Block Length Distribution Research Articles

Rheological Behavior of Aqueous Micellar Solutions of a Triblock Copolymer of Ethylene Oxide and 1,2-Butylene Oxide: B10E410B10

A triblock copolymer of ethylene oxide and 1,2-butylene oxide, denoted B10E410B10, was prepared by sequential oxyanionic polymerization and characterized by 13C NMR spectroscopy and gel permeation chromatography. Micellization and the formation of micelle clusters in dilute aqueous solution, the latter a consequence of micelle bridging, was confirmed by dynamic light scattering, and average association numbers of the micelles were determined by static light scattering for T = 20-40 degrees C. The frequency dependence of the dynamic storage and loss moduli was investigated for solutions in the range of 5-20 wt %. Comparison with results for poly(oxyethylene) dialkyl ethers (10 wt %, T = 25 degrees C) indicated that the viscoelasticity of a copolymer with terminal B10 hydrophobic blocks was roughly equivalent to one with terminal C14 alkyl chains. The temperature dependence of the modulus was investigated for 15 wt % solutions at T = 5-40 degrees C. Superposition of the data led, via an Arrhenius plot, to an activation energy for the relaxation process of -40 kJ mol(-1). The negative value contrasts with the positive values found for poly(oxyethylene) dialkyl ethers and related HEUR copolymers with urethane-linked terminal alkyl chains. This difference is attributed to the block-length distribution in copolymer B10E410B10, whereby the activation energy of the relaxation process has a positive contribution from the disengagement of B blocks from micelles but a negative contribution from micellization. The negative value of the activation energy for solutions of B10E410B10 was confirmed by determining the temperature dependence of the zero-shear viscosity of its 15 wt % solution.

Isotactic Block Length Distribution in Polypropylene: Bernoullian vs Hemiisotactic

Derivation of the isotactic block length distribution is made for polypropylenes having Bernoullian (chain-end control) or hemiisotactic microstructures. For each of these tacticities, the isotactic block length distribution depends on a single stereochemical parameter and Mn, the number-average molecular weight. For polypropylene with Bernoullian statistics, the number of isotactic blocks of length n is given by Nn = (1 − σ)2(σ)(n-1)(Mn/42.08). For hemiisotactic polypropylene, the number of isotactic blocks of length one is given by N1 = [(0.5)(1 − α)2 + (0.5)(1 − α)](Mn/42.08) and the number of isotactic blocks of length n (where n is an odd integer greater than one) is given by Nn = (0.5)(1 − α)2(α)(n-1)/2(Mn/42.08). The distributions are compared and contrasted for hypothetical polypropylenes and real polypropylenes for which σ, α (13C NMR) and Mn (GPC) have been determined. For polypropylene with Mn = 100 000 an elastomeric morphology is calculated to exist for σ = 0.752−0.827 (Bernoullian) and for α...

Effects of Poloxamer Inhomogeneities on Micellization in Water

Pluronic P85 (poloxamer 235), which is a symmetrical PEO−PPO−PEO triblock copolymer of poly(ethylene oxide) and poly(propylene oxide), has been investigated by differential scanning calorimetry and chromatography. Interaction chromatography at critical conditions for PEO was used for chromatographic characterization and preparative separation of P85 according to PPO block lengths. The results show that the P85 sample is heterogeneous with respect to chemical composition and molar mass. P85 contains 12 wt % lower size impurities, which do not contribute to the main micellization transition. The shapes and widths of the micellization peaks observed in P85 thermograms are influenced by the distribution of PPO block lengths in P85, as shown from measurements on chromatographic fractions. PPO block lengths of the main P85 fraction follow a Poisson distribution closely. The characteristic temperatures of micellization, sphere-to-rod, and phase separation transitions observed in thermograms are influenced by polydispersity.

