Interfacial properties of diblock copolymers at penetrable interfaces: Density profile,stretching, and interfacial tension

The interfacial properties of diblock (AB) copolymers near an interface between two solvents are studied by using the exact Green's function of a Gaussian copolymer chain at an attractive penetrable interface. We have studied the mean‐square end‐to‐end distance of the copolymer, 〈R²(z)〉, as a function of the distance of the joint point of the copolymer to the interface, z, the segment density distribution ρ(z), and the reduction of the interfacial tension Δγ_c due to the presence of the diblock copolymer. The density profile and the stretching of the copolymer chain are in agreement with both experimental results and simulations. The reduction in the interfacial tension is found to decrease with the increase in the degree of polymerization of the copolymer chain.     

Influence of excluded volume on the conformational property of tail-like chain on the simple cubic lattice

The influence of excluded volume on the conformational property of linear tail-like chain with one end attached to a flat surface is investigated by means of dynamic Monte Carlo method. Conformational properties such as mean-square end-to-end distance 〈R²〉, mean-square radius of gyration 〈S²〉 and mean asphericity parameter 〈A〉 are calculated for random walking (RW) and self-avoiding walking (SAW) tail-like chains on the simple cubic lattice. We find that the EV has nearly the same effect on 〈R²〉 as on 〈S²〉: (1) 〈R²〉_SAW/〈R²〉_RW≈〈S²〉_SAW/〈S²〉_RW∝n^0.204±0.05, where n is the chain length, and (2) the limiting value of 〈R²〉/〈S²〉≈7.7 for both chains. The distribution P(R) of the SAW tail-like chain can be expressed as a R⁴ correction of that of the RW one. We find that the value 〈A〉 of the SAW tail-like chain is bigger than that of the RW tail-like chain for all chain lengths, and the limiting values are 0.446±0.006 and 0.403±0.005 respectively.     

Concentration dependence of the global and anisotropic dimensions of confined macromolecules

The chain dimensions 〈R²〉 of nondilute polymer solutions confined to a slit of the width D were studied using lattice simulations. It was found that the chain compression induced in good solvents by the concentration ϕ is enhanced in a slit relative to the bulk. The global dimensions of chains also change with ϕ in confined and unconfined theta solutions. At intermediate slit widths, a region was noted where coils are squeezed along all three axes. This region is manifested as a channel on the three‐dimensional surface 〈R²〉(D,ϕ) in both good and theta solvents. The coil anisotropy, given by the ratio of the parallel and perpendicular components of the chain dimensions 〈R_y²〉/〈R_x²〉, reaches high values at strong confinements, where coils form quasi‐two‐dimensional pancakes. The concentration‐induced reduction of the global chain dimensions in good solvents is almost fully transmitted to the parallel component 〈R_y²〉. The computed effects of concentration and confinement were compared with the predictions of mean‐field and scaling theories, and implications of the results to ultrathin films and layered nanocomposites were discussed. In addition, the distribution functions of the components of the end‐to‐end distance R perpendicular and parallel to the plates, W (R_x) and W (R_y), were calculated. The function W (R_x) combined with the concentration profile ϕ (x) along the pore provided details of the chain structure close to walls. A marked difference in the pace of the filling up of the depletion layer was noticed between chains in theta and good solvents. From the distribution functions W (R_x) and W (R_y), the highly anisotropic force‐elongation relations imply the deformation of chains in confined solutions and ultrathin bulk films.     

Excluded-volume effect for various chain models. I. Application to optical anisotropy and end-to-end distance of linear polymers

A study of the effect of excluded volume on the mean-square optical anisotropy 〈γ²〉 and the mean-square end-to-end distance 〈R²〉 has been carried out for polymer chains of up to 2000 bonds. The calculations have been made for models assuming (a) equiprobability of internal rotations and (b) interdependence of short-range intramolecular interactions. All the results indicate that 〈γ²〉 is practically insensitive to the excluded-volume effect. Concomitantly the behavior of 〈R²〉 has been analyzed.     

