Topology effects on associative polymers

Abstract

Tailoring the topology of associative polymers offers a means to control macromolecular responses that in turn enables the design of new responsive soft materials. The current study probes the conformation and response of ring associative polymers in comparison with their entangled linear analogues using molecular dynamics simulations of a coarse-grained bead-spring model. The uniqueness of ring polymers lies in their topology where the chains have no free ends, resulting in considerably faster dynamics compared to their linear analogs, whereas the associative groups drive assembly that constrains the polymer motion. Here, polymers consisting of randomly distributed associative groups, with a fraction f = 0.02 to 0.1 and interaction strength varying from 2 to 8k_BT, were studied. We find that with increasing f and association strength, larger clusters of associative groups are formed, where their size and dynamics are strongly affected by chain topology. While the associative groups do not impact the chain conformation, they slow stress relaxation, with a distinctively stronger effect on the linear chains. This is attributed to the lower number of unique chains associated with clusters of the same size in ring melts compared with linear ones. Overall, the coupling of associating groups with entanglements results in slower stress relaxation, where the distinctive topologies affect the association of the chains.

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I. Introduction

The viscoelastic response of polymers is affected by their chemistries coupled with the size and shape of the molecules.^1–3 Among the chemistries that impact polymers are associative interactions with energies exceeding those of van der Waals forces, such as hydrogen bonds, π–π interactions groups as well as ionizable ones that are often critical to the functionality of these polymers in their many applications. They often drive the assembly of the macromolecules, which affects their structure and often constrains their motion. Tethering the associating groups (AGs) to chains with distinctive topologies opens the way to design new responsive polymers. The delicate balance between chain topology and the constraints exerted by the AGs remains to be determined. It is fundamental to systems that are controlled by two distinctive energy scales and is key to the function and stability of polymers in current and potential applications.

The topology of chains can be linear, branched, comb or star-like, circular, as well as brush-like. Combined with associative groups, moieties whose interaction energies are typically higher than van der Waals, tethered to their backbone, polymers exhibit markedly diverse characteristics, forming a formidable landscape of macromolecular responses.^4–7 A notable number of studies have focused on either the effects of topology^8–12 or associative groups on the polymer structure, dynamics, and response but none have examined the combined effect of topology and associating groups.

Only a limited number of experimental studies have probed the correlations involving polymer topology, among which are polymer brushes, where only one end is free, while the other is confined. In these systems, the electrostatic environment strongly affects chain conformation and in turn affects the mechanical response of these systems.^13,14

Associative ring polymers and loopy segments are prevalent in nature, where, for example, topology-associated group correlations affect protein folding as well as assembly of DNA into networks¹⁵ and are critical in understanding the assembly into chromatin.^16–18 In these bio systems, specific association of amino acids coupled with topology dictates the ability of the chains to assemble. In the realm of synthetic polymers, the conjunction of topology and associative groups offer a design tool for macromolecular response. The interrelation between the topology and the impact of associative groups, however, remains a convoluted uncharted territory with hardly any experimental studies.

Here, using a coarse grain bead-spring model, we probe using molecular dynamics simulations^19,20 the structure, chain mobility and mechanical response of ring AG decorated polymers in comparison with their linear analogue as the strength of the interactions of associative groups is varied. We find that topology affects the number of chains that constitute each of the clusters, determining the response of the polymers.

Ring polymers are distinguished by the simple fact that they lack free ends, affecting their structure and dynamics.^12,21 Linear chains in a melt assume a Gaussian conformation with their size scaling as N^1/2, where N is the degree of polymerization.² The topological constraint of no free ends forces ring polymers to form globularly compact structures whose size scales as N^1/3.¹² Ring polymers are less entangled compared with linear chains with similar N, resulting in higher mobility. The motion of rings proceeds as loops of increasing size rearrange progressively where linear polymer dynamics is constrained by entanglements.^22,23 The enhanced dynamics that stems from the topology of the molecules expresses itself in much faster stress-relaxation in ring melts compared to linear chain melts.^24–26

