Interfacial diffusion of a single cyclic polymer chain

Brownian motion of flexibly linked colloidal rings

Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on the conformation and diffusion of molecular ring polymers simultaneously are challenging due to their inherently small size. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly linked micron-sized colloids with n=4-8 segments. We characterize the conformations of these flexible colloidal rings and find that they are freely jointed up to steric restrictions. We measure their diffusive behavior and compare it to hydrodynamic simulations. Interestingly, flexible colloidal rings have a larger translational and rotational diffusion coefficient compared to colloidal chains. In contrast to chains, their internal deformation mode shows slower fluctuations for n≲8 and saturates for higher values of n. We show that constraints stemming from the ring structure cause this decrease in flexibility for small n and infer the expected scaling of the flexibility as function of ring size. Our findings could have implications for the behavior of both synthetic and biological ring polymers, as well as for the dynamic modes of floppy colloidal materials.

Effect of Topology on the Statics and Dynamics of a Polymer Chain at the Fluid-Fluid Interface: A Molecular Dynamics Simulation Study

The effect of chain topology on the statics and dynamics of a chain at the interface of two immiscible fluids is studied by means of molecular dynamic simulations. For three topologically different chains, namely, linear, ring, and trefoil-knot, of the same molecular weight, the effect of varying both polymer-fluid and fluid-fluid interaction nature on the width of the fluid interface, chain conformation, shape, and chain dynamics is investigated. For a sharp-interface binary-fluid system, the interface width is insensitive to both topology and polymer-fluid interaction nature, while a weak nonmonotonic variation is seen for a broad-interface system. Chain extension normal to the interface plane is significantly affected by the topology with a trefoil-knot chain, due to the additional constraint, which has the largest value compared to both linear and ring polymers. Instantaneous shapes are also quantified through shape parameters. Furthermore, it is observed that the qualitative behavior of the center-of-mass mean-square displacement (MSD) is independent of topology, i.e., all the chain types show the same diffusion exponent α ( ∼ 1). However, the self-diffusion constant depends on the topology and it is the largest for the trefoil-knot chain. An interesting observation pertaining to the early time behavior of monomeric MSD is that, within the subdiffusive regime, the values of α for different parameters (independent of topology) are grouped into two distinct ranges (0.52 - 0.59 and 0.62 - 0.67), which are related to the different chain conformation for the polymer-fluid interaction range below and above a threshold value equal to that of the self-interaction of the pure fluid phase.

Cyclic Topology Enhancing Structural Ordering and Stability of Comb-Shaped Polypeptoid Thin Films against Melt-Induced Dewetting

We investigated the effect of cyclic chain topology on the molecular ordering and thermal stability of comb-shaped polypeptoid thin films on silicon (Si) substrates. Cyclic and linear poly(N-decylglycine) (PNDG) bearing long n-decyl side chains were synthesized by ring-opening polymerization of N-decylglycine-derived N-carboxyanhydrides. When the spin-coated thin films were subjected to thermal annealing at temperatures above the melting temperature (T > T m), the cyclic PNDG films exhibited significantly enhanced stability against melt-induced dewetting than the linear counterparts (l-PNDG). When recrystallized at temperatures below the crystallization temperature (T < T c), the homogeneous c-PNDG films exhibit enhanced crystalline ordering relative to the macroscopically dewetted l-PNDG films. Both cyclic and linear PNDG molecules adopt cis-amide conformations in the crystalline film, which transition into trans-amide conformations upon melting. A top-down solvent leaching treatment of both l/c-PNDG films revealed the formation of an irreversibly physisorbed monolayer with similar thickness (ca. 3 nm) on the Si substrate. The physisorbed monolayers are more disordered relative to the respective thicker crystalline films for both cyclic and linear PNDGs. Upon heating above T m, the adsorbed c-PNDG chains adopt trans-amide backbone conformation identical with the free c-PNDG molecules in the molten film. By contrast, the backbone conformations of l-PNDG chains in the adsorbed layers are notably different from those of the free chains in the molten film. We postulate that the conformational disparity between the chains in the physically adsorbed layers versus the free chains in the molten film is an important factor to account for the difference in the thermal stability of PNDG thin films. These findings highlight the use of cyclic chain topology to suppress the melt-induced dewetting in polymer thin films.

Lateral diffusion of single polymer molecules at interfaces between water and oil

Lateral diffusion of polymer molecules at the interfaces between immiscible oil and water is investigated at the single molecular level. The interfaces between water and alkanes are chosen as the model systems and polyethylene oxide (PEO) is the model polymer. Fluorescence correlation spectroscopy is used to measure the interfacial diffusion of fluorescence-labeled PEO with its molecular weight ranging over more than an order of magnitude. It is discovered that the interfacial diffusion coefficient scales with the molecular weight by the exponent of -0.5. Detailed analysis shows that the PEO chain takes an ideal two-dimensional random coil conformation at these fluidic interfaces and the bigger contribution from water's hydrodynamic friction is discovered.

