The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.     

Compositionally symmetric diblock copolymer blends of moderate polydispersity

Recent experimental evidence and theoretical predictions indicate that binary blends of relatively monodisperse diblock copolymers remain miscible if the molecular weight disparity of the constituent copolymers is not too great. In this work, we examine the effect of moderate copolymer polydispersity on both the microstructural characteristics and phase behavior of blends prepared from four compositionally symmetric poly(styrene-b-isoprene) (SI) diblock copolymers ranging in polydispersity (M̄_w/M̄_n) from 1.02 to 1.30. Blend periodicities, measured by small-angle X-ray scattering, compare favorably with predictions from a strong segregation theory proposed for lamellar diblock copolymer blends composed of monomolecular copolymers. Transmission electron microscopy, employed to ascertain the real-space morphological characteristics of these blends, reveals that a lamellar → cylindrical transition occurs in macrophase-separated blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2653–2658, 1997     

PE/PEO/PE-PEO 对称三元共混体系相行为的耗散粒子动力学模拟研究

建立了对应实验体系聚乙烯/聚氧化乙烯/聚乙烯-聚氧化乙烯嵌段共聚物(PE/PEO/PE-PEO)的对称三元共混模型,并采用耗散粒子动力学(DPD)模拟方法对其相行为进行了理论研究.研究结果表明,随着均聚物体积分数的增加,体系的平衡相态发生由层状相(LAM)到双连续微乳液(BME)再到相分离(PS)的转变,相态演化规律和...     

Spinodal decomposition of two homopolymers with their block copolymer: A comparison of models

The dynamics of phase separation in the presence of a diblock copolymer have been studied using ternary and quaternary models of spinodal decomposition. The ternary model treats the block copolymer as a third component that is compatible with each of the mutually incompatible homopolymers. The quaternary model treats the block copolymer as a pair of specially constrained homopolymers. Both models predict core-shell morphologies with the copolymer concentrated at the interface. Both models predict larger domain sizes and less sharp phase boundaries in the early stages of spinodal decomposition. In the late stages, domain sizes are largest for the system of homopolymers without copolymer and smallest when a system containing copolymer is modeled as a quaternary blend. The scaling exponent observed for the quaternary model was s = 0.25 ± 0.02 compared to s ≅ 0.3 for the homopolymers without copolymer and for the ternary model. The quaternary model predicts internal phase separation within a pure diblock copolymer, whenever the corresponding homopolymers are sufficiently incompatible. © 1996 John Wiley & Sons, Inc.     

Dynamic light scattering from ternary polymer blends: critical behavior and bicontinuous microemulsions

We have used dynamic light scattering to study the dynamics of ternary polymer blends consisting of poly(dimethylsiloxane) (PDMS) and poly(ethylethylene) (PEE) homopolymers and a PDMS‐PEE diblock copolymer nearly symmetric in composition. The intensity autocorrelation functions for the binary blend are single‐exponential, and the associated correlation length ξ scales with reduced temperature ϵ in accordance with the Ising universality class (i.e., ξ ∼ ϵ^−ν, with ν = 0.63). An addition of copolymer depresses the critical temperature, but also increases the magnitude of ν. For compositions within the microemulsion channel, ξ exhibits a distinct maximum with decreasing temperature, near the Lifshitz line obtained from the static structure factor. For a particular composition, there is a “re‐entrant” microemulsion, as the system passes into and then out of the phase‐separated region upon cooling.     

Non‐equilibrium phase behavior of diblock copolymer melts and binary blends in the intermediate segregation regime

The phase behavior of intermediately segregated (χN = 45) poly(ethylene)‐poly(ethylethylene) (PE–PEE) diblock copolymers and PE–PEE binary blends are characterized using transmission electron microscopy and small‐angle X‐ray scattering. Surprisingly, the preparation‐dependent, nonequilibrium phase behavior can be overwhelming even at this degree of segregation. A pure diblock with a poly(ethylene) volume fraction of f_PE = 0.46 exhibited coexisting lamellae and perforated layers when prepared using a precipitation technique, but contained only the lamellar morphology when solvent cast. This preparation dependence was more dramatic in binary diblock copolymer blends with average compositions of 〈f_PE〉 = 0.44, 0.46, and 0.48. Precipitated blends exhibited a microphase separated structure that was disordered and bicontinuous; however, solvent cast samples exhibited either a cylindrical, coexisting cylindrical and lamellar, or lamellar morphology. This nonequilibrium behavior is attributed to the high degree of segregation and the proximity to the cylinder/lamellae phase boundary. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2229–2238, 1999     

Molecular design of multicomponent polymer systems. III. Comparative behavior of pure and tapered block copolymers in emulsification of blends of low-density polyethylene and polystyrene

Poly(hydrogenated butadiene-b-styrene) copolymers are very effective emulsifiers for blends of polystyrene and low-density or high-density polyethylene. It is shown that the extent of improvement in mechanical properties is dependent not only on the molecular weight but also on the structure of the diblock copolymer. A comparative study of the morphology and the mechanical behavior of modified low-density polyethylene/polystyrene blends demonstrates that a tapered diblock is more efficient than a pure diblock with the same composition and molecular weight. It is assumed that the unique behavior of the tapered sample results from its particular miscibility characteristics at the blend interface. The tapered copolymer could behave essentially as a solu-bilizing agent for the homopolymers at the interface and provide a “graded” modulus responsible for the improved mechanical response of the material.     

