Lattice Monte Carlo investigations on copolymer systems, 3. Alternating and random copolymers

Alternating and random copolymers in dilute solution are investigated by means of Monte Carlo simulations on a cubic lattice. Each molecule consists of an equal number of A and B segments, either randomly distributed along the chain or forming an alternating sequence. The energy parameters chosen represent selective solvent conditions (the solvent is a good one for monomers of type A and a θ-solvent for B; between A and B repulsive interactions are operative). Comparison with di- and triblock copolymers of equal overall composition reveals that the behaviour of random or alternating copolymers (subject to the same selective solvent) is quite different. Their properties rather resemble those of homopolymers in a solvent of intermediate quality. The absolute chain dimensions (e.g. the mean square radius of gyration, 〈s²〉, and the mean square end-to-end distance, 〈h²〉) of random and alternating copolymers as well as their scaling exponents are significantly larger than those of block copolymers. The ratio between 〈h²〉 and 〈s²〉 as well as the shape of the polymer (expressed by the asphericity δ) are similar to those of athermal polymers indicating that there is no pronounced selectivity of the solvent. In contrast to block copolymers, these parameters exhibit no significant chain-length dependence. The number of the various types of polymer-polymer contacts (A-A, B-B and A-B) is almost independent of the type of contact at least for the solvent conditions investigated. This is in contrast to block copolymers where A-B contacts are widely suppressed and where the number of B-B contacts is approximately twice as high as that of A-A contacts.     

Monte Carlo investigations of dense copolymer systems, 1. Pivot algorithm and pair distribution function

ABA triblock copolymers (the solvent being a θ-solvent for B and an athermal one for A) as well as their constituent homopolymers were investigated by means of Monte Carlo simulations in a 5-choice cubic lattice. The polymer concentration (represented by the fraction ϕ of sites occupied by the polymer) varied from 0 (isolated chain) to 0.80. An investigation of the usefulness of the pivot algorithm in dense systems resulted in reasonable acceptance fractions up to a volume fraction of 0.12 (athermal chain and ABA copolymer) and 0.05 (θ-chain). For larger volume fractions only the chain-ends remain mobile. The overlap concentration of the polymers defined by several quantities was approximately 0.07 (athermal chain), 0.12 (θ-chain) and 0.09 (ABA copolymer). At a polymer fraction of 0.32, the chains had the same number of inter- and intramolecular contacts on average. At higher concentrations, the behaviour of the chains was primarily determined by intermolecular interactions. Contrary to isolated pairs, the pair distribution function g(r) of two athermal chains in a (cubic) box exceeded unity at intermediate distances because of the influence of the finite size of the box. The larger the size of the box, the smaller the (positive) deviation was. In the limit of r → 0 the pair distribution function g(r) – being smaller than unity – increased with increasing concentration while the maximum at intermediate distances simultaneously decreased. Ultimately, at the highest concentration, the pair distribution function resembled that of isolated θ-chains. The concentration dependence of the θ-pair distribution function itself, however, is negligible. At low concentrations the pair distribution function of the ABA triblock copolymer behaved like that of an athermal chain (up to ϕ ≈ 0.40) where characteristic oscillations around 1 developed. This might be taken as indicative of the formation of a lamellar phase.     

Monte Carlo investigations of dense copolymer systems. III. Properties of triblock copolymers in good and theta solvent

The present article gives an analysis of XYX triblock copolymers in a good solvent and in a theta solvent, the segments of type X and type Y being repulsive for each other. The results are compared to homopolymers as well as to copolymers in a selective solvent that is a good one for the outer blocks and a theta solvent for the inner one and vice versa, the strength of repulsion between blocks being the same as in the present types of copolymers. A lattice model is used for the investigations and the concentration ranges from a volume fraction phi = 0 up to phi = 0.8. In the limit phi --> 0 the triblocks in good solvent are slightly more expanded than homopolymers and in theta solvent mean square dimensions of triblocks are considerably increased compared to homopolymers due to the repulsion between blocks. With increasing concentration the dimensions decrease but then they increase again and for large concentrations they become similar for all types of copolymers studied, as the effect of the solvent levels off making the repulsive interaction between blocks the dominant interaction. This leads to an orientation effect and as a consequence to microphase separation which is demonstrated by the concentration dependence of various quantities as well as by visualization of snapshots.     

