Statistical Segment Length Research Articles

Nanostructured Block Polymer Electrolytes: Tailoring Self-Assembly to Unlock the Potential in Lithium-Ion Batteries.

ConspectusIon-containing solid block polymer (BP) electrolytes can self-assemble into microphase-separated domains to facilitate the independent optimization of ion conduction and mechanical stability; this assembly behavior has the potential to improve the functionality and safety of lithium-ion batteries over liquid electrolytes to meet future demands (e.g., large capacities and long lifetimes) in various applications. However, significant enhancements in the ionic conductivity and processability of BPs must be realized for BP-based electrolytes to become robust alternatives in commercial devices. Toward this end, the controlled modification of BP electrolytes' intra-domain (nanometer-scale) and multi-grain (micrometer-scale) structure is one viable approach; intra-domain ion transport and segmental compatibility (related to the effective Flory-Huggins parameter, χeff) can be increased by tuning the ion and monomer-segment distributions, and the morphology can be selected such that the multi-grain transport is less sensitive to grain size and orientation.To highlight the characteristics of intra-domain structure that promote efficient ion transport, this Account begins by describing the relationship between BP thermodynamics (namely, χeff and the statistical segment length, b, which is indicative of chain stiffness) and local ion concentration. These thermodynamic insights are vital because they inform the selection of synthesis and formulation variables, such as polymer and ion chemistry, polymer molecular weight and composition, and ion concentration, which boost electrolyte performance. In addition to its relationship with local ion transport, χeff is also an important factor with respect to electrolyte processability. For example, a reduced χeff can allow BP electrolytes to be processed at lower temperatures (i.e., lower energy input), with less solvent (i.e., reduced waste), and/or for shorter times (i.e., higher throughput) yet still form desired nanostructures. This Account also examines the impact of electrolyte preparation and processing on the ion transport across nanostructured grains because of grain size and orientation. As morphologies with a 3D-connected versus 2D-connected conducting phase show different sensitivities to conductivity losses that can occur because of the fabrication methods, it is necessary to account for electrolyte processing effects when probing ion transport.The intra-domain and micrometer-scale structure also can be tuned using either tapered BPs (macromolecules with modified monomer-segment composition profiles between two homogeneous blocks) or blends of BPs and homopolymers, independent of the BP molecular weight and composition, as detailed herein. The application of TBPs or BP/HP blends as ion-conducting materials leads to improved ion transport, reduced χeff, and greater availability of morphologies with 3D connectivity relative to traditional (non-tapered and unblended) BP electrolytes. This feature results from the fact that ion transport is related more closely to the monomer-segment distributions within a domain than the overall nanoscale morphology or average polymer/ion mobilities. Taken together, this Account describes how ion transport and processability are influenced by BP architecture and nanostructural features, and it provides avenues to tune nanoassemblies that can contribute to improved lithium-ion battery technologies to meet future demands.

Sub-Rouse Dynamics in Poly(isobutylene) as a Function of Molar Mass

We report on the molar mass dependence of the segmental, sub-Rouse, and terminal relaxation processes of poly(isobutylene). For this purpose, seven samples were synthesized with molar masses in the range from 2.8 to 172 kg·mol–1 and investigated by temperature-modulated differential scanning calorimetry, dielectric spectroscopy, and rheology. Rheology provided access to the terminal times that were found to scale as τterm ∼ Μ3.2. On the other hand, the sub-Rouse dielectric process shows a very weak molar mass dependence (τsub – Rouse/τSM ∼ M0.1), that is, distinctly different from the Rouse and terminal dynamics. We infer that the sub-Rouse mode has a lengthscale intermediate to the statistical segment length (∼1.25 nm) and the length of an entanglement strand (∼2.3 nm).