Analytical resolution of a parallel second‐order reaction mechanism

The competition among the three different elementary second‐order processes involving the radicals A and B, (1) (2) (3) is frequently established in many combustion and atmospheric chemistry systems. The analytical resolution of the above mechanism for k_AB = 2k_AA and k_AB = 2k_BB, that is, for a cross‐combination ratio ? = k_AB/(k_AAk_BB)^1/2 = 2, is well‐known, but it has been claimed not to exist for ? ≠ 2. In the present paper an analytical resolution of the system (1)–(3), performed under the condition k_AB ≠ 2k_AA and k_AB ≠ 2k_BB, leads to The mathematical procedure leading to this equation and the equation itself are valid independently of the nature of the products of the reactions ( 1 ), ( 2 ) and ( 3 ), that is, recombination or disproportionation products, provided that the reactants and the order of the reactions remain the same. The comparison with numerical integration for exemplary cases is performed. The solutions for the particular cases k_AB ≠ 2k_BB or k_AB ≠ 2k_AA are also presented. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 246–251, 2003     

Studies on equilibrium structures of complex polymers in condensed systems

The thermodynamic‐equilibrium structures of four copolymers with different chain architectures are compared. They are AB diblock, BAB triblock, and ABC triblock copolymers and AB₂ star‐branched graft copolymers. Their morphological transitions meaningfully differ from one another, reflecting the difference in chain architecture. Two‐component polymers barely form bicontinuous structures; however, symmetric ABC triblock copolymers easily form tricontinuous structures composed of two surfaces parallel to a Gyroid minimal surface. All four ABC equilibrium structures have a superlattice structure. Block polymer chains in microphase‐separated bulk are elongated in the longitudinal direction in lamellar microphases. Although the deformation manner of the chains restricted in microphases depends on the chain architectures, the volumes of the deformed coils are always the same as those of the unperturbed chains regardless of their architectures. The measured polystyrene/poly(2‐vinylpyridine) interfacial thickness is fairly thin, but the observed value is much thicker than the theoretically predicted one. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1645–1655, 2000     

Anisotropy in the dimensional and elastic parameters of confined macromolecules

Using lattice simulations the effect of confinement on the size, orientation and elastic properties of athermal chains was investigated. For chains confined in a slit or in a “cylinder” with square profile a minimum was observed in the dependence of the mean‐square end‐to‐end distance 〈R²〉 on the plate distance D. However, the components of the mean chain dimensions perpendicular and parallel to the walls, 〈R²_⟂〉 and 〈R²_∥〉, steadily diverge with reduction of the pore size. In a slit the distribution functions of the chain vector perpendicular and parallel to the plates, W〈R²_⟂ 〉 and W〈R²_∥〉, respectively, were computed. The marked difference between these distribution functions is interpreted as a sign of enhanced alignment of chains of the shape of elongated ellipsoids along the pore walls. A major part of the free energy of confinement ΔA_cf stems from this mechanism of pore‐induced macromolecular orientation. A striking anisotropy was observed in the elastic free energies A^el_⟂ and A^el_∥ of chains deformed in the direction perpendicular and parallel to the walls and in the corresponding force‐displacement functions. Finally, the relation between the elastic free energy A^el and the free energy of confinement ΔA_cf and between the forces f and f_solv derived thereof is analysed.     

Tuning block copolymer phase behavior with a selectively associating homopolymer additive

We use polymer random phase approximation (RPA) theory to calculate the microphase separation transition (MST) spinodal for an AB + C diblock copolymer–homopolymer blend where the C homopolymers are strongly attracted to the A segment of the copolymers. Our calculations indicate that one can shift the MST spinodal value of the A ? B segmental interaction parameter (χ_ABN)_S to significantly lower values [i.e., (χ_ABN)_S < 10.5] upon the addition of a selectively attractive C homopolymer. For a sufficiently attractive C homopolymer, (χ_ABN)_S can be pushed to negative values, indicating microphase separation in what would appear to be a completely miscible diblock copolymer. Furthermore, we show that microphase separation can occur in diblock copolymer–homopolymer blends where the segmental interactions between all polymer constituents are attractive. By tuning the value of (χ_ABN)_S with a homopolymer additive, one is therefore able to tune the effective copolymer segregation strength and thus dramatically affect the blend phase behavior. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2083–2090, 2009     

Random-coil dimensions of poly(methylphenylsiloxane) and their dependence on stereochemical structure