Block copolymer containing poly(3‐hexylthiophene) and poly(4‐vinylpyridine): Synthesis and its interaction with CdSe quantum dots for hybrid organic applications

Poly(3‐hexylthiophene)‐b‐poly(4‐vinylpyridine) diblock copolymer was synthesized by RAFT polymerization of 4‐vinyl pyridine using a trithiocarbonate‐terminated poly(3‐hexylthiophene) macro‐RAFT agent. The optoelectronic properties and the morphology of the block copolymer blends with CdSe quantum dots were investigated. UV‐vis and fluorescence experiments were performed to prove the charge transfer between CdSe and poly(3‐hexylthiophene)‐b‐poly(4‐vinylpyridine) diblock copolymer. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Polyethylene‐poly(L‐lactide) diblock copolymers: Synthesis and compatibilization of poly(L‐lactide)/polyethylene blends

A model polyethylene‐poly(L ‐lactide) diblock copolymer (PE‐b‐PLLA) was synthesized using hydroxyl‐terminated PE (PE‐OH) as a macroinitiator for the ring‐opening polymerization of L ‐lactide. Binary blends, which contained poly(L ‐lactide) (PLLA) and very low‐density polyethylene (LDPE), and ternary blends, which contained PLLA, LDPE, and PE‐b‐PLLA, were prepared by solution blending followed by precipitation and compression molding. Particle size analysis and scanning electron microscopy results showed that the particle size and distribution of the LDPE dispersed in the PLLA matrix was sharply decreased upon the addition of PE‐b‐PLLA. The tensile and Izod impact testing results on the ternary blends showed significantly improved toughness as compared to the PLLA homopolymer or the corresponding PLLA/LDPE binary blends. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2755–2766, 2001     

From the plateau problem to periodic minimal surfaces in lipids,surfactants and diblock copolymers

A novel method is presented for generating periodic surfaces. Such periodic surfaces appear in all systems which are characterized by internal interfaces and which additionally exhibit ordering. One example are systems of AB diblock copolymers, where the internal interfaces are formed by the chemical bonds between the A and B blocks. In these systems at least two bicontinuous phases are formed: the ordered bicontinuous double diamond phase and the gyroid phase. In these phases the ordered domains of A monomers and B monomers are separated by a periodic interface of the same symmetry as the phases themselves. Here we present a novel method for the generation of such periodic surfaces based on the simple Landau-Ginzburg model of microemulsions. We test the method on four known minimal periodic surfaces, find two new surfaces of cubic symmetry, and show how to obtain periodic surfaces of high genus and n-tuply continuous phases (n > 2). So far only bicontinuous (n = 2) phases have been known. We point out that the Landau model used here should be generic for all systems characterized by internal interfaces, including the diblock copolymer systems.     

Phase separation induced by shear quenching in polymer blends with a diblock copolymer

The effects of adding A–B diblock copolymer to a polymer blend (A/B) on phase‐separation kinetics and morphology have been investigated in a fixed shallow‐quench condition (ΔT = 1.5 °C) by in situ time‐resolved light scattering and phase‐contrast optical microscopy. A shear‐quench technique was used in this study instead of a conventional temperature‐quench method. Mixtures of nearly monodisperse low relative‐molecular masses of polybutadiene (M_w = 2.8 kg/mol), polystyrene (M_w = 2.6 kg/mol), and a near‐symmetric butadiene–styrene diblock copolymer (M_w = 6.3 kg/mol) as an interfacial modifier were studied. We observed that the addition of the diblock copolymer could either retard or accelerate the phase‐separation kinetics depending on the concentration of the diblock copolymer in the homopolymer blends. In contrast to the conventional temperature quench, we observed complex phase‐separation kinetics in the intermediate and late stages of phase separation by the shear‐quench technique. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 819–830, 2001     

Block copolymer compatibilizers for polystyrene/poly(dimethylsiloxane) blends

Symmetric polystyrene (PS)–poly(dimethylsiloxane) (PDMS) diblock copolymers were mixed into a 20% dispersion of PDMS in PS. The effect of adding the block copolