Local Polymer Dynamics and Diffusion in Cylindrical Nanoconfinement

Increase in the effective viscosity of polyethylene under extreme nanoconfinement

Understanding polymer transport in nanopores is crucial for optimizing heterogeneously catalyzed processes in polymer upcycling and fabricating high-performance nanocomposite films and membranes. Although confined polymer dynamics have been extensively studied, the behavior of polyethylene (PE)-the most widely used commodity polymer-in pores smaller than 20 nm remains largely unexplored. We investigate the effects of extreme nanoconfinement on PE transport using capillary rise infiltration in silica nanoparticle packings with average pore radii ranging from ∼1 to ∼9 nm. Using in situ ellipsometry and the Lucas-Washburn model, we discover a previously unknown inverse relationship between effective viscosity (ηeff) and average pore radius (Rpore). Additonally, we determine that PE transport under these extreme conditions is primarily governed by physical confinement, rather than pore surface chemistry. We refine an existing theory to provide a generalized formalism to describe the polymer transport dynamics over a wide range of pore radii (from 1 nm and larger). Our results offer valuable insights for optimizing catalyst supports in polymer upcycling and improving infiltration processes for nanocomposite fabrication.

Fluorescence-readout as a powerful macromolecular characterisation tool

The last few decades have witnessed significant progress in synthetic macromolecular chemistry, which can provide access to diverse macromolecules with varying structural complexities, topology and functionalities, bringing us closer to the aim of controlling soft matter material properties with molecular precision. To reach this goal, the development of advanced analytical techniques, allowing for micro-, molecular level and real-time investigation, is essential. Due to their appealing features, including high sensitivity, large contrast, fast and real-time response, as well as non-invasive characteristics, fluorescence-based techniques have emerged as a powerful tool for macromolecular characterisation to provide detailed information and give new and deep insights beyond those offered by commonly applied analytical methods. Herein, we critically examine how fluorescence phenomena, principles and techniques can be effectively exploited to characterise macromolecules and soft matter materials and to further unravel their constitution, by highlighting representative examples of recent advances across major areas of polymer and materials science, ranging from polymer molecular weight and conversion, architecture, conformation to polymer self-assembly to surfaces, gels and 3D printing. Finally, we discuss the opportunities for fluorescence-readout to further advance the development of macromolecules, leading to the design of polymers and soft matter materials with pre-determined and adaptable properties.

Structure and dynamics of a 1,4-polybutadiene melt in an alumina nanopore: A molecular dynamics simulation

We present results of Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene (PBD)confined in a cylindrical alumina nanopore of diameter 10 nm. The simulations are done at three different temperaturesabove the glass transition temperature T g . We investigate the density layering across the nanopore as well as theorientational ordering in the polymer melt, brought about by the confinement, on both the segmental and chain scales.For the chain scale ordering, the magnitude and orientation of the axes of the gyration tensor ellipsoid of single chainsare studied and are found to prefer to align parallel to the pore axis. Even though double bonds near the wall arepreferentially oriented along the pore walls, studying the nematic order parameter indicates that there is no nematicordering at the melt-wall interface. As for the dynamics in the melt, we focus here on the mean-square-displacement ofthe monomers for several layers across the nanopore as well as the movement of the chain center of mass which bothdisplay a slowing down of the dynamics in the layer at the wall. We also show the strong adsorption of the monomersto the pore wall at lower temperatures.

