Polydisperse Polymer Research Articles

Synthesis of Polydispersed P(St-MMA-AA) Microspheres and Fabrication of Colloidal Crystals with Non-Compact Morphology

Great attention has been given to the synthesis of monodispersed and uniform colloidal polymer particles with controllable particle sizes. However, investigations on the preparation, characterization and fabrication of polydisperse polymeric particles are very few. Polydisperse polymers are also needed to meet the new demands of the modern markets due to the ease of their synthesis. This study, therefore, synthesized polydispersed poly(styrene-methyl-methacrylate acrylic-acid) (P(St-MMA-AA)) via emulsion polymerization synthetic approach under unstable reaction conditions. The synthesized P(St-MMA-AA) microparticles were characterized using Fourier transform infrared spectroscopy (FTIR), dynamic light scattering (DLS), a thermo-gravimetric analyzer (TGA) and scanning electron microscope (SEM). The DLS results revealed a highly polydispersed P(St-MMA-AA) microparticles with an average particle diameter of 803.4 nm. SEM, TEM (transmission electron microscopy) and AFM (atomic force microscopy) analyses showed that the particles were spherical and polydispersed. The unequal diameters and non-compact nature of the fabricated colloidal crystals may have affected its possible uses in some specific applications such as decorative coatings, biomedical and sensing applications. However, other materials can be incorporated into the polydispersed prepared P(St-MMA-AA) colloidal microspheres to improve their properties and possible applications.
 Keywords: Emulsion polymerization; Polydispersed; Polymer; P(St-MMA-AA).

Modelling elongational viscosity overshoot and brittle fracture of low-density polyethylene melts

The Hierarchical Multi-mode Molecular Stress Function (HMMSF) model predicts the elongational and multiaxial extensional viscosities of polydisperse linear polymer melts based exclusively on their linear viscoelastic characterization and a single nonlinear material parameter, the so-called dilution modulus {G}_{D}. For long-chain branched (LCB) polymer melts such as low-density polyethylene (LDPE), the HMMSF model describes quantitatively the elongational stress growth coefficient up to the maximum of the elongational viscosity but fails to predict the existence of the maximum and the following steady-state viscosity. By taking into account branch point withdrawal in elongational flow of LCB melts, we extend the HMMSF model and show that the maximum of the elongational viscosity can be characterized by a single additional parameter, the characteristic stretch {overline{lambda }}_{m}, while the steady-state tensile stress and the elongational viscosity depend only on the dilution modulus {G}_{D} as in the case of linear polydisperse melts. Comparison of predictions of the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model to experimental data of 5 LDPE melts with widely different molecular weights, polydispersities and densities, and a model polystyrene pom-pom polymer shows good agreement within experimental accuracy in constant elongational-rate flow as well as stress relaxation after steady and reversed elongational flow. For the LCB melts considered, we report differences in the specific Hencky strain at the maximum of the tensile stress as quantified by the characteristic stretch {overline{lambda }}_{m}, and we discuss correlations between polydispersity, dilution modulus {G}_{D}, and strain hardening potential of the LDPE melts. We also extend the fracture criterion for brittle fracture of monodisperse polymer melts to the case of polydisperse polymers and find reasonable agreement with experimental evidence.

Percolation in Polydisperse Polymer Systems: A Computer Simulation Study

AbstractThe structure of polymer chains at interfaces still is not fully understood. A coarse‐grained lattice model is used to study the structure of macromolecules strongly adsorbed on a flat surface. As a result, the polymers are strictly two‐dimensional. Chains are flexible and athermal. A dynamic Monte Carlo algorithm consisting of local and non‐local modification of chains’ conformations is employed. The scaling behavior of chains’ size is found to be similar to monodisperse systems. It is also shown that the introduction of polydispersity increases values of the percolation threshold, especially for longer chains. The influence of the type of polydispersity on the percolation threshold in two‐dimensional polymer films is found to be significant.

Machine Learning for Melting Temperature Predictions and Design in Polyhydroxyalkanoate-Based Biopolymers.

Diminishing fossil fuel-based resources and ever-growing environmental concerns related to plastic pollution demand for the development of sustainable and biodegradable polymeric material alternatives. Polyhydroxyalkanoates (PHAs) represent an eco-friendly and economically viable class of polymers with a wide range of applications. However, the chemical diversity combined with tunable physical properties available within PHAs poses discovery and optimization challenges with respect to identifying optimal application-specific chemical compositions. Here we use an example of melting temperature (Tm) prediction to demonstrate the promise of machine learning (ML)-based techniques for establishing efficient structure-property mappings in PHA-based chemical space. We employ a manually curated data set of experimentally measured Tm values for a wide range of PHA homo- and copolymer chemistries along with their reported polymer molecular weights and polydispersity indices. Descriptors based on topology, shape, and charge/polarity of specific motifs forming the polymer backbone were then used to numerically represent the polymers. The ML models developed by using available data were used to rapidly predict the property of multicomponent PHA-based copolymers, while estimating uncertainties underlying the predictions. Combined with a previously developed glass transition temperature (Tg) prediction model and an evolutionary algorithm-based search strategy, the approach is demonstrated to address polymer design with multiobjective optimization challenges.

