Nonlinear Elongation Flows in Associating Polymer Melts: From Homogeneous to Heterogeneous Flow
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We analyze the onset of "necking" and subsequent filament failure during the transient uniaxial elongation of viscoelastic fluid samples in extensional rheometers. In the limit of rapid elongation (such that no molecular relaxation occurs), the external work applied is all stored elastically and the Considere criterion originally developed in solid mechanics can be used to quantitatively predict the critical Hencky strain to failure. By comparing the predictions of the Doi-Edwards model for linear homopolymer melts with those of the "Pom-Pom" model for prototypical branched melts we show that the critical strain to failure in rapid elongation of a rubbery material is intimately linked to the molecular topology of the chain, especially the degree of chain branching. The onset of necking instability is monotonically shifted to larger Hencky strains as the number of branches is increased. Numerical computations at finite Deborah numbers also show that there is an optimal range of deformation rates over which homogeneous extensions can be maintained to large strain. We also consider other rapid homogeneous stretching deformations, such as biaxial and planar stretching, and show that the degree of stabilization afforded by inclusion of material with long-chain branching is a sensitive function of the imposed mode of deformation.
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X-ray photon correlation spectroscopy measurements were used to quantify the dynamics of bare and bimodal grafted silica nanoparticles mixed with PEO melts of different molecular weights. In dilute polymer nanocomposite (PNC) samples, we find diffusive NP behavior as described by the Stokes–Einstein relationship so long as the adsorbed PEO polymer layer is taken into account in determining both the effective NP size and its role on composite viscosity. The size of this bound layer was found to be approximately 2R g , where R g is the chain radius of gyration. We also expanded our system to investigate how the dynamics of grafted NPs differ from bare NPs with an adsorbed layer. We showed that the dynamics again can be determined by an effective NP radius at a scale smaller than the effective interparticle spacing; however, at larger length scales, the morphology and grafting parameters play a major role in the system dynamics. These results allow us to quantify NP ordering driven by polymer crystallization. It has previously been speculated that behavior is controlled by the relative ratio of time scale of crystal growth and the diffusive time scale of the NPs, a Peclet number. When the former time scale is longer, then the NPs are expected to be segregated into the interlamellar amorphous zones, while the NPs are too slow to be reorganized in the opposite case. We show here that this conjecture is quantitatively correct and the demarcation in behavior occurs for Pe = 1. Thus, we provide a way to estimate a critical spherulite growth rate for any semicrystalline PNC, at which a given NP can be ordered. Together, the results of this study permit us to tunably design PNCs through directed dispersion of NPs in a polymer matrix.
High-performance polymers that have improved processing characteristics, and a method of making them, have been invented. One of the improved characteristics is low (relative to corresponding prior polymers) melt viscosities at given temperatures. This characteristic makes it possible to utilize such processes as resin-transfer molding and resin-film infusion and to perform autoclave processing at lower temperatures and/or pressures. Another improved characteristic is larger processing windows that is, longer times at low viscosities. Other improved characteristics include increased solubility of uncured polymer precursors that contain reactive groups, greater densities of cross-links in cured polymers, improved mechanical properties of the cured polymers, and greater resistance of the cured polymers to chemical attack. The invention is particularly applicable to poly(arylene ether)s [PAEs] and polyimides [PIs] that are useful as adhesives, matrices of composite materials, moldings, films, and coatings. PAEs and PIs synthesized according to the invention comprise mixtures of branched, linear, and star-shaped molecules. The monomers of these polymers can be capped with either reactive end groups to obtain thermosets or nonreactive end groups to obtain thermoplastics. The synthesis of a polymeric mixture according to the invention involves the use of a small amount of a trifunctional monomer. In the case of a PAE, the trifunctional monomer is a trihydroxy- containing compound for example, 1,3,5-trihydroxybenzene (THB). In the case of a PI, the trifunctional monomer is a triamine for example, triamino pyrimidine or melamine. In addition to the aforementioned trifunctional monomer, one uses the difunctional monomers of the conventional formulation of the polymer in question (see figure). In cases of nonreactive end caps, the polymeric mixtures of the invention have melt viscosities and melting temperatures lower than those of the corresponding linear polymers of equal molecular weights. The lower melting temperatures and melt viscosities provide larger processing windows. In cases of reactive end caps, the polymeric mixtures of the invention have lower melt viscosities before curing and the higher cross-link densities after curing (where branching in the uncured systems would become cross-links in the cured systems), relative to the corresponding linear polymers of equal molecular weights. The greater cross-link densities afford increased resistance to chemical attack and improved mechanical properties.
