Confined Polymer Melts Research Articles

Local viscoelastic properties and shear stress propagation in bulk and confined polymer melts and low-molecular weight liquids

Through the analysis of the spatial correlations of local stress, we detect the propagation of long-ranged liquid-elasticity-mediated shear stress waves in polymeric and low-molecular weight liquids. The propagation of shear waves is effectively planar; i.e., σαβ propagates in the αβ plane. The autocorrelation functions of the local stress of a region are affected by both the relaxation of stress in that region and the propagation of stress from the region to the rest of the sample. However, due to the planar propagation of shear waves, the transfer of σαβ from those slices of the simulation box that are periodic in the αβ plane is negligible. This allows direct probing of the position-dependent local stress relaxation modulus of liquid in the vicinity of a confining surface. Published by the American Physical Society 2024

Universal scaling of the osmotic pressure for dense, quasi-two-dimensionally confined polymer melts reveals transitions between fractal dimensions.

A scaling law for the osmotic pressure of quasi-two-dimensional polymer melts as a function of concentration is obtained, which shows fractal characteristics. Structural properties such as the chains' contour length and their inner-monomer pair distribution function display fractal scaling properties as well. These predictions are confirmed with mesoscale numerical simulations. The chains are swollen and highly entangled, yet Flory's exponent is always ν = 1/2. The melt can be considered a fluid of "blobs" whose size becomes renormalized in terms of the contour's length while the fractal dimension df increases monotonically between 5/4 and 2, as the monomer concentration is increased. The semidilute scaling of the pressure is recovered when df = 1. Our results agree with recent experiments and with numerical reports on quasi-2d melts. This work provides a new paradigm to study and interpret thermodynamic and structural data in low-dimensional polymer melts, namely as fractal macromolecular objects.

From Hidden Shear‐Elasticity to Opto‐ and Thermo‐Elastic Properties in Confined Polymer Melts and Viscous Liquids

AbstractThe newly identified low frequency elasticity of mesoscopic liquids opens the route to the identification of novel dynamic liquid properties. Two experimental examples illustrating the impact of the liquid elasticity in optics and thermodynamics are presented. It is revealed that at mesoscopic scale, liquids are able to convert the mechanical energy in optical and thermal effects. The fluids are submitted to a low frequency (∼Hz) mechanical shear strain (external stress), thus excluding a coupling with molecular time scales. The dynamic response is probed using two in situ methods accessing in real time optical response of the isotropic phase of liquid crystals and probing the thermal response upon shear deformation. In both cases, a dynamic response is identified: the isotropic phase of liquid crystals exhibits a low frequency dynamic birefringence while ordinary liquids exhibit cold and hot thermal waves synchronous to the low frequency excitation.

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 () 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 and less variation in in the weak-to-intermediate flow regimes. Accordingly, the interfacial SCB ring system displayed the lowest 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.

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.

Efficient equilibration of confined and free-standing films of highly entangled polymer melts

Equilibration of polymer melts containing highly entangled long polymer chains in confinement or with free surfaces is a challenge for computer simulations. We approach this problem by first studying polymer melts based on the soft-sphere coarse-grained model confined between two walls with periodic boundary conditions in two directions parallel to the walls. Then, we insert the microscopic details of the underlying bead-spring model. Tuning the strength of the wall potential, the monomer density of confined polymer melts in equilibrium is kept at the bulk density even near the walls. In a weak confining regime, we observe the same conformational properties of chains as in the bulk melt showing that our confined polymer melts have reached their equilibrated state. Our methodology provides an efficient way of equilibrating large polymer films with different thicknesses and is not confined to a specific underlying microscopic model. Switching off the wall potential in the direction perpendicular to the walls enables to study free-standing highly entangled polymer films or polymer films with one supporting substrate.

Statistics and Dynamics of Polymer Melt in Neutral Diblock Copolymer Single-Crystal Platelets.

Polymer single-crystal (SC) platelets of poly(butylene oxide)-b-poly(lactic acid) (PBO-b-PLLA) of a well-defined shape, size, and grafting density have been fabricated and embedded into PBO melt for the study of the statistics and dynamics of the host polymers. The colloidal liquid-crystalline order of SCs above a threshold concentration of ∼2.2 vol % provides a confining environment for the molten PBO. Meanwhile, the peculiar type-A characteristics of PBO allow us to simultaneously probe the dielectric chain dimensions and the hierarchical dynamics of polymers under confinement. We observe negligible changes to the mean-square end-to-end distance of the polymer melt as well as the chain and segment dynamics, even the interlayer distance approaches the length scale comparable to the size of the host polymers. Our results provide direct evidence of the impacts of neutral walls on both the statistics and the dynamics of confined polymer melts, which can be also enlightening for the field of polymer nanocomposites.

