Entanglements of Macromolecules and Their Influence on Rheological and Mechanical Properties of Polymers

Flexible macromolecules easily become entangled with neighboring macromolecules. The resulting network determines many polymer properties, including rheological and mechanical properties. Therefore, a number of experimental and modeling studies were performed to describe the relationship between the degree of entanglement of macromolecules and polymer properties. The introduction presents general information about the entanglements of macromolecule chains, collected on the basis of studies of equilibrium entangled polymers. It is also shown how the density of entanglements can be reduced. The second chapter presents experiments and models leading to the description of the movement of a single macromolecule. The next part of the text discusses how the rheological properties change after partial disentangling of the polymer. The results on the influence of the degree of chain entanglement on mechanical properties are presented.

Microscopic versus Macroscopic Glass Transitions and Relevant Length Scales in Mixtures of Industrial Interest

We have combined X-ray diffraction, neutron diffraction with polarization analysis, small-angle neutron scattering (SANS), neutron elastic fixed window scans (EFWS), and differential scanning calorimetry (DSC) to investigate polymeric blends of industrial interest composed by isotopically labeled styrene-butadiene rubber (SBR) and polystyrene (PS) oligomers of size smaller than the Kuhn length. The EFWS are sensitive to the onset of liquid-like motions across the calorimetric glass transition, allowing the selective determination of the "microscopic" effective glass transitions of the components. These are compared with the "macroscopic" counterparts disentangled by the analysis of the DSC results in terms of a model based on the effects of thermally driven concentration fluctuations and self-concentration. At the microscopic level, the mixtures are dynamically heterogeneous for blends with intermediate concentrations or rich in PS, while the sample with highest content of the fast SBR component looks as dynamically homogeneous. Moreover, the combination of SANS and DSC has allowed determining the relevant length scale for the α-relaxation through its loss of equilibrium to be ≈30 Å. This is compared with the different characteristic length scales that can be identified in these complex mixtures from structural, thermodynamical, and dynamical points of view because of the combined approach followed. We also discuss the sources of the non-Gaussian effects observed for the atomic displacements and the applicability of a Lindemann-like criterion in these materials.

Decoding polymer self-dynamics using a two-step approach

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a "two-step" approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

Fluorescence Resonance Energy Transfer Measurements in Polymer Science: A Review

Fluorescence resonance energy transfer (FRET) is a non-invasive characterization method for studying molecular structures and dynamics, providing high spatial resolution at nanometer scale. Over the past decades, FRET-based measurements are developed and widely implemented in synthetic polymer systems for understanding and detecting a variety of nanoscale phenomena, enabling significant advances in polymer science. In this review, the basic principles of fluorescence and FRET are briefly discussed. Several representative research areas are highlighted, where FRET spectroscopy and imaging can be employed to reveal polymer morphology and kinetics. These examples include understanding polymer micelle formation and stability, detecting guest molecule release from polymer host, characterizing supramolecular assembly, imaging composite interfaces, and determining polymer chain conformations and their diffusion kinetics. Finally, a perspective on the opportunities of FRET-based measurements is provided for further allowing their greater contributions in this exciting area.

Disentangling Component Dynamics in an All-Polymer Nanocomposite Based on Single-Chain Nanoparticles by Quasielastic Neutron Scattering

We have investigated an all-polymer nanocomposite (NC) consisting of single-chain nanoparticles (SCNPs) immersed in a matrix of linear chains of their precursors (25/75% composition in weight). The SCNPs were previously synthesized via “click” chemistry, which induces intramolecular cross-links in the individual macromolecules accompanied by a slight shift (5–8 K) of the glass transition temperature toward higher values and a broadening of the dynamic response with respect to the raw precursor material. The selective investigation of the dynamics of the NC components has been possible by using properly isotopically labeled materials and applying quasielastic neutron scattering techniques. Results have been analyzed in the momentum transfer range where the coherent scattering contribution is minimal, as determined by complementary neutron diffraction experiments with polarization analysis. We observe the development of dynamic heterogeneity in the intermediate scattering function of the NC components, which grows with increasing time. Local motions in the precursor matrix of the NC are accelerated with respect to the reference bulk behavior, while the displacements of SCNPs’ hydrogens show enhanced deviations from Gaussian and exponential behavior compared with the pure melt of SCNPs. The resulting averaged behavior in the NC coincides with that of the pure precursor, in accordance with the macroscopic observations by differential scanning calorimetry (DSC) experiments.