Conformation and dynamics of ring polymers under symmetric thin film confinement

Understanding the structure and dynamics of polymers under confinement has been of widespread interest, and one class of polymers that have received comparatively little attention under confinement is that of ring polymers. The properties of non-concatenated ring polymers can also be important in biological fields because ring polymers have been proven to be a good model to study DNA organization in the cell nucleus. From our previous study, linear polymers in a cylindrically confined polymer melt were found to segregate from each other as a result of the strong correlation hole effect that is enhanced by the confining surfaces. By comparison, our subsequent study of linear polymers in confined thin films at similar levels of confinements found only the onset of segregation. In this study, we use molecular dynamics simulation to investigate the chain conformations and dynamics of ring polymers under planar (1D) confinement as a function of film thickness. Our results show that conformations of ring polymers are similar to the linear polymers under planar confinement, except that ring polymers are less compressed in the direction normal to the walls. While we find that the correlation hole effect is enhanced under confinement, it is not as pronounced as the linear polymers under 2D confinement. Finally, we show that chain dynamics far above Tg are primarily affected by the friction from walls based on the monomeric friction coefficient we get from the Rouse mode analysis.

Proper adsorptive confinement for efficient production of cyclic polymers: a dissipative particle dynamics study

Efficient production of cyclic polymers has been a hot topic in the past few decades. In this work, we found that an adsorptive porous template with an appropriate size has the capability to accelerate the ring closure of a linear polymer chain in a dilute solution with a higher yield. The restricted pore provides a confined space and the effect of its characteristics, such as pore size, shape and adsorption strength on cyclization time, is systematically studied by using dissipative particle dynamics simulations. As a prerequisite of cyclization in confinement, the entry process of linear precursors has been studied as well. Total production time is governed by a tradeoff between the size effect caused by decreasing the size of the pore and the adsorption of the pore. The strong size effect suppresses polymer entry but accelerates cyclization. The stronger adsorption promotes polymer entry but decelerates cyclization. According to our defined total production time, a small spherical confinement with strong adsorption results in a shorter total production time of cyclic polymers compared to that in free solution. If chain cyclization is permitted during its entering the confinement, the interplay between steric hindrance caused by pore size and adsorption provides an additional 'virtual' confinement at the boundary between confinement and free solution. In this case, an optimal cyclization time is observed with an appropriate adsorption strength under small confinement. Our results provide useful guidance for designing suitable porous templates for producing cyclic polymers with high efficiency.

Poly(diethylene glycol methylether methacrylate) Brush-Functionalized Anodic Alumina Nanopores: Curvature-Dependent Polymerization Kinetics and Nanopore Filling

We report on the synthesis and characterization of poly(diethylene glycol methylether methacrylate) (PDEGMA) brushes by surface-initiated atom transfer radical polymerization inside ordered cylindrical nanopores of anodic aluminum oxide with different pore radii between 20 and 185 nm. In particular, the dependence of polymerization kinetics and the degree of pore filling on the interfacial curvature were analyzed. On the basis of field emission scanning electron microscopy data and thermal gravimetric analysis (TGA), it was concluded that the polymerization rate was faster at the pore orifice compared to the pore interior and also as compared to the analogous reaction carried out on flat aluminum oxide substrates. The apparent steady-state polymerization rate near the orifice increased with decreasing pore size. Likewise, the overall apparent polymerization rate estimated from TGA data indicated stronger confinement for pores with increased curvature as well as increased mass transport limitations due to the blockage of the pore orifice. Only for pores with a diameter to length ratio of ∼1, PDEGMA brushes were concluded to grow uniformly with constant thickness. However, because of mass transport limitations in longer pores, incomplete pore filling was observed, which leads presumably to a PDEGMA gradient brush. This study contributes to a better understanding of polymer brush-functionalized nanopores and the impact of confinement, in which the control of polymer brush thickness together with grafting density along the nanopores is key for applications of PDEGMA brushes confined inside nanopores.

Nanoscale viscosity of confined polyethylene oxide

Complex fluids near interfaces or confined within nanoscale volumes can exhibit substantial shifts in physical properties compared to bulk, including glass transition temperature, phase separation, and crystallization. Because studies of these effects typically use thin film samples with one dimension of confinement, it is generally unclear how more extreme spatial confinement may influence these properties. In this work, we used x-ray photon correlation spectroscopy and gold nanoprobes to characterize polyethylene oxide confined by nanostructured gratings (<100nm width) and measured the viscosity in this nanoconfinement regime to be ∼500 times the bulk viscosity. This enhanced viscosity occurs even when the scale of confinement is several times the polymer's radius of gyration, consistent with previous reports of polymer viscosity near flat interfaces.

