Average Block Length Research Articles

Microstructure and mechanical properties of a statistical aromatic-aliphatic copolyester synthesized by catalytic transesterification

Copolymerising polyethylene terephthalate (PET) and polycaprolactone (PCL) could provide a cost-effective method to recycle PET waste into a compostable plastic. In this work we investigated the relationship between formulation, microstructure, and mechanical properties during catalytic transesterification. It was found that the wt.% PCL was most effective in reducing the average PET block length and determining the copolymer's microstructure at equilibrium. Catalytic transesterification is a random process and can only give a narrow distribution when the average homopolymer block length is less than three, as determined by 1H NMR spectroscopy. A statistical copolymer marks reaction equilibrium where the average PCL block length is greater than one, contradicting the theoretical limit of a single PCL block length. It was proposed that the number of PCL ester groups available for reaction diminishes as transesterification progresses, leading to a favouring of the more abundant PET ester groups to undergo neutral or reverse reactions, resulting in equilibrium. As a result of the imbalance in the availability of PET and PCL ester groups at equilibrium, secondary factors, such as increasing the catalyst amount, were ineffective in further propagating transesterification. Copolymers formed in this study were either amorphous or semi-crystalline. The mechanical properties had minimal correlation with crystallinity and instead was mainly influenced by the ratio between the “hard” (PET) and “soft” (PCL and copolymer) segments in the microstructure and the molecular mass. In this study it was demonstrated that the microstructure of aromatic-aliphatic copolymers, synthesized through catalytic transesterification, can be manipulated to tailor physical properties to meet application requirements.

Effect of PLGA raw materials on in vitro and in vivo performance of drug-loaded microspheres.

Poly(lactide-co-glycolide) and poly(lactic-co-glycolic acids) (PLGAs) play a critical role in the development of commercial long-acting injectable microsphere formulations. However, very little information is available describing the impact of PLGA manufacturer and monomer distribution along the polymer chain (e.g., glycolic blockiness (Rc) and average lactic block length (LL)) on the degradation and release behavior of PLGA drug carriers in vitro and in vivo. Here, we compared the in vitro and in vivo performance of (a) four leuprolide-loaded microsphere formulations prepared from similar low-molecular-weight acid-capped PLGAs (10-14 kD, i.e., Expansorb® DLG 75-2A, Purasorb® PDLG 7502A, Resomer® RG 752H and Wako® 7515) and (b) two triamcinolone acetonide-loaded (Tr-A) microsphere formulations from similar medium-molecular-weight ester-capped PLGAs (i.e., Expansorb® DLG 75-4E and Resomer® RG 753S). Lupron Depot® and Zilretta® were used as reference commercial products. The six 75/25 PLGAs displayed block lengths that were either above or below values expected from a random copolymer. Drug release and polymer degradation were monitored simultaneously in vitro and in vivo using a cage implant system. The four leuprolide-loaded formulations showed similar release and degradation patterns with some notable differences between each other. Microspheres from the Expansorb® polymer displayed lower LL and higher Rc relative to the other 3 PLGA 75/25 microspheres, and likewise exhibited distinct peptide release and degradation behavior compared to the other 3 formulations. For each formulation, leuprolide release was erosion-controlled up to about 30% release after the initial burst followed by a faster than erosion release phase. In vitro release was similar as that in vivo over the first phase but notably different from the latter release phase, particularly for the most blocky Expansorb® formulation. The Purasorb® and Wako® formulations displayed highly similar performance in release, degradation, and erosion analysis. By contrast, the two ester-capped Expansorb® DLG 75-4E and Resomer® RG 753S used to prepare Tr-A microspheres shared essentially identical LL and higher Rc and behaved similarly although the Expansorb® degraded and released the steroid faster in vivo, suggestive of other factors responsible (e.g., residual monomer). The in vivo release performance for both drugs from the six microsphere formulations was similar to that of the commercial reference products. In summary, this work details information on comparing the similarities and differences in in vitro and in vivo performance of drug-loaded microspheres as a function of manufacturing and microstructural variables of different types of PLGA raw materials utilized and could, therefore, be meaningful in guiding the source control during development and manufacturing of PLGA microsphere-based drug products. Future work will expand the analysis to include a broader range of LL and higher Rc, and add additional important formulation metrics (e.g., thermal analysis, and residual monomer, moisture, and organic solvent levels).