The correlation of topology effects with the presence of AGs presents a challenge given that the addition of even a small fraction of interacting associating groups on the polymer backbone dramatically changes the properties of the system and drives the assembly.^4–7 These AGs either form pairwise associations, such as hydrogen bonds, or larger directional assemblies, such as π–π stacks, or clusters such as ionizable groups.⁷ The latter exhibit long range interactions that drive collective assemblies to form ionic clusters.^27–29 The size, shape, and lifetime of these clusters all affect the structure and dynamics of the chains. The current work seeks to resolve the interrelation between associating groups in rings compared with linear entangled polymers.

The unique dynamics of associative polymers and their technological potential have driven significant efforts including various computational studies using both fully atomistic simulations of model polymers, such as polystyrene sulfonate, and coarse-grained chains, each providing insight into distinct length scales. Using fully atomistic models, Agrawal et al.³⁰ have shown that for polystyrene sulfonate, increasing the dielectric constant of the media, which reduces the strength of the ionic interaction between associating SO₃⁻ groups, decreases the size of the ionic cluster and enhances the dynamics. Mohottalalage et al.³¹ have shown that the distribution of ionic groups along the polymer backbone affects the size and shapes of these ionizable groups and their dynamics. Studies of segmental motion by Frischknecht et al.³² and Winey and Frischknecht³³ on precise poly(ethylene-co-acrylic acid) ionomers showed that the local motion of the chains slows down as clusters are formed. They showed that the ionic aggregates form various shapes ranging from isolated aggregates to percolated aggregates depending on the separation of the space length. Paren et al.³⁴ found that the ionic groups on precise single-ion conductors, consisting of a polyethylene backbone with sulfonated phenyl pendant groups, nanophase separate from the polymer backbone to form percolating ionic aggregates. Using a coarse grained bead-spring model, Hall et al.^35,36 embedded charged beads and studied their effects on the structure. Sadeghi et al.³⁷ extended this model to study polyampholyte ionomers in which both types of ions are incorporated in the polymer chain and compared their dynamics and structures with the conventional cationic ionomers, where only cations are incorporated into the polymer chain.

With the realization that topology plays a significant role, Senanayake et al.³⁸ studied the effect of strength of the associating groups on chain mobility and viscoelastic response of melts of unentangled linear chains and star polymers. They found that for a 3-arm star polymer melt, the average size of the assemblies is similar to a linear polymer melt of the same molecular weight. However, the number of unique chains associated with each cluster is smaller for the associative star melt compared with the linear chain melt.

To understand the effect of chain topology on the assembly process of associating groups, we use molecular dynamics (MD) simulations of a coarse-grained bead-spring model in which the interacting groups are incorporated in the form of associating beads randomly distributed along the backbone.³⁸ We compare the structure, chain mobility, and stress relaxation for entangled linear chain melts with ring polymer melts of the same chain length.

Specifically, we study a range of associating group interactions from 2 to 8k_BT for associating group fractions of f = 0.02 to 0.10. Experimentally, changing the associated group interaction would entail changing the chemistry of the association group. The lower interaction range is characteristic of co-polymers where the interactions of minority species are stronger than those of the majority component. With increasing interactions, the model captures the association of AGs, such as those present in non-ionic surfactants, and the stronger interactions typical of ionizable groups, all driving collective assembly. A visualization of a linear and a ring chain with associative beads extracted from ring and linear melts is shown in Fig. 1.

Fig. 1 Visualizations of an individual (a) linear and (b) ring chain for f = 0.05 with the strength of the associating bead interactions of 5k_BT. Each chain contains 400 beads. The associating beads (yellow) are increased in size for clarity.

Similar to melts of non-associative polymers, the linear chains are more extended compared with the rings. The conformational difference between individual ring and linear chains in non-associative polymers is attributed to the nature of confinement of the macromolecules. The extended conformation of the linear chains arises from their confinement to a tube of their neighbors where the ends move more freely. Rings, however, do not have free ends and are thus more globular. As the strength of attraction between the associating groups and their concentration increases, the size of the clusters of associating beads increases, leading to long lived, transient networks, in both linear and ring melts.