Multiscale relaxation dynamics and diffusion of myelin basic protein in solution studied by quasielastic neutron scattering

We report an analysis of high-resolution quasielastic neutron scattering spectra from Myelin Basic Protein (MBP) in solution, comparing the spectra at three different temperatures (283, 303, and 323 K) for a pure D₂O buffer and a mixture of D₂O buffer with 30% of deuterated trifluoroethanol (TFE). Accompanying experiments with dynamic light scattering and Circular Dichroism (CD) spectroscopy have been performed to obtain, respectively, the global diffusion constant and the secondary structure content of the molecule for both buffers as a function of temperature. Modeling the decay of the neutron intermediate scattering function by the Mittag-Leffler relaxation function, ϕ(t) = E_α(-(t/τ)^α) (0 < α < 1), we find that trifluoroethanol slows down the relaxation dynamics of the protein at 283 K and leads to a broader relaxation rate spectrum. This effect vanishes with increasing temperature, and at 323 K, its relaxation dynamics is identical in both solvents. These results are coherent with the data from dynamic light scattering, which show that the hydrodynamic radius of MBP in TFE-enriched solutions does not depend on temperature and is only slightly smaller compared to the pure D₂O buffer, except for 283 K, where it is much reduced. In accordance with these observations, the CD spectra reveal that TFE induces essentially a partial transition from β-strands to α-helices, but only a weak increase in the total secondary structure content, leaving about 50% of the protein unfolded. The results show that MBP is for all temperatures and in both buffers an intrinsically disordered protein and that TFE essentially induces a reduction in its hydrodynamic radius and its relaxation dynamics at low temperatures.

The challenges of controlling polymer synthesis at the molecular and macromolecular level

In this Perspective, we outline advances and challenges in controlling the structure of polymers at various size regimes in the context of structural features such as molecular weight distribution, end groups, architecture, composition and sequence.

Local Dynamics of the Hydration Water and Poly(Methyl Methacrylate) Chains in PMMA Networks

The dynamic behavior of water molecules and polymer chains in a hydrated poly(methyl methacrylate) (PMMA) matrix containing a small amount of water molecules was investigated. Water molecules have been widely recognized as plasticizers for activating the segmental motion of polymer chains owing to their ability to reduce the glass transition temperature. In this study, combined with judicious hydrogen/deuterium labeling, we conducted quasi-elastic neutron scattering (QENS) experiments on PMMA for its dry and hydrated states. Our results clearly indicate that the dynamics of hydrated polymer chains are accelerated, and that individual water molecules are slower than bulk water. It is therefore suggested that the hydration water affects the local motion of PMMA and activates the local relaxation process known as restricted rotation, which is widely accepted to be generally insensitive to changes in the microenvironment.

Dynamic Processes and Mechanisms Involved in Relaxations of Single-Chain Nano-Particle Melts

We present a combined study by quasielastic neutron scattering (QENS), dielectric and mechanical spectroscopy, calorimetry and wide-angle X-ray diffraction on single-chain nano-particles (SCNPs), using the corresponding linear precursor chains as reference, to elucidate the impact of internal bonds involving bulky cross-links on the properties of polymer melts. Internal cross-links do not appreciably alter local properties and fast dynamics. This is the case of the average inter-molecular distances, the β-relaxation and the extent of the atomic displacements at timescales faster than some picoseconds. Contrarily, the α-relaxation is slowed down with respect to the linear precursor, as detected by DSC, dielectric spectroscopy and QENS. QENS has also resolved broader response functions and stronger deviations from Gaussian behavior in the SCNPs melt, hinting at additional heterogeneities. The rheological properties are also clearly affected by internal cross-links. We discuss these results together with those previously reported on the deuterated counterpart samples and on SCNPs obtained through a different synthesis route to discern the effect of the nature of the cross-links on the modification of the diverse properties of the melts.

