Confined Polymer Chains Research Articles

Probing Temperature‐Dependence of Hydrogen Bonding in Condensed Polymeric Materials with Aggregation‐Induced Emission

AbstractHydrogen bonding is pivotal in chemical and biological systems, yet detecting it in condensed matter, especially polymers, remains challenging. We propose a straightforward method using an aggregation‐induced emission luminogen (AIEgen) probe, demonstrated in a specially designed hydrogen‐bonded polymer with UPy groups. Unlike conventional covalent bonding, our approach involves mixing the AIEgen probe with polymers, inducing a significant change in fluorescence intensity due to the exceptional AIE characteristics. Validation involved comparative analyses with traditional methods, including dynamic mechanical analysis and infrared spectroscopy, across various temperatures. Our AIEgen‐based approach offers a more intuitive assessment of hydrogen bonding dynamics than the complexity of infrared spectroscopy. Importantly, hydrogen‐bonding transition temperatures determined by our AIEgen‐based method are only 6–8 degrees higher than those from dynamic mechanical analyses, confirming accuracy under faster, simpler conditions. This innovative technique not only opens a new avenue for investigating hydrogen bonding dynamics within confined polymer chains but also enhances the precision of transition temperature determination in solid‐state materials. Our study highlights the vital role of hydrogen bonding in functional materials, promising exciting possibilities for further advancements in this field.

Revisiting the second Vassiliev (In)variant for polymer knots

Knots in open strands such as ropes, fibers, and polymers, cannot typically be described in the language of knot theory, which characterizes only closed curves in space. Simulations of open knotted polymer chains, often parameterized to DNA, typically perform a closure operation and calculate the Alexander polynomial to assign a knot topology. This is limited in scenarios where the topology is less well-defined, for example when the chain is in the process of untying or is strongly confined. Here, we use a discretized version of the Second Vassiliev Invariant for open chains to analyze Langevin Dynamics simulations of untying and strongly confined polymer chains. We demonstrate that the Vassiliev parameter can accurately and efficiently characterize the knotted state of polymers, providing additional information not captured by a single-closure Alexander calculation. We discuss its relative strengths and weaknesses compared to standard techniques, and argue that it is a useful and powerful tool for analyzing polymer knot simulations.

Thermodynamics of a confined macromolecule: An analytical approach

We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long flexible polymer chain and also to mimic confirmations of a short flexible chain under confined conditions. The confinement conditions is achieved using two parallel impenetrable plates. The confined chain is under good solvent conditions and we revisit this problem to solve the real (self avoiding) polymer's model for any length of the chain and also for any given separation in between the confining plates. The equilibrium statistics of the confined polymer chain are derived using analytical approach of the generating function technique. The force of the confinement, the surface tension and the monomer density profile of the confined chain are obtained analytically. We propose that the methods of calculation are suitable to understand thermodynamics of an arbitrary length confined polymer chain under other possible conditions of the confinement.

Kinetics of nanoconfined benzyl methacrylate radical polymerization

AbstractThe effect of nanoconfinement on the kinetics of benzyl methacrylate radical polymerization is investigated using differential scanning calorimetry. Controlled pore glass (CPG), ordered mesoporous carbons, and mesoporous silica are used as confinement media with pore sizes from 2 to 8 nm. The initial polymerization rate in CPG and mesoporous silica increases relative to the bulk and increases linearly with reciprocal pore size; whereas, the rate in the carbon mesopores decreases linearly with reciprocal pore size; the changes are consistent with the rate being related to the ratio of the pore surface area to pore volume. Induction times are longer for nanoconfined polymerizations, and in the case of CPG and carbon mesopores, autoacceleration occurs earlier, presumably due to the limited diffusivity and lower termination rates for the confined polymer chains. The molecular weight of the polymer synthesized in the nanopores is generally higher than that obtained in the bulk except at the lowest temperatures investigated. The equilibrium conversion under nanoconfinement decreases with decreasing temperature and with confinement size, exhibiting what appears to be a floor temperature at low temperatures.

Dynamics of polymer chains confined to a periodic cylinder: molecular dynamics simulation vs. Lifson-Jackson formula.