II. Model and methodology

The Kremer–Grest coarse-grained model^19,20 with beads of mass m and diameter σ connected by finite extensible nonlinear elastic (FENE) bonds was used to compare the structure and dynamics of associating polymer melts of linear and ring polymers. Non-connected beads interact with a Lennard-Jones potential,where the cutoff r_cut = 2.5σ for all beads. The chains contain two types of beads, non-associating beads (type 1), which interact with strength ε₁₁ and associating beads (type 2), which interact with strength ε₂₂ > ε₁₁. The cross term ε₁₂ = ε₁₁. The ratio of the interaction strengths ε_s = ε₂₂/ε₁₁ was varied from 1 to 8, which captures the interaction energies of random copolymers to ionic interaction energies. The fraction of random associating beads f = 0.02, 0.05 and 0.10. This range of associating bead strength and concentration is sufficient to qualitatively affect the size of clusters of associating groups and reduce chain mobility.

All simulations are carried out using the large scale atomic molecular massively parallel simulator (LAMMPS) software.³⁹ Melts of 400 chains of length N = 400 were prepared following the procedure described by Auhl et al.⁴⁰ Ring melts of 1600 chains of length N = 400 were prepared following the procedure developed by Smrek et al.⁴¹ The equations of motion were integrated with a time step at Δt = 0.01τ, where τ = (mσ²/ε₁₁)^1/2 is the standard time unit for a Lennard-Jones fluid, where m is the mass of the bead. The beads are coupled to a Langevin thermostat to maintain the temperature T = ε₁₁/k_B with a damping time constant of 10τ.^42,43 The glass transition T_g ∼ 0.48ε₁₁/k_B for a linear, homopolymer melt with no associating beads.⁴⁴ The beads are connected by FENE bonds with a spring constant K = 30 ε₁₁ and R₀ = 1.5σ. The polymers are semiflexible with a 3-body cosine angle interaction V_angle(θ) = k_θ [1 + cos(θ)] with k_θ = 1.5ε. The entanglement length N_e ∼ 28 for linear chains for this model.^45,46 Thus, for the linear chain melts studied here, the number of entanglements per chain Z = N/N_e ∼ 14. Following equilibration with no associating groups, a fraction f of the beads in the systems was randomly changed to associating beads, type 2. The evolution of the associating groups was then followed as a function of time for ε_s = 2–8 at constant pressure. After the density and average cluster size of the associating groups reached a steady state, the systems were run at constant volume for 3–4 × 10⁷τ. The number density of each system is ρ ≈ 0.89–0.92σ⁻³, depending on the value of the associating bead strength ε_s and fraction f. The measured radius of gyration of the chains is found to be independent of the fraction and strength of the associating beads as shown in Fig. S1 (ESI†).

The static structure factor S(q) for the associating beads is calculated by

where b_i is the scattering length density for monomer i. Due to the periodic boundary conditions, the wavevector q is limited to , where L is the simulation cell length and n_x, n_y, and n_z are integers. The scattering length density is set to b_i = 1 for associating beads and to b_i = 0 for non-associating beads.

III. Structure of linear and ring melts

The assembly process of associating groups was followed over time with varying the interaction strength ε_s and associating bead fraction f. The visualization of a section of the ring and linear melts for f = 0.05 for three values of ε_s is shown in Fig. 2. Similar illustrations for ε_s = 5 for varying f are shown in Fig. S1 (ESI†). With increasing ε_s the AGs assemble to form clusters that become significantly more defined at higher interactions.

Fig. 2 Visualization of a section of the melts of linear and ring chains for f = 0.05 after the systems have reached a steady state. The associating beads are yellow, and the non-interacting beads are blue. The associating beads are increased in size for clarity.