Dynamics & Spectroscopy with Neutrons-Recent Developments & Emerging Opportunities

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

Diffusivelike Motions in a Solvent-Free Protein-Polymer Hybrid

The interaction between proteins and hydration water stabilizes protein structure and promotes functional dynamics, with water translational motions enabling protein flexibility. Engineered solvent-free protein-polymer hybrids have been shown to preserve protein structure, function, and dynamics. Here, we used neutron scattering, protein and polymer perdeuteration, and molecular dynamics simulations to explore how a polymer dynamically replaces water. Even though relaxation rates and vibrational properties are strongly modified in polymer coated compared to hydrated proteins, liquidlike polymer dynamics appear to plasticize the conjugated protein in a qualitatively similar way as do hydration-water translational motions.

Disentangling Self-Atomic Motions in Polyisobutylene by Molecular Dynamics Simulations

We present fully atomistic molecular dynamics simulations on polyisobutylene (PIB) in a wide temperature range above the glass transition. The cell is validated by direct comparison of magnitudes computed from the simulation and measured by neutron scattering on protonated samples reported in previous works. Once the reliability of the simulation is assured, we exploit the information in the atomic trajectories to characterize the dynamics of the different kinds of atoms in PIB. All of them, including main-chain carbons, show a crossover from Gaussian to non-Gaussian behavior in the intermediate scattering function that can be described in terms of the anomalous jump diffusion model. The full characterization of the methyl-group hydrogen motions requires accounting for rotational motions. We show that the usually assumed statistically independence of rotational and segmental motions fails in this case. We apply the rotational rate distribution model to correlation functions calculated for the relative positions of methyl-group hydrogens with respect to the carbon atom at which they are linked. The contributions to the vibrational density of states are also discussed. We conclude that methyl-group rotations are coupled with the main-chain dynamics. Finally, we revise in the light of the simulations the hypothesis and conclusions made in previously reported neutron scattering investigations on protonated samples trying to address the origin of the dielectric β-process.

On the Mutual Relationships between Molecular Probe Mobility and Free Volume and Polymer Dynamics in Organic Glass Formers: cis-1,4-poly(isoprene)

We report on the reorientation dynamics of small spin probe 2,2,6,6-tetramethylpiperidinyl-1-oxyl (TEMPO) in cis-1,4-poly(isoprene) (cis-1,4-PIP10k) from electron spin resonance (ESR) and the free volume of cis-1,4-PIP10k from positron annihilation lifetime spectroscopy (PALS) in relation to the high-frequency relaxations of cis-1,4-PIP10k using light scattering (LS) as well as to the slow and fast processes from broadband dielectric spectroscopy (BDS) and neutron scattering (NS). The hyperfine coupling constant, 2A_zz '(T), and the correlation times, τ _c(T), of cis-1,4-PIP10k/TEMPO system as a function of temperature exhibit several regions of the distinct spin probe TEMPO dynamics over a wide temperature range from 100 K up to 350 K. The characteristic ESR temperatures of changes in the spin probe dynamics in cis-1,4-PIP10k/TEMPO system are closely related to the characteristic PALS ones reflecting changes in the free volume expansion from PALS measurement. Finally, the time scales of the slow and fast dynamics of TEMPO in cis-1,4-PIP10k are compared with all of the six known slow and fast relaxation modes from BDS, LS and NS techniques with the aim to discuss the controlling factors of the spin probe reorientation mobility in polymer, oligomer and small molecular organic glass-formers.

