Block Length Distribution Research Articles

Block length distribution, morphology, and property of thermoplastic polyurethanes affected by production method: A polymer‐by‐process investigation

AbstractTwo thermoplastic polyurethanes (TPUs) based on the same monomers and composition were produced by two different production methods – hand mix batch process and continuous band casting. The soft segment was poly(hydrofuran) (PTHF) with a molar mass of 1000 and the hard segment was made of 1,4‐butanediol (BD) and 4,4′‐methylene diphenyl diisocyanate (MDI). The hard segment content amounted to 42%. The distinctions in crystallization and thermal behavior and mechanical properties of the two TPUs were ascribed to differences in the hard and soft block length distribution caused by the different production methods. Using thermal fractionation – a series of successive self‐nucleation and annealing steps – the minor differences in hard block length distribution could be shown and quantified. The length distribution of the hard and soft blocks of the machine‐produced sample was narrower than that of the hand‐cast sample. The former with the narrow block distribution showed thicker and mechanically and thermally more stable hard domains. The more uniform block length distribution facilitated crystallization and resulted in improved tensile recovery behavior and elasticity. The second with the broader distribution, however, showed the highest tensile strength at break, which was ascribed to an improved strain‐induced hardening of the soft phase.

Molecular Architecture of Multiblock Copolymers Synthesized by the Chain Shuttling Technology

AbstractRecent advances in the characterization of ethylene/1‐octene‐based statistical multiblock copolymers (MBCs) synthesized via chain shuttling copolymerization are illustrated. The Perspective focuses on the peculiarity of MBC systems that consists in the nonuniform chain architecture of these intriguing systems due to compositional heterogeneity occurring at inter‐ and intra‐chain level. In the first part, the effect of dispersity on the phase behavior and properties of MBCs and block copolymers in general is discussed along with the consequences of crystallization of one of the blocks on microphase separation, domain spacing, and morphology. In the second part, the main results achieved in the elucidation of details of the chain microstructure in terms of average length of the blocks and block length distribution are presented. It is shown that solvent and thermal fractionation techniques, coupled with other techniques such as transmission electron microscopy (TEM) and small angle X‐ray scattering (SAXS) represent powerful tools to elucidate the inter‐ and intra‐chain heterogeneous composition of the MBCs. Guidelines on how to establish structure/properties relationships for such polydisperse systems are also provided.

Principles and potential of solvent gradient size-exclusion chromatography for polymer analysis

The properties of a polymeric material are influenced by its underlying molecular distributions, including the molecular-weight (MWD), chemical-composition (CCD), and/or block-length (BLD) distributions. Gradient-elution liquid chromatography (LC) is commonly used to determine the CCD. Due to the limited solubility of polymers, samples are often dissolved in strong solvents. Upon injection of the sample, such solvents may lead to broadened or poorly shaped peaks and, in unfavourable cases, to “breakthrough” phenomena, where a part of the sample travels through the column unretained. To remedy this, a technique called size-exclusion-chromatography gradients or gradient size-exclusion chromatography (gSEC) was developed in 2011. In this work, we aim to further explore the potential of gSEC for the analysis of the CCD, also in comparison with conventional gradient-elution reversed-phase LC, which in this work corresponded to gradient-elution reversed-phase liquid chromatography (RPLC). The influence of the mobile-phase composition, the pore size of the stationary-phase particles, and the column temperature were investigated. The separation of five styrene/ethyl acrylate copolymers was studied with one-dimensional RPLC and gSEC. RPLC was shown to lead to a more-accurate CCD in shorter analysis time. The separation of five styrene/methyl methacrylate copolymers was also explored using comprehensive two-dimensional (2D) LC involving gSEC, i.e. SEC × gSEC and SEC × RPLC. In 2D-LC, the use of gSEC was especially advantageous as no breakthrough could occur.