Effect of Poly(acrylic acid) Block Length Distribution on Polystyrene-b-poly(acrylic acid) Block Copolymer Aggregates in Solution. 2. A Partial Phase Diagram

The first paper of the series, which focused on the effect of polydispersity on the self-assembly of block copolymer vesicles, showed that an increase in the width of the poly(acrylic acid) (PAA) block length distribution resulted in a decrease in the size of the vesicles formed. In this paper, the rest of the phase diagram is explored. For the present study, a series of polystyrene-b-poly(acrylic acid) copolymers of an identical polystyrene length of 325 units but of varying degrees of polymerization of PAA was synthesized. Mixtures of the copolymers were made to artificially broaden the molecular weight distribution of PAA at a constant number average of 48 in the polydispersity index (PDI) range of 1.1-3.3. The mixtures were dissolved in dioxane, and water was added slowly to predetermined amounts. Transmission electron microscopy was used to observe aggregate morphologies at different water contents and PAA PDIs. At low water contents, dynamic light scattering was also used to measure the sizes of the aggregates. A partial phase diagram as a function of the water content and PAA PDI was obtained. Large compound micelles and spherical micelles (average diameter of 40 nm) were found at low water contents; however, at a water content of 12% (w/w), a continuum of morphologies from spheres to rods to vesicles was found with increasing PAA PDI. In addition, each copolymer was investigated by itself under identical conditions to those used for the mixtures to determine if there was any segregation of the individual polymers into separate aggregates. No evidence for such segregation was found.

Core/Shell Structures of Proteinlike Copolymers: Are Finite Aggregates Thermodynamically Stable?

We propose a theory of aggregation in solutions of amphiphilic copolymers consisting mostly of insoluble H (hydrophobic) units with a small fraction of soluble (P, polar) monomer units. When P units are arranged along the sequence in a periodic (regular) fashion, the resultant HP copolymers are essentially insoluble: they precipitate. The main result is that finite aggregates of HP copolymers can be made stable by an appropriate smart arrangement of the same number of soluble P units in the chemical sequence. An analytical approach yielding the thermodynamic quantities of H-core/P-shell copolymer structures in the weak stretch limit is developed. We show that different types of copolymer aggregates and microdomain structures can be thermodynamically stable depending on the copolymer chemical sequence. The relationship between the block-length distribution and copolymer aggregation is illustrated by a few phase diagrams. Copolymers that can form stable finite aggregates with H-core/P-shell structure (including single-chain globules) are often referred to as the proteinlike copolymers. Thus, the present theory sheds a new light as to the essential features of proteinlike copolymer sequences.

Characterization of poly(ethylene oxide)-b-poly(L-lactide) block copolymer by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

A poly(ethylene oxide)-b-poly(L-lactide) diblock copolymer (PEO-b-PLLA) is characterized by matrixassisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) and a block length distribution map is constructed. Although the MALDI-TOF mass spectrum of PEO-b-PLLA is very complicated, most of the polymer species were identified by isolating the overlapped isotope patterns and by fitting the overlapped peaks to the Schulz-Zimm distribution function. Reconstructed MALDI-TOF MS spectrum was nearly identical to the measured spectrum and this method shows its potential to be developed as an easy and fast analysis method of low molecular weight block copolymers.

Effects of polydispersity on the phase coexistence diagrams in multiblock copolymers with Laser block length distribution

Phase behavior of AB-multiblock copolymer melts which consists of chains with laser distribution of A and B blocks have been investigated in the framework of the mean-field theory, where the polydispersity of copolymer is a function of two parameters K and M. The influence of the Laser distribution on higher-order correlation functions (up to sixth order) are computed for various values of K and M, and their contributions on the phase diagrams and phase coexistence are presented. It is shown that, with increasing polydispersity (decreasing K and increasing M) the transition lines of all phases shift upwards, consequently polydispersity destabilize the system.

Laser block length distribution and influence of its parameters (K and M) on the phase behavior of statistical multiblock copolymers

The phase diagram of AB-multiblock copolymer melts containing A and B blocks obeying the Laser distribution, has been investigated for various values of the parameters K and M. As M→∞ it reduces to the ordinary Schultz–Zimm distribution. With decreasing M, the transition lines of the lamellar, hexagonally close-packed cylinders and body-centered-cubic phases shift to greater N× χ, so that for high K these shifts are very large while for low K they are very small.