Entanglement dynamics at flat surfaces: Investigations using multi-chain molecular dynamics and a single-chain slip-spring model.

The dynamics of an entangled polymer melt confined in a channel by parallel plates is investigated by Molecular Dynamics (MD) simulations of a detailed, multi-chain model. A primitive path analysis predicts that the density of entanglements remains approximately constant throughout the gap and drops to lower values only in the immediate vicinity of the surface. Based on these observations, we propose a coarse-grained, single-chain slip-spring model with a uniform density of slip-spring anchors and slip-links. The slip-spring model is compared to the Kremer-Grest MD bead-spring model via equilibrium correlation functions of chain orientations. Reasonably good agreement between the single-chain model and the detailed multi-chain model is obtained for chain relaxation dynamics, both away from the surface and for chains whose center of mass positions are at a distance from the surface that is less than the bulk chain radius of gyration, without introducing any additional model parameters. Our results suggest that there is no considerable drop in topological interactions for chains in the vicinity of a single flat surface. We infer from the slip-spring model that the experimental plateau modulus of a confined polymer melt may be different to a corresponding unconfined system even if there is no drop in topological interactions for the confined case.

Dynamics of Entangled Polymers Confined between Graphene Oxide Sheets as Studied by Neutron Reflectivity

For graphene-based composites, the dynamics of polymers confined between graphene sheets are a key parameter governing the overall mechanical properties of bulk materials. Here, we used neutron reflectivity (NR) to measure the diffusion dynamics of polymer melts confined between graphene oxide (GO) surfaces. From the NR results, we found that the diffusion coefficients of poly(methyl methacrylate) (PMMA) between the GO sheets were dramatically reduced by more than 1 order of magnitude when the film thickness was less than ∼3 times the gyration radius of the bulk polymer (Rg), whereas the diffusion of the polystyrene (PS) films sandwiched between GO sheets was only three times slower as the PS thickness decreased from ∼8 Rg to 1 Rg. This difference was due to the fact that the polymer-GO interaction significantly influences the dynamics of confined polymer melts.

Relaxation processes and glass transition of confined polymer melts: A molecular dynamics simulation of 1,4-polybutadiene between graphite walls.

Molecular dynamics simulations of a chemically realistic model for 1,4-polybutadiene in a thin film geometry confined by two graphite walls are presented. Previous work on melts in the bulk has shown that the model faithfully reproduces static and dynamic properties of the real material over a wide temperature range. The present work studies how these properties change due to nano-confinement. The focus is on orientational correlations observable in nuclear magnetic resonance experiments and on the local intermediate incoherent neutron scattering function, Fs(qz, z, t), for distances z from the graphite walls in the range of a few nanometers. Temperatures from about 2Tg down to about 1.15Tg, where Tg is the glass transition temperature in the bulk, are studied. It is shown that weakly attractive forces between the wall atoms and the monomers suffice to effectively bind a polymer coil that is near the wall. For a wide regime of temperatures, the Arrhenius-like adsorption/desorption kinetics of the monomers is the slowest process, while very close to Tg the Vogel-Fulcher-Tammann-like α-relaxation takes over. The α-process is modified only for z≤1.2 nm due to the density changes near the walls, less than expected from studies of coarse-grained (bead-spring-type) models. The weakness of the surface effects on the glass transition in this case is attributed to the interplay of density changes near the wall with the torsional potential. A brief discussion of pertinent experiments is given.

Local Chain Segregation and Entanglements in a Confined Polymer Melt.

The reptation mechanism, introduced by de Gennes and Edwards, where a polymer diffuses along a fluffy tube, defined by the constraints imposed by its surroundings, convincingly describes the relaxation of long polymers in concentrated solutions and melts. We propose that the scale for the tube diameter is set by local chain segregation, which we study analytically. We show that the concept of local segregation is especially operational for confined geometries, where segregation extends over mesoscopic domains, drastically reducing binary contacts, and provide an estimate of the entanglement length. Our predictions are quantitatively supported by extensive molecular dynamics simulations on systems consisting of long, entangled chains.