Fluorinated amorphous silica–alumina (F-ASA) prepared by the thermolysis of Krossing’s Al(OC(CF 3 ) 3 ) 3 (PhF) Lewis superacid supported on silica is a very reactive catalyst that promotes the pyrolysis (cracking) of aliphatic polymer melts to produce low molecular weight hyperbranched oils. Initial spectroscopic studies reported previously (Gao, J.; Perras, F. A.; Conley, M. P. J. Am. Chem. Soc . 2025 , 147, 18145–18154) showed that this material contains a distribution of four-, five-, and six-coordinate aluminum sites and a small amount of Brønsted acid sites, similar to typical amorphous silica–alumina materials that are far less reactive in the pyrolysis of aliphatic polymer melts. The objective of this study was to determine whether other active sites present in F-ASA could facilitate pyrolysis reactions. This study provides evidence for the presence of a redox-active silicon oxycarbide persistent radical ((≡Si) 3 C•) in F-ASA. Mims ENDOR EPR experiments show that (≡Si) 3 C• is located close to aluminum. Contacting F-ASA with thianthrene (Th) results in oxidation to form the [Th •+ ][F–ASA] ion-pair, while reactions with 1-hydroxy-2,2,6,6-tetramethylpiperidine (TEMPOH) result in H atom transfer to form TEMPO radical and F-ASA-H containing a mildly acidic (≡Si) 3 C–H. Poisoning studies show that both Lewis acidity and (≡Si) 3 C• are required for polymer pyrolysis reactivity. Finally, we propose that F-ASA promotes the formation of alkyl radicals in polymer melts, which are key intermediates in the thermal pyrolysis reactions of aliphatic polymers, involving the cooperative reactivity of both the Lewis acid and (≡Si) 3 C•.
There has been considerable interest in the nucleation and crystallization of polymers in the presence of nanoparticles (NPs, or nanofillers in general, NFs). Most of the extensive work in this area has focused on anisotropic, non-Brownian NFs (e.g., clay sheets, carbon nanotubes) whose spatial dispersion state in these nanocomposites is controlled by the process by which they are formed. Hence, NF spatial dispersion is generally limited and often remains poorly characterized. Thermodynamic handles that can be used to control NF dispersion state in the polymer melt include (a) favorable interactions between the polymer chains and the bare NP surfaces, or (b) the density and length of the chains, with the same chemistry as the matrix, grafted to the NP surface. These relatively large NFs merely act as stationary objects that affect the kinetics of nucleation by providing heterogeneous sites, and the crystallization rate by confining the polymer in the melt state. The dispersion state of the NFs can dramatically affect the nucleation and crystallization of the matrix, but in most cases reported, the NFs increase nucleation efficiency relative to the neat polymer. At higher NF loadings, the effect of polymer confinement by the NFs dominates, leading to a decrease in crystal growth rates. This review describes the most important lessons learned from these commonly studied systems and then extends to polymer composite systems containing small, mobile spherical NPs (typically smaller than 100 nm in size). The role of NP mobility, which provides for dynamic confinement of the polymer melt, on the kinetics of polymer crystallization (nucleation, growth, and overall crystallization) and how this behavior is mostly consistent with the case of immobile NF is a second important focus of this review. In addition to the role of NFs on crystallization kinetics, recently reported nanoparticle ordering phenomena such as the effect of matrix crystallization on the organization of small spherical NPs within the amorphous regions of the semicrystalline morphology are discussed. In conclusion, such phenomena are clearly not observed for large NFs and hence provide a point of departure from past works in this area.