Molecular Inhomogeneity and Amplitude of Scattering of the Products of Diblock Copolymer Degradation

Expressions are derived for the distributions in size and composition of the macromolecular products of random degradation of diblock copolymers with arbitrary block length distributions. Equations for the calculation of the angular dependence of the static structure factor of these products formed at different depths of degradation are presented. General regularities of the evolution of the spinodal of the polymer melt in the course of this reaction are analyzed. Proceeding from the general theory developed, examples concerning degradation processes of diblock copolymers with particular block length distributions are provided.

Detailed structural analysis of diblock copolymers by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

The individual block length distributions of poly(α-methylstyrene)-b-poly(4-vinylpyridine) diblock copolymers have been determined by the MAC MALDI-TOFMS method of analysis of copolymers, which combines matrix assisted laser desorption/ionization time-of-flight mass spectrometry with computational data treatment. The problem of the possibility of multiple assignments of chemical composition to the mass spectral peaks is discussed in detail. A solution based on the pattern of peak clusters is proposed and verified using the statistical random coupling hypothesis test. The progress of the anionic polymerization in a series of polymers prepared by sequential addition of the second monomer to a living chain system is studied and shown in three-dimensional (3-D) plots of experimental individual blocks length distributions. The presence of unreacted homopolymer has been observed as well as bimodal and trimodal distributions for the poly(α-methylstyrene) and the poly(4-vinylpyridine) segments. A depolymerization process of the homopoly(α-methylstyrene) in the series of poly(α-methyl-styrene)-b-poly(4-vinylpyridine) diblock copolymers was detected following a temperature rise. It was confirmed that it is impossible to place a single unit of 4VP at the end of each PαMS chain. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of Diblock Copolymers of Poly(α-methylstyrene)-block-polystyrene by Mass Spectrometry

The individual block length distributions of a series of diblock copolymers, polystyrene-b-poly(α-methylstyrene), were determined by the MAC MALDI/TOF MS method of analysis of copolymers which combines matrix-assisted laser desorption/ionization time-of-flight mass spectrometry with computational data treatment. The robustness of the calculation technique was evaluated. The presence of unreacted homopolymer was observed as well bimodal and trimodal distributions for the poly(α-methylstyrene) segments. A new method to verify the random coupling hypothesis has been proposed. The hypothesis was verified to hold within the experimental error of the technique for all the correct assignments of polymers studied. The experimental distributions have been compared with the Poisson, Schulz−Zimm, Tung, and logarithmic-normal models, modified to account for the change of variables. The equations of the Tung model, which was found to have the best predictive capability for the PαMS blocks, were transformed into the an...

Determination of Block Length Distributions of Poly(oxypropylene) and Poly(oxyethylene) Block Copolymers by MALDI-FTICR Mass Spectrometry

Matrix-assisted laser desorption/ionization (MALDI) was performed on an external ion source Fourier transform ion cyclotron resonance mass spectrometer (FTICR-MS) to analyze the block length distributions of triblock polymers of poly(oxypropylene) and poly(oxyethylene). The first series of results presented demonstrate that the apparent molecular weight distributions are distorted. This distortion is induced by the flight-time-induced mass discrimination inherent in the experimental technique, the variation of isotopic patterns over the measured mass range, and the overlap of peaks in the spectrum. Subsequently, a method for the treatment of molecular weight distributions measured by MALDI on an external ion source FTICR-MS is developed to yield the actual molecular weight distribution and, from that, the individual block length distributions. For the first time, detailed and accurate molecular weight data were obtained on a complex sample using this methodology, which independently validates the data provided by the manufacturer. The experimentally verified random coupling hypothesis proves the validity of the methodology.