Covalent adaptable networks and thermosets of multi-block ethylene/1-octene copolymers made by free-radical processing: Effects of melt flow index and crystallinity on thermomechanical properties and reprocessability

Chain shuttling polymerization has facilitated the rapid development of olefin block copolymers (OBCs) such as ethylene/1-octene multi-block copolymers. The properties of OBCs stem from various parameters such as average block length, number of blocks per chain, etc., which lead to complexity associated with establishing structure–property relationships between precursor OBCs and properties of cross-linked OBCs. Additionally, permanent cross-linking of OBCs sacrifices their recyclability, and cross-linked OBCs capable of being reprocessed have seldom been reported. Here, permanently cross-linked OBCs (OBCXs) and dynamically cross-linked OBCs, or OBC covalent adaptable networks (CANs), were synthesized by melt-state reactive processing of neat OBCs with various crystallinities and melt flow indices (MFIs). The OBC CANs are capable of dialkylamino disulfide dynamic chemistry via the grafting of bis(2,2,6,6-tetramethyl-4-piperidyl methacrylate) disulfide, or BiTEMPS methacrylate, cross-linkers onto OBC backbone chains. Thermomechanical characterizations indicate that increasing crystallinity and decreasing MFI in precursor OBCs lead to higher cross-link densities in OBCXs and OBC CANs. Dynamically cross-linking OBCs into CANs also significantly improves their elevated-temperature creep resistance. Stress relaxation results of OBC CANs indicate an increased average relaxation time with greater cross-link density. Distinct from other CANs capable of dialkylamino disulfide chemistry, the stress relaxation behaviors of OBC CANs of higher cross-link density show evident dependence on their network viscoelasticities. In OBC CANs of lower cross-link density, the dynamic chemistry more strongly governs their stress relaxation behaviors. Finally, the OBC CANs exhibit full cross-link density and thermomechanical property recovery after reprocessing, whereas the OBCXs cannot be reprocessed due to their irreversible cross-links.

Linkage disequilibrium, historical effective population size and haplotype blocks in selected native sheep breeds

This study was conducted to investigate linkage disequilibrium (LD), historical effective population size (Ne) and haplotype blocks structure in genomes of nine Polish conserved sheep breeds or varieties: Black-headed (BH), Colored Mountain Sheep (CMS), Old-type Merino (MPOT), Podhale Zackel (PZ), Polish Merino of Coloured Variety (MPC), Polish Mountain Sheep (PMS), Świniarka (SW), Uhruska (UHR) and Wrzosówka (WRZ), based on single nucleotide polymorphisms (SNPs) from the OvineSNP50 DNA Analysis Kit (Illumina, San Diego, CA). LD analysis was performed based on the pairwise r2 statistic of SNPs at a distance up to 5 Mb. At a short distance, up to 100 kb, the lower average r2 was observed in PZ (0.10) breed and the highest average r2 was observed in MPC (0.21) breed. At a distance of 4–5 Mb, the highest average r2 was observed in SW (0.08) breed and the lowest average r2 was observed in PZ (0.02) and PMS (0.02) breeds. All studied Polish sheep breeds, showed mean r2 > 0.3 (‘useful’ LD level for QTL mapping) at shorter distances than average distances between adjacent SNP markers and only for MPC, SW, UH, WRZ breeds mean r2 > 0.2 (high enough to attain an accuracy of 0.85 for genomic breeding value estimation) was observed at similar or longer distances than average distances between adjacent SNP markers. Obtained results showed that the Illumina OvineSNP50 BeadChip assay is not a suitable tool to perform reliable genome-wide association for all studied Polish sheep breeds and only for MPC, SW, UH and WRZ it is potentially possible to perform reliable genomic breeding value estimation. For most of the studied sheep breeds, effective population size 5 generations ago was close or less to the FAO recommended Ne of 50 per generation required to maintain fitness in breed. From 2,051 (SW) to 1,265 (PZ) haplotype block structures, spanning from 148.9 (SW) to 26.3 (PZ) of the genome were detected. Across all studied sheep breeds the highest average block length was observed in MPC (82.5 ± 114 kb) breed and the lowest average block length was observed in PZ (20.9 ± 43 kb) breed. For all studied Polish sheep breeds, as many as 280 haplotype block structures with overlapping segments were detected, within which 182 genes were identified.