Estimating effective permeability using connectivity and branch length distribution of fracture network

In this study, a new approach to estimate the effective permeability of the fracture network is proposed. New functional expressions are derived considering laminar fluid flow through fracture networks. Effective permeability of the fracture network is expressed as a function of topological connectivity, statistical branch segment length distributions, maximum, and minimum branch segment lengths. It is observed that the statistical cumulative branch segment length distribution of fracture networks can follow both fractal and multi-fractal patterns. Hence, analytical expressions of effective permeability are proposed considering both fractal and multi-fractal distribution of branch segment lengths. Obtained expressions are validated using numerical simulation results from past studies. It is observed from derived expressions that, effective permeability of fracture networks increases non-linearly with increasing topological connectivity and fractal dimensions of statistical branch segment length distributions. However, the non-linearity in the relationship is mainly governed by the scaling exponent and scaling coefficient of the fracture network. With increasing scaling exponent and scaling coefficient, non-linearity in the relation between effective permeability and topological connectivity increases. It is observed from the derived relation that, effective permeability of a fracture network is more sensitive to longer branch segments compared to the shorter branch segments. Effective permeability of fracture networks increases rapidly with increase in length of the branch segments. Hence it is interpreted, longer branch segments in fracture networks play a critical role in determining the effective permeability of the fractured reservoir.

Synthesis and Self-Assembly of ABn Miktoarm Star Polymers

The stability of tetrahedrally close-packed (TCP) phases in block copolymer melts is predicted by theory to depend on molecular architecture, yet no experimental studies to date have probed its effect. Motivated by this open question, here we report an efficient synthesis of asymmetric ABn miktoarm star polymers using functionalized sugars as cores for orthogonal grafting-from block copolymerizations. A combination of ring-opening and atom transfer radical polymerization produced model low dispersity materials comprising a single A = poly(lactide) (L) and multiple B = poly(dodecyl acrylate) (D) arms that amplify "conformational asymmetry" through two concerted effects: the mikto architecture and disparate block statistical segment lengths. Analyzing the self-assembly of LD2 and LD3 samples resulted in the discovery of two TCP phases, σ and A15, that remained stable to significantly higher A-block volume fractions as the number of B arms increased. These results experimentally establish the importance of conformational asymmetry and molecular architecture as powerful design tools for the self-assembly of block copolymers into nonclassical phases.

Dependence of reinforcement degree of nanocomposites polymer/carbon nanotubes on nanofi ller structure and molecular characteristics of polymer matrix

The possibility for simulation of carbon nanotubes structure in polymer matrix as complex reinforcing element, consisting of nanofiller and covered it interfacial layer is shown. It is concluded that size (radius) of annular formations of such complex element is determined by normalized content of interfacial regions or ability of nanofiller to generate interfacial regions. The change of phase state of polymer matrix from glassy to rubber-like one leads to change of its molecular characteristics, namely, the length of statistical segment of polymer chain. The qualitative jump in reinforcement degree of nanocomposites is realized at transition from closed annular formations of carbon nanotubes to open (circular arc) one.

Investigating the Effect of Added Salt on the Chain Dimensions of Poly(ethylene oxide) through Small-Angle Neutron Scattering

We have measured the effect of added salt on the chain dimensions of mixtures of poly(ethylene oxide) (PEO) and lithium bis(trifluoromethanesulfonyl)imide salt (LiTFSI) in the melt state through small-angle neutron scattering (SANS) experiments. Scattering profiles from blends of hydrogenated and deuterated PEO mixed with LiTFSI were measured as a function of salt concentration. Scattering profiles from pure deuterated PEO/LiTFSI mixtures were used for background-subtraction purposes. The densities of PEO/LiTFSI mixtures of varying salt concentrations were measured to calculate partial molar monomer volumes of PEO and LiTFSI to account for nonideal mixing. Kratky plots of the scattering profiles were used to calculate the salt concentration dependence of statistical segment length. At low salt concentrations, segment length decreases with increasing salt concentration, before increasing with increasing salt concentration in the high salt concentration regime. The random phase approximation was used to predict theoretical scattering profiles from the calculated segment lengths and partial molar volumes; there is excellent agreement between the theoretical and measured scattering profiles at all salt concentrations. There appears to be a correlation between chain dimensions and coordination between lithium ions and EO monomers. The scattering profiles of the pure deuterated PEO/LiTFSI mixtures suggested the presence of ion clusters of characteristic size of 0.6 nm at high salt concentrations.