Chain-Growth Sulfur(VI) Fluoride Exchange Polycondensation: Molecular Weight Control and Synthesis of Degradable Polysulfates.

Sulfur(VI) fluoride exchange (SuFEx) click chemistry has offered a facile and reliable approach to produce polysulfates and polysulfonates. However, the current SuFEx polymerization methods lack precise control of target molecular weight and dispersity. Herein, we report the first chain-growth SuFEx polycondensation process by exploiting the unique reactivity and selectivity of S–F bonds under SuFEx catalysis. Given the higher reactivity of iminosulfur oxydifluoride versus fluorosulfate, the chain-growth SuFEx polycondensation is realized by using an iminosulfur oxydifluoride-containing compound as the reactive chain initiator and deactivated AB-type aryl silyl ether-fluorosulfates bearing an electron-withdrawing group as monomers. When 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) was utilized as the polymerization catalyst, precise control over the polymer molecular weight and polydispersity was achieved. The resulting polymers possess great thermal stability but are easily degradable under mild acidic and basic conditions.

Dynamics of Nanoparticles in Polydisperse Polymer Networks: from Free Diffusion to Hopping

Using molecular dynamics simulations we study the static and dynamic properties of spherical nanoparticles (NPs) embedded in a disordered and polydisperse polymer network. Purely repulsive (RNP) as well as weakly attractive (ANP) polymer-NP interactions are considered. It is found that for both types of particles the NP dynamics at intermediate and at long times is controlled by the confinement parameter $C=\sigma_N/\lambda$, where $\sigma_N$ is the NP diameter and $\lambda$ is the dynamic localization length of the crosslinks. Three dynamical regimes are identified: i) For weak confinement ($C \lesssim 1$) the NPs can freely diffuse through the mesh; ii) For strong confinement ($C \gtrsim 1$) NPs proceed by means of activated hopping; iii) For extreme confinement ($C \gtrsim 3$) the mean squared displacement shows on intermediate time scales a quasi-plateau since the NPs are trapped by the mesh for very long times. Escaping from this local cage is a process that depends strongly on the local environment, thus giving rise to an extremely heterogeneous relaxation dynamics. The simulation data are compared with the two main theories for the diffusion process of NPs in gels. Both theories give a very good description of the $C-$dependence of the NP diffusion constant, but fail to reproduce the heterogeneous dynamics at intermediate time scales.

Thermodynamic insights on the liquid-liquid fractionation of gluten proteins in aqueous ethanol

Wheat gluten includes two major proteins classes, gliadin (25–60 kg/mol) and glutenin polymers (100 to > 2,000 kg/mol) each comprising several polypeptides routinely identified by size-exclusion chromatography and electrophoresis. Gluten proteins are rich in glutamine (30%) and contain several repeated sequences, linking them to the wide class of intrinsically disordered protein (IDP). Here we showed that an ethanol/water (EtOH/W, 50/50, v/v) extract of an industrial gluten, comprising 1/3 of glutenin polymers and 2/3 of gliadin, underwent liquid-liquid phase separation (LLPS) below 14 °C, leading to two coexisting phases, respectively rich and poor in protein. As the quenching depth increased, proteins of lower and lower molecular weight joined the rich phase, akin to what would have been obtained for a polydisperse polymer sample. Within the rich phase the mass ratio of glutenin over gliadin decreased from 2.5 to 0.5 as the temperature dropped from 14 °C to −0.8 °C. Concomitantly the concentration in glutenin polymers increased up to 143 ± 6 g/L (at 9 °C) and then stopped to evolve, suggesting that the binodal line intersected the gelation line below this temperature. Applying the Flory-Huggins (FH) lattice model for each gluten protein classes, we demonstrated that their partitioning in the coexisting phases followed a same temperature dependency. However, some gliadin species joined the rich phase above their critical temperature. Here, specific interactions with the glutenin polymers through weak forces were exemplified. The study demonstrated the relevance of the Flory-Huggins (FH) lattice model in predicting phase behavior even when applied to complex protein mixtures.