Exploring haplotype block structure, runs of homozygosity, and effective population size among dairy cattle breeds of India

The present study aimed to explore haplotype structure, runs of homozygosity (ROH), effective population size and persistence of gametic phase among three indigenous dairy cattle breeds, viz., Sahiwal (n = 19), Tharparkar (n = 17), and Gir (n = 16) by using BovineHD single nucleotide polymorphism (SNP) genotyping assay. The filtered SNPs after quality control ranged from 44% in Sahiwal to 53% in Gir. The highest number of haplotype blocks was observed in Tharparkar (15,640) and the lowest in Sahiwal (8027) spanning 17.3% and 7.8% of genome, respectively. The average block length was found close to 26kb which suggests that multiple recombination events fragmented the ancestral haplotypes into smaller sizes. Gir cattle had the largest number of runs of homozygosity (ROH) regions (1762) followed by Tharparkar (1528) and Sahiwal (1138). Without pedigree information, inbreeding coefficients estimated from ROH (FROH) revealed that Gir had the highest FROH (0.099) proposing more inbreeding rate in this population. Effective population size (Ne) decreased slowly over the last 60 generations and at 13 generations ago; Ne was estimated as 70 for all the three dairy breeds. The highest gametic phase correlation (r = 0.78) was observed for Sahiwal and Tharparkar breed pair suggesting formulation of multi-breed reference population for successful implementation of genomic selection among dairy breeds. The decline in effective population size among native Indian cattle breeds may help in formulating strategies for conservation and genetic improvement of native germplasm for future use.

Microphase Separation of Statistical Multiblock Copolymers

Random multiblock copolymers are characterized by a number of parameters, and their self-assembly is controlled, in particular, by correlations in monomer unit sequences. We investigate the microphase separation of random multiblock copolymers composed of A and B homo-oligomers (macromonomers) in melts. The copolymer synthesis and self-assembly are studied by computer simulations using the dissipative particle dynamics technique. The copolymers are formed by irreversible step-growth polymerization in an equimolar melt of end-functionalized macromonomers of length M up to a high conversion degree. Correlations between macromonomers of different types along the chains are controlled by the reaction probabilities. The molar mass and block mass distributions are described for linear macromolecules and for cycles. Macromonomer sequences in linear chains are well described by the first-order Markov statistics. With an increase in the Flory–Huggins parameter χ, microphase separation into a lamellar structure, for close-to-alternating block copolymers, and into irregularly arranged domains, for Bernoullian sequences of macromonomers, occurs. The transition χM values are approximately twice those obtained with weak segregation theory [Fredrickson, G. H. Macromolecules1992, 25, 6341−6354] and approximately half the values for which microphases were previously detected in the simulations of random copolymer melts [Gavrilov, A. A. J. Chem. Phys.2013, 139, 224901]. Microphase separation is described by the static structure factor and local composition, besides the block positions are monitored visually. The lamellar thickness H is always between the unperturbed sizes of one- and two-macromonomer blocks, and we characterize the separation as a moderate segregation regime. For the close-to-alternating block copolymers at a fixed χ, the thickness scales with the average block length approximately as H ∼ N̅bl2/3 that is in agreement with the theoretical description (Supporting Information) considering the elastic response of the shortest blocks only.