The cluster evolution is shown in Fig. 3a for f = 0.05. Associating groups are defined to reside in the same cluster if they are within 1.5σ of each other. This distance was chosen to capture all the nearest neighbor pairs as shown in Fig. S2 (ESI†) for the pair correlation function between associating bead g_aa(r). Similar trends are found for f = 0.02 and 0.10. For low association strength, ε_s = 2–4, the average cluster size reaches its final value almost instantly. For ε_s ≥ 5, the average cluster size initially rapidly increases with time as nearby associating groups form clusters and then continue to slowly grow, reaching a plateau only at later times. The average cluster size 〈N_c〉 at the plateau is presented in Fig. 3b as a function of ε_s for f = 0.02, 0.05 and 0.1. With increasing ε_s, the final average cluster size first increases and then decreases. With increasing ε_s, the energy barrier for the clusters to rearrange increases and the system becomes kinetically trapped. For large ε_s, the associating beads are locked in which ever cluster they first associate with and the cluster size does not change. At lower ε_s, the associating beads can exchange between clusters, resulting in an increase in cluster size compared to large ε_s. Except for the smallest association strength ε_s, 〈N_c〉 for the rings is larger than for the linear chains with the largest difference for intermediate interaction strength between AG ε_s ∼ 5.

Fig. 3 (a) Average cluster size 〈N_c〉 as a function of time for linear chains (open) and rings (closed) in polymer melts for f = 0.05 at ε_s = 2 (circles), ε_s = 3 (squares), ε_s = 4 (triangles), ε_s = 5 (diamonds), and ε_s = 8 (stars). (b) Average cluster size 〈N_c〉 for f = 0.02, 0.05, and 0.10, at the end of the simulation as a function of association strength ε_s for linear (open) and ring (filled) polymer chains.

The formation of the AG clusters does not affect the overall dimensions of the chains. The measured radius of gyration of the chains is found to be independent of the fraction and strength of the associating beads as shown in Fig. S3 (ESI†) for both the ring and linear melts. This is presumably because the AGs do not move very far to assemble into clusters, in which case the overall dimensions of the chain are not affected.

The mesoscopic correlations in both melts were studied through calculating the static structure factor S(q) of the associating beads. The results are shown in Fig. 4, where the calculated static structure factor is normalized to the number of beads. For both linear and ring melts, the patterns consist of two distinct features, one at low q, which reflects correlations between the associative clusters, and another at high q that corresponds to the packing of the associating beads. At ε_s = 2, there is no low q peak in S(q), as most AGs are not in clusters for both linear and ring melts. As ε_s increases, the intensity of both the low q peaks, and their width decreases.

Fig. 4 (a) Static structure factor S(q) of the associating groups as a function of q for (a) linear chains and (b) rings at the indicated values of ε_s for f = 0.05. Intensity for the low q peak for S(q) as a function of association strength ε_s for linear (open) and ring (filled) polymer melts is shown in the inset.

Experimentally, the intensity of any peak in a scattering pattern corresponds to the number of objects that contribute to a given signature and its width is inversely proportional to the degree of correlation. Here as S(q) is normalized to the number of the associating beads, both the intensities and peak widths reflect the degree of correlation. The insert captures the peak intensity as a function ε_s for the values of f studied. For linear chains, both the intensity and width of the low q peak gradually increase with increasing ε_s and then level off. For rings, the intensity of the low q peak exhibits an abrupt increase between ε_s = 4 and 5 followed by a plateau. At low and intermediate ε_s, the intensity of the low q peak increases with increasing ε_s. At higher ε_s, the peak intensity decreases for all systems except linear chains at f = 0.05. The f = 0.05, as the systems become kinetically trapped, as shown in the next section, indicating that the clusters are most likely not completely equilibrated. Linear chains exhibit higher peak intensities than rings at low and intermediate ε_s. The larger peak intensity for linear chains compared to the rings indicates more well-defined inter-cluster distances, as shown in the visualization in Fig. 2.