Efficient Design to Monitor the Site‐specific Sustained Release of a Non‐Emissive Anticancer Drug

A pH-responsive smart nanocarrier with significant components was synthesized by conjugating the non-emissive anticancer drug methyl orange and polyethylene glycol derived folate moiety to the backbone of polynorbornene. Complete synthesis procedure and characterization methods of three monomers included in the work: norbornene-derived Chlorambucil (Monomer 1), norbornene grafted with polyethylene glycol, and folic acid (Monomer 2) and norbornene attached methyl orange (Monomer 3) connected to the norbornene backbone through ester linkage were clearly discussed. Finally, the random copolymer CHO PEG FOL METH was synthesized by ring-opening metathesis polymerization (ROMP) using Grubbs' second-generation catalyst. Advanced polymer chromatography (APC) was used to find the final polymer's molecular weight and polydispersity index (PDI). Dynamic light scattering, scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were utilized to explore the prodrug's size and morphology. Release experiments of the anticancer drug, Chlorambucil and the coloring agent, methyl orange, were performed at different pH and time. Cell viability assay was carried out for determining the rate of survived cells, followed by the treatment of our final polymer named CHO PEG FOL METH.

Dynamics and stress relaxation of bidisperse polymer melts with unentangled and moderately entangled chains

Polydispersity is inevitable in industrially produced polymers. Established theories of polymer dynamics and rheology, however, were mostly built on monodisperse linear polymers. Dynamics of polydisperse polymers is yet to be fully explored—specifically how chains of different lengths affect the dynamics of one another in a mixture. This study explored the dynamics of bidisperse polymer melts using molecular dynamics and a bead–spring chain model. Binary mixtures between a moderately entangled long-chain species and an unentangled or marginally entangled short-chain species were investigated. We found that adding short chains can significantly accelerate the dynamics of the long chains by substantially lessening their extent of entanglement. Meanwhile, although introducing long chains also hinders the motion of the short chains, it does not qualitatively alter the nature of their dynamics—unentangled short chains still follow classical Rouse dynamics even in a matrix containing entangled chains. Detailed Rouse mode analysis was used to reveal the effects of entanglement at chain segments of different scales. Stress relaxation following a step shear strain was also studied, and semi-empirical mixing rules that predict the linear viscoelasticity of polydisperse polymers based on that of monodisperse systems were evaluated with simulation results.

Recovery of Polyhydroxyalkanoates From Single and Mixed Microbial Cultures: A Review.

An overview of the main polyhydroxyalkanoates (PHA) recovery methods is here reported, by considering the kind of PHA-producing bacteria (single bacterial strains or mixed microbial cultures) and the chemico-physical characteristics of the extracted polymer (molecular weight and polydispersity index). Several recovery approaches are presented and categorized in two main strategies: PHA recovery with solvents (halogenated solvents, alkanes, alcohols, esters, carbonates and ketones) and PHA recovery by cellular lysis (with oxidants, acid and alkaline compounds, surfactants and enzymes). Comparative evaluations based on the recovery, purity and molecular weight of the recovered polymers as well as on the potential sustainability of the different approaches are here presented.

Calculation of molecular weight distribution using extended Cole-Cole model and quadratic mixing rule

We suggest a numerical method to calculate molecular weight distribution from linear viscoelastic data. The calculation method consists of three components: (1) a viscoelastic model of a monodisperse polymer as a function of molecular weight; (2) the mixing rule connecting viscoelastic data of monodisperse and polydisperse polymers through molecular weight distribution; (3) an algorithm which calculates the molecular weight distribution from the chosen mixing rule. Since we cannot measure the relaxation modulus of all monodisperse samples, we need an accurate monodisperse model for any molecular weight. It is known that a dynamic test is more reliable than a relaxation test, while the mixing rule needs relaxation modulus. Hence, we should have a smart numerical method that can convert dynamic data to relaxation modulus with the minimum conversion error. If we use the numerical method, then we have to generate numerical data from the model. Then it takes quite a long time. On the other hand, if we have a monodisperse model with the analytical relaxation spectrum, then calculation time can be reduced dramatically. Since the conversion from relaxation modulus to dynamic modulus suffers from smaller errors than the reverse conversion because of ill-posedness of the interconversion, the analytical conversion can be implemented more quickly at an acceptable level of errors. This paper proposes a new method satisfying the requirements.

