer, in association with its larger chain dimension in the neutral direction via short-chain branching, exhibits a relatively smaller proportion of center-loop tumbling in comparison with the pure ring polymer.
In respect to the overall chain dimension, the closed-loop ring topology tends to enhance G zz but diminish both G xx and G yy , while short-chain branching tends to enhance both G yy and G zz but diminish G xx .