Co-nonsolvency in concentrated aqueous solutions of PNIPAM: effect of methanol on the collective and the chain dynamics

The polymer dynamics in concentrated solutions of poly(N-isopropyl acrylamide) (PNIPAM) in D2O/CD3OD mixtures is investigated in the one-phase region. Two polymer concentrations (9 and 25 wt%) and CD3OD contents in the solvent mixture of 0, 10 and 15 vol% are chosen. Temperature-resolved dynamic light scattering (DLS) reveals the collective dynamics. Two modes are observed, namely the fast relaxation of polymer segments within the blobs and the slow collective relaxation of the blobs. As the cloud point is approached, the correlation length related to the fast mode increases with CD3OD content. It features critical scaling behavior, which is consistent with mean-field behavior for the 9 wt% PNIPAM solution in pure D2O and with 3D Ising behavior for all other solutions. While the slow mode is not very strong in the 9 wt% PNIPAM solution in pure D2O, it is significantly more prominent as CD3OD is added and at all CD3OD contents in the 25 wt% solution, which may be attributed to enhanced interaction between the polymers. Neutron spin-echo spectroscopy (NSE) reveals a decay in the intermediate structure factor which indicates a diffusive process. For the polymer concentration of 9 wt%, the diffusion coefficients from NSE are similar to the ones from the fast relaxation observed in DLS. In contrast, they are significantly lower for the solutions having a polymer concentration of 25 wt%, which is attributed to the influence of the dominant large-scale dynamic heterogeneities. To summarize, addition of cosolvent leads to enhanced large-scale heterogeneities, which are reflected in the dynamic behavior at small length scales.

Resolving Segmental Polymer Dynamics in Nanocomposites by Incoherent Neutron Spin-Echo Spectroscopy

The segmental dynamics of styrene-butadiene nanocomposites with embedded silica nanoparticles (NPs, ca. 20 vol. %) has been studied by broadband dielectric (BDS) and neutron spin-echo spectroscopy (NSE). It is shown by BDS that overlapping contributions only allow us to conclude on a range of distributions of relaxation times in simplified industrial nanocomposites formed with highly polydisperse NPs. For comparison, structurally similar but less aggregated colloidal nanocomposites have a well-defined distribution of relaxation times due to the reduced influence of interfacial polarization processes. This distribution is widened with respect to the neat polymer, without change in the position of the maximum and at most a small slowing down visible in the average time. We then demonstrate that incoherent NSE can be used to resolve small modifications of segmental dynamics of the industrial samples. By carefully choosing the q-vector of the measurement, experiments with fully hydrogenated polymer give access to the self-dynamics of the polymer in the presence of silica on the scale of approximately 1 nm. Our high-resolution measurements show that the segmental motion is slightly but systematically slowed also by the presence of the industrial filler NPs.

A practical method to account for random phase approximation effects on the dynamic scattering of multi-component polymer systems

Investigations of polymer systems that rely on the interpretation of dynamical scattering results as, e.g., the structure factor S(Q, t) of single chains or chain sections may require the inclusion of effects, as described within the framework of the random phase approximation (RPA) for polymers. To do this in practice for the dynamic part of S(Q, t) beyond the initial slope is a challenge. Here, we present a method (and software) that allows a straightforward assessment of dynamical RPA effects and inclusion of these in the process/procedures of model fitting. Examples of applications to the interpretation of neutron spin-echo data multi-component polymer melts are shown.