Theory of Polydisperse Multiblock Copolymers

We study the self-organization of a polydisperse A−B multiblock copolymer melt with repulsive interactions between the different monomers. In the framework of the one-loop (Hartree) approximation we consider the influence of the polydispersity parameter u, which is the ratio of the first two moments of the block length distribution u = (〈l2〉/〈l〉2) − 1, on the condition for the order−disorder transition. At low polydispersity (u < 0.3) the system undergoes the ordinary block copolymer microphase separation transition. The value of the Flory parameter χ on the line of the order−disorder transition increases with increasing polydispersity of the system. The transition to macrophase separation at the classical Lifshitz point u = 0.5 is precluded by a fluctuation-induced instability of the homogeneous state with respect to finite-wavelength composition fluctuations. The characteristic length scale L of these critical fluctuations above the microphase separation transition and the period of the domain structure below changes weakly with temperature as ((T − Tc)/Tc)-1/6. In the case of an exponential block length distribution (u ≈ 1), the period of the domain structure exhibits stronger temperature dependence L ≈ ((T − Tc)/Tc)-1/4 than that derived for this system near the Lifshitz point due to strong coupling between composition fluctuations. For values of the polydispersity parameter u > 0.4 the value of the Flory parameter on the line of the first-order order-disorder phase transition decreases with increasing polydispersity of the system.

Polymer electrolytes based on triblock-copoly(oxyethylene/oxypropylene/oxyethylene) systems

Polymer electrolytes based on triblock copolymers of ethylene oxide (EO)/propylene oxide (PO)/ethylene oxide of moderate molecular weight and narrow block-length distributions, doped with M(CF3SO3)2 and M[N(CF3SO2)2]2 (M = Mg, Ca, Sr and Ba), LiCF3SO3 and LiN(CF3SO2)2 have been investigated using infrared spectroscopy, differential scanning calorimetry and conductivity measurements. The effects of varying the EO/PO block length, composition and temperature on the phase behaviour, ion-pair formation and conductivity of the polymer electrolytes have been studied. A two-phase microstructure has been observed. Ion pairing occurs for the triflate salts and the amount was found to be sensitive to the relative block sizes rather than the molecular weight of the copolymer.

Studies on sequence distribution of aliphatic/aromatic copolyesters by high‐resolution 13C nuclear magnetic resonance spectroscopy for evaluation of biodegradability

AbstractCopolyesters with different stoichiometric compositions, obtained from 1,4‐butanediol, adipic acid, and terephthalic acid by molten‐state polycondensation, are studied by means of high resolution 13C NMR spectroscopy with respect to copolymer composition and block length distribution. The ratio of aliphatic and aromatic dicarboxylic acids in the polymer, which sensitively influences the biodegradability of the polymers, reflects the initial monomer composition during polycondensation. This indicates that under the conditions applied for polycondensation no loss for example of terephthalic acid due to sublimation occurs. It was found that the aliphatic and aromatic repeating units are randomly distributed within the polymer chain. The experimentally determined average sequence length distribution dependence on stoichiometric copolymer compositions are in accord with ideal polycondensation statistics. In combination with the results of the degradability of aromatic oligomers, predictions about the degradation characteristics of the aliphatic/aromatic copolymers can be made.

Individual Block Length Distributions of Block Copolymers of Polystyrene-block-Poly(α-methylstyrene) by MALDI/TOF Mass Spectrometry

The block length distributions of two block copolymers of α-methylstyrene and styrene, of different molecular weights and relative block lengths, were analyzed by matrix-assisted laser desorption/ionization time-of-flight (MALDI/TOF) mass spectrometry. A method for the treatment of mass spectroscopic data for block copolymers is proposed. The random coupling hypothesis has been verified experimentally and found to hold for this type of triblock copolymers. The experimental distributions have been compared with the Poisson and Schulz−Zimm models modified to accommodate the change of variables. The agreement between the experimental and calculated distributions is very good for the Schulz−Zimm model and fair for the Poisson model. Mass spectrometry proved to be a useful technique providing unique information on the experimental distributions of both constituent parts in a block copolymer. It was confirmed that block copolymers with narrow molecular weight distributions may have broad, complex, and even bimo...

