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Spatial correlations of entangled polymer dynamics
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Furthermore, comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.
Viscoelastic properties of entangled polymers - Ternary blends of monodisperse homopolymers
In a previous publication from this laboratory, the Rouse-Bueche-Zimm molecular theory of viscoelasticity has been extended by using a transient network model to apply to binary blends of monodisperse polymers with chain entanglements. The dynamics of the entanglements were modeled both by the enhanced frictional coefficients and by the additional elastic couplings. It was recognized that entanglements not only may form between chains of the same lengths (intracomponent entanglements) but also between those of different lengths (intercomponent entanglements). At a given intercomponent entanglement, the longer chain was assumed to have the frictional coefficient of the shorter chain. Similarly, for blends consisting of several monodisperse components with different molecular weights, such modifications are also required to predict their linear viscoelastic behavior. The frequency of these interactions is assumed to be proportional to the weight ratio of the respective component chains in the blend. Equations of motion are formulated for each component and solved numerically for the relaxation time spectra. Linear viscoelastic properties such as the dynamic mechanical moduli, stress relaxation moduli, and zero-shear viscosity can then be computed for these systems by linear summation of those of the components.
Smoother Surfaces Enhance Diffusion of Nanorods in Entangled Polymer Melts
Coarse-grained molecular dynamics simulations are used to study the diffusion of thin nanorods in entangled polymer melts for varying nanorod length and roughness. While prior studies observed a nanorod parallel diffusion constant scaling inversely with rod length D ∥ ~ l –1 , here, we show that this scaling is not universal and depends sensitively on the nanorod surface roughness. We observe D ∥ ~ l –k , where k < 1 and decreases with decreasing surface roughness. The weaker scaling is driven by the non-Gaussian diffusion of nanorods due to the emergence of an intermittent hopping process that becomes more pronounced with decreasing roughness at the monomer scale. Analysis shows that the mean hop size grows for smoother rods but shows little to no variation with rod length. The mean hopping frequency shows no dependence on either rod length or roughness, suggesting it originates from the polymer melt environment. Further, our results show that the small-scale features of the nanorod surface strongly influence the large-scale and long-time transport of nanorods in polymer matrices, creating new material design opportunities for precisely engineered nanocomposites.
Nonlinear Shear Rheology of Entangled Polymer Rings
Steady-state shear viscosity η($\bar{γ}$) of unconcatenated ring polymer melts as a function of the shear rate $\bar{γ}$ is studied by a combination of experiments, simulations, and theory. Experiments using polystyrenes with Z ≈ 5 and Z ≈ 11 entanglements indicate weaker shear thinning for rings compared to linear polymers exhibiting power law scaling of shear viscosity η ~ $\bar{γ}$ –0.56 ± 0.02 , independent of chain length, for Weissenberg numbers up to about 10 2 . Nonequilibrium molecular dynamics simulations using the bead-spring model reveal a similar behavior with η ~ $\bar{γ}$ -0.57 ± 0.08 for 4 ≤ Z ≤ 57. Viscosity decreases with chain length for high $\bar{γ}$. In our experiments, we see the onset of this regime, and in simulations, which we extended to Wi ~ 10 4 , the nonuniversality is fully developed. In addition to a naive scaling theory yielding for the universal regime η ~ $\bar{γ}$ –0.57 , we developed a novel shear slit model explaining many details of observed conformations and dynamics as well as the chain length-dependent behavior of viscosity at large $\bar{γ}$. The signature feature of the model is the presence of two distinct length scales: the size of tension blobs and much larger thickness of a shear slit in which rings are self-consistently confined in the velocity gradient direction and which is dictated by the size of a chain section with relaxation time 1/$\bar{γ}$. These two length scales control the two normal stress differences. In this model, the chain length-dependent onset of nonuniversal behavior is set by tension blobs becoming as small as about one Kuhn segment. This model explains the approximate applicability of the Cox–Merz rule for ring polymers.