Assessment of molecular dynamics simulations for amorphous poly(3-hexylthiophene) using neutron and X-ray scattering experiments

The molecular morphology and dynamics of conjugated polymers in the bulk solid state play a significant role in determining macroscopic charge transport properties. To understand this relationship, molecular dynamics (MD) simulations and quantum mechanical calculations are used to evaluate local electronic properties. In this work, we investigate the importance of system and simulation parameters, such as force fields and equilibration methods, when simulating amorphous poly(3-hexylthiophene) (P3HT), a model semiconducting polymer. An assessment of MD simulations for five different published P3HT force fields is made by comparing results to experimental wide-angle X-ray scattering (WAXS) and to a broad range of quasi-elastic neutron scattering (QENS) data. Moreover, an in silico analysis of force field parameters reveals that atomic partial charges and torsion potentials along the backbone and side chains have the greatest impact on structure and dynamics related to charge transport mechanisms in P3HT.

Dynamics of Hyperbranched Polymers under Confinement: A Dielectric Relaxation Study

The effect of severe confinement on the dynamics of three different generations of hyperbranched polyesters of the Boltorn family is investigated by dielectric relaxation spectroscopy (DRS). The polymer chains are intercalated within the galleries of natural montmorillonite (Na+-MMT), thus forming 1 nm polymer films confined between solid walls. The structure of the nanocomposites is studied with X-ray diffraction and the thermal behavior of the polymers in bulk and under confinement is determined by differential scanning calorimetry. The glass transition temperatures of the polymers show a clear dependence on the generation whereas the transition is completely suppressed when all the polymer chains are intercalated. The dynamic investigation of the bulk polymers reveals two sub-Tg processes, with similar behavior for the three polymers with the segmental relaxation observed above the Tg of each polymer. For the nanocomposites, where all the polymer chains are severely confined, the dynamics show significant differences compared to that of the bulk polymers. The sub-Tg processes are similar for the three generations but significantly faster and with weaker temperature dependence than those in the bulk. The segmental process appears at temperatures below the bulk polymer Tg, it exhibits an Arrhenius temperature dependence and shows differences for the three generations. A slow process that appears at higher temperatures is due to interfacial polarization.

Effects of nanoscopic-confinement on polymer dynamics

The static and dynamic behavior of polymers in confinement close to interfaces can be very different from that in the bulk. Among the various geometries, intercalated nanocomposites, in which polymer films of ∼1 nm thickness reside between the parallel inorganic surfaces of layered silicates in a well-ordered multilayer, offer a unique avenue for the investigation of the effects of nanoconfinement on polymer structure and dynamics by utilizing conventional analytical techniques and macroscopic specimens. In this article, we provide a review of research activities mainly in our laboratory on polymer dynamics under severe confinement utilizing different polymer systems: polar and non-polar polymers were mixed with hydrophilic or organophilic silicates, respectively, whereas hyperbranched polymers were studied in an attempt to probe the effect of polymer-surface interactions by altering the number and the kinds of functional groups in the periphery of the branched polymers. The polymer dynamics was probed by quasielastic neutron scattering and dielectric relaxation spectroscopy and was compared with that of the polymers in the bulk. In all cases, very local sub-Tg processes related to the motion of side and/or end groups as well as the segmental α-relaxation were identified with distinct differences recorded between the bulk and the confined systems. Confinement was found not to affect the very local motion in the case of the linear chains whereas it made it easier for hyperbranched polymers due to modifications of the hydrogen bond network. The segmental relaxation in confinement becomes faster than that in the bulk, exhibits Arrhenius temperature dependence and is observed even below the bulk Tg due to reduced cooperativity in the confined systems.

Multi-component modeling of quasielastic neutron scattering from phospholipid membranes

We investigated molecular motions in the 0.3-350 ps time range of D2O-hydrated bilayers of 1-palmitoyl-oleoyl-sn-glycero-phosphocholine and 1,2-dimyristoyl-sn-glycero-phosphocholine in the liquid phase by quasielastic neutron scattering. Model analysis of sets of spectra covering scale lengths from 4.8 to 30 Å revealed the presence of three types of motion taking place on well-separated time scales: (i) slow diffusion of the whole phospholipid molecules in a confined cylindrical region; (ii) conformational motion of the phospholipid chains; and (iii) fast uniaxial rotation of the hydrogen atoms around their carbon atoms. Based on theoretical models for the hydrogen dynamics in phospholipids, the spatial extent of these motions was analysed in detail and the results were compared with existing literature data. The complex dynamics of protons was described in terms of elemental dynamical processes involving different parts of the phospholipid chain on whose motions the hydrogen atoms ride.