Ancient splice junction shadows with relation to blocks in protein structure

Splice junction shadows (ancient exon-exon junctions) presumably reflect the existence of amino acid primary blocks which were used in the course of evolution for the construction of new proteins. The lengths of such blocks (i.e. regions between splice junctions), as the lengths of corresponding inserted or duplicated ancient exons, should be divisible by three in order to store the preexisting coding frame in the course of evolution. In this paper, we will test the hypothesis of intron-mediated recombination in a model of block molecular evolution (exon shuffling) by revealing corresponding blocks in existing database-contained coding sequences. For this purpose, we use a weight matrix prediction of ancient splice junction shadows in coding regions of the nucleotide sequences in current databases. The usage of splice junction shadows allows us to test the block evolution hypothesis in better detail in comparison with previous methods which were based only on currently existing recent exons. Our result of block length distribution at the nucleotide level shows a clear tendency to be divisible by three. At the protein level, several unexpected favorable block lengths, which are six, nine, 12 and 15 amino acids in length, were observed. Further refinements in our method for revealing splice junction shadows (structural block boundaries) might reveal peptides which probably maintain stable folds in different structures. The latter can in turn be used for protein structure prediction.

The interaction of acrylic diblock‐copolymers with aluminum oxide surfaces and their application for ceramic powder processing

AbstractAmphiphilic diblock copolymers were prepared by anionic copolymerization of t.‐butylmethacrylate (TBMA) with methylmethacrylate (MMA) and n‐butylmethacrylate (NBMA) respectively, followed by polymer analogous conversion of the TBMA‐into methacrylic acid‐ (MAA) blocks. These materials are highly efficient dispersants for oxide and nitride ceramic powders. A series of samples with Mn ranging from 4.000 to 135.000, and with block length ratios from 0.5 to 14 (MMA/MAA) with polydispersities close to 1.0 were obtained.The influence of total molecular weight and block length distribution of the copolymers and quality of the solvent system on their interaction with α‐Al2O3 were studied by sedimentation, adsorption experiments and surface plasmon resonance (SPR). The acrylic diblock copolymers are adsorbed irreversibly at the alumina surface. The conformation of the adsorbed macromolecules depends on the “quality” of the solvent. With respect to powder dispersing efficiency, an optimum is found when the polymers consist of short anchoring and stabilizing blocks.

Multiblock copolymers as polymeric surfactants: are “pancakes” better than “dumbbells”?

AbstractIt is suggested that multiblock copolymers which form a pancake at the interface between two incompatible homopolymers would be more efficient as compatibilizers than di‐ or triblock copolymers. Less of the multiblock copolymers would be lost into the bulk phases as micelles or mesophases than di‐ or triblock copolymers if some degree of irregularity is included in the multiblock architecture, either in block length or chemical sequence distribution, without compromising the thermodynamic driving forces which localize the copolymers at the interface. This molecular design strategy is aimed at reducing the ability of the surfactant to form a separate phase, thereby increasing the interfacial activity in a nonequilibrium system with a large interfacial area. The multiblock loops which would preferentially orient into the most compatible homopolymer phases would have to exceed a certain critical size in order to avoid the entropic penalty of having an extremely flat pancake, and to provide good adhesion between the bulk phases.

Use of crown ether in the anionic polymerization of propylene oxide—3. Preparation and micellization of diblock-copoly(oxypropylene/oxyethylene)

Diblock-copoly(oxypropylene/oxyethylene)s with moderately-long P-blocks (about 200 P units) and narrow block-length distributions were prepared by use of 18-crown-6 ether and the potassium salt of methoxypropanol in the sequential anionic polymerization of bulk propylene oxide at room temperature and ethylene oxide at 40–80°C (melt). The micellization of one of these copolymers, denoted P 200E 560, was studied by a number of techniques: surface tension, gel permeation chromatography, photon correlation spectroscopy, electron microscopy. The quantities obtained (critical micelle concentration, hydrodynamic radius, micelle size distribution) were compared with published results for other diblock and triblock copolymers.