Macromolecular reaction and interdiffusion in a compatible polymer blend

A theory describing slow macromolecular reaction and interdiffuion in a compatible polymer blend is suggested based on the linear non-equilibrium thermodynamic principles. A simple model system is considered. In a blend consisting initially of homopolymers A and B, the transformation A → B proceeds with the B units accelerating the reaction. A system of diffusive-reaction equations for relevant macroscopic variables is derived. The randomness of the reacting chains' structure gives rise to a new interdiffusion mode in addition to the reacting polymer-homopolymer B interdiffusion. Numerical calculations reveal that the diffusive intermixing of reacting chains of different composition may significantly affect the reaction rate and the local compositional heterogeneity as well. It is possible to discriminate the fast- and the slow-mode theories of interdiffusion using reaction kinetics data. Under certain conditions, the reaction may proceed in a non-trivial autowave-like regime.     

Macromolecular reaction and interdiffusion in a compatible polymer blend, 2. The role of H‐bonding

A theory describing slow macromolecular reaction and interdiffusion in a compatible polymer blend is extended to consider H‐bonding. The known treatments of H‐bonding influence on the free energy of mixing and chains' mobilities are combined to calculate mutual diffusion coefficients in the framework of linear non‐equilibrium thermodynamics. Numerical calculations are performed for a blend of two random copolymers AC and BC to reveal the effect of H‐bonding (between A and B, B and B units) on the interdiffusion profiles. Then, the transformation of A units into B ones is included and the reaction‐diffusion equations are solved with the parameters corresponding to the blend of poly(tert‐butyl acrylate‐co‐styrene) with poly‐(acrylic acid‐co‐styrene) in which the thermal decomposition of tert‐butyl acrylate units takes place. The numerical calculations show that this system is suitable for the experimental verification of theoretical predictions concerning the interplay between macromolecular reaction and interdiffusion in polymer blends.     

The effect of copolymer composition on the dynamics of random copolymers in a homopolymer matrix

The effect of copolymer composition on the dynamics of random copolymers in a homopolymer matrix is studied using computer simulations within the framework of the bond-fluctuation model on blends containing low concentrations (10%) of A-B copolymers, where A and B are two different types of monomers, dispersed in a homopolymer matrix of chains with only A-type monomers. Four copolymer compositions were studied, phi(A)=0.33, phi(A)=0.5, phi(A)=0.66, and phi(A)=0.82, while maintaining a statistically random sequence distribution. For this study, we have only included intermolecular interactions between A and B monomers. Our results indicate, in agreement with experimental data, that copolymer composition has an impact on system dynamics. Analysis of the structure reveals that copolymers with majority A content are expanded in the homopolymer matrix, have fewer interchain copolymer-copolymer contacts, and are well dispersed in the homopolymer matrix. On the other hand, copolymers with lower A content form a more compact structure, have more interchain contacts, and form aggregates that are short lived. This in turn leads to slower system dynamics. Both the radius of gyration (Rg) and copolymer end-to-end vectors (Re) increase with increasing A content until phi(A)=0.66 and then decrease. Copolymers with lower A content form more compact structures as the repulsive interactions between unlike species are minimized by the copolymers folding back on themselves and forming aggregates of copolymer chains. Thus, these results provide insight into the variation of copolymer dynamics with composition in the system by documenting the correlation between the thermodynamics of this mixture, the conformation of a copolymer chain in a homopolymer matrix, and the dynamics of both components in this blend.     

Modern problems of the theory of macromolecular reactions in polymer blends

The main task of the theory of macromolecular reactions in polymer blends is to describe an evolution of the blend structure under the concerted action of the reaction and interdiffusion. For a polymeranalogous reaction proceeding with autoacceleration in a compatible blend, the task has been solved by methods of linear non-equilibrium thermodynamics. The set of reaction-diffusion equations derived permits to describe the blend structure in details, including the parameters characterizing compositional heterogeneity and units' distribution of the reacting chains in any local region of the blend. For incompatible blend of two homopolymers, the competition between a phase separation and the reaction of end-coupling with a formation of diblock-copolymer has been considered. The peculiarities of the processes mentioned as well as the actual problems in this field are discussed.     