Kinetic Polymer Arrest in Percolated SWNT Networks

Particle-polymer attractions in nanocomposites can cause significant heterogeneities in the polymer dynamics and remarkably impact the material properties. Dynamical perturbations are generally expected to be limited to interfacial polymer segments. However, composites with highly anisotropic nanoparticles usually exhibit very low percolation thresholds. In such systems, the overlapping interfacial regions could result in a complex polymer relaxation behavior that is unanticipated from dilute nanoparticle dispersions in polymer matrices. To understand this behavior, we examine a system of percolated single-wall carbon nanotubes (SWNT) in a polymer matrix, PMMA, which is known to have strong interfacial binding. Neutron spectroscopy measurements on the composites reveal not only an interfacial polymer layer that is transiently pinned to the SWNT surface, but suggest that the percolated network forms a kinetic cage that dramatically restricts both local and cooperative relaxations of noninterfacial polymer segments. These findings should help guide theories and simulations of hierarchical polymer dynamics in nanocomposites.

Dynamics and thermodynamics of polymer glasses

The fate of matter when decreasing the temperature at constant pressure is that of passing from gas to liquid and, subsequently, from liquid to crystal. However, a class of materials can exist in an amorphous phase below the melting temperature. On cooling such materials, a glass is formed; that is, a material with the rigidity of a solid but exhibiting no long-range order. The study of the thermodynamics and dynamics of glass-forming systems is the subject of continuous research. Within the wide variety of glass formers, an important sub-class is represented by glass forming polymers. The presence of chain connectivity and, in some cases, conformational disorder are unfavourable factors from the point of view of crystallization. Furthermore, many of them, such as amorphous thermoplastics, thermosets and rubbers, are widely employed in many applications. In this review, the peculiarities of the thermodynamics and dynamics of glass-forming polymers are discussed, with particular emphasis on those topics currently the subject of debate. In particular, the following aspects will be reviewed in the present work: (i) the connection between the pronounced slowing down of glassy dynamics on cooling towards the glass transition temperature (Tg) and the thermodynamics; and, (ii) the fate of the dynamics and thermodynamics below Tg. Both aspects are reviewed in light of the possible presence of a singularity at a finite temperature with diverging relaxation time and zero configurational entropy. In this context, the specificity of glass-forming polymers is emphasized.

Structure and polymer dynamics within PNIPAM-based microgel particles

The synthesis of temperature-responsive microgels of poly(N-isopropylacrylamide) (PNIPAM) was first reported in 1986 and, since then, there have been hundreds of publications describing the preparation, characterization and applications of these systems. This paper reviews the developments concerning the study of the structure of PNIPAM-based microgels performed over the last years using small angle neutron scattering (SANS) and also the investigations of the polymer-chain dynamics within the microgels carried out with incoherent elastic and quasielastic neutron scattering, and pulse field gradient nuclear magnetic resonance (PFG-NMR) techniques. Furthermore, the self-diffusion coefficient of the water molecules within the microgel, determined by means of solvent relaxation NMR, is also discussed as a function of the polymer volume fraction of the microgels.

Time resolved analysis of water drainage in porous asphalt concrete using neutron radiography

Porous asphalt as a road surface layer controls aquaplaning as rain water can drain through its highly porous structure. The process of water drainage through this permeable layer is studied using neutron radiography. Time-resolved water configuration and distribution within the porous structure are reported. It is shown that radiography depicts the process of liquid water transport within the complex geometry of porous asphalt, capturing water films, filled dead end pores and water islands.