Bottom-up Multiscale Simulation of Nonlinear Rheology for Entangled Polymer Melts: Using Atactic Polystyrene as An Example
Not Available
Generalized vs. fractional: a comparative analysis of Maxwell models applied to entangled polymer solutions
Fractional viscoelastic models provide an excellent description of rheological data for polymer systems with power-law behaviour. However, the physical interpretation of their model parameters, which carry fractional units of time, often remains elusive. We show that for poly(ethylene oxide) (PEO) solutions, the fractional Maxwell model (FMM) requires much fewer model parameters than the classical generalized Maxwell model for a good description of the data and that it can be applied consistently to solutions with varying degrees of viscoelasticity. Despite their fractional units, the parameters exhibit scaling laws similar to classical parameters as a function of polymer concentration.
Computer Simulations of Entangled Polymer Melts: From Segmental Dynamics to Viscoelastic Response.
Abstract not provided.
Viscoelastic properties of entangled polymer. IV - Binary blends of monodisperse homopolymers
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Elucidating Polymer Binder Entanglement in Freestanding Sulfide Solid-State Electrolyte Membranes
This study advances the development of flexible, sheet-type sulfide solid-state electrolytes (SSEs) for use in all-solid-state batteries, emphasizing the important and previously insufficiently investigated role of polymer binder entanglement. Here, the molecular weight of polymer binders is pivotal in crafting robust, freestanding SSE films. Our research uncovers a dual impact: higher molecular weight binders bolster the structural integrity of SSE films but elevate grain boundary resistance and diminish critical current density, whereas lower molecular weight poly(isobutylene) films, despite their more uniform distribution, lack the essential strain hardening or strength for sustained active material contact. Crucially, full cells employing higher molecular weight binders demonstrate improved discharge capacity retention, contrasting sharply with the notable capacity degradation in lower molecular weight cells. Our findings not only deepen the comprehension of binder influences in solid-state batteries but also chart a course for refining all-solid-state battery technologies, a key stride for the future of energy storage solutions.
Mechanically Accelerated Depolymerization of Entangled Linear Polymer Melts
Mechanical forces can enhance the chemical depolymerization of synthetic polymers when shear flow accelerates chain scission. To quantify the extent of mechanically-accelerated scission, the effect of simple shear flow (duration and strength) with low Weissenberg and Deborah numbers was investigated by considering the impact of applied work in both simple shear and shear dominated mixed flows. Hydrogenated polyisoprene was chosen as a model linear, entangled system. The conditions (strain amplitude, frequency, and shearing time) necessary to increase chain scission were assessed in the rubbery melt. Shear flow accelerated chain scission at higher temperatures, suggesting an activated process. Isothermal scission versus work curves were superposed by applying shift factors a T,S , whose Arrhenius-like temperature dependence gave an apparent activation energy for chain scission of ~ 110 kJ/mol, which is likely a combination of the activation energy of viscosity and bond energy. This work provides a base for quantifying the impact of shear on depolymerization of polymer melts and highlight the connection between viscous dissipation and scission chemistry.
Molecular Dynamics Simulations of the Effects of Entanglement on Polymer Crystal Nucleation
Not provided.