Rotational isomeric state theory was used to study the unperturbed dimensions 〈r²〉₀ of poly(methylphenylsiloxane) (PMPS) chains [Si(CH₃)(C₆H₅)? O? ]_x as a function of their stereochemical structure. The required conformational energies were obtained from semi-empirical, interatomic potential energy functions and from known results on poly(dimethylsiloxane). PMPS chains were found to differ from monosubstituted and disubstituted vinyl chains primarily in the larger distance of separation between groups in conformations giving rise to “pentanetype interactions.” In PMPS, the relatively large distance of separation, 3.8 Å, makes such in teractions attractive, particularly in the case of two phenyl groups; in contrast, such interactions are strongly repulsive at the ～2.5 Å separation characterizing vinyl chains. According to the calculated results, PMPS chains are very different from vinyl chains in that increase in isotacticity should cause a significant decrease in 〈r²〉₀ and increase in d ln 〈r²〉₀/dT. Comparison of theory with experimental results in the literature suggests that PMPS polymers which have been studied in this regard must have been significantly syndiotactic in stereochemical structure.     

Local order and shape of a polymer chain in an external electric field

A solution of polymer chains in the presence of an external electric field is considered. Dipole-like interactions between polymer chain segment-vectors and the electric field are assumed to be proportional to the cosine of the angle between the segment-vector and the direction of the electric field. Parameters characterizing the shape of the chain (i.e., the chain end-to-end distance and cross-section per chain), and parameters describing the local order at the segmental and chain level (i.e., moments of the first and second Legendre polynomials 〈P₁〉 and 〈P₂〉 are calculated. The optical anisotropy and the molecular shape change induced by the external electric field are discussed.     

Unperturbed chain dimensions of isotactic polypropylene in theta solvents

The unperturbed mean-square end-to-end distance 〈R₀²〉 and its temperature variation d In 〈R₀²〉/dT for isotactic polypropylene have been estimated from intrinsic viscosity data in three theta solvents, i.e., diphenyl, diphenyl ether, and dibenzyl ether, measured at their θ temperatures as determined by precipitation temperature measurements. The characteristic ratios, 〈R₀²〉/nl², where n is the number of bonds of length l in the main chain, evaluated by assuming Φ = 2.87 × 10²¹, are 5.80 in diphenyl (at θ = 125.1°C.), 5.41 in diphenyl ether (at θ = 142.8°C.), and 4.56 in dibenzyl ether (at θ = 183.2°C.). These values lead to the temperature coefficient d In 〈R₀²〉/dT = ?4.09 × 10^?3 deg.^?1 Results are compared with the data previously reported on polyethylene.     

Aggregation behavior of polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer in N‐methylpyrrolidone

Solution property of hydrogenated polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer (SEBS copolymer) was studied by using static light scattering and dynamic light scattering for cyclohexane and N‐methylpyrrolidone (NMP) solutions. From the values of dimensionless parameters ρ, defined as the ratio of radius of gyration 〈S²〉^1/2 to hydrodynamic radius R_H, and solubility parameters, SEBS copolymer proved to exist as single chain close to random coil in nonpolar cyclohexane, whereas aggregate into the core‐shell micelle consisting of poly(ethylene/butylene) (PEB) core surrounded by PS shell in polar NMP. The core‐shell micelle formed in NMP is composed of 65 polymer chains, having three times larger average chain density (d = 0.12 g cm^?3) than a single polymer chain (d = 0.04 g cm^?3) in cyclohexane. The comparison with the aggregation behaviors in other solvents demonstrated that the aggregate compactness of the copolymer depended largely on solvent polarity, resulting in formation of the highly dense PEB core (R_c = 4.5 nm) and the thick PS shell (ΔR = 22.9 nm) in high‐polar NMP. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 588–594, 2010     

Crystallization of markoffian copolymers

An equilibrium theory is proposed for crystallization of (A, B) binary copolymers whose comonomeric unit sequences are statistically described by conditional pair probabilities P_AA, P_AB, P_BA, and P_BB. These are linked to the product of the reactivity ratios by r = r_Ar_B = (P_AAP_BB)/(P_ABP_BA). Three cases are considered here, (i) B units are rejected from the crystals, (ii) cocrystallization of A and B comonomeric units is possible in the full range of compositions within a single crystal structure (copolymer isomorphism), (iii) cocrystallization takes place either in a poly(A)-type or in a poly(B)-type structure, depending on composition (copolymer isodimorphism). For case (i) crystallization the theory demonstrates, according to expectation, that alternating copolymers (r = 0) produce the largest melting point depression, whereas in case (ii) they give rise to the smallest composition difference between the crystals and the liquid. The theory developed here further illustrates that for binary copolymers which are isodimorphic (case iii), a phase diagram is obtained similar to that for a classical binary system of small molecules.     