Influence of Electrostatic Long-Range and Short-Range Effects on the Conformations of Flexible-Chain Linear Polyelectrolyte Macromolecules with Different Charge Density in Salt-Free Aqueous Solutions

A series of copolymers of N-methyl-N-vinylacetamide and N-methyl-N-vinylamine hydrochloride with an average content of charged groups of (4.4 ± 0.2) mol % and molecular mass in the range of 22 < M × 10–3, g/mol < 630 are synthesized and characterized. Fractions are studied by sedimentation-diffusion methods in 0.2 mol/L NaCl under almost suppressed polyelectrolyte effects. In salt-free aqueous solutions, their viscous flow is investigated and intrinsic viscosity is determined as [η] ≡ lim(∂lnηr/∂c) at c → 0. The results are compared with the previous data obtained for the copolymer containing (15.7 ± 0.5) mol % of charged groups and the homopolymer. It is shown that the type of intrinsic viscosity dependence on the molecular mass of the copolymer containing 4.4 mol % of charged groups is typical of chains manifesting intrachain volume interactions, while at a 15.7 mol % content of charged groups the type of the dependence is characteristic of chains demonstrating intrachain short-range effects; hence, the chains behave as rigid-chain, permeable. The statistical segment lengths of copolymer macromolecules in salt-free solutions and in 0.2 mol/L NaCl are determined. The data are analyzed in terms of the normalized Kuhn–Mark–Houwink–Sakurada relation.

Effects of Segment Length Asymmetry in Ternary Diblock Co-polymer–Homopolymer Mixtures

Self-consistent field theory is used to study the effect of asymmetry between A and B statistical segment lengths on interfacial properties and phase behavior in ternary mixtures of AB diblock co-p...

Small Angle Neutron Scattering Study of the Thermodynamics of Highly Interacting PαMSAN/dPMMA Blends

Poly(methyl methacrylate) (PMMA) and poly(α-methylstyrene-co-acrylonitrile) (PαMSAN) form partially miscible blends with lower critical solution temperature (LCST) behavior. We revisit this system using small angle neutron scattering (SANS), examining the effect of molecular weight (Mw) of deuterated PMMA (dPMMA), blend composition (ϕ), and temperature (T) in the homogeneous region. All data are well-described by the Random Phase Approximation (RPA) theory, enabling us to determine thermodynamic and structural parameters, including the correlation length ξ, G″ (the second derivative of the free energy of mixing with respect to composition), and the statistical segment length a of each component. Phase boundaries are computed by extrapolation of G″ with temperature, to yield the spinodal, and inspection of Kratky plots to yield the binodal. For PαMSAN, a is determined to be 10.1 ± 0.4 A. Unsurprisingly, this system deviates strongly from Flory–Huggins expectations, exhibiting a minimal Mw dependence of the...

Multi-resolution polymer Brownian dynamics with hydrodynamic interactions

A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. A Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale approach, a modeller can efficiently look at different regions of the polymer in different spatial and temporal resolutions with scalings given for the number of beads, statistical segment length, and bead radius in order to maintain macro-scale properties of the polymer filament. The Boltzmann distribution of a Gaussian chain for differing statistical segment lengths gives a diffusive displacement equation for the multi-resolution model with a mobility tensor for different bead sizes. Using the pre-averaging approximation, the translational diffusion coefficient is obtained as a function of the inverse of a matrix and then in closed form in the long-chain limit. This is then confirmed with numerical experiments.

Solution Properties of Polysarcosine: From Absolute and Relative Molar Mass Determinations to Complement Activation

Polysarcosine (pSar) was one of the first polymers synthesized in a controlled living manner, but it was only recently when it was reconsidered as a promising alternative for poly(ethylene glycol) (PEG) in biomedical applications. Despite receiving more and more attention, very little is known about the solution properties of pSar, such as coil dimensions and thermodynamic interactions. In this article, we report on these properties of pSar with degrees of polymerization 50 < Xn < 400 that were prepared by controlled living ring-opening polymerization. The polymers are characterized by gel permeation chromatography (GPC), MALDI-TOF mass spectrometry, dynamic and static light scattering (SLS), and viscometry. The chain stiffness of pSar in PBS in terms of the Kuhn statistical segment length, lk, was estimated to lk = 1.5 nm by application of the Yamakawa–Fujii wormlike chain theory to the experimentally determined hydrodynamic radii, Rh, thus being higher than lk = 1.1 nm for PEG in PBS. Also, the second v...