The dynamics of polymer chains confined to a periodic cylinder is explored using molecular dynamics simulation and theoretical analysis. The cylinder is divided into two cavities in one periodicity: one cavity consists of a channel of length L1 and diameter D1 and another cavity is a channel of length L2 and diameter D2. For L1 = L2 = L/2, the diffusion coefficient D of a single confined polymer chain decreases rapidly with increase in periodicities L. For a fixed periodicity with L = L1 + L2 = constant, the diffusion coefficient D of a single confined polymer chain shows strong dependence on L1 (or L2). Moreover, for a multi-chain system with L1 = L2, the diffusion coefficient D shows strong non-monotonic dependence on the chain monomer density ρ, and the confined polymer chains diffuse fastest for ρ = 0.068, in which there are three polymer chains in two periodicities as well as two opposing effects: one is that the excluded volume effect between polymer chains can reduce the free energy barrier, and another is that when the chain monomer density ρ increases further, the entanglement effect increases, which leads to that the diffusion coefficient D decreases as ρ increases. Finally, we found that the diffusion coefficient D has a similar oscillation relationship with the ratio of R/L for different chain lengths N and different periodicity L, and the oscillation amplitude decreases gradually as R/L increases; here R is the mean end-to-end distance of a single confined polymer chain, i.e., . From the view of free energy potential, both the width of the free energy potential well and the height of the free energy potential barrier govern simultaneously the diffusion behavior of confined polymer chains. According to the mean force potential (PMF) based on the weighted histogram analysis method (WHAM), we found that our results agree very well with the theoretical analysis using the Lifson-Jackson formula. Our investigation may help us understand the dynamics of particles in a periodic medium, which is one of the interesting problems in many different fields of science, such as physics, chemistry and biology.

Relation between mechanical response of reinforced elastomers and dynamics of confined polymer chains

Elastomers used in everyday life are always reinforced with rigid nanoparticles (carbon black or silica). The addition of rigid nanoparticles to an elastomer gives it very specific viscoelastic properties. In this article, we discuss the current understanding of mechanical properties of a polymer matrix around its glass transition, focusing on the situation of polymers confined between two rigid surfaces with a nanometric gap. Then, we will explain how the properties of the matrix can help to understand the properties of filled or reinforced elastomers. We will then explain that in reinforced rubbers, the mechanical properties are dominated by stress propagation between neighboring aggregates through a nanometric polymer gap, thus by confined polymer bridges. We will discuss how knowledge of the dynamics of confined polymers allows us to understand the temperature dependence, the pressure dependence and the non-linearities observed for strain below 0.1 of reinforced elastomers.

Diffusion of Short Semiflexible DNA Polymer Chains in Strong and Moderate Confinement.

In many technological applications, DNA is confined within nanoenvironments that are smaller than the size of the unconfined polymer in solution. However, the dependence of the diffusion coefficient on molecular weight and characteristic confinement dimension remains poorly understood in this regime. Here, convex lens-induced confinement (CLiC) was leveraged to examine how the diffusion of short DNA fragments varied as a function of slit height by using single-molecule fluorescence tracking microscopy. The diffusion coefficient followed approximate power law behavior versus confinement height, with exponents of 0.27 ± 0.01, 0.32 ± 0.02, and 0.42 ± 0.06 for 692, 1343, and 2686 base pair chains, respectively. The weak dependence on slit height suggests that shorter semiflexible chains may adopt increasingly rodlike conformations and therefore experience weaker excluded-volume interactions as the confinement dimension is reduced. The diffusion coefficient versus molecular weight also exhibited apparent power law behavior, with exponents that varied slightly (from -0.89 to -0.85) with slit height, consistent with hydrodynamic interactions intermediate between Rouse and Zimm model predictions.

De Novo Ion-Exchange Membranes Based on Nanofibers.

The unique functions of nanofibers (NFs) are based on their nanoscale cross-section, high specific surface area, and high molecular orientation, and/or their confined polymer chains inside the fibers. The introduction of ion-exchange (IEX) groups on the surface and/or inside the NFs provides de novo ion-exchangers. In particular, the combination of large surface areas and ionizable groups in the IEX-NFs improves their performance through indices such as extremely rapid ion-exchange kinetics and high ion-exchange capacities. In reality, the membranes based on ion-exchange NFs exhibit superior properties such as high catalytic efficiency, high ion-exchange and adsorption capacities, and high ionic conductivities. The present review highlights the fundamental aspects of IEX-NFs (i.e., their unique size-dependent properties), scalable production methods, and the recent advancements in their applications in catalysis, separation/adsorption processes, and fuel cells, as well as the future perspectives and endeavors of NF-based IEMs.

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.

Self-Avoiding Random Walks as a Model to Study Athermal Linear Polymers under Extreme Plate Confinement.

Monte Carlo (MC) simulations, built around chain-connectivity-altering moves and a wall-displacement algorithm, allow us to simulate freely-jointed chains of tangent hard spheres of uniform size under extreme confinement. The latter is realized through the presence of two impenetrable, flat, and parallel plates. Extreme conditions correspond to the case where the distance between the plates approaches the monomer size. An analysis of the local structure, based on the characteristic crystallographic element (CCE) norm, detects crystal nucleation and growth at packing densities well below the ones observed in bulk analogs. In a second step, we map the confined polymer chains into self-avoiding random walks (SAWs) on restricted lattices. We study all realizations of the cubic crystal system: simple, body centered, and face centered cubic crystals. For a given chain size (SAW length), lattice type, origin of SAW, and level of confinement, we enumerate all possible SAWs (equivalently all chain conformations) and calculate the size distribution. Results for intermediate SAW lengths are used to predict the behavior of long, fully entangled chains through growth formulas. The SAW analysis will allow us to determine the corresponding configurational entropy, as it is the driving force for the observed phase transition and the determining factor for the thermodynamic stability of the corresponding crystal morphologies.