Molecular dynamics simulations of polymer crystallization under confinement: Entanglement effect

We carried out molecular dynamics simulations to study the crystallization of polymer melts subjected to confinement between two parallel walls. Two types of walls, bare and grafted walls, are studied. The bare walls are slippery for chain motions, and the interactions between polymer chains and the walls are moreover chosen either attractive or repulsive. The crystallization in the case of bare walls generally consists of surface-induced processes close to the walls followed by homogeneous nucleation in both the boundary and middle regions. In the case of grafted walls, parts of polymer chains residing close to the walls are adhesive to the surfaces and become permanent graft points. We find that the surface-induced crystallization is increasingly suppressed with increasing grafting density. At high grafting densities, only crystallization in the middle regions is observed. We calculated the spatial distribution of entanglement lengths and related it to the crystallization behavior. The entanglement length close to the walls is found to decrease with increasing grafting density, as the adhesion points act as effective entanglement knots. In light of our recent results that less entangled polymer melts lead to faster crystallization and higher crystallization order, we now show that this conclusion stands also for the case of confined polymer melts. Our results suggest entanglements to be an universal factor towards the understanding of polymer crystallization under different situations, in particular at supercooling.

Structure and dynamics of confined polymer melts from attractive interaction to repulsive interaction between polymer and smooth wall

We studied the static and dynamic properties of unentangled polymer chains which have a variable strength of interaction with the confining smooth walls by means of the lattice Monte Carlo simulation based on the bond-fluctuation model, that is, investigated the wall-polymer interactions which systematically vary from attraction to repulsion. A critical value of attractive potential(ewc) is found to be–0.6kBT, and only below it can the adsorption layer of monomers be formed near the wall. At the critical point of attraction ewc, attractive interaction counterbalances the wall-polymer excluded volume effect, which minimizes the confinement effects on both chain dimension and mobility. Influences on both chain dimension and mobility increase with the increasing of either attraction or repulsion imposed by the walls. Despite of the nature and strength of the wall-polymer interaction, with the decrease of film thickness, configurations more parallelly aligned and flattened are adopted by confined chains, and a systematic trend of deceleration is found. Variations of chain dynamics with both film thickness and wall-polymer interaction can be well explained by the corresponding changes in the confinement of the nearest-neighboring particles that surround the chains. Besides, the thickness of the interfacial layer inside polymer films, where chains adopt a flattened “pancake” shape, is about two times the bulk radius of gyration and independent of the wall-polymer interaction.

SPATIAL-TEMPORAL OSCILLATIONS OF THE ORDER PARAMETER IN CONFINED DIBLOCK COPOLYMER MIXTURES

The mathematical model describing the evolution of the order parameter in confined polymer melts is under consideration. The corresponding equation is derived from a special energy functional introduced by Fredrickson and Binder to describe the behavior of polymer chains in block copolymer melts. This equation is modified to take into account the "memory" of correlated blends. The resulting hyperbolic partial differential equation is of order six in space variable. The Puri–Binder dynamical boundary conditions with "feedback" describe processes of cyclic surface crystallization and melting. Two types of polymer mixtures (ideal and non-ideal) are studied. In the case of the ideal mixture, the attractor of the boundary problem consists of asymptotically periodic piecewise constant functions with finite or infinite number of discontinuities per period (spatial-temporal structures of relaxation or turbulent type). In the non-ideal case, the attractor contains quasi-periodic functions or it is so-called strange chaotic or strange non-chaotic. The bifurcation diagram is constructed.

Slow process in confined polymer melts: Layer exchange dynamics at a polymer solid interface

Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.

Nanotribological Properties of Molecularly Thin Polymer Melt Films Studied using the Surface Forces Apparatus

The nanotribological properties of molecularly thin films of polymer melts were investigated using a surface forces apparatus (SFA). When the droplet of a polymer melt was injected between two smooth mica surfaces and confined by normal compression, the dynamic properties of the polymer melt shifted from bulk rheological to thin film tribological features. The shift of the dynamics was evaluated by measuring the effective viscosity of the confined films and by comparing the viscosity with its bulk value; the results were discussed in terms of confinement-induced glasslike transition. Molecular ordering (layering) in confined polymer melts was also studied. The tribological properties of the thin films of poly(dimethylsiloxane) (PDMS) were evaluated. The results implied well-ordered layer structures in the confined films, which are very different from most of the hydrocarbon-type polymeric lubricants (having disordered molecular conformations in confinement). The experiments described here reveal the unique dynamics of molecularly confined polymer melts, which cannot be obtained by any other experimental techniques than SFA.