Sequence distribution determination by SWAMP‐MS a systematic way of analyzing multiple fragmented polymers with mass spectrometry

AbstractA new method to determine the blockiness and especially the block length distribution (BLD) of copolymers is described. This Systematic Workflow to Analyze Multi‐fragmented Polymers with Mass Spectrometry (SWAMP‐MS) is developed to characterize the sequence distribution of synthetic polymers. Copolymerization of polyamide 4,6 and polyamide 4,10 is used as a model system. Supercharged polymer ions, generated by electrospray ionization, swamp the mass spectrum due to <1> different chemical related distributions (chain composition, end groups), <2> the number of repeating units, <3> the charge and adduct distribution, and <4> isotopes distribution. Without selecting specific substrate ions, MSMS will transform this total ion‐SWAMP into chemical rich information of the polymer backbone. The generated fragments contain up to 20 monomers. The reduction of blockiness is evaluated by the decreasing abundancy of specific ions originating from the starting polymers. Moreover, evaluation of all significant fragments and applying Monte Carlo simulations can rebuild the polymer backbone and generate sequence distributions of the copolymerized samples, which is currently still a holy grail in co‐chemical polymer analysis.

Hard block length distribution of thermoplastic polyurethane determined by polymerization-induced phase separation

Three thermoplastic polyurethanes (TPUs) based on the same monomers and composition were produced in bulk by hand and machine casting methods. The soft segment was PTHF® 1000 and the hard segment was made of 1,4-butanediol and 4,4′-methylene diphenyl diisocyanate (MDI). The hard segment content amounted to 30%. The hand cast TPUs were prepared at 80 and 125 °C. The temperature conditions for the machine prepared sample were comparable to that of the hand casting process at 125 °C. The samples prepared at high temperature were transparent, whereas the sample produced at low temperature was translucent. The latter showed some crystallinity and in crystallization studies it crystallized more readily than the transparent samples. The distinctions in transparency and crystallization behavior were ascribed to differences in the hard block length distribution. Using thermal fractionation – a series of successive self-nucleation and annealing steps – the minor differences in hard block length distribution could be shown and quantified. The TPU synthesized at low temperatures possessed the longer hard blocks. These facilitated crystallization by enhancing nucleation and crystal growth. Superstructures, induced by the longer hard blocks, scattered visible light and reduced the transparency.

Testing for population decline using maximal linkage disequilibrium blocks

Only 6% of known species have a conservation status. Methods that assess conservation statuses are often based on individual counts and are thus too laborious to be generalized to all species. Population genomics methods that infer past variations in population size are easy to use but limited to the relatively distant past. Here we propose a population genomics approach that tests for recent population decline and may be used to assess species conservation statuses. More specifically, we study Maximal Recombination Free (MRF) blocks, that are segments of a sequence alignment inherited from a common ancestor without recombination. MRF blocks are relatively longer in small than in large populations. We use the distribution of MRF block lengths rescaled by their mean to test for recent population decline. However, because MRF blocks are difficult to detect, we also consider Maximal Linkage Disequilibrium (MLD) blocks, which are runs of single nucleotide polymorphisms compatible with a single tree. We develop a new method capable of inferring a very recent decline (e.g. with a detection power of 50% for populations whose size was halved to N, 0.05 ×N generations ago) from rescaled MLD block lengths. Our framework could serve as a basis for quantitative tools to assess conservation status in a wide range of species.

Mesoscopic Simulation of Dispersed Copolymers: Effects of Chain Length, Chemical Composition, and Block Length Distributions on Self‐Assembly

AbstractPolymer materials are normally constituted by chains of different sizes and compositions due to the stochastic nature of most polymerization mechanisms. For this reason, dissipative particle dynamics (DPD) simulations are carried out in the present work to investigate the effect of chain length distribution (CLD), chemical composition distribution (CCD), and block length distribution (BLD) on the process of self‐assembly of diblock copolymers. Flory and Poisson distributions are used to study CLD and BLD effects and bidispersed distributions are used for the study of CCD effects. Visual inspection and the static structure factor S(q) are used to evaluate the obtained structures. The results show that high dispersion in the CCD and different levels of dispersion in the BLDs of different components of the system increase the sizes of the segregated domains and decisively affect the structure and the purity of the formed mesophases.