Strategy for reducing molecular ensemble size for efficient rheological modeling of commercial polymers

We develop a method for efficient prediction of linear and nonlinear rheology of polydisperse polymers by judicious selection of a small number of representative polymer molecules from the large ensemble of chains comprising the molecular weight and branching distribution. Specifically, we use a numerical inversion of the double reptation model to select five or six representative molecular species to optimally fit the linear rheology of commercial polymers and then use the regressed parameters to compute the nonlinear rheology via the Rolie-double-poly (RDP) model. The method is tested for several model systems, namely, two polydisperse linear polystyrene (PS) samples described in Shivokhin et al. [Polym. Eng. Sci. 56, 1012–1020 (2016)] and Munstedt [J. Rheol. 24, 847–867 (1980)], a commercial linear low density polyethylene (LLDPE), and a low density polyethylene (LDPE) whose rheological properties are measured in the current study. For the linear polymers including the PS samples and the LLDPE, the predictions of the “representative” RDP model of the start-up extensional rheology are comparable to those of the “full” RDP model based on all the species drawn from the gas permeation chromatography characterization. The method then successfully predicts the linear rheology of blends of LLDPE and LDPE using the same representative molecules found by fitting each of the pure polymers. Further fitting the extensional rheology of the LDPE requires using the “priorities” q i and stretch relaxation times τ s , i of the representative molecules as adjustable parameters, whose values are then held fixed when predicting the extensional rheology of blends of the LDPE with the LLDPE roughly as successfully as does branch-on-branch model. The reduction in the number of representative polymer species offers new opportunities for faster simulations of flowing polymers, as well as for the prediction of segmental orientation to be used in the modeling of flow-induced crystallization.

Shear induced demixing in bidisperse and polydisperse polymer blends: Predictions from a multifluid model

In light of recent advancements in the constitutive modelling of bidisperse and polydisperse entangled linear polymers, we present a new multi fluid generalization of the classic two fluid approximation for flows of inhomogeneous polymer blends. As an application of the model, we consider predictions for the linear and nonlinear dynamics of shear induced demixing (SID) instabilities in blends with bidisperse and lognormal molecular weight distributions. We find that even in the absence of any chemical contrast between component chains, an imposed flow can induce a demixing instability provided there is sufficient contrast in the size of the two chains. The lower bound polydispersity for SID coincides with the point where elastic forces (kT per entanglement) scaled by the contrast between chains (e.g. polydispersity index minus one) exceed the entropic forces for mixing (kT per chain). For bi-disperse blends, we show that the non-linear dynamics of SID strongly resemble what has previously been shown for SID in entangled polymer solutions.

Polymer Chains of a Large Persistence Length in a Polymer Brush Require a Lower Force to Be Compressed Than Chains with a Short Persistence Length

The force on a polydisperse polymer brush with chains of increasing persistence length, LP, is obtained by numerical simulations. Unexpectedly, the force needed to compress a stiff brush is smaller...

Long-Range Ordered Water Correlations between A–T/C–G Nucleotides

Summary The interactions between complementary base pairs are crucial to the helical duplex structure of DNA. Although base-base interactions have been widely reported, the study of long-range interactions in the base-pairing processes is still a major challenge in this field. Here, we first study the long-range interactions between the base pairs by atomic force microscopy-based single-molecule force spectroscopy (SMFS). The SMFS results of A–T/C–G imply that there are weak long-range interactions between them, which have a range of 15–25 nm. Raman spectroscopy results imply that these weak interactions can be attributed to multiplex hydrogen bond interaction of ordered water structure between A–T/C–G nucleotides. In addition, the theoretical calculations deduce that the ideal structure of these water molecules exhibits a specific helical structure. Our findings might open up a new understanding of biological assembly processes and provide helpful strategies for bio-nanotechnology.

Flow-induced fractionation effects on slip of polydisperse polymer melts

The slip behavior of several high-density polyethylenes with a broad range of molecular weights (MWs) including bimodal is studied as a function of MW and its distribution (MWD). A formulation inspired by the reptation theory is used to predict the slip velocity of the studied polymers as a function of MWD coupled with a model of surface MW fractionation that includes (i) the entropy driven migration of short chains toward the die wall due to the concentration gradient and (ii) the flow (stress)-induced migration effects. While surface fractionation has a minor effect on slip of narrow to moderate MWD polymers (particularly unimodal), its role is significant for broad bimodal MWD polymers. The inclusion of both effects (concentration and flow gradients) accurately captures the slip velocity of broad MWD polymers.

How Many Monodisperse Fractions are Required to Discretize Polydisperse Polymers?