Scaling and structural properties of a polymer in a simple solvent: A study based on integral equations

We present a statistical mechanical theory for polymer–solvent systems based on integral equations derived from the polymer Kirkwood hierarchy. Integral equations for pair monomer–monomer, monomer–solvent, and solvent–solvent correlation functions yield polymer–solvent distribution, chain conformation in three dimensions, and scaling properties associated with polymer swell and collapse in athermal, good, and poor solvents. Variation of polymer properties with solvent density and solvent quality is evaluated for chains having up to 100 bonds. In good solvents, the scaling exponent v has a constant value of about 0.61 at different solvent densities computed. For the athermal solvent case, the gyration radius and scaling exponent decrease with solvent density. In a poor solvent, the chain size scales as N^v with the value of the exponent being about 0.3, compared with the mean field value of ⅓. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3025–3033, 1998     

Multiblock copolymers of styrene and isoprene. II. Microstructure and dilute solution properties

Dilute solution properties of linear (SI)₃ six-block copolymers of styrene and isoprene are compared to those of random, two-block, and three-block copolymers of the same system. All the copolymers were prepared with sec-butyllithium in benzene. The microstructure of the polyisoprene blocks is close to that of homopolyisoprene prepared under the same conditions. In contrast, the random copolymer shows a larger amount of trans-1,4 isoprene units. The intrinsic viscosities of the copolymers in methylisobutyl ketone, a poor solvent for both polystyrene and polyisoprene, and in toluene, a good solvent for both homopolymers, are examined on the basis of the Fox–Flory relation for homopolymers. All the copolymers behave similarly in each solvent. In methylisobutyl ketone, the viscosity results indicate a random coil conformation with a small expansion owing to the extra repulsive interactions between the dissimilar units. In all cases, the heterocontact repulsive interactions are small and can be characterized by an interaction parameter χ_ab close to 0.025. In toluene, the perturbation caused by the heterocontacts becomes negligible and the expansion factor α_η can be predicted from a weighted average of those of the parent homopolymers of the same molecular weight as the copolymer.     

Aggregate morphologies of amphiphilic ABC triblock copolymer in dilute solution using self-consistent field theory

The complex microstructures of amphiphilic ABC linear triblock copolymers in which one of the end blocks is relatively short and hydrophilic, and the other two blocks B and C are hydrophobic in a dilute solution, have been investigated by the real-space implementation of self-consistent field theory (SCFT) in two dimensions (2D). In contrast to diblock copolymers in solution, the aggregation of triblock copolymers are more complicated due to the presence of the second hydrophobic blocks and, hence, big ranges of parameter space controlling the morphology. By tailoring the hydrophobic degree and its difference between the blocks B and C, the various shapes of vesicles, circlelike and linelike micelles possibly corresponding to spherelike, and rodlike micelles in 3D, and especially, peanutlike micelles not found in diblock copolymers are observed. The transition from vesicles to circlelike micelles occurs with increasing the hydrophobicity of the blocks B and C, while the transition from circlelike micelles to linelike micelles or from the mixture of micelles and vesicles to the long linelike micelles takes place when the repulsive interaction of the end hydrophobic block C is stronger than that of the middle hydrophobic block B. Furthermore, it is favorable for dispersion of the block copolymer in the solvent into aggregates when the repulsion of the solvent to the end hydrophobic block is larger than that of the solvent to the middle hydrophobic block. Especially when the bulk block copolymers are in a weak segregation regime, the competition between the microphase separation and macrophase separation exists and the large compound micelle-like aggregates are found due to the macrophase separation with increasing the hydrophobic degree of blocks B and C, which is absent in diblock copolymer solution. The simulation results successfully reproduce the existing experimental ones.     