Catalyst: Size Distribution in Self-Assembly Matters

Dafni Moatsou completed her PhD in chemistry at the University of Warwick in 2015, was a Marie Sklodowska-Curie fellow at the Adolphe Merkle Institute until 2017, and is a junior research group leader at the Karlsruhe Institute of Technology, where she focuses on sequence control and self-assembly of polymers. Rachel O’Reilly completed her PhD in 2003 at Imperial College London. She currently holds a chair in chemistry within the College of Engineering and Physical Sciences at the University of Birmingham. In August 2018 she became the head of the School of Chemistry. Her research targets the design, synthesis, and application of polymeric materials, where control over architecture, functionality, and reactivity are central to their application.

Low friction poly(amide-imide) coatings with silicones as tethered liquids

In the production of enamelled copper wires, coated with the high-performance polymer PAI (poly(amide-imide)), friction between multiple polymer surfaces as well as between the polymer and the slot substrate are significant issues. These effects drastically reduce the achievable packing density of the wires, which directly correlates to efficiency of the products. Conventional methods of lubrication involve use of leeching lubricants or addition of wax layers, which in return produces other problems. Moreover, the most potent lubricant PDMS cannot be used due to incompatibilities with the PAI matrix.A desirable solution for these issues is the covalent attachment of lubricating substances, ideally PDMS, to the PAI matrix. To achieve this, block copolymers from PAI and PDMS of different shapes and block length distributions were synthesized and cured as coatings. It was found that, depending on the specific type of block copolymer, friction can be drastically reduced by up to one order of magnitude. This effect was observed in lab scale experiments as well as in industrially produced enamelled copper wires.AFM investigations furthermore revealed a surface structure with distinct PDMS domains, which show liquid-like behavior as well as strong covalent binding to the matrix. Several parameters of the domains can be fine-tuned by variation of block copolymer parameters.

Efficient Search of Girth-Optimal QC-LDPC Codes

In this paper, we study the cycle structure of quasi-cyclic (QC) low-density parity-check (LDPC) codes with the goal of obtaining the shortest code with a given degree distribution and girth. We focus on QC-LDPC codes, whose Tanner graphs are cyclic liftings of fully connected base graphs of size 3 × n, n ≥ 4, and obtain minimal lifting degrees that result in girths 6 and 8. This is performed through an efficient exhaustive search, and as a result, we also find all the possible non-isomorphic codes with the same minimum block length, girth, and degree distribution. The exhaustive search, which is ordinarily a formidable task, is made possible by pruning the search space of many codes that are isomorphic to those previously examined in the search process. Many of the pruning techniques proposed in this paper are also applicable to QC-LDPC codes with base graphs other than the 3 × n fully connected ones discussed here, as well as to codes with a larger girth. To further demonstrate the effectiveness of the pruning techniques, we use them to search for QC-LDPC codes with girths 10 and 12, and find a number of such codes that have a shorter block length compared with the best known similar codes in the literature. In addition, motivated by the exhaustive search results, we tighten the lower bound on the block length of QC-LDPC codes of girth 6 constructed from fully connected 3 × n base graphs, and construct codes that achieve the lower bound for an arbitrary value of n ≥ 4.

A unified picture of hard-soft segmental development along olefin chain shuttling copolymerization

It is the dual nature of chain shuttling polymerization (CSP) that makes control of olefin block copolymer (OBC) composition difficult and difficult, but at the same time, stimulating. Although recent investigations on OBCs brought some insights to the kinetics and microstructure of block copolymers differentiating from ethylene and α-olefins, some crucial features of these systems are not uncovered because of experimental difficulties. Thus, attention is still placed upon theoretical concepts that enable deeper understanding of behavior of end-of-batch OBCs. Extending the predictability of a well-developed Monte Carlo algorithm, we present for the first time an explicit image of hard-soft segmental growth at the course of CSP process. The stochastically tailored ethylene/1-octene copolymers with diverse architectural characteristics were simulated and characterized in terms of mole fraction of soft and hard segments, block length distribution, sequence length distribution, longest ethylene sequence distribution, and the distribution of the number of blocks per growing copolymer chain to be used as unique signatures of this reaction mechanism.