Early Stages of Interchange Reactions in Polymer Blends

Summary: Simple models are studied for better understanding of the early stages of interchange reactions in polymer blends. For a homogeneous blend of homopolymers A and B, parameters of copolymer AB formed at the reaction beginning are explicitly calculated. It is shown that the analysis of the copolymer composition can help to establish the prevailing interchange mechanism. For a bilayer blend of immiscible homopolymers A and B, the reactive compatibilization through interchange is studied by continual Monte Carlo modeling. The analysis of the local distribution in block length shows that the interdiffusion of blend components may start only after the formation of rather short copolymer blocks in the course of interchange.     

Molecular weight distribution in emulsion polymerization. II. The copolymer case

A model for evaluating instantaneous degree of polymerization distribution and the chain composition distribution of copolymers produced in emulsion is developed. The approach adopted is based on the mathematics of Markov processes and represents an extension of the one developed for homopolymers in Part I. As in the homopolymer case, the main aspect of the theoretical treatment is the definition of the proper one step transition probability matrix through the so called subprocess-main process procedure. The model accounts for monomolecular and bimolecular termination (both by combination and disproportionation) and, in principle, it can be applied to any number of reacting monomer species as well as to any number of active chains per particle. However, only the 0–1–2 and 0–1–2–3 emulsion copolymerization systems are discussed in detail. In the case of the chain composition distribution, the model allows the calculation of its moments only, through the method of the Generating Function associated with the probability density function. The expression obtained for the instantaneous probability density functions, as well as for the corresponding cumulative distributions, are all in explicit form and involve only algebraic operations among matrices. Efficient numerical procedure for their application are reported in the Appendix. Illustrative calculations are reported for a 0–1–2–3 copolymerization system, simulating the copolymer styrene–methylmethacrylate. The effect of the various termination mechanisms on the distribution of degrees of polymerization and on the first two moments of the chain composition distribution is discussed in detail. Finally, the three dimensional overall distribution function of both chain length and composition is shown under the assumption of Gaussian type chain composition distribution.     

Observation of single-chain scattering from homopolymer blended with a triblock copolymer

A small-angle neutron scattering method has been developed to determine the chain conformation of homopolymer chains dispersed in a block copolymer matrix. Two contrast matching techniques are used to achieve this result and are demonstrated for a system based on a styrene-hydrogenated butadiene-styrene triblock copolymer and a hydrogenated butadiene homo-polymer. Composition matching uses a blend of labeled and unlabeled molecules to match the scattering density of another component. Phase matching requires a block copolymer which has been synthesized such that the scattering densities of the blocks are equal. This polymer provides a transparent matrix in which a composition-matched blend of homopolymer can be dispersed to isolate the single-chain scattering function of the homopolymer chains.     

A control of primary structure in the products of macromolecular reactions

Basing on the theory of macromolecular reactions, an influence of various factors on a units' distribution (UD) of the forming macromolecules is considered. In diluted solutions UD is determined by a competition between external reagent and intrachain interaction of reacted and unreacted units, first by neighbor effect. Should accelerating action of remote units is commensurable with that of nearest neighbors, such a conformational effect enlarges the formation of alternating sequences. In a melt, interchain effect shifts UD to a random one. In a polymer blend consisting of reacting and non-reacting but influencing the reactivity components, UD of transforming macromolecules is formed under concerted action of the reaction and interdiffusion. Thus modern achievements of the theory permit to analyze peculiarities of a wide set of reaction systems and facilitate a choice of optimal conditions for the preparation of tailor-made macromolecules.     

Polymer Melt Intercalation in Clay Modified by Diblock Copolymers

Summary: The thermodynamic equilibrium in a melt of homopolymer C mixed with clay modified by a diblock copolymer AB is considered in theory. It is assumed that mixing is carried out in two stages. At first, the diblock copolymer penetrates into the interlayers formed by long clay sheets. Then, the clay with adsorbed diblock copolymer chains is added to the homopolymer melt. It is shown that the first process is thermodynamically favorable only if the interlayer width exceeds some threshold value that depends mostly on the difference in the adsorption energy of units A and B. A spontaneous mixing at the second stage is possible only if the enthalpic interactions between homopolymer and copolymer units are not very unfavorable. If so, the formation of an intercalated state is expected for a homopolymer of length comparable to the copolymer length, while for a long homopolymer the anticipated equilibrium state is exfoliation. The spatial distribution of A, B, and C units across the interlayer has been studied for different parameters of the system. The most readily adsorbing units A occupy almost all clay surface. However, the layer of block A is considerably swelled by both B and C units. The mutual distribution of units B and C may vary from almost homogeneous to having rather sharp boundary depending on the value of the Flory‐Huggins parameter χ_BC. The formation of a pure homopolymer layer at the center of the interlayer indicates about a tendency to exfoliate.