AbstractThe linear viscoelasticity of polydisperse samples and their discretization into a blend of nf monodisperse fractions is compared. The molecular weight distribution of the polydisperse sample is described using a lognormal distribution, which has two parameters that are related to the weight‐averaged molecular weight, Zw, and the polydispersity index, ρ. Due to its success on similar systems, a variant of the double reptation model is used to describe the linear rheology. Given Zw and ρ, the optimal number of monodisperse fractions is obtained using the Bayesian information criterion. It quantifies and negotiates the tradeoff between accuracy (discrepancy with the response of the polydisperse sample) and complexity (number of fractions). The optimal number of fractions was found to be somewhat insensitive to Zw; however, it increased with ρ from about 6 for ρ = 1.01 to about 20 for ρ = 2.0. Changing the underlying viscoelastic model had only a weak effect on the conclusions. Furthermore, using a blend of monodisperse fractions was found to be preferable to direct sampling even when an ensemble of chains was requested.

Size-Selective Catalytic Polymer Acylation with a Molecular Tetrahedron

Selective catalysis at the molecular level represents a cornerstone of chemical synthesis. However, it still remains an open question how to elevate tunable catalysis to larger length scales to functionalize whole polymer chains in a selective manner. We now report a hydrazone-linked tetrahedron with wide openings, which acts as a catalyst to size-selectively functionalize polydisperse polymer mixtures. Our experimental and computational evidence supports a dual role of the hydrazone-linked tetrahedron. To accelerate functionalization of the polymer substrates, the tetrahedron (i) unfolds the polymer substrates and/or breaks the polymer aggregates as well as (ii) enables target sites (amino groups) on the polymers to coordinate with catalytic units (triglyme) attached to the tetrahedron. With the tetrahedron as the catalyst, we find that the reactivity of the shorter polymers increases selectively. Our findings enable the possibility to engineer hydrolytically stable molecular polyhedra as organocatalysts for size-selective polymer modification.

Elucidating the 1H NMR Relaxation Mechanism in Polydisperse Polymers and Bitumen Using Measurements, MD Simulations, and Models.

The mechanism behind the 1H nuclear magnetic resonance (NMR) frequency dependence of T1 and the viscosity dependence of T2 for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an extended range of frequencies (f0 = 0.01-400 MHz) and viscosities (η = 385-102 000 cP) using T1 and T2 in static fields, T1 field-cycling relaxometry, and T1ρ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times T1LM ∝ f0 and T2LM ∝ (η/T)-1/2 with a phenomenological model of 1H-1H dipole-dipole relaxation, which includes a distribution in molecular correlation times and internal motions of the nonrigid polymer branches. We show that the model also accounts for the anomalous T1LM and T2LM in previously reported bitumen measurements. We find that molecular dynamics (MD) simulations of the T1 ∝ f0 dispersion and T2 of similar polymers simulated over a range of viscosities (η = 1-1000 cP) are in good agreement with measurements and the model. The T1 ∝ f0 dispersion at high viscosities agrees with previously reported MD simulations of heptane confined in a polymer matrix, which suggests a common NMR relaxation mechanism between viscous polydisperse fluids and fluids under nanoconfinement, without the need to invoke paramagnetism.

Critical Role of Confinement in the NMR Surface Relaxation and Diffusion of n-Heptane in a Polymer Matrix Revealed by MD Simulations.

The mechanism behind the NMR surface-relaxation times (T1S,2S) and the large T1S/T2S ratio of light hydrocarbons confined in the nanopores of kerogen remains poorly understood and consequently has engendered much debate. Toward bringing a molecular-scale resolution to this problem, we present molecular dynamics (MD) simulations of 1H NMR relaxation and diffusion of n-heptane in a polymer matrix. The high-viscosity polymer is a model for kerogen and bitumen that provides an organic "surface" for heptane. Diffusion of n-heptane shows a power-law dependence on the concentration of n-heptane (ϕC7) in the polymer matrix, consistent with Archie's model of tortuosity. We calculate the autocorrelation function G(t) for 1H-1H dipole-dipole interactions of n-heptane in the polymer matrix and use this to generate the NMR frequency (f0) dependence of T1S,2S as a function of ϕC7. We find that increasing molecular confinement increases the correlation time, which decreases the surface-relaxation times for n-heptane in the polymer matrix. For weak confinement (ϕC7 > 50 vol %), we find that T1S/T2S ≃ 1. Under strong confinement (ϕC7 ≲ 50 vol %), we find that T1S/T2S ≳ 4 increases with decreasing ϕC7 and that the dispersion relation T1S ∝ f0 is consistent with previously reported measurements of polydisperse polymers and bitumen. Such frequency dependence in bitumen has been previously attributed to paramagnetism; instead, our studies suggests that 1H-1H dipole-dipole interactions enhanced by organic nanopore confinement dominate the NMR response in saturated organic-rich shales.