Synthesis and properties of long‐chain branched poly(ether sulfone)s by self‐polycondensation of AB2 type macromonomers

Long‐chain branched poly(ether sulfone)s (PESs) were synthesized via self‐polycondensation of AB₂ macromonomers. The linear PES oligomers synthesized by self‐polycondensation of 4‐chloro‐4′‐(4‐hydroxyphenyloxy)diphenyl sulfone were terminated with 4‐(3,5‐methoxyphenoxy)‐4′‐fluorodiphenyl sulfone to form AB₂ macromonomer precursors. After conversion from methoxy to hydroxy groups, the AB₂ macromonomers were self‐polycondensed to form long‐chain branched PESs. NMR measurements support the formation of the target macromonomers ( = 2930–67,800 (g mol^?1); M_n = number average molecular weight) and long‐chain branched PESs. Gel permeation chromatography with multiangle light scattering measurements indicated the formation of high‐molecular‐weight (M_w) polymers over 10⁴. The root‐mean‐square radius of gyration (R_g) suggests that the shape of the long‐chain branched PES synthesized from small AB₂ macromonomers in solution is similar to that of hyperbranched polymers. Increasing resulted in larger R_g, suggesting a transition from hyperbranched to a linear‐like architecture in the resulting long‐chain branched PESs. Rheological measurements suggested the presence of strongly entangled chains in the long‐chain branched PES. Higher tensile modulus and smaller elongation at the break were observed in the tensile tests of the long‐chain branched PESs. It is assumed that the enhanced molecular entanglement points may act as physical crosslinks at room temperature. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1825–1831     

Hydrogen bond mediated self-assembly of two diblock copolymers

Two chemically dissimilar diblock copolymers, polybutadiene-b-poly(acrylic acid), PBd-b-PAA (M_w = 5.8–4 kg mol⁻¹) and poly(styrene)-b-poly(ethylene oxide), PS-b-PEO (M_w = 9–5 kg mol⁻¹) were blended in an effort to achieve morphologies typical of triblock copolymers. Blend compatibility was achieved by the hydrogen bond driven association of the PAA block of one diblock with the PEO block of the other. Small angle X-ray scattering was used to determine the morphologies of the compositions, which were further investigated using transmission electron microscopy and selective staining techniques. The crystallinity of the PEO block was determined by differential scanning calorimetry. The hydrogen bond interactions between PEO and PAA yielded a complex triblock lamellar morphology of the form PS-b-(PEO/PAA)-b-PBd-b-(PEO/PAA). This morphology was stable when crystallization of PEO was suppressed by sufficient interaction with PAA.     

The parameter dependence of calculated koopmans'defects in the framework of a model hamiltonian verified in the case of transition metal compounds

The validity of Koopmans' theorem in the lower energy region of trimethylenemethane iron tricarbonyl (1) is studied by means of a semi-empirical IN Reorganization energies are investigated as a function of the one-electron resonance integral β_μυ^AB and as a function of the one- and two interaction (γ_μυ^AA, K_μυ^AA and γ_μυ^AB). β_μυ^AB determines the kinetic energy of the interacting enlarged kinetic energy. The two-center electron repulsion intergral γ_μυ^AB have been calculated by means of an exponential formula with a short-range potentials with large γ_μυ^AB gradients pronounced reorganization energies are predicted while negligible defects even for stro case of smooth repulsion potentials with small γ_μυ^AB gradients. The largest parameter dependence of the calculated reorganization energie one-center electron—electron interaction integrals. With enlarged γ_μυ^AA and K_μυ^AA values enhanced Koopmans' defects are calculted in the framework of many body perturbation theory based on the Green's function formalism. A renormalized diagonal approximation for the self and correlation increments. The net defects are predominantly determined by electronic relaxation and modifications of the correlation energy in the ca of ground state pair-correlation (pair-removal) is only of minor importance.     