Competition Between Interfacial Interaction and Microphase Separation in Crystallization of Filled Block Copolymers

Understanding the effect of repulsive interaction between blocks on crystallization in block copolymers is beneficial for the design and development of sophisticated nanostructures. Dynamic Monte Carlo simulations were performed to reveal the crystallization mechanism of block copolymers containing one‐dimensional nanofiller under different repulsive interaction strengths between crystallizable and noncrystallizable blocks. During crystallization, crystalline morphology is determined by the competition between segmental orientation perpendicular to microphase interfaces dominated by microphase separation and that along the direction of the long axis of the nanofiller controlled by interfacial interaction. As the repulsive interaction between different blocks is strengthened, the competition between microphase separation and interfacial interaction is intensified, eventually leading to an increase in crystallization rate and a degradation in crystalline morphology. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1516–1526     

Synthesis of phenylenevinylene and naphthylenevinylene homopolymers and block copolymers by ring‐opening metathesis polymerization

Homopolymers and copolymers containing phenylenevinylenes and naphthylenevinylenes can be synthesized by ring‐opening metathesis polymerization of strained monomers such as tetraoctyloxy‐substituted cyclophanedienes and naphthalenophanedienes initiated by the third‐generation Grubbs’ initiator. The resulting homopolymers exhibited low polydispersities. The block copolymers can also be synthesized by the sequential ring‐opening metathesis polymerization of two individual monomers. The structures of homopolymers and block copolymers were fully characterized by nuclear magnetic resonance spectroscopy. The molecular weight distribution of the block copolymers is relatively broad compared to their parent homopolymers possibly due to chain transfer reaction. The molar ratio of the two blocks can be tailored by the ratio of the monomers employed. The block copolymers exhibited a more efficient energy transfer in the solid state between the different blocks than those carried out in solution. The optical and electrochemical properties of the polymers were investigated and exhibited the potential uses in optoelectronics devices. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 67–74     

Properties of polystyrene-poly(methylmethacrylate) random and diblock copolymers in dilute and semidilute solutions

Solution properties for random and diblock copolymers of polystyrene (PS) and poly(methyl methacrylate) (PMMA) have been measured by dynamic and total intensity light scattering in solvents of differing quality. The results are compared with the corresponding properties for PS and PMMA homopolymers of similar molecular weight, in order to determine if interactions between unlike monomers are significant. The hydrodynamic radius (R_h) and diffusion second virial coefficient (k_d) for the random copolymer are found to be larger than the corresponding values for the homopolymers in a solvent which is near-theta for the two homopolymers, whereas no such effect is observed for the block copolymer. This suggests that most intrachain interactions occur a relatively short distance along the chain backbone. In a mutual good solvent R_h and k_d of the random copolymer are comparable to the average of the values for the homopolymers, indicating that in a good solvent monomer/solvent interactions dominate over monomer/monomer interactions. For an isolated diblock copolymer in a mutual good solvent, there is no evidence that interactions between unlike monomers lead to additional expansion of the entire molecule, as measured by R_h, nor expansion of the individual blocks as probed by light scattering with one block optically masked. However, at low but finite concentration there is evidence (the coefficients of the binary interaction terms in the viscosity and the mutual diffusion coefficient, and the second and third virial coefficients) that a weak ordering effect may exist in block copolymer solutions, far from the conditions where microphase separation occurs. Finally, measurements of ternary polymer-polymer-solvent solutions show no dependence on monomer composition or monomer distribution for the tracer diffusion of probe PS-PMMA copolymers in a PMMA/toluene matrix. This indicate that the frictional interaction is largely unaffected by interactions between unlike monomers. However, there is evidence that the thermodynamic interaction is more unfavorable between a random copolymer and the homopolymer matrix than between a diblock and the matrix. © 1994 John Wiley & Sons, Inc.     