Response of adhesive polymer interfaces to repeated mechanical loading and the spatial variation of diffusion coefficient and stresses in a deforming polymer film

Comprehensive molecular simulations are conducted to show that polymer crosslinks preserve the strength of solid-polymer (melt) interfaces when they are subjected to repeated mechanical loading. The spatial variation of the diffusion coefficient and local stresses is also investigated along the polymer thickness, during deformation. After each loading cycle, a reduction in entanglement strength is observed at the fracture site. The work of adhesion also decreases over consecutive loading cycles, when fracture is induced at the same site. Reduction in both, the work of adhesion and the entanglement strength, decreases as the crosslink density increases. Diffusion coefficient and stresses vary significantly and in a complex manner along the film thickness during the entire deformation process. These variations were due to peculiar configurations occurring at each instance of separation, which are analyzed and explained in this work. The variation of diffusion coefficient during deformation suggests that other dynamic properties, such as viscosity, also vary spatially during polymer deformation.

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions.

Bacterial chromosome organization. II. Few special cross-links, cell confinement, and molecular crowders play the pivotal roles

Using a coarse-grained bead-spring model of bacterial chromosomes of Caulobacter crescentus and Escherichia coli, we show that just 33 and 38 effective cross-links in 4017 and 4642 monomer chains at special positions along the chain contour can lead to the large-scale organization of the DNA polymer, where confinement effects of the cell walls play a key role in the organization. The positions of the 33/38 cross-links along the chain contour are chosen from the Hi-C contact map of bacteria C. crescentus and E. coli. We represent 1000 base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA polymer. Thus, 4017/4642 beads on a flexible ring polymer represent the C. crescentus/E. coli DNA polymer with 4017/4642 kilo-base pairs. Choosing suitable parameters from Paper I, we also incorporate the role of compaction of the polymer coil due to the presence of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the bacterial chromosomes with available experimental data and also give a prediction of the approximate positions of different segments within the cell. In the absence of confinement, the minimal number of effective cross-links required to organize the DNA chains of 4017/4642 monomers was 60/82 [Agarwal et al., Europhys. Lett. 121, 18004 (2018) and Agarwal et al., J. Phys.: Condens. Matter 30, 034003 (2018)].

Critical Contact Angle to Induce Capillary Rise of Polymers in Nanopores Does Not Depend on Chain Length

We study the effect of physical confinement on the capillary infiltration of polymers into cylindrical nanopores using molecular dynamics simulations. In particular, we probe whether the critical contact angle (θ_c) above which capillary rise infiltration ceases to occur changes for long-chain polymers, possibly due to loss of conformation entropy induced by chain confinement. Surprisingly, θ_c does not strongly depend on the length of polymer chains and stays constant for large N. A free energy model is developed to show that θ_c depends strongly on the size of statistical segments rather than N, which we confirm by performing MD simulations of infiltration with semiflexible polymers. These results could provide guidelines in manufacturing polymer nanostructures and nanocomposites using capillary rise infiltration.

Molecular dynamics simulation of the capillary leveling of viscoelastic polymer films

Surface tension-driven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface topography, we present results on the capillary relaxation of a square pattern at the free surface of a viscoelastic polymer film, using molecular dynamics simulations of a coarse-grained polymer model. Height profiles are monitored as a function of time after heating the system above its glass-transition temperature and their time dependence is fitted to the theory of capillary leveling. Results show that the viscosity is not constant, but time dependent. In addition to providing a complementary insight about the local inner mechanisms, our simulations of the capillary-leveling process therefore probe the viscoelasticity of the polymer and not only its viscosity, in contrast to most experimental approaches.