Stable domain size and conformational segregation of short and long blocks during microphase separation in random block copolymers

In this Letter we use computer simulations and test microphase separation for AB-diblock copolymers with different block's statistics. We show that the domain size during microphase separation is stable only for the system with large enough polydispersity, namely with exponential (Flory-type) block length distribution. The reason for stable domain size is a conformational segregation of short and long blocks during the increase of the incompatibility in the system. While short blocks became elongated and occupy the surface of the interphase region, long blocks pushed out to the center of the domain and formed their compact conformations.

Thermal fractionation of vinyl acetate-vinyl alcohol copolymers

Thermal fractionation via the method of successive self-nucleation and annealing was used for the first time to study the crystallinity of vinyl acetate-vinyl alcohol copolymers with different random distributions of chain units. The lamella-thickness distribution was calculated through the Gibbs-Thomson equation. It was shown that, for all samples, the minimum lamella thickness is the same and corresponds to a block of no less than 15 vinyl alcohol units. On the basis of these data and with the use of the computer simulation of the polymer-analogous reaction via the Monte Carlo method, the block-length distribution in the crystalline phase was found. It was shown through a comparison of the lamella-thickness and block-length distributions that the maximum lamella thickness increases with the block length and vinyl alcohol content in the copolymer. In crystallites, blocks with lengths exceeding the maximum lamella thickness comprise a significant fraction. Thus, it is probable that these blocks form folds. The dependences of melting temperatures of crystalline lamellas on their thicknesses, as well as the dependences of the melting temperatures of copolymers not subjected to thermal fractionation on the chain-structure parameters, are adequately described by the Flory crystallization theory.

On-line fractionated size exclusion chromatography–nuclear magnetic resonance of polymers with 1H and 2H nuclear magnetic resonance detection

A new approach for on-line SEC–NMR is introduced. The method combines time slicing, fractionation with adjusted loop collection and automatic stop-flow NMR analysis. It will be called on-line fractionated SEC–NMR. This technique allows the precise determination of molar mass distributions for any polymer which can be detected by NMR. It is a significant improvement of sensitivity and accuracy compared to onflow SEC–NMR and exhibits a much easier experimental setup than off-line SEC–NMR fractionation. The new method was applied to protonated and deuterated block copolymers by using 1H NMR and for the first time also 2H NMR detection. In this case block copolymers can be correctly characterized according to their block length distributions. As the consequence very precise molar mass parameters Mn and Mw can be determined. The results of the on-line fractionated SEC–NMR are in very good agreement with the multi detector analysis. The new technique also proposes a method for separating the true copolymer and low molar mass fractions in the mixture, whose structures are confirmed by HPLC–FTIR and 2D chromatography.

Alginate Sequencing: An Analysis of Block Distribution in Alginates Using Specific Alginate Degrading Enzymes

Distribution and proportion of β-D-mannuronic and α-L-guluronic acid in alginates are important for understanding the chemical-physical properties of the polymer. The present state of art methods, which is based on NMR, provides a statistical description of alginates. In this work, a method was developed that also gives information of the distribution of block lengths of each of the three block types (M, G, and MG blocks). This was achieved using a combination of alginate lyases with different substrate specificities, including a novel lyase that specifically cleaves diguluronic acid linkages. Reaction products and isolated fragments of alginates degraded with these lyases were subsequently analyzed with (1)H NMR, HPAEC-PAD, and SEC-MALLS. The method was applied on three seaweed alginates with large differences in sequence parameters (F(G) = 0.32 to 0.67). All samples contained considerable amounts of extremely long G blocks (DP > 100). The finding of long M blocks (DP ≥ 90) suggests that also algal epimerases act by a multiple attack mechanism. Alternating sequences (MG-blocks) were found to be much shorter than the other block types. In connection with method development, an oligomer library comprising both saturated and unsaturated oligomers of various composition and DP 2-15 was made.

Distribution of Parental Genome Blocks in Recombinant Inbred Lines

We consider recombinant inbred lines obtained by crossing two given homozygous parents and then applying multiple generations of self-crossings or full-sib matings. The chromosomal content of any such line forms a mosaic of blocks, each alternatively inherited identically by descent from one of the parents. Quantifying the statistical properties of such mosaic genomes has remained an open challenge for many years. Here, we solve this problem by taking a continuous chromosome picture and assuming crossovers to be noninterfering. Using a continuous-time random walk framework and Markov chain theory, we determine the statistical properties of these identical-by-descent blocks. We find that successive block lengths are only very slightly correlated. Furthermore, the blocks on the ends of chromosomes are larger on average than the others, a feature understandable from the nonexponential distribution of block lengths.