Assessing Measurement Invariance of a Land Use Environment Construct Across Levels of Urbanicity.

Variation in the land use environment (LUE) impacts the continuum of walkability to car dependency, which has been shown to have effects on health outcomes. Existing objective measures of the LUE do not consider whether the measurement of the construct varies across different types of communities along the rural/urban spectrum. To help meet the goals of the Diabetes Location, Environmental Attributes, and Disparities (LEAD) Network, we developed a national, census tract‐level LUE measure which evaluates the road network and land development. We tested for measurement invariance by LEAD community type (higher density urban, lower density urban, suburban/small town, and rural) using multiple group confirmatory factor analysis. We determined that metric invariance does not exist; thus, measurement of the LUE does vary across community type with average block length, average block size, and percent developed land driving most shared variability in rural tracts and with intersection density, street connectivity, household density, and commercial establishment density driving most shared variability in higher density urban tracts. As a result, epidemiologic studies need to consider community type when assessing the LUE to minimize place‐based confounding.

Olefin cross-metathesis of polynorbornene with polypentenamer: New norbornene–cyclopentene multiblock copolymers

Statistical multiblock copolymers of norbornene (NB) and cyclopentene (CP) with different compositions and average block lengths are synthesized via the metathesis of polynorbornene (PNB) with polypentenamer (PCP) mediated by Grubbs’ catalysts of the 1st (G1) and 2nd (G2) generations. Interest in the copolymerization of NB and CP is dictated by the attractive properties of their homopolymers, whereas its realization is hampered by the mismatch in their metathesis polymerization activities. This difficulty can be circumvented by starting from the homopolymers, which are well-known industrial products. Our study demonstrates that the interaction of PNB with PCP in dilute solutions at room temperature in the presence of G1 leads to the copolymers with short CP blocks of 1–3 units separating longer NB blocks. In situ 1H NMR monitoring of the process reveals nearly full depolymerization of PCP via the ring-closing intramolecular metathesis and the formation of NB–CP copolymers presumably via the interaction of CP with PNB. The depolymerization can be suppressed by increasing the concentration of reacting polymers and replacing G1 with more active G2. Under these conditions, the cross-metathesis of PNB with PCP results in the multiblock NB–CP copolymers with composition close to that of the initial homopolymer mixture, but short blocks of the both comonomers. A copolymer with longer blocks that can inherit properties of the parent homopolymers is obtained by decreasing the reaction temperature to 5 °C. Additional information about the structure of NB–CP copolymers is obtained via their hydrogenation followed by spectral and thermal characterization. Thus, the macromolecular cross-metathesis of unsaturated polymers appears to be a versatile method to synthesize copolymers with different backbone structures that are hard to reach by other methods.

Synthesis and mechanochemical properties of biobased ABCBA‐type pentablock copolymers comprising poly‐d‐lactide (A), poly‐l‐lactide (B) and poly(1,2‐propylene succinate) (C)

AbstractThe ABCBA pentablock copolymers (p‐d‐l‐PPS) comprising poly(d‐lactide) (PDLA: A), poly(l‐lactide) (PLLA: B) and poly(propylene succinate) (PPS: C) were successfully synthesized by two‐step ring‐opening polymerization (ROP) of d‐ and l‐lactide using a dihydroxy‐terminated PPS as a macro‐initiator. The pentablock copolymers revealed the high stereocomplex (sc) crystallinity, thermal stability and elastomeric property in their solution‐cast films. It was found that the Tg was found to be proportional to the PPS content, whereas the Tm was proportional to their average block length. The thermal resistivity of the copolymer films was found to be as high as 202°C owing to their sc formation. The copolymers also showed improved stereocomplexibility compared to the enantiomeric mixtures of triblock copolymers (PLLA‐PPS‐PLLA and PDLA‐PPS‐PDLA) having similar PLLA and PDLA chain lengths. These pentablock copolymers can afford thermoplastic elastomers or flexible plastic materials having a 100% bio‐based content, showing high heat‐resistive property.