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections.

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

Water-Ethanol and Methanol-Ethanol Separations Using in Situ Confined Polymer Chains in a Metal-Organic Framework.

This study presents a straightforward approach for the in situ polymerization of poly(N-isopropylacrylamide) (PNIPAM) chains within the one-dimensional (1D) pores of the five-coordinated zinc-based metal–organic framework DMOF in order to obtain new MOF-based composites. The loading amount of PNIPAM within DMOF ⊃ PNIPAM composites can be tuned by changing the initial weight ratio between NIPAM, which is the monomer of PNIPAM, and DMOF. The guest PNIPAM chains in the composites block partially the 1D pores of DMOF, thus leading to a narrowed nanospace. The water adsorption studies reveal that the water uptake increased by increasing the loading of PNIPAM in the final DMOF ⊃ PNIPAM composites, indicating that the exposed amide groups of PNIPAM gradually alter the hydrophobicity of pristine DMOF and lead to hydrophilic DMOF ⊃ PNIPAM composites. The composite with the highest loading of PNIPAM displays a selective adsorption for water and methanol over ethanol when using equimolar mixtures of methanol–ethanol and water–ethanol. This is confirmed by the single-component adsorption measurements as well as ideal adsorbed solution theory molecular simulations. Additionally, the water stability of pristine DMOF has been greatly improved after the incorporation of PNIPAM in its pores. PNIPAM can undergo a phase transition between hydrophobic and hydrophilic phases in response to a low temperature change. This property is used in order to control the desorption of water and methanol molecules, thus enabling an efficient and cost-effective regeneration process.

Description of poly(ethylenepropylene) confined in nanopores by a modified Rouse model.

A recent model for unentangled polymer chains in confinement [M. Dolgushev and M. Krutyeva, Macromol. Theory Simul. 21, 565 (2012)] is scrutinized by small-angle neutron scattering (SANS) with respect to its static prediction, the single-chain structure factor. We find a remarkable agreement although the model simplifies the effect of the confinement to a harmonic potential. The effective confinement size from fits of SANS data with the model agrees well with the actual pore size. Starting from this result we discuss the possibility of an experiment on the dynamic structure factor predicted by the model. It turns out that such an experiment would need a large ratio polymer dimension/pore size which is difficult but not impossible to achieve.

Failure mechanism of the polymer infiltration of carbon nanotube forests

Polymer melt infiltration is one of the feasible methods for manufacturing filter membranes out of carbon nanotubes (CNTs) on large scales. Practically, however, its process suffers from low yields, and the mechanism behind this failure is rather poorly understood. Here, we investigate a failure mechanism of polymer melt infiltration of vertical aligned (VA-) CNTs. In penetrating the VA-CNT interstices, polymer melts exert a capillarity-induced attractive force laterally on CNTs at the moving meniscus, leading to locally agglomerated macroscale bunches. Such a large configurational change can deform and distort individual CNTs so much as to cause buckling or breakdown of the alignment. In view of membrane manufacturing, this irreversible distortion of nanotubes is detrimental, as it could block the transport path of the membranes. The failure mechanism of the polymer melt infiltration is largely attributed to steric hindrance and an energy penalty of confined polymer chains. Euler beam theory and scaling analysis affirm that CNTs with low aspect ratio, thick walls and sparse distribution can maintain their vertical alignment. Our results can enrich a mechanistic understanding of the polymer melt infiltration process and offer guidelines to the facile large-scale manufacturing of the CNT-polymer filter membranes.

Super-Resolution Genome Mapping in Silicon Nanochannels

Optical genome mapping in nanochannels is a powerful genetic analysis method, complementary to deoxyribonucleic acid (DNA) sequencing. The method is based on detecting a pattern of fluorescent labels attached along individual DNA molecules. When such molecules are extended in nanochannels, the labels create a fluorescent genetic barcode that is used for mapping the DNA molecule to its genomic locus and identifying large-scale variation from the genome reference. Mapping resolution is currently limited by two main factors: the optical diffraction limit and the thermal fluctuations of DNA molecules suspended in the nanochannels. Here, we utilize single-molecule tracking and super-resolution localization in order to improve the mapping accuracy and resolving power of this genome mapping technique and achieve a 15-fold increase in resolving power compared to currently practiced methods. We took advantage of a naturally occurring genetic repeat array and labeled each repeat with custom-designed Trolox conjugated fluorophores for enhanced photostability. This model system allowed us to acquire extremely long image sequences of the equally spaced fluorescent markers along DNA molecules, enabling detailed characterization of nanoconfined DNA dynamics and quantitative comparison to the Odijk theory for confined polymer chains. We present a simple method to overcome the thermal fluctuations in the nanochannels and exploit single-step photobleaching to resolve subdiffraction spaced fluorescent markers along fluctuating DNA molecules with ∼100 bp resolution. In addition, we show how time-averaging over just ∼50 frames of 40 ms enhances mapping accuracy, improves mapping P-value scores by 3 orders of magnitude compared to nonaveraged alignment, and provides a significant advantage for analyzing structural variations between DNA molecules with similar sequence composition.