A multi-chain polymer slip-spring model with fluctuating number of entanglements: Density fluctuations, confinement, and phase separation

Coarse grained simulation approaches provide powerful tools for the prediction of the equilibrium properties of polymeric systems. Recent efforts have sought to develop coarse-graining strategies capable of predicting the non-equilibrium behavior of entangled polymeric materials. Slip-link and slip-spring models, in particular, have been shown to be capable of reproducing several key aspects of the linear response and rheology of polymer melts. In this work, we extend a previously proposed multi-chain slip-spring model in a way that correctly incorporates the effects of the fluctuating environment in which polymer segments are immersed. The model is used to obtain the equation of state associated with the slip-springs, and the results are compared to those of related numerical approaches and an approximate analytical expression. The model is also used to examine a polymer melt confined into a thin film, where an inhomogeneous distribution of polymer segments is observed, and the corresponding inhomogeneities associated with density fluctuations are reflected on the spatial slip-spring distribution.

Glass transition of polymers in bulk, confined geometries, and near interfaces

When cooled or pressurized, polymer melts exhibit a tremendous reduction in molecular mobility. If the process is performed at a constant rate, the structural relaxation time of the liquid eventually exceeds the time allowed for equilibration. This brings the system out of equilibrium, and the liquid is operationally defined as a glass-a solid lacking long-range order. Despite almost 100 years of research on the (liquid/)glass transition, it is not yet clear which molecular mechanisms are responsible for the unique slow-down in molecular dynamics. In this review, we first introduce the reader to experimental methodologies, theories, and simulations of glassy polymer dynamics and vitrification. We then analyse the impact of connectivity, structure, and chain environment on molecular motion at the length scale of a few monomers, as well as how macromolecular architecture affects the glass transition of non-linear polymers. We then discuss a revised picture of nanoconfinement, going beyond a simple picture based on interfacial interactions and surface/volume ratio. Analysis of a large body of experimental evidence, results from molecular simulations, and predictions from theory supports, instead, a more complex framework where other parameters are relevant. We focus discussion specifically on local order, free volume, irreversible chain adsorption, the Debye-Waller factor of confined and confining media, chain rigidity, and the absolute value of the vitrification temperature. We end by highlighting the molecular origin of distributions in relaxation times and glass transition temperatures which exceed, by far, the size of a chain. Fast relaxation modes, almost universally present at the free surface between polymer and air, are also remarked upon. These modes relax at rates far larger than those characteristic of glassy dynamics in bulk. We speculate on how these may be a signature of unique relaxation processes occurring in confined or heterogeneous polymeric systems.

Enhanced gas separation factors of microporous polymer constrained in the channels of anodic alumina membranes

New composite membranes based on porous anodic alumina films and polymer of intrinsic microporosity (PIM-1) have been prepared using a spin-coating technique. According to scanning electron microscopy, partial penetration of polymer into the pores of alumina supports takes place giving rise to selective polymeric layers with fiber-like microstructure. Geometric confinement of rigid PIM-1 in the channels of anodic alumina causes reduction of small-scale mobility in polymeric chains. As a result, transport of permanent gases, such as CH4, becomes significantly hindered across composite membranes. Contrary, the transport of condensable gases (CO2, С4H10), did not significantly suffer from the confinement due to high solubility in the polymer matrix. This strategy enables enhancement of selectivity towards CO2 and C4H10 without significant loss of the membrane performance and seems to be prospective for drain and sweetening of natural gas.

Spatial distribution of entanglements in thin free-standing films

We simulate entangled linear polymers in free-standing thin film geometries where the confining dimension is on the same scale as or smaller than the bulk chain dimensions. We compare both film-averaged and layer-resolved, spatially inhomogeneous measures of the polymer structure and entanglement network with theoretical models. We find that these properties are controlled by the ratio of both chain- and entanglement-strand length scales to the film thickness. While the film-averaged entanglement properties can be accurately predicted, we identify outstanding challenges in understanding the spatially resolved character of the heterogeneities in the entanglement network, particularly when the scale of both the entanglement strand and the chain end-to-end vector is comparable to or smaller than the film thickness.