Tuning Organic Semiconductor Packing and Morphology through Non-equilibrium Solution Processing (Final Report)
Organic semiconductors (OSCs) are a promising candidate to produce low-cost, large area, and flexible electronics. There has previously been successful development of organic field effect transistors (OFETs), photovoltaics (OPV), and bioelectronics using OSCs. Solution processing of these materials allows for the fabrication of large-area devices in the kinetic crystallization regime. The charge transport capabilities have been shown to depend on the morphology and molecular packing of the OSC within thin films. Our hypothesis is that solution processing conditions may significantly impact OSC morphology and as a result the charge transport. Therefore, this work has focused on obtaining a fundamental understanding of the morphology and molecular packing of OSCs for optimal device performance. Through our work, we have gained a better understanding of how these structural conditions were influenced by the solution processing conditions. Our studies have led to a more systematic understanding of the various parameters that impact OSC morphology. Solution processing leads to non-equilibrium films, thus allowing for the formation of diverse morphologies that are inaccessible by other fabrication methods. Previously, our group has focused on tuning the morphology of small-molecular OSCs [53, 55-57]. However, little work had been devoted to polymer OSCs. There was a lack of detailed studies characterizing the solution-state of polymer OSCs in terms of their conformation, degree of entanglement, polymer aggregation, and chain relaxation dynamics. The solution state properties are also likely to be influenced by the rigidity and molecular weight of the polymer OSCs investigated. Thus, we have focused our attention on gaining a better insight of polymer OSC films and solution processing methods. Through this proposal, our approach is to investigate the correlation between solution-state properties and the morphology of the resulting polymer OSC films. We worked three specific aims: investigate the effects of 1) polymer OSC solution-state properties on final film morphology; 2) molecular additives on the solution-state and final film properties; 3) controlled pre-aggregation in the solution-state in the final film morphology. More rigid and planar polymer backbones should promote interchain charge transport and more efficient interchain hopping between polymer chains. Through tailoring the polymer backbone, polymer sidechains, and molecular weight, we expected the altered solution-state properties to affect the final film morphology. In addition, reducing the entanglements and promoting chain alignment will likely prevent charge carrier trapping through conformation disorders. We thus studied different mechanisms, such as molecular additives, to reduce entanglements in solution. Devices fabricated from these solutions were expected to have improved charge transport abilities. In addition to tailoring the solution-state characteristics of the polymer OSCs, we investigated the effect of solution processing methods on the molecular packing and morphology of polymer OSC films. Two main solution processing techniques, e.g., spin-coating and solution shearing, were employed to fabricate OFETs. Spin coating was employed to prepare OSC films, which produce isotropic films. This technique creates several parameters to tune such as spin coating speed, acceleration, and time. Additionally, our research group developed the solution shearing method, which consists of the solution initially sandwiched between two plates. By sliding the top plate, the solution front is exposed and drying begins. This technique allows for the creation of aligned large crystalline domains. Solution shearing consists of different processing parameters which can affect the final morphology, such as shearing speed, substrate temperature and temperature gradient, distance between both plates, and the tilt angle of the top plate. Due to the complexity of the polymer systems investigated, numerous techniques were employed to characterize the polymer OSC solution state and films. All the materials were characterized using the DOE supported synchrotron X-ray scattering facilities at the Stanford Synchrotron Radiation Lightsource (SSRL). Using grazing incidence X-ray scattering (GIXS) and Near Edge X-ray Absorption Fine Structure (NEXAFS) techniques, the crystalline structure and molecular orientations of the thin films were measured. Optical absorption (UV-Vis) spectroscopy was employed to determine the aggregation state in solution and films of the polymer systems. Polarized UV-Vis also allowed for the determination of the relative degree of polymer chain alignment for solution sheared films. Additionally, various other techniques were used to investigate other properties within the film, such as atomic force microscopy (AFM) and solution rheology. Finally, the device performance is quantified through the fabrication and characterization of OFETs, which will highlight the effects of morphology on charge transport.
The Work of Mechanical Degradation in Elongating Polymer Melts
Molecular dynamics simulations are used to study the mechanical degradation of well-entangled polymer melts during uniaxial extensional flow. Simulations measure the transient rise in extensional stresses and relate them to the molecular alignment and scission of chain backbones. Intermolecular entanglements couple chain scission in space and time, making degradation sensitive to deformation history and strain rate in ways not displayed by dilute polymer solutions. The rate of chain scission is nonmonotonic and peaks at strains corresponding to the maximum extensibility of entanglement segments but prior to the full extension of chain backbones. We measure a specific work per scission event w* and decompose it into separate contributions associated with chain alignment, chemical bond breaking, and scission-induced plasticity. We find chain scission in melts requires activating plastic dissipation that is multiple orders of magnitude larger than the chemical work required to break a covalent backbone bond. Our findings underscore the critical need to consider bulk polymer mechanics and rheology in designing efficient mechanical degradation and mechanochemical processes.