Development of a simple model to characterize the complex constrained polymer chains in polymer nanocomposites at the interphase of amorphous/semicrystalline ethylene vinyl acetate and nanosheets

A simple model was developed to characterize the constrained polymer chains at the interphase of amorphous/semicrystalline polymer nanocomposites based on ethylene vinyl acetate copolymer and some nanosheets such as expanded graphite, graphene and organo-modified montmorillonite. It was found that this method is a useful tool to describe the reinforcement efficiency of nanoparticles. Models were developed using dynamical mechanical thermal analysis data to identify the interphase properties. The volume fraction of constrained polymer chains shows power law relationship with filler content. Since the total volume fraction consists of the confined polymer chains at the surface of nanoparticles and in crystal lamellas, the contribution of nanosheet interphase was evaluated separately. Moreover, the thickness of constructed interphase between polymer chains and nanosheets were predicted using the filler characteristics in the polymer nanocomposites. This implies that the dispersion state of nanofiller in polymeric nanocomposites can be obtained by using this simple model.

Equilibrium statistics of an infinitely long chain in the severe confined geometry: exact results

We analyse the equilibrium statistics of a long linear homopolymer chain confined in between two flat geometrical constraints under good solvent conditions. The chain is occupying two-dimensional space and geometrical constraints are two impenetrable lines for the two-dimensional space. A fully directed self-avoiding walk lattice model is used to derive analytical expression of the partition function for the given value of separation () in between the impenetrable lines. The exact values of the critical exponents ( and ) were obtained for given values of separations in between the impenetrable lines. The probability of polymerization of the confined polymer chain conformations (bridges and trains) with any or both the ends in contact with the impenetrable lines was obtained and the dominant contribution of the canonical partition function of an N-monomer-long chain is also analysed to discuss the effect of confinement on equilibrium statistics of the confined chain. An exact expression of the grand canonical partition function of the confined semi-flexible chain is also calculated using the generating function technique.

A Simple Method for Complex Monomer Creation in the Matrix Method for the Statistics and Thermodynamics of a Confined Polymer Chain

We extend earlier work that gave exact results for the thermodynamics and size parameters of a confined polymer to the case where the monomers have complex structure. The only restriction on the co...

Interfacial interactions and complex segmental dynamics in systems based on silica-polydimethylsiloxane core–shell nanoparticles: Dielectric and thermal study

Effects of two types of silica particles, with different characteristics of porosity, on segmental mobility of poly(dimethylsiloxane), PDMS, in core–shell nanocomposites with two contents of polymer, 40 and 80 wt%, were studied by employing thermal (DSC) and dielectric (DRS, TSDC) techniques, under different annealing procedures. Filler morphology and polymer–particle interactions were found to affect PDMS crystallinity and segmental mobility. The dielectric techniques allowed the detection of four contributions to the segmental dynamics associated with the glass transition arising, in the order of decreasing mobility, from confined polymer chains in the pores of silica gel (αp relaxation), from the bulk (unaffected) amorphous polymer fraction (α relaxation), from polymer chains restricted between condensed crystal regions (αc) and from semibound polymer in an interfacial layer close to the nanoparticle surface (α′). For the core–shell nanocomposites with high PDMS content (80 wt%) the interfacial α′ relaxation process is found to have similar characteristics with that in conventional PDMS/silica nanocomposites, for lower PDMS content (40 wt%), however, the interfacial relaxation process exhibits distinct differences. The experimental findings are discussed in terms of models proposed for the description of conformations of polymers adsorbed onto a solid surface.

Polymers in 2-D confinement

2-D confined polymer chains were observed using small angle neutron scattering. The signal of unwanted background needed to be removed, and so the scattering of 2-D confined polymer chains was recorded and interpreted. Due to finite thickness of the polymer layer the concept of self-avoiding trails was applied, contrary to self-avoiding walks for the single layer thickness. The limitations by the finite clay particle diameter were not observed for the larger platelets, but additional confinement effects appeared for the series of smaller clay particles in the lateral direction. The concept of single pores explains the latter findings.