Testing the Universality of Entropic Segregation at Polymer Surfaces

This study addresses entropic segregation effects at the surfaces of monodisperse and bidisperse melts. For the monodisperse melts, we focus on the segregation of chain ends to the surface, and for the bidisperse melts, we examine the segregation of short polymers to the surface. Universal shapes have been predicted for their concentration profiles, but the derivations rely on the mean-field approximation, which only treats the excluded-volume interactions in an approximate manner. To test whether or not the predictions hold up when the polymers are rigorously prevented from overlapping, we compare mean-field calculations with Monte Carlo simulations performed on the exact same model. Apart from a significant increase in the statistical segment length, the rigorous enforcement of excluded-volume interactions has a relatively small effect on the mean-field predictions. In particular, the universal profiles predicted by mean-field theory are found to be accurate.

The Statistical Segment Length of DNA: Opportunities for Biomechanical Modeling in Polymer Physics and Next-Generation Genomics.

The development of bright bisintercalating dyes for deoxyribonucleic acid (DNA) in the 1990s, most notably YOYO-1, revolutionized the field of polymer physics in the ensuing years. These dyes, in conjunction with modern molecular biology techniques, permit the facile observation of polymer dynamics via fluorescence microscopy and thus direct tests of different theories of polymer dynamics. At the same time, they have played a key role in advancing an emerging next-generation method known as genome mapping in nanochannels. The effect of intercalation on the bending energy of DNA as embodied by a change in its statistical segment length (or, alternatively, its persistence length) has been the subject of significant controversy. The precise value of the statistical segment length is critical for the proper interpretation of polymer physics experiments and controls the phenomena underlying the aforementioned genomics technology. In this perspective, we briefly review the model of DNA as a wormlike chain and a trio of methods (light scattering, optical or magnetic tweezers, and atomic force microscopy (AFM)) that have been used to determine the statistical segment length of DNA. We then outline the disagreement in the literature over the role of bisintercalation on the bending energy of DNA, and how a multiscale biomechanical approach could provide an important model for this scientifically and technologically relevant problem.

Molecular Structure, Chain Dimensions, and Linear Rheology of Poly(4-vinylbiphenyl)

The linear viscoelasticity and molecular structure of a series of poly(4-vinylbiphenyl) (PVBP) samples with polydispersities ranging from 1.08 to 2.75 are investigated using wide-angle X-ray scattering (WAXS), small-angle neutron scattering (SANS), and rheological measurements. PVBP chain dimensions, such as statistical segment length, persistence length, and packing length, are obtained from SANS measurements. Because of the bulkiness of the biphenyl monomer, PVBP has the lowest chain flexibility and the largest reptation tube diameter among most common thermoplastics, including polystyrene and polyvinylcyclohexane. Nevertheless, PVBP follows the universal power law dependence between elastic modulus and packing length (GN0 ∝ p–3). X-ray diffraction of PVBP consist of two main amorphous peaks: one associated with the interchain (backbone) correlations and a second one arising from phenyl–phenyl correlations. The latter are due to π–π stacking of the phenyl rings, mostly arranged in the T-shaped configura...

Toughened Isotactic Polypropylene: Phase Behavior and Mechanical Properties of Blends with Strategically Designed Random Copolymer Modifiers

A series of poly(cyclohexylethylene-ran-ethylene) (CE) copolymers were synthesized with statistical segment lengths designed to match that of isotactic poly(propylene) (iPP). Melt blending the CE compounds containing 50–70 wt % cyclohexylethylene repeat units with iPP at loadings between 5 and 20 wt % resulted in a dispersion of CE droplets with number-average diameters between 150 and 500 nm as determined by scanning electron microscopy. Linear dynamic mechanical elastic (G′) and loss (G″) moduli data were fit to the Palierne model providing estimates for the interfacial tension between iPP and CE, which was interpreted based on enthalpic (χH) and entropic (χS) contributions to the overall segment–segment interaction parameter, χ = χH + χS, attributed to density and statistical segment length differences, respectively. The small particle sizes are explained by a reduced interfacial tension, driven by minimization of χS (≈0), counterbalanced by χH > 0, establishing an optimal balance between phase separat...