Interlayer profiles of the fractions of units A, B, and C, respectively.     

Lateral ordering during self-organization of statistical multiblock copolymers

The self-organization of statistical multiblock and Bernoulli AB copolymers is studied. The initial ensemble is generated via the polymer-analogous reaction A→B that proceeds with the accelerating effect of neighboring B units. In a two-dimensional model, the reaction is performed in a rectangle composed of stretched chains. Then, the rectangle is closed into a cylinder, so that ring chains are located on its side surface. The self-organization of the ensemble is simulated via the successive rotation of each upper ring over the lower ring until arrangement with the maximum (in modulus) energy of attraction between chains is attained. Self-organization by energy is accompanied by lateral ordering: the sizes of clusters—accumulations of the one-type units—and mean heights H _A (H _B) of stems—columns consisting of A or B units perpendicular to chains—increase. The ratio between the values of H _A, as well as H _B, for ordered and initial ensembles is independent of the average composition of the system and as a rule increases as the length of blocks increases and the length of chains decreases. Features of generation of the ensemble of short chains and their ordering are revealed. It is shown that, during ordering of multiblock copolymers, the probabilistic properties (the stochastic behavior) of the ensemble are disturbed. The self-organization of statistical multiblock copolymers in a three-dimensional model is investigated via rotation of rings in the torus of the rectangular cross-section. The effects of various factors on self-organization by energy and local ordering in 2D and 3D models are similar; however, the efficiency of ordering in the three-dimensional system is always lower because, in this case, arrangements with the maximum energy of attraction simultaneously to two neighboring chains, rather than to one, are implemented for the majority of chains.     

Theoretical Study of the Effects of Templated Materials on Aggregate Formation

Summary: We have conducted Monte Carlo simulations to investigate a greatly simplified model for a blend composed of templated materials (polymers or monomers), smaller reacting particles and solvents on a two‐dimensional lattice. In the simulations, we compute the mean chain conformation of flexible templated polymers, and the distribution of the number of adjacent reacting particles aligned along the same axis to rationalize how templated materials affect the physical aggregation of smaller particles in a blend. We first examine the effects of the effective interactions between templated materials and smaller reacting particles. For repulsive interactions, flexible templated polymers tend to contract to reduce repulsions arising from smaller reacting particles, but for attractive interactions, mean chain dimension increases to maximize attraction. When templated material composition is increased, the conformational deformation of templated polymers becomes more pronounced. Moreover, in the presence of attractive interactions, reacting particles are more dispersed in the blend. In contrast, repulsive interactions increase the probability of aggregation of reacting particles. Also, our findings show that templated monomers (without chain connectivity) interact with reacting particles more effectively than with templated polymers due to the greater interacting area per monomer, which enhances the dispersion and segregation of reacting particles in the blend due to the attractive and repulsive interaction, respectively. In addition, as templated material composition is increased, the probability of forming a larger aggregate decreases. This simple model allows us to elucidate the role of templated materials on the physical aggregation of smaller particles in a blend.

Probability distribution P(m) of finding m adjacent reacting particles along the same axis in the presence of templated polymers (open symbols) and templated monomers (solid symbols) for different monomer‐reacting particle ratio, 1:3 (□/▪), 1:1 (○/•) and 3:1 (▵/▴):.     