Using light to study boundary lubrication: spectroscopic study of confined fluids

Several instrumental developments to examine the spectroscopic response of molecularly thin fluids confined between mica sheets are described. They are predicated on using a redesigned surface forces apparatus where dielectric coatings, transparent to light at needed optical wavelengths, retain the ability to measure interferometric thickness at other optical wavelengths. Examples of recent measurements are presented using confocal laser Raman spectroscopy to evaluate how molecules orient as well as to perform chemical imaging. Other examples are presented using confocal fluorescence recovery after photobleaching to evaluate translational diffusion of confined polymer melts. The advantage of separating the mechanical average (force and friction) from direct information about structure and mobility at the molecular level is stressed.

Chain dynamics in mesoscopically confined polymer melts. A field-cycling NMR relaxometry study

Polymer chain dynamics were studied with the aid of field-cycling NMR relaxometry (time scale: 10-9s... 10-4s) supplemented by field gradient NMR diffusometry (time scale: 10-4s...100s). Three sorts of samples of mesoscopically confined polymer melts were examined. In the first sample series, linear poly(ethylene oxide) was incorporated in strands embedded in a quasi-solid and impenetrable methacrylate matrix. The strand diameters ranged from 10 to 60 nm. It was shown that chain dynamics becomes dramatically different from bulk behavior. This so-called “corset effect” occurs both above and below the critical molecular mass and reveals dynamic features predicted for reptation. On the time scale of spin-lattice relaxation, the frequency and molecular weight, signature of reptation, T1 ∼M0 ν3/4, that is limit II of the Doi/Edwards formalism corresponding to the mean squared segment displacement law 〈r2 〉∼M0 t1/4, showed up. A “tube” diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. The corset effect is traced back to the lack of the local fluctuation capacity of the free volume under nanoscopic confinements. The confinement dimension at which the cross-over from confined to bulk chain dynamics is expected was estimated to be micrometers. Using the so-called roll-coating technique, micrometer thick polymer melt layers between Kapton foils were prepared. Perceptible differences from the bulk materials were found. The polymer species studied in this case was perfluoropolyether with Flory radii in the order of 7 nm. Remarkably, the confinement effect was shown to reach polymer-wall distances of the order 100 Flory radii. As a third confinement system, melts of perfluoropolyether were filled into a porous silica glass (Vycor; 4 nm nominal pore size). In this case, a crossover from Rouse dynamics in the bulk to reptation in the Doi/Edwards limit III (T1∼M-1/2 ν1/2 corresponding to 〈r2 〉∼M-1/2 t1/2) was observed.

Measurement of Viscosity of Confined Polymer Melt Using Capillary Kinetics

We present a simple method to measure viscosity of thin polymer melt that is confined between a substrate and a permeable plate using a modified Poiseuille equation. When a patterned polydimethylsiloxane (PDMS) mold is placed on a styrene-butadiene-styrene (SBS) block copolymer film spin-coated onto a substrate and heated above the polymer's glass transition temperature, capillarity forces the polymer melt into the void of the channel. To calculate the viscosity of the confined polymer melt, the height of capillary rise was measured as a function of time for a number of film thicknesses (220, 350, 540, 1000, and 1300 nm) and at two different temperatures (70 and 100°C). It was found that the viscosity increases with decreasing film thickness at 70°C, whereas it decreases with decreasing film thickness at 100°C. This discrepancy might be related to the confinement-induced solid-like behavior of the polymer melt and wall slip at the polymer/solid interface. Furthermore, the viscosity turned out to be nearly equal to the bulk value for relatively large film thickness (> ∼ 500 nm) regardless of the temperature, which corresponds to earlier findings.

Surface forces in a confined polymer melt: Self-consistent field analysis of full and restricted equilibrium cases

In full equilibrium the self-consistent field theory for a homopolymer melt confined between two surfaces predicts pronounced oscillatory interaction forces on the monomer length scale. However, when not all the polymer molecules can reversibly equilibrate with the bulk, the trapped molecules may be squeezed, adding a repulsive contribution to the interaction energy. The classical constrained or restricted equilibrium approach by Scheutjens and Fleer two decades ago to deal with this for polymers adsorbed from dilute solutions, breaks down in semidilute and concentrated polymer solutions. We present a generalized restricted equilibrium ansatz applicable also for concentrated polymer solutions. The key idea is that only the adsorbed polymer molecules, i.e., molecules that touch the surface at least once, are forced to remain inside the gap, whereas the nonadsorbing chains are free to move out of the gap when the surfaces approach each other. As in dilute solutions, the forces found in confined melt with trapped adsorbed chains become repulsive. We analyse the dependence of the interaction forces both in full as well as in restricted equilibrium cases as a function of the chain length and the interactions with the surface for a compressible polymer melt.