Nematogenic block copolymers via the yamazaki reaction

A novel extension of the Yamazaki reaction is used to prepare block copolymers having rigid blocks of poly-(p-benzamide) (PBA) and semiflexible blocks of polyamide-hydrazide. A PBA prepolymer having M ? 10,000 was synthesized by the usual Yamazaki reaction using triphenylphosphite. As previously reported, higher-molecular-weight PBA could be obtained using 4-N-(4′-aminobenzamido)benzoic acid containing a preformed amide linkage. Addition of p-aminobenzhydrazide and terephthalic acid then led to formation of the polyamide-hydrazide blocks using as the active reactant the diphenylphosphite formed as a by-product in the first polymerization. Evidence that a block copolymer is produced includes an increase in inherent viscosity during the second step, differences in the solubility of the copolymer compared to the homopolymers, and comparison of the phase diagram of the block copolymer in N-methylpyrrolidone having 4% added LiCl with those of a random copolymer, and of mixtures of the two homopolymers. The critical concentration required to form a nematic phase in solutions of the block copolymers is correlated with the length (or axial ratio) of the rigid block, and with its proportion in the copolymer.     

Synthesis of tertiary amine‐based pH‐responsive polymers by RAFT Polymerization

Well‐defined tertiary amine‐based pH‐responsive homopolymers and block copolymers were synthesized via reversible addition‐fragmentation chain transfer (RAFT) polymerization using 4‐cyanopentanoic acid dithiobenzoate (CPAD) as the RAFT agent for homopolymers and a poly(ethylene glycol) (PEG) macro‐RAFT agent for the block copolymers. ¹H NMR and gel permeation chromatography results confirmed the successful synthesis of these homopolymers and block copolymers. Kinetics studies indicated that the formation of both the homopolymers and the block copolymers were well defined. The pKa titration experiments suggested that the homopolymers and the related block copolymers have a similar pKa. The dynamic light scattering investigation showed that all of the block copolymers underwent a sharp transition from unimers to micelles around their pKa and the hydrodynamic diameter (D_h) was not only dependent on the molecular weight but also on the composition of the block copolymers. The polymer solution of PEG‐b‐PPPDEMA formed the largest micelle compare to the PEG‐b‐PDPAEMA and PEG‐b‐PDBAEMA with a similar molecular weight. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1010–1022     

Macromolecular self-assembly in dilute sequence-controlled block copolymer/homopolymer blends

Conventional block copolymers consist of two long contiguous monomer sequences (‘blocks’) that can, in the same fashion as low-molar-mass surfactants, self-assemble into various microstructural elements (e.g., micelles at low copolymer concentrations) to minimize repulsive contacts in the presence of a parent homopolymer. In this work, we explore the existence of segment-specific interactions, as well as the possibility of tailoring these blend morphologies (and producing altogether new ones), with novel sequence-controlled block copolymers. These copolymers are comprised of at least one block that is a random segment composed of both constituent monomer species. Transmission electron microscopy is employed here to examine the bilayered membranes and channel structures that form in two different series of such copolymers in dilute copolymer/homopolymer blends.     

Interface stabilization and micelle formation in blends with a block copolymer

The phase separation behavior of ternary blends of two homopolymers, PMMA and PS, and a block copolymer of styrene and methylmethacrylate, P(S-b-MMA), was studied. The homopolymers were of equal chain length and were kept at equal amounts. Two copolymers were used with blocks of equal length, which exceeded or equaled that of the homopolymer chains. Varied was the copolymer contentf. Films were cast from toluene, which is a nonselective solvent. The morphologies of the cast films were compared with the structure of the critical fluctuations in solution, which were calculated in mean field approximation. The axis of blend compositionsf can be divided into parts of dominating macrophase and microphase separation. Above a transition concentrationf _o, all copolymer chains are found in phase interfaces. Belowf _o, part of them form micelles within the homopolymer phases.     