Effect of block length on the network connectivity and temperature resistance of model, soft thermoplastic elastomers

We discuss the connection between high-temperature mechanics, block structure, and composition of a model series of industrially relevant, soft, thermoplastic elastomers (TPEs) containing polydisperse hard blocks (HBs). The high-strain deformation behavior of these materials results from the combination of multiple dynamics in the system, i.e., the HB associations and the mobile and entangled amorphous phase. Many soft-TPEs show a reduction in toughness with increasing temperature. Molecular weight (Mw) has been shown to improve the temperature-dependent mechanics by increasing network connectivity. In this work, we investigate the possibility to increase the network connectivity by tuning block length at constant Mw and composition. The average number of HBs per chain can be used to quantify network connectivity; however, by using block statistics, we show how increasing this value is not enough to increase the high-temperature mechanics, especially in the case of polydisperse HBs. Since temperature affects the HB ability to associate with each other, only the number of associated HBs per chain determines network connectivity. The experimental results are consistent with modeling predictions, revealing how decreasing the average block length influences the crystal stability, which ultimately controls network connectivity, and how this relationship is affected by temperature.

Impact of drying on the sodium alginate obtained after polyphenols ultrasound-assisted extraction from Ascophyllum nodosum seaweeds

Ultrasound-assisted extraction (UAE) of polyphenols from the brown seaweeds Ascophyllum nodosum leaves a solid phase where alginates can be extracted. This study characterizes alginates extracted after the UAE process, with and without an intermediate drying stage at different temperatures (50 and 90 °C) producing sequentially two bioactive compounds from a unique raw material. FT-IR and 1H NMR analyses showed the high purity of alginates with features in the range of commercial alginates. Drying at high temperature decreased average block length and viscosity average molecular weight (Mv) of alginate from 428 to 133 kg/mol. Steady-shear curves (shear-thinning behaviour) and viscoelasticity (liquid like character) features depended clearly on Mv. Solutions of alginates with high Mv were more viscous and the elastic character was more relevant. Cox-Merz rule was only accomplished within the semi-dilute regimes of alginate concentration. Tested process conditions allow the production of alginates with different properties.

Conformation-dependent sequence design of polymer chains in melts

Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice are considered as typical microphase-separated morphologies of block copolymers. Random trajectories of polymer chains are described by the diffusion-type equations and, in parallel, simulated in the computer modeling, the probability distributions of block length k being calculated. The problem is similar to that of gambler’s ruin and first passage time in probability theory but the consideration is generalized to 3D and the domains of different shapes are considered. In any domain, the probability distribution can be described by the asymptote ∼k −3/2 at moderate values of k if the spatial size of the block is less than the smallest characteristic size of the domain. For large blocks, the exponential asymptote exp(−const ) is valid, d as being the asymptotic domain length (a is the monomer unit size). The number average block lengths and their dispersities change linearly with the domain size for lamellae, cylinders, and balls, when the domain is characterized by a single characteristic size. If the domain is described by more than one size, the number average block length can grow nonlinearly with the domain sizes and the length d as can depend on all of them.