Polymeric materials are ubiquitous in modern society and they play an instrumental role in almost all industries, undoubtedly including the energy and environment sectors. Increased demand of energy and awareness to sustainability both necessitates the development of novel polymers with enhanced properties. Unfortunately, their structural and behavioral complexity render such discovery challenging and impeded. To address this problem, scientists are developing various computational modeling techniques and leveraging their power to depict the relationship between structural characteristics of polymers and their properties (such as rheological behaviors), and use such prediction to guide the design and syntheses of novel polymeric materials with enhanced performances. Unfortunately, predicting the relationships between polymer structure and composition with rheological properties via atomistic modeling is still a major challenge because of the extended time and length scales involved. Studying dynamic shear viscosity and linear viscoelasticity using molecular models requires capabilities that have been elusive, including representation of large molecular weight chains with an effective internal scale capable of describing entanglement, shear-rates that are in the s-1 scale with accurate quantitative stresses, and chemically-realistic combinations of both homogeneous and heterogeneous systems. Motivated by these unmet challenges, the overall technical objective of this DOE-STTR Phase II project is to develop robust molecular predictive methods for advanced polymer discovery and applications and especially for designing and demonstrating the “smart” polymer-based waterflooding enhanced oil recovery (EOR) process. In particular, we apply state-of-the-art molecular modeling methods developed by our academic partner, Materials Stimulation Center (MSC) at California Institute of Technology (Caltech), to facilitate and accelerate the experimental discovery processes. During the Phase I of this project, we had focused on development and demonstration of the molecular modeling methods to describe rheological properties of non-Newtonian polymer fluids, and to improve our fundamental understandings of shear-thickening mechanism and kinetics. In Phase II, we further apply the theoretical models to guide our experimental programs to improve our design of smart rheology modifier (SRM) polymers and their optimization for EOR. Specifically, we have three objectives in the Phase II study: (1) to further improve out computational modeling methods, coupling with the advanced machine learning algorithms; (2) to develop cost-effective and efficient SRM-flooding process suitable for EOR applications under typical reservoir conditions; and (3) to further explore the application of our molecular predictive models for innovative material discovery in other industrial applications. The recent development of our multiscale predictive framework allows the successful prediction of rheological properties from the chemical structure for polymers of experimentally relevant molecular weights, and provides an in-silico machine learning engine for screening novel compositions and structures with optimized non-Newtonian response, required for both shear-thinning and shear-thickening applications. Our framework provides: (1) procedures and tools for systematic coarsening from atomistic models and reverse mapping of coarse-grain models to atomistic, (2) unique ab initio methods to characterize the atomistic origin of colloidal and interfacial interactions and phenomena, (3) systematic structure and composition builders based on practical descriptors that drive rheological changes in polymer melts and diluted polymer mixtures, (4) a rheological properties engine capable of predicting viscosity in the zero-shear limit and under realistic dynamic conditions (for shear-rates commensurate with experiments) for large heterogeneous systems, (5) coarse-grain force fields with improved non-bond descriptions based on accurate quantum mechanics, (6) an in-silico screening machine learning engine that feeds from the systematic model builders to cover the descriptors search space, computes the rheological properties from converged trajectories spanning sub-milliseconds and ranks them for each structure/composition using an automated viscosity-vs-shear rate fitness function that can be tuned for shear-thickening, shear-thinning and other rheological responses.
Dielectric spectroscopy measures the dynamics of polymer melts over a broad frequency range. Developing a theory for the spectral shape can extend the analysis of dielectric spectra beyond determining relaxation times from the peak maxima and adds physical meaning to shape parameters determined with empirical fit functions. Toward this goal, we use the experimental results on unentangled poly(isoprene), and unentangled poly(butylene oxide), polymer melts, to test whether the concept of end blocks could be one reason for the Rouse model deviating from experimental data. These end blocks have been suggested by simulations and neutron spin echo spectroscopy and are a consequence of the monomeric friction coefficient depending on the position of the bead in the chain. The concept of an end block is an approximation which partitions the chain in a middle and two end blocks to avoid overparameterization by a continuous position dependent change of the friction parameter. Analysis of dielectric spectra shows that the deviations of the calculated from the experimental normal mode cannot be related to the end block relaxation. However, the results do not contradict an end block hiding below the segmental relaxation peak. Finally, it seems that the results are compatible with an end block being the specific part of the sub-Rouse chain interpretation close to the chain ends.
Melt-flow instability of extruded polymers - failure criterion and equations of state, and linearized stability analysis in Newtonian fluid, power-law fluid, and elastic fluids