Cluster formations comprise associating groups that could belong to different polymers, defined as unique chains, or reside on the same chain. The number of unique polymer chains associated with each cluster, along with the cluster's size and shape, significantly impacts the overall dynamics of the melts. Fig. 5 presents the average number of unique chains 〈N_uc〉 in a cluster as a function of cluster size N_c. For both the linear and ring melts, 〈N_uc〉 is independent of the AG strength ε_s for a given cluster size. For the smallest clusters at low interaction strengths, associations are primarily interchain, with 〈N_uc〉 ≈ N_c. As the cluster size grows, 〈N_uc〉/N_c decreases, as the number of intra chain associations in the same cluster grows. For a given cluster size, 〈N_uc〉 is significantly larger for the linear chains compared to the rings as each cluster contains more inter-chain associating groups. This difference is presumably because the rings are much more compact (〈R_g²〉^1/2 = 7.2σ) than the linear chains (13.3σ). This is also manifested in the fact that the largest cluster size for the rings is larger than for the linear chain melts.

Fig. 5 Average number of unique chains 〈N_uc〉 in a cluster of size N_c as a function of cluster size for linear chains (a) and rings (b) for f = 0.05 for the indicated ε_s values. Visualizations of an average size cluster of associative groups are observed in a melt of linear chains and rings for f = 0.05 with the associating bead strength of 5k_BT. Each chain contains 400 beads and is marked by different colors. The associated beads are yellow and are increased in size for clarity for the highlighted cluster, which has 23 associating beads in each case. There are 11 unique chains for the linear chains and 8 for the rings.

III. Dynamics and viscoelastic response

Association groups constantly break and reform clusters over time. To obtain an insight into the lifetime of the clusters, we measured the survival time of pairs of associating beads that remain in the same cluster as a function of time. This is calculated by first identifying all pairs of associating beads that are within the same cluster and following the number of pairs that remain in the same cluster as a function of time.

The number of such pairs N_pair(t) that remain in the same cluster as a function of time is shown in Fig. 6. N_pair(t) decreases either by single associating beads leaving the cluster or the cluster breaking into two or more smaller clusters. Although for the present systems, the decay is predominantly by an associating bead leaving the cluster.

Fig. 6 Number of pairs N_pair(t) that remain in the same cluster as a function of time for (a) linear and (b) ring melts with f = 0.05 for the indicated ε_s values. The solid lines are fits to a sum of two exponentials.

The results for N_pair(t) are fitted to the sum of two exponentials,

N_pair(t)/N_pair(0) = A₁e^−t/τ₁ + A₂e^−t/τ₂,

where τ_i are the relaxation times (τ₁ > τ₂) and A_i are the weighting functions for the two contributions. The sum was constrained in the fit so that A₁ + A₂ = 1. Results for τ_i are shown in Fig. 7 and the values of τ_i and A_i are tabulated in Tables S1 and S2 in the ESI.† For low association strength ε_s, N_pair(t) for both the linear and ring melts decays quickly as the associating clusters are small and very dynamic and as a result have minimal effect on the long-time mobility of the chains. As ε_s increases, the decay times for N_pair(t) increases rapidly, with the decay time always being longer for the linear chains compared to the rings, as the linear chains are more entangled than the rings. For associating strength ε_s = 8, the clusters are kinetically trapped. For large ε_s, these long-lived clusters constrain the mesoscopic mobility of the polymer, as is shown in Fig. 8.

Fig. 7 Relaxation times τ_i as a function of association strength ε_s for linear chains (open) and rings (filled).

Fig. 8 Mean square displacement, g₁(t) of the beads for (a) linear chains and (b) rings as a function of time and for the center of mass (COM) g₃(t) for (c) linear chains and (d) rings for f = 0.05 for the indicated ε_s values.