Synthesis of New of Norbornene–1,5-Bis(hexenyl)hexamethyltrisiloxane Copolymers via Olefin Metathesis Reaction

New copolymers of norbornene and 1,5-bis(hexenyl-5)-1,1,3,3,5,5-hexamethyltrisiloxane containing flexible siloxane and rigid norbornene fragments in the main chain are synthesized. Synthesis is carried out using three types of olefin metathesis reactions: the ring-opening metathesis polymerization of norbornene, the metathesis of nonconjugated diene 1,5-bis(hexenyl-5)-1,1,3,3,5,5-hexamethyltrisiloxane, and the interchain macromolecular cross-metathesis between polynorbornene and siloxane-containing polyene. The latter reaction is studied for the first time. With its help, new statistical multiblock copolymers of norbornene and 1,5-bis(hexenyl-5)-1,1,3,3,5,5-hexamethyltrisiloxane with different average block lengths are obtained and characterized by 1H and 13C NMR and IR spectroscopy. The effect of the copolymer structure on their thermal properties is investigated.

Printability and Critical Insight into Polymer Properties during Direct-Extrusion Based 3D Printing of Medical Grade Polylactide and Copolyesters.

Various 3D printing techniques currently use degradable polymers such as aliphatic polyesters to create well-defined scaffolds. Even though degradable polymers are influenced by the printing process, and this subsequently affects the mechanical properties and degradation profile, degradation of the polymer during the process is not often considered. Degradable scaffolds are today printed and cell-material interactions evaluated without considering the fact that the polymer change while printing the scaffold. Our methodology herein was to vary the printing parameters such as temperature, pressure, and speed to define the relationship between printability, polymer microstructure, composition, degradation profile during the process, and rheological behavior. We used high molecular weight medical-grade (co)polymers, poly(l-lactide-co-ε-caprolactone) (PCLA), poly(l-lactide-co-glycolide) (PLGA), and poly(d,l-lactide-co-glycolide) (PDLGA), with l-lactide content ranging from 25 to 100 mol %, for printing in an extrusion-based printer (3D Bioplotter). Optical microscopy confirmed that the polymers were printable at high resolution and good speed, until a certain degree of degradation. The results show also that printability can not be claimed just by optimizing printing parameters and highlight the importance of a careful analysis of how the polymer's structure and properties vary during printing. The polymers thermally decomposed from the first processing minute and caused a decrease in the average block length of the lactide blocks in the copolymers and generated lower crystallinity. Poly(l-lactide) (PLLA) and PCLA are printable at a higher molecular weight, less degradation before printing was possible, compared to PLGA and PDLGA, a result explained by the higher complex viscosity and more elastic polymeric melt of the copolymer containing glycolide (GA) and lactide (LA). In more detail, copolymers comprised of LA and ε-caprolactone (CL) formed lower molecular weight compounds over the course of printing, while the PLGA copolymer was more susceptible to intermolecular transesterification reactions, which do not affect the overall molecular weight, but cause changes in the copolymer microstructure. This results in a longer printing time for PLGA than PLLA and PCLA.

Cross-Metathesis between Polynorbornene and Poly(5,6-epoxy-1-octenamer)

The macromolecular reaction of interchain cross-metathesis between polynorbornene and poly(5,6-epoxy-1-octenamer) in the presence of the first-generation Grubbs catalyst is studied. Chemically stable poly(5,6-epoxy-1-octenamer) is obtained through metathesis polymerization of 5,6-epoxycyclooct-1-ene with the second-generation Grubbs ruthenium catalyst. New random multiblock copolymers of norbornene and 5,6-epoxycyclooct-1-ene with different average block lengths determined by the reaction time, solvent type, and concentrations of the catalyst and initial homopolymers are synthesized and characterized by NMR, GPC, and DSC. Despite a distance between the epoxy substituent and the reaction center (double bond), poly(5,6-epoxy-1-octenamer) shows a lower activity in the cross-metathesis reaction with polynorbornene compared to unsubstituted polyoctenamer. The influence of epoxy groups present in the backbones of homopolymer and norbornene–cyclooctene multiblock copolymers on their thermal characteristics is studied. It is shown that the glass transition and melting temperatures increase with the concentration of epoxy groups upon the incorporation of an oxirane fragment into both homopolymers and copolymers. The crystallinity of poly(5,6-epoxy-1-octenamer) increases with the content of trans-С=С bonds in the polymer.