Entanglements in polymer nanocomposites containing spherical nanoparticles

We investigate the polymer packing around nanoparticles and polymer/nanoparticle topological constraints (entanglements) in nanocomposites containing spherical nanoparticles in comparison to pure polymer melts using molecular dynamics (MD) simulations. The polymer-nanoparticle attraction leads to good dispersion of nanoparticles. We observe an increase in the number of topological constraints (decrease of total entanglement length Ne with nanoparticle loading in the polymer matrix) in nanocomposites due to nanoparticles, as evidenced by larger contour lengths of the primitive paths. An increase of the nanoparticle radius reduces the polymer-particle entanglements. These studies demonstrate that the interaction between polymers and nanoparticles does not affect the total entanglement length because in nanocomposites with small nanoparticles, the polymer-nanoparticles topological constraints dominate.

The dynamics of unentangled polymers during capillary rise infiltration into a nanoparticle packing

Although highly packed polymer nanocomposites (PNCs) are important for a wide array of applications, preparing them remains difficult because of the poor dispersion of NPs at high loading fractions. One method to successfully prepare PNCs with high loadings is through capillary rise infiltration, as previously shown by Huang et al., although the mechanism of polymer infiltration remains largely unknown. We use molecular dynamics simulations to directly simulate the process of capillary rise infiltration, and we show that the polymers follow Lucas-Washburn dynamics. We observe a wetting front that precedes bulk infiltration, and chains belonging to this front are highly adsorbed to NPs. We also investigate the viscosity of the model polymers both globally and locally in supported and free-standing films, and we find reduced viscosity near the surface of the films and increased viscosity near the supporting substrate, similar to the results of local relaxation times. The reduction in the viscosity at the free surface for short, oligomeric polymers is smaller than for higher molecular weight polymers, and the ratio of the surface viscosities is most consistent with the predictions of the Lucas-Washburn equation. Our results introduce the mechanism by which polymers infiltrate a highly packed NP film, which may shed light on better ways to prepare these materials for energy storage applications and protective coatings.

Effect of geometric curvature on vitrification behavior for polymer nanotubes confined in anodic aluminum oxide templates

The glass transition behavior of polystyrene (PS) nanotubes confined in cylindrical alumina nanopores was studied as a function of pore diameter (d) and polymer tube thickness (δ). Both the calorimetric glass transition temperature and the microstructure measured by a nonradiative energy transfer method indicated that the polymer nanotube, or concave polymer thin film, exhibited significant differences in vitrification behavior compared to the planar one. A closer interchain proximity and an increased T_{g} were observed for polymer nanotubes with respect to the bulk polymer. T_{g} for polymer nanotubes was primarily dependent on the curvature radius d of the template, while it was less dependent on the thickness δ of the PS tube wall in the range of 11-23 nm. For small nanotubes (d=55nm), the T_{g} increased as high as 18 °C above the bulk value. This vitrified property reverted back to the bulk value when the substrate was chemically removed, which indicated the crucial importance of the interfacial effect imposed by the hard wall with a concave geometry.

Large-Scale Diffusion of Entangled Polymers along Nanochannels

Changes in large-scale polymer diffusivity along interfaces, arising from transient surface contacts at the nanometer scale, are not well understood. Using proton pulsed-gradient NMR, we here study the equilibrium micrometer-scale self-diffusion of poly(butadiene) chains along ∼100 μm long, 20 and 60 nm wide channels in alumina, which is a system without confinement-related changes in segmental relaxation time. Unlike previous reports on nonequilibrium start-up diffusion normal to an interface or into particulate nanocomposites, we find a reduction of the diffusivity that appears to depend only upon the pore diameter but not on the molecular weight in a range between 2 and 24 kg/mol. We rationalize this by a simple volume-average model for the monomeric friction coefficient, which suggests a 10-fold surface-enhanced friction on the scale of a single molecular layer. Further support is provided by applying our model to the analysis of published data on large-scale diffusion in thin films.