As the mesoscopic dynamics is coupled to the lifetime of the clusters, we measured the mean squared displacement (MSD) of the monomers g₁(t) = 〈(r_i(t) − r_i(0))²〉 and of the center of mass (COM) g₃(t) of polymer chains. For the linear chains, g₁(t) was averaged over the inner 50 beads of the chain, while for the rings, g₁(t) was averaged over all the monomers of the chain. Results for g₁(t) and g₃(t) are presented in Fig. 8 for the linear and ring chains for f = 0.05 for different strengths ε_s.

For small associating group strength, ε_s < 4, the mobility of beads in the linear chains, presented in Fig. 8a, shows the characteristic crossover from Rouse scaling t^1/2 at early times to reptation scaling t^1/4 at intermediate times at crossover time τ_e ∼ 2800τ. At much later times, a crossover to the diffusive regime, g₃(t) ∼ t, is observed for times greater than the diffusive time τ_d. For N = 400 with ε_s = 1, τ_d = 2.6 × 10⁷τ is determined as the time for the inner beads to move 3 〈R_g²〉. For ε_s = 2, which would model a random copolymer, τ_d is unchanged for f = 0.02 and increases slightly to τ_d = 2.8 × 10⁷τ for f = 0.05 and to τ_d = 3.9 × 10⁷ for f = 0.10. For larger ε_s, g₁(t) does not reach the diffusive regime within the time scales currently accessible as the associating groups act effectively as crosslinks.

As the interaction between associating groups increases, the mobility of the beads, even at short distances, becomes significantly suppressed, with an effective power law smaller than 1/4 expected for reptation. This suppression in the chain mobility is seen very clearly in the mobility of the center of mass g₃(t), shown in Fig. 8c. The mobility of the beads for the ring polymers is shown in Fig. 8b. For ring melts with no associating groups, Halverson et al.⁴⁷ observed a significant slowing down in the mean-square displacement from the initial t^1/2 scaling to a power law very close to the t^1/4 expected for reptation of linear polymers, even though rings cannot entangle in the classical sense.²³ As for the linear chains, this behavior is largely unchanged for ε_s ≤ 4 for f = 0.05 as shown in Fig. 8b. Only for larger ε_s, do the associating group begin to dominate the chain mobility. For f = 0.05, the diffusive time τ_d = 2.4 × 10⁵τ for ε_s = 1 and 2 and increases only slightly to τ_d = 2.5 × 10⁵τ for ε_s = 3 and then starts to increase more rapidly with increasing associating strength, τ_d = 3.6 × 10⁵τ for ε_s = 4 and τ_d = 8.0 × 10⁵τ for ε_s = 5, and τ_d = 6.0 × 10⁶τ for ε_s = 6. For larger ε_s values, the diffusive regime is beyond the accessible time scales. Similar results are observed for f = 0.02 and 0.10. Similar effects of increasing ε_s on the overall chain mobility are shown in Fig. 8d for the motion of the COM of the rings.

These linear and ring melts constitute heterogeneous media where the AG beads form distinctive domains whose dynamics controls the macroscopic motion of the chains and their mechanical response. The mobility of the molecules affects the mechanical response of the system as reflected in stress relaxation G(t) after a small perturbation, which is a prevalent experimental measure of polymer rheology. Stress relaxation is measured using the Green–Kubo relation G(t) = (V/k_BT)〈σ_αβ(t)σ_αβ(0)〉, where σ_αβ(t) is the off-diagonal components xy, xz, and yz of the stress and V is the volume of the system. The results are shown in Fig. 9 and 10 for linear and ring melts.

Fig. 9 (a) Stress autocorrelation G(t) for linear chains as a function of time at f = 0.05 for the indicated ε_s values. (b) G(t) for ε_s = 5 for f = 0.02, 0.05 and 0.10.

Fig. 10 Stress autocorrelation G(t) for ring polymer melts as a function of time for (a) f = 0.05 and (b) f = 0.10 for the indicated ε_s values.