Properties of vinylpyrrolidone-tert-butylphenyl methacrylate copolymers in solution

Copolymers of vinylpyrrolidone-p-tert-butylphenyl methacrylate (VP-MBPh) of several compositions were prepared by polymerization in benzene at 50°C using α′α′-azobisisobutyronitrile as initiator. Three of the copolymers were fractionated. Number-average molecular weights of fractionated samples were determined by osmotic pressure in benzene or 2-propanol. Kuhn–Mark–Houwink relations were established in benzene, chloroform, and 2-propanol. From the relation between M _n and the intrinsic viscosity (η), it appears that these random copolymers behave as predicted by the theory for flexible polymers. Abnormal viscometric behavior shown by one of the copolymers in nitromethane at 29°C (the theta temperature) is discussed. The Stockmayer–Fixman semiempirical method was used for estimating unperturbed dimensions from viscosity data obtained in chloroform, a good common solvent. Values of the viscosity parameter K_θ increase with the content of p-tert-butylphenyl methacrylate. In general, experimental K_θ values are higher than those calculated for the homopolymers. Excluded-volume parameters are estimated and discussed in relation to repulsive interactions between unlike monomer units.     

Monte Carlo simulation of phase separations of block copolymers and of corresponding blends

The Monte Carlo method has been used to simulate the phase separations of block copolymers and of corresponding blends with very high concentration (sum of volume fractions of blocks A and B: ϕ_A + ϕ_B = 0,9545). Our main findings are as follows: (1) The mixing is nonrandom even in the athermal limit. (2) The nonselective good solvent molecules (ϕ_V = 0,0455) are mostly located at the interface between A- and B-rich phases, thus, it is not true that solvent and monomeric units will remain mixed at all temperatures. (3) Even for the same microscopic A-B interaction energy, ε, and at the same temperature, the Flory-Huggins parameter χ of block copolymers is always higher than that of corresponding blends, and the χ values of block copolymers and corresponding blends have different ε-dependencies. (4) The critical values of χ both for block copolymer and corresponding blend are obtained and compared with the meanfield theoretical predictions. It is found that the ratio of χ_c (block)/χ_c (blend) is qualitatively compatible with the prediction of the Flory-Leibler theory.     

Stoichiometric polyelectrolyte complexes of ionic block copolymers and oppositely charged polyions

Micellization in dilute solutions of diblock copolymers with a polyelectrolyte and a hydrophilic nonionic blocks and oppositely charged polyions is studied using mean-field theory. In aqueous solutions the micelle core consists of the polyelectrolyte complex (PEC) while the corona is formed by hydrophilic blocks of the block copolymers. Describing PEC as a globule in the framework of the Lifshitz [Zh. Eksp. Teor. Fiz. 55, 2408 (1968)] globule theory we calculate the surface tension of the micellar core/solvent interface as a function of the polyion degree of ionization, solvent quality, and concentration of low-molecular-mass salt. The equilibrium aggregation number of starlike micelles formed by block copolymers and homopolymers of opposite charge at stoichiometric mixture compositions is found as a function of the system parameters. It is shown that micelles disintegrate upon addition of salt.     

Styrene-methyl acrylate copolymers and acrylate homopolymers in solution

Molecular weight determinations by light scattering and osmometry and intrinsic viscosity measurements were made in various solvents on fractions of styrene–methyl acrylate copolymers with different compositions and on acrylate homopolymers prepared by free-radical reaction. Relations between intrinsic viscosity [η] and molecular weight M thus established are compared with those reported by other authors. 2-Methylcyclohexanol was found to be a theta solvent for the copolymers and both parent homopolymers, and isoamyl acetate was a theta solvent for poly(methyl acrylate). From theta point viscosity data obtained with these solvents, unperturbed chain dimensions were estimated. The results are compared with the unperturbed dimensions estimated from the [η]–M relations obtained in good solvents. On the basis of the experimental data it was found that the unperturbed dimension depends linearly on the copolymer composition, in contrast to the case of styrene–methyl methacrylate copolymers. Composition dependences of the theta temperature and of the parameter describing the long-range interactions between nonadjacent segments in polymer chains were investigated. The result implies that long-range interactions between monomeric units never disappear even when those between the same monomeric units vanish. The Huggins constant for copolymer is discussed in terms of the excluded volume variable.     