Inversion of the Kirkwood–Buff Theory of Solutions: Application to Tetrahydrofuran + Aromatic Hydrocarbon Binary Liquid Mixtures

The Kirkwood–Buff (K-B) integrals play an important role in characterizing the intermolecular interactions in liquid mixtures. The interaction is represented by the K-B parameters, G _AA,G _BB, and G _AB, which reflect correlation between like-like and like-unlike species in the mixture. The K-B integrals of binary mixtures of tetrahydrofuran with benzene, toluene, o-xylene, m-xylene, p-xylene and mesitylene at 298.15 K and atmospheric pressure have been computed from the experimental data of ultrasonic speed and density. We have used the similar inverse procedure (as proposed by Ben-Naim) to compute the K-B parameters of the mixture, in which thermodynamic information on mixtures, such as partial molar volumes, isothermal compressibility and experimental data of partial vapor pressures were used. A new route has been incorporated by using regular solution theory in the computation of excess Gibbs energy for obtaining the partial vapor pressures of binary liquid mixtures. The low values of excess entropy, S ^E≈0, obtained for these mixtures indicate the applicability of regular solution theory to the mixtures. The values of the K-B parameter, G _AB, obtained using this procedure indicate that the correlation/affinity between THF and aromatic hydrocarbon molecules follows the order: benzene > toluene > o-xylene > m-xylene > p-xylene > mesitylene, which is in good agreement with the results obtained from the trends exhibited by the excess functions of these mixtures.     

Conformational Analysis,RIS Models and Single‐Chain Properties of Structurally Modified Polycarbonates, 1. Effect of Cyclohexyl and Phenyl Ring Substitutions

Conformational properties of segments and chains of structurally different polycarbonates are investigated in detail. Conformational analysis and rotational isomeric state (RIS) models for some of the polycarbonates and single‐chain properties of all the polycarbonates are reported here for the first time. Substitution of the methyl group on the bisphenol phenyl rings results in increased energy barriers to rotations as well as changes in positions of local minima, compared to the case without substitutions. Conformational structure about the isopropylidene linkage C_α atom is not altered by ortho methyl substitutions on the rings. Substitution by a cyclohexyl ring rigidly attached to the C_α atom restricts conformational mobility within the bisphenol unit. Rotational flexibility of the phenyl–oxygen bond is hindered by additional substitutions on the cyclohexyl ring. The carbonate group prefers the trans–trans conformation in all the polycarbonates. The energy difference between the cis–trans and trans–trans states of the carbonate group is lowered by the ortho methyl substituent on the phenyl rings. There is a reduction in 〈R²〉, 〈S²〉, and C_n accompanying the substitutions. The introduction of other substituents on a cyclohexyl polycarbonate results in an increase in all chain dimensions including the persistence length. Also, the cyclohexyl or trimethylcyclohexyl substituents do not significantly alter the overall average shape of the chains. Substitutions both on the phenyl rings and at the isopropylidene linkage lead to a compaction of the polymer chain, but the effect is more pronounced when due to substituents on phenyl rings.     

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.     

Microphase Separation within a Comb Copolymer with Attractive Side Chains: A Computer Simulation Study

Computer simulation modelling of a flexible comb copolymer with attractive interactions between the monomer units of the side chains is performed. The conditions for the coil‐globule transition, induced by the increase of attractive interaction, ε, between side chain monomer units, are analysed for different values of the number of monomer units in the backbone, N, in the side chains, n, and between successive grafting points, m. It is shown that the coil‐globule transition of such a copolymer corresponds to a first‐order phase transition. The energy of attraction (ε) required for the realisation of the coil‐globule transition decreases with increasing n and decreasing m. The coil‐globule transition is accompanied by significant aggregation of side chain units. The resulting globule has a complex structure. In the case of a relatively short backbone (small value of N), the globule consists of a spherical core formed by side chains and an enveloping shell formed by the monomer units of the backbone. In the case of long copolymers (large value of N), the side chains form several spherical micelles while the backbone is wrapped on the surfaces of these micelles and between them.