Improving Miscibility of Polymer Donor and Polymer Acceptor by Reducing Chain Entanglement for Realizing 18.64 % Efficiency All Polymer Solar Cells
All-polymer solar cells have experienced rapid development in recent years by the emergence of polymerized small molecular acceptors (PSMAs). However, the strong chain entanglements of polymer donors (P D s) and polymer acceptors (P A s) decrease the miscibility of the resulting polymer mixtures, making it challenging to optimize the blend morphology. Herein, we designed three P A s, namely PBTPICm-BDD, PBTPICγ-BDD and PBTPICF-BDD, by smartly using a BDD unit as the polymerized unit to copolymerize with different Y-typed non-fullerene small molecular acceptors (NF-SMAs), thus achieving a certain degree of distortion and giving the polymer system enough internal space to reduce the entanglements of the polymer chains. Such effects increase the chances of the P D being interspersed into the acceptor material, which improve the solubility between the P D and P A . The PBTPICγ-BDD and PBTPICF-BDD displayed better miscibility with PBQx-TCl, leading to a well optimized morphology. As a result, high power conversion efficiencies (PCEs) of 17.50 % and 17.17 % were achieved for PBQx-TCl : PBTPICγ-BDD and PBQx-TCl : PBTPICF-BDD devices, respectively. In conclusion, with the addition of PYFT-o as the third component into PBQx-TCl : PBTPICγ-BDD blend to further extend the absorption spectral coverage and finely tune microstructures of the blend morphology, a remarkable PCE of 18.64 % was realized finally.
Reversible Nanocomposite by Programming Amorphous Polymer Conformation Under Nanoconfinement
Nanoconfinements are utilized to program how polymers entangle and disentangle as chain clusters to engineer pseudo bonds with tunable strength, multivalency, and directionality. When amorphous polymers are grafted to nanoparticles that are one magnitude larger in size than individual polymers, programming grafted chain conformations can "synthesize" high-performance nanocomposites with moduli of ≈25GPa and a circular lifecycle without forming and/or breaking chemical bonds. These nanocomposites dissipate external stresses by disentangling and stretching grafted polymers up to ≈98% of their contour length, analogous to that of folded proteins; use both polymers and nanoparticles for load bearing; and exhibit a non-linear dependence on composition throughout the microscopic, nanoscopic, and single-particle levels.
The entanglement chain length and polymer composition
Dependence of entanglement chain length on polymer composition of linear, amorphous polymers - Rheology
[Results of Simulation Studies]
Lattice Monte Carlo and off-lattice molecular dynamics simulations of h(sub 1)t(sub 4) and h(sub 4)t(sub l) (head/tail) amphiphile solutions have been performed as a function of surfactant concentration and temperature. The lattice and off-lattice systems exhibit quite different self-assembly behavior at equivalent thermodynamic conditions. We found that in the weakly aggregating regime (no preferred-size micelles), all models yield similar micelle size distributions at the same average aggregation number, albeit at different thermodynamic conditions (temperatures). In the strongly aggregating regime, this mapping between models (through temperature adjustment) fails, and the models exhibit qualitatively different micellization behavior. Incipient micellization in a model self-associating telechelic polymer solution results in a network with a transient elastic response that decays by a two-step relaxation: the first is due to a heterogeneous jump-diffusion process involving entrapment of end-groups within well-defined clusters and this is followed by rapid diffusion to neighboring clusters and a decay (terminal relaxation) due to cluster disintegration. The viscoelastic response of the solution manifests characteristics of a glass transition and entangled polymer network.