Common-Message Broadcast Channels With Feedback in the Nonasymptotic Regime: Stop Feedback

We investigate the maximum coding rate for a given average blocklength and error probability over a K-user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiy et al. (2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e., zero dispersion. In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message K-user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.

Self-Assembly of PEO-b-PCL-b-PMOXA Binary Mixtures

We report about aqueous self-assembly of binary mixtures of poly(ethylene oxide)-block-polycaprolactone-block-poly(2-methyl-2-oxazoline) (PEO-b-PCL-b-PMOXA) triblock copolymers containing identical PEO (45 units) and different PCL (48–153 units) and PMOXA (3–25 units) block lengths. All mixtures targeted a certain triblock copolymer; that is, mixtures had the same average block lengths as the targeted polymer. Self-assembled morphologies formed by mixtures were compared with the morphologies formed by the corresponding targeted polymers, which were polymersomes or cloudlike aggregates. The mixtures were prepared using premixing and postmixing protocols. In the premixing protocol, polymers were mixed before self-assembly. In the postmixing protocol, structures were mixed after self-assembly. Self-assembly was performed at 62 °C using the film rehydration method, and the microscale structures were visualized using laser scanning microscopy. In postmixing protocol, polymersomes stayed intact, whereas cloudli...

Unveiling the molecular structure of ethylene/1-octene multi-block copolymers from chain shuttling technology

A method for assessing the puzzling molecular architecture of ethylene/1-octene multi-block copolymers, synthesized via chain-shuttling technology, is proposed. They are commercial elastomers characterized by alternating segments with low (hard blocks) and high (soft blocks) octene concentration. Our molecular assessment allows determining plausible value for the average length of blocks and number of blocks/chain, setting the basis for a definitive elucidation of structure-properties relationships of these elusive systems. Namely, the molecular basis which explains the similar crystallization properties, and the large difference in mechanical properties of this class of copolymers is unveiled thanks to our approach. We demonstrate that at 25 °C we have similar values of Young modulus and deformation at break higher than 1400%, but large strain hardening before breaking or flat mechanical behavior up to the break, depending on the short or long average block length of the multiblock copolymers, respectively, coupled with a high or low number of blocks/chain, respectively. At 60 °C these differences are amplified entailing no strain hardening but preservation of high ductility for copolymers with short average block length and high number of blocks/chain, remarkable decrease of strain at break of about two orders of magnitude (from ≈2000 to ≈90%) for copolymers with long average block length and lower number of blocks/chain.

Epoxidation of Multiblock Copolymers of Norbornene and Cyclooctene

The epoxidation of double bonds in random multiblock copolymers of norbornene and cyclooctene is studied for the first time. The initial copolymers with different composition and average block length are synthesized via the cross-metathesis reaction between polynorbornene and polycyclooctene in the presence of the first-generation Grubbs catalyst. New multiblock copolymers containing oxirane fragments in the backbone are obtained with a yield of 85–92% through epoxidation conducted under the action of m-chloroperbenzoic acid in toluene. The kinetics of epoxidation of polynorbornene, polycyclooctene, and their multiblock copolymers in deuterochloroform and deuterobenzene is investigated via the in situ monitoring of transformation of double bonds using 1Н NMR spectroscopy. It is shown that on the whole the modification of cyclooctene units occurs more easily in copolymers than that in the homopolymer. The thermal properties of epoxidized homo- and copolymers are examined. It is found that upon epoxidation the glass-transition temperature and the melting temperature of multiblock copolymers increase by 40–50 and 20–30°С, respectively, wherein the degree of crystallinity and the temperature of melting grow with the length of the cyclooctene block.

Common-Message Broadcast Channels With Feedback in the Nonasymptotic Regime: Full Feedback

We investigate the maximum coding rate for a given average blocklength and error probability over a $K$ -user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiy et al. (2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e., zero dispersion . In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message $K$ -user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.