Anti-HIV Activities of Precisely Defined, Semirigid, Carboxylated Alternating Copolymers

Di-tert-butyl (E)-4,4'-stilbenedicarboxylate and tert-butyl 4-vinylbenzoate were copolymerized with maleic anhydride and tert-butyl 4-maleimidobenzoate, individually and respectively. After conversion into polyanions, these four copolymers exhibited activity against four HIV-1 strains: IIIb, BaL, JR-CSF, and 92UG037. For both the IIIb and BaL HIV-1 strains, the lowest IC50 (0.095 and 0.23 μg/mL, respectively) values were obtained with poly(4,4'-stilbenedicarboxylate-alt-maleic acid) (DCSti-alt-MA). For JR-CSF and 92UG037, both tier 2 clinical isolates but different clades, DCSti-alt-MA exhibited the lowest IC50 (0.76 and 0.75 μg/mL, respectively). Although DCSti-alt-MA had the lowest IC50 in μg/mL for each strain, the other copolymers had IC50s less than 2-fold higher. Further, these copolymers achieved high selectivity indices (>100) for these clinical isolates. Polymer rigidity, as measured by the statistical segment length, emerged as a key property when comparing anti-HIV activities with those of other polyanions. A speculative illustration was proposed for possible modes of inhibition.

Conformational and dynamic characteristics of copolymers of N,N-dimethylaminoethyl methacrylate and 2-deoxy-2-methacrylamido-D-glucose

The conformational and relaxation properties of N,N-dimethylaminoethyl methacrylate and 2-deoxy-2-methacrylamido-D-glucose copolymers in solutions are studied by the methods of molecular hydrodynamics (sedimentation, diffusion, viscometry), polarized luminescence, and flow birefringence. Kuhn-Mark-Houwink equations are obtained, and Kuhn statistical segment lengths at various degrees of protonation of amino groups are estimated. It is found that there is a correlation between the Kuhn statistical segment length and the intramolecular mobility of the copolymers.

Strong Linear Polyelectrolytes in Solutions of Extreme Concentrations of One–One Valent Salt. Hydrodynamic Study

Two series of highly charged linear aliphatic polymers—sodium polystyrene-4-sulfonate and random copolymer of N-methyl-N-vinylacetamide and N-methyl-N-vinylamine hydrochloride—were studied in water solution without added salts and in solutions containing up to 5 M NaCl. Intrinsic viscosity in salt-free solutions was estimated by a method proposed earlier [Pavlov et al. Russ. J. Appl. Chem. 2006, 79, 1407–1412]. Molecular characteristics were obtained in 0.2 M NaCl. The polyelectrolytes were studied in more than 10-fold range of molar mass. Qualitatively, the conformational status of the polyelectrolyte chains in different ionic strength was defined with the Kuhn–Mark–Houwink–Sakurada plots normalized by the value of linear chain density. In salt-free solution both polyelectrolytes could be attributed to extra rigid chains with the statistical segment length of 650 nm for sodium polystyrene-4-sulfonate and 100 nm for copolymer chains. Such statistical segment lengths are provided by short-range electrostatic intrachain interactions and are comparable with the Debye screening length. At extremely high NaCl concentration polyelectrolyte chains became discriminated by their degree of hydrophobicity. Chains of hydrophobic nature are compacted up to preglobular state, whereas the chains of the hydrophilic nature stay in the conformation of swelling coils at the highest concentration of NaCl.

Birefringence in triphenylamine-containing polyheteroarylene films

When a polarized ray is obliquely incident on a film, rotating the film around an axis perpendicular to its surface results in birefringence (BR), which has been studied in a previous paper. Surface BR in triphenylamine-containing polyheteroarylene films has been investigated as a function of the angle of incidence of the light and the film thickness. The results made it possible to estimate the orientational-order parameter of fragments of the macromolecules in the near-surface layers, as well as to estimate the statistical segment length of the polyheteroarylene chains.

Entropy-driven segregation of nanoparticles in polymer melts

We present a Monte Carlo study of the dispersibility of nanoparticles in polymer melts based on the relative entropic contributions of particles and polymer chains. Our model predictions are in terms of the particle diameter d and the chain statistical segment length ℓ. In the limit of small (d=ℓ) particles, a good dispersion is predicted, as the high entropy contribution of the small particles largely offsets the loss in polymer chain entropy. This is not the case, however, at larger d ≈ 3ℓ and particle segregation at the surfaces of thin polymer films is observed. That model prediction is in good agreement with experimental observation for systems with little or no enthalpic interaction between polymer and particles.