嵌段共聚物和星型均聚物共混体系相行为的自洽场理论研究

用自洽场理论方法(Self-consistent field theory, SCFT)计算了嵌段共聚物AB和三等臂星型均聚物A共混体系的微相形态. 为了简化计算, 着重讨论了固定嵌段共聚物本体的相形态(如层状相)时, 所加入的均聚物的体积分数及均聚物与嵌段共聚物链长之比对体系相形态的影响; 并结合体系的熵和相互作用能的变化, 讨论了星型均聚物在体系微相结构中的分布.     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

Dissipative particle dynamics study on the interfaces in incompatible A/B homopolymer blends and with their block copolymers

Dissipative particle dynamics, a simulation technique appropriate at mesoscopic scales, has been applied to investigate the interfaces in immiscible binary A/B homopolymer blends and in the ternary systems with their block copolymers. For the binary blends, the interfacial tension increases and the interface thickness decreases with increasing Flory-Huggins interaction parameter chi while the homopolymer chain length is fixed. However, when the chi parameter and one of the homopolymer chain length is fixed, increasing another homopolymer chain length will induce only a small increase on interfacial tension and slight decrease on interface thickness. For the ternary blends, adding the A-b-B block copolymer will reduce the interfacial tension. When the mole number of the block copolymer is fixed, longer block chains have higher efficiency on reducing the interfacial tension than the shorter ones. But for the block copolymers with fixed volume fraction, shorter chains will be more efficient than the longer ones on reducing the interfacial tension. Increasing the block copolymer concentration reduces interfacial tension. This effect is more prominent for shorter block copolymer chains.     

The phase behavior of comblike block copolymer A(m+1)B(m)/homopolymer A mixtures

The phase behaviors of comblike block copolymer A(m+1)B(m)/homopolymer A mixtures are studied by using the random phase approximation method and real-space self-consistent field theory. From the spinodals of macrophase separation and microphase separation, we can find that the number of graft and the length of the homopolymer A have great effects on the phase behavior of the blend. For a given composition of comblike block copolymer, increasing the number of graft does not change the macrophase separation spinodal curve but decreases the microphase separation region. The addition of a small quantity of long-chain homopolymer A increases the microphase separation of comblike block copolymer/homopolymer A mixture. However, the addition of short-chain homopolymer A will decrease the phase separation region of comblike block copolymer/homopolymer A mixture. It is also found that the microstructure formed by diblock copolymer is easier to be swelled by homopolymer than that formed by comblike block copolymer. This can be attributed to the architecture difference between the comblike block copolymer and linear block copolymer.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245     

Thermal degradation of styrene-butadiene diblock copolymer: Part 2—Characteristics and mechanism of degradation of the copolymer

The degradation behaviour of the copolymer has been studied under programmed heating conditions and isothermally at 380°C and compared with the characteristics of the degradation of polystyrene (PS), polybutadiene (PB) and a 1:1 by weight blend of the homopolymers, under the same conditions. The degradation shows many similarities to that of the blend. Evolution of styrene from the PS sections is at first inhibited by early volatile products from the PB parts of the chains and is subsequently retarded by other products. The extent of these stabilisation effects is greater in the copolymer than in the blend. In consequence, greater amounts of PS and PB chain structures can persist to higher degradation temperatures than in the case of homopolymer or blend: this explains the considerably higher proportion of toluene in the volatile products and the greater extent of aromatisation of the PB chain fragments.     

Interdiffusion in polymer blends: The effect of compressibility

The polymer/polymer interdiffusion in a binary compressible blend consisting of long and short chains is investigated within the framework of the dynamic random phase approximation (RPA). The relative contributions of two (fast and slow) stages into the total relaxation of compositional heterogeneities are explicitly shown to be strongly dependent on the initial conditions and the degree of asymmetry of the blend. Special emphasis is given to the influence of the initial distribution of free volume on the apparent rate of the composition relaxation. The evolution of the dynamic struture factor is described as well. It is shown that most of the peculiarities usually ascribed to the “fast‐mode” behavior can be derived within the RPA approach.     

Ferrocene containing polymers

Polymers with pendent ferrocene units are synthesized by radical and anionic methods. It has been demonstrated that polymer-analogous reactions are an attractive alternative to prepare those polymers. Polymers with ferrocene units in the main chain are available from interfacial condensation reaction between ferrocene-1,1′-dicarbonic acid dichloride with α, ω-diamines. Addition of ferrocene-1,1′-dithiol onto norbornadiene yields a polymer with repeating units from ferrocene disulfide and norbornene and nortricyclane end-groups. End-capping reactions of α, ω-dimercapto-telechelics with vinylferrocene yield polymers with ferrocene end-groups.