Extracting Intramolecular Sequence Information from Intermolecular Distributions: Highly Nonrandom Methylester Substitution Patterns in Homogalacturonans Generated by Pectinmethylesterase

The ratio of the two component sugar residues comprising the anionic polysaccharide homogalacturonan (HG; namely, methylesterified or unmethylesterifed galacturonic acid (GalA)) has been controlled chemically or enzymatically in order to produce samples comprised of varying degrees and distributions of methylesterification (DM). Capillary electrophoresis (CE) has been used to characterize the samples produced and, by mapping the measured electrophoretic mobilities to biopolymer charge density, intermolecular distributions of the DM have been extracted. For chemically modified samples with random intramolecular patterns of methylesterification, the experimentally extracted intermolecular DM distributions agree well with the predictions of calculations based on the binomial theorem, demonstrating that the random nature of the demethylesterification process and, hence, the intramolecular DM patterns themselves, are directly reflected in the intermolecular distribution. Furthermore, this principle has been demonstrated by extending the work to the study of substrates with highly nonrandom DM distributions generated using a processive plant-pectinmethylesterase (pPME). An ensemble of polymer chains, generated in silico by a simulation optimized to match the experimentally measured intermolecular DM distribution, contains all possible information regarding the substrate and can further be interrogated to obtain, for example, the full Gal-A blocklength distribution.

Simulation of Crystallization Analysis Fractionation (Crystaf) of Linear Olefin Block Copolymers

AbstractSummary: Linear olefin block copolymers (OBCs) have microstructures that are unique among polyolefins and exhibit properties that are different from those of other polyolefin elastomers. Characterizing their chain microstructures is a challenging task, as conventional characterization techniques cannot probe directly block length distribution or composition. In this work, we used a Monte Carlo model to predict the microstructure details of OBCs and a modified version of the Crystaf model previously developed in our groups to describe theoretical Crystaf profiles for model OBCs. This model can be used as a tool to interpret Crystaf results of these interesting new polyolefins and to relate them to OBC microstructures. Effects of polymerization parameters on OBC microstructure and Crystaf profiles were also discussed.

Solvent-Induced Morphology of the Binary Mixture of Diblock Copolymer in Thin Film: The Block Length and Composition Dependence of Morphology

A series of binary SB blend samples with various overall volume fraction of PS (Phi(PS)) and different discrete distribution of the block length (denoted as d(PS) or d(PB)) were prepared by mixing various asymmetric poly(styrene)-block-poly(butadiene) (SB) block copolymers with a symmetric SB block copolymer. The influences of the external solvent field, composition, and the block length distribution on the morphologies of the blends in the thin films were investigated by atomic force microscopy (AFM) and transmission electron microscopy (TEM). The experimental results revealed that after solvent annealing, the interface of the blend thin films depended mainly on the cooperative effects of the annealing solvent and the inherently interfacial curvature of the blends. Upon exposure to the saturated vapor of cyclohexane, which has preferential affinity for the PB block, a "threshold" of Phi(PS) (approximate 0.635-0.707) was found. Below such threshold, the influence of the annealing solvent played an important role on the interfacial curvature of the blend thin film. The morphologies of the thin films and the long-range order of the structures were related to the value of d(PS), regardless of the change of d(PB).

Microwave-assisted synthesis and micellization behavior of soy-based copoly(2-oxazoline)s

Polymers based on renewable resources are promising candidates for replacing common organic polymers, and thus, for reducing oil consumption. In this contribution we report the microwave-assisted synthesis of block and statistical copolymers from 2-ethyl-2-oxazoline and 2-“soy alkyl”-2-oxazoline via a cationic ring-opening polymerization mechanism. The synthesized copolymers were characterized by gel permeation chromatography and 1H-NMR spectroscopy. The micellization of these amphiphilic copolymers was investigated by dynamic light scattering and atomic force microscopy to examine the effect of hydrophobic block length and monomer distribution on the resulting micellar characteristics.