Inconsistency of Diffusion and Relaxation of Ring Polymers Adsorbed on Rough Surfaces

We explore the diffusion and relaxation dynamics of a single ring polymer strongly adsorbed on rough surfaces with different roughnesses by means of molecular dynamics simulations. Our simulations demonstrate that on rough surfaces the intrachain topological constraint deriving from the closed architecture induces the inconsistency of diffusion and relaxation of ring polymers. When the lateral chain size is larger than the obstacle distance (2R_g∥,r > d), the ring closure induces the polymers to anchor on a single obstacle and dramatically reduces their diffusivity, where R_g∥,r and d are the lateral components of the mean-square radius of gyration and the obstacle distance, respectively. However, the single obstacle anchoring has no effect on the relaxation of ring polymers, which implies a deviation between the diffusion and the relaxation. With the lateral chain size beyond twice of the obstacle distance (R_g∥,r > d), the ring polymers are totally confined in the array of obstacles and can only diffuse through hopping over the obstacles, resulting in an exponential reduction of their diffusion coefficient. However, the relaxation of ring polymers mainly depends on their rotating reptation and satisfies the reptation-like dynamics, which means that the diffusion and the relaxation are nearly irrelevant. This inconsistency between the diffusion and relaxation is a unique property of adsorbed ring polymers, which would be meaningful to understand the physical nature of polymers with ring closure and significant to develop the corresponding applications.

Cross-over in the dynamics of polymer confined between two liquids of different viscosity

Using molecular dynamics simulations, we analysed the polymer dynamics of chains of different molecular weights entrapped at the interface between two immiscible liquids. We showed that on increasing the viscosity of one of the two liquids the dynamic behaviour of the chain changes from a Zimm-like dynamics typical of dilute polymer solutions to a Rouse-like dynamics where hydrodynamic interactions are screened. We observed that when the polymer is in contact with a high viscosity liquid, the number of solvent molecules close to the polymer beads is reduced and ascribed the screening effect to this reduced number of polymer-solvent contacts. For the longest chain simulated, we calculated the distribution of loop length and compared the results with the theoretical distribution developed for solid/liquid interfaces. We showed that the polymer tends to form loops (although flat against the interface) and that the theory works reasonably well also for liquid/liquid interfaces.

Viscoelastic Properties of Unentangled Multicyclic Polystyrenes

We report on the viscoelastic properties of linear, monocyclic, and multicyclic polystyrenes with the same low molecular weight. All polymers investigated were found to exhibit unentangled dynamics. For monocyclic polymers without inner loops, a cyclic-Rouse model complemented by the contribution of unlinked chains (whose fraction was determined experimentally) captured the observed rheological response. On the other hand, multicyclic polymers with inner loops were shown to follow a hierarchical cyclic-Rouse relaxation with the outer loops relaxing first, followed by the inner loop relaxation. The influence of unlinked linear chains was less significant in multicyclic polymers with inner loops. The isofrictional zero-shear viscosity decreased with increasing number of constrained segments on the coupling sites, which was attributed to the decreasing loop size and the dilution effect due to the hierarchical relaxation.

Effects of surface roughness on the self-diffusion dynamics of a single polymer

We employ molecular dynamics simulations to simulate the diffusion dynamics of a single polymer adsorbed on surfaces with different roughnesses, which are characterized by the separation distance between obstacles and the height of obstacles. Our simulations demonstrate that for strong adsorption and when the confinement of obstacles is strong enough for all chains, the scaling exponent α of the diffusion coefficient on the chain length exhibits three cases with increase of the height of obstacles: a Rouse plateau with α ≈ -1 (the lateral motion of the polymer chains is free), a reptationlike plateau with α ≈ -1.5 (the polymer chains can hardly stride over the obstacles in the perpendicular direction) and a transition from the Rouse plateau to the reptationlike plateau with -1.5 < α < -1 (the obstacles hinder the lateral motion of the polymer chains). However, with increase of the separation distance between obstacles, the confinement from the obstacles exhibits a decrease (more lateral motions of the polymer chains are allowed), which results in a higher plateau (no longer separate reptationlike dynamics). Our results clarify the effects of surface roughness on the diffusion mechanism of polymer chains strongly adsorbed on solid surfaces in dilute solutions and the resulting transition mechanism from the Rouse scaling to the reptationlike scaling, which is significant for the understanding of the physical nature and the development of the corresponding applications.

The effect of alcohols as the third component on diffusion in mixtures of aromatics and ketones

The Fick diffusion coefficient matrix of three ternary mixtures composed of an aromatic (benzene), a ketone (acetone) and one of three different alcohols (methanol, ethanol or 2-propanol) is investigated with laboratory and numerical work.