n-Butyllithium/α-methylstyrene/benzene/diethyl ether: A suitable initiation system for anionic syntheses of model co- and homopolymers of styrene and isoprene

An initiation system of the anionic polymerization, intended for the syntheses of homopolymers and block copolymers with narrow molar mass distribution, was tested with styrene and isoprene. The actual initiating species, viz., the oligomeric α-methylstyryl anion, originates by the reaction of n-butyllithium with α-methylstyrene in a benzene/diethyl ether 1:1 (v:v) solvent mixture at room temperature. The homopolymers and two-block copolymers of styrene and isoprene, prepared by using this system, were characterized by light scattering, membrance osmometry, GPC, and ¹H NMR spectroscopy. By using the suggested initiation system, it is possible to synthesize well-defined homopolymers and block copolymers with low polydispersity (as judged by the shape of the GPC peaks and by the values of the polydispersity index), especially in a molar mass region between 4 × 10⁴ and 1.5 × 10⁵ g/mol. Above the upper limit of this interval, an appropriate decrease of the diethyl ether/benzene volume ratio is recommended, though the polymerization time must then be prolonged.     

Cleavage of polystyrene‐b‐poly(ethylene oxide) block copolymers with a trithiocarbonate linkage in solutions

In this work, the polystyrene‐b‐poly(ethylene oxide) (PS‐b‐PEO) block copolymers with a trithiocarbonate group between the blocks were prepared by polymerization of styrene in the presence of a trithiocarbonate reversible addition fragmentation chain transfer (RAFT) agent connected with PEO. Decomposition of the trithiocarbonate group by UV irradiation was investigated in three different types of solvent: tetrahydrofuran (THF, common solvent for both blocks), cyclohexane/dioxane mixture (selective solvent for the PS block) and N,N‐dimethylformamide (DMF)/ethanol mixture (selective solvent for the PEO block). It is found that cleavage of the block copolymers can take place in all these three solvents and the cleavage ratio ranges from 76 to 86%. The micellar morphologies in selective solvents before and after cleavage were examined. It is observed that the size of the micelles is reduced after cleavage and sometimes aggregation of the micelles occurs due to removal of the corona of micelles. It shows that this work provides a facile and general method for synthesis of cleavable block copolymers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3834–3840, 2010     

Hydrodynamic properties of model 3-miktoarm star copolymers

The synthesis of well-defined, nearly monodispersed, 3-miktoarm (from the greek word μlkτós meaning mixed) star copolymer of the A₂B type is described. A and B is either polystyrene (PS), polybutadiene (PBd), or polyisoprene (PI). The sequential controlled addition of living anionic B and A chains to methyltrichlorosilane leads to narrow molecular weight distribution miktoarm star copolymers with homogeneous composition. Characterization was carried out by size exclusion chromatography, low-angle laser light scattering, laser differential refractometry, membrane and vapor pressure osmometry, nuclear magnetic resonance and ultraviolet spectroscopy. Analysis of [η], R_H and R_v of the A₂B and one A₂B₂ miktoarm copolymers, suggests that a small expansion of the copolymer occurs either in a good solvent for both species or in a Θ solvent for one of them, as compared with the corresponding star homopolymers. This is in contrast to results obtained on linear block copolymers, and is due to the increased occurrence of heterocontacts in the miktoarm starshaped architecture. © 1995 John Wiley & Sons, Inc.