For entangled non-associative linear polymers, at short times, G(t) decays as the chains locally relax in response to the perturbation. At intermediate times beyond the entanglement time τ_e, G(t) plateaus at , before decaying to zero after the chains have reached the diffusive regime at τ_d. The results for non-associating melts are in agreement with those of Hsu and Kremer²⁰ who observed a well-defined plateau at intermediate times for G(t) with N_e = 28 for a range of chain lengths. For ε_s < 3, we observe little effect on stress relaxation for f = 0.05 as shown in Fig. 9a. For larger ε_s, the stress relaxes slowly and decays only for very long times. The effect of varying the concentration of associating beads is shown in Fig. 9b for ε_s = 5. Increasing the fraction of associating beads has a strong effect on stress relaxation.

The stress relaxes significantly faster in ring melts than in linear ones. For intermediate chain lengths where the rings do not entangle, the fractal loopy globular model²³ predicts that G(t) decays as t^−3/7, in agreement with the MD simulations of Halverson et al. and Tu et al.⁴⁸ For very high molecular weight rings, recent experiments and simulations show non-power-law stress relaxation as the rings interpenetrate.⁴⁸

For ε_s < 3, we observe little effect on stress relaxation for f = 0.05 as shown in Fig. 9a. For larger ε_s, the stress relaxes slower and decays only for very long times. The combination of entanglements and strongly interacting associating groups dramatically increases the plateau modulus, consistent with what one finds for crosslinked networks.^49–51 The effect of varying the concentration of associating beads is shown in Fig. 9b for ε_s = 5. Increasing the fraction of associating beads retards stress relaxation and increases the plateau modulus.

For rings, the relaxation times are much shorter than for linear chains of the same length as shown in Fig. 10. Measurable deviations from the expected t^−3/7 power law in G(t) occur for ε_s ≥ 6 for f = 0.05 and ε_s ≥ 5 for f = 0.10. However, except for the highest AG strength, G(t) is still reasonably well described by a power law, albeit with a smaller amplitude exponent.

Though both linear and ring melts reach a plateau for large ε_s, the magnitude differs significantly with the plateau for the linear systems being much higher. This is attributed to the lock-in of entanglements by the AGs that do not occur in the ring melts.

IV. Conclusions

The structure, dynamics and response of ring associative polymer melts were studied in comparison with those of linear melts. Although for both melts the associating beads form clusters with increasing interaction strength between the associate beads, the topology of the polymer affects the nature, size, and stability of the associative domains and hence, their stress relaxation. The clusters for the linear chains form at lower association strength compared with rings and exhibit a narrower distribution. The lifetime of a pair of associating groups in a melt of ring polymers is shorter than that in linear melts.

The linear and ring melt response to stress is distinctive. In linear chains, the AGs lock the entanglements, increasing the plateau moduli, which is similar to a crosslinked network. For ring melts with weakly interacting associating groups, the stress relaxes as a power law with an exponent that is smaller in magnitude compared to rings without associating groups. At high ε_s, stress relaxation exhibits a plateau.

These simulations show that combining topology and associating groups can lead to interesting new phenomena and can be used as a design tool for new materials.

Conflicts of interest

There are no conflicts to declare.

Data availability

The trajectories from the molecular dynamics simulations and resulting analysis are available from one of the corresponding authors upon request.

Acknowledgements

D. P. gratefully acknowledges the financial support given by NSF Grant No. DMR-1905407. This research used in part resources on Palmetto Cluster at Clemson University under NSF awards MRI 1228312, II NEW 1405767, MRI 1725573, and MRI 2018069. This research used resources at the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science user facility, operated under Contract No. DE-AC02-05CH11231. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy and Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multimission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. NSF, DOE or the U.S. Government.

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Footnotes

† Electronic supplementary information (ESI) available: Visualization of a section of the melts of linear and ring chains for ε_s = 5 for f = 0.02, 0.05 and 0.10 together with graphs for the pair correlation function, g_aa(r) for the associating bead, and root mean squared radius of gyration as a function of association strength ε_s. Tables with the fitting parameters τ_i and A_i. See DOI: https://doi.org/10.1039/d5sm00368g

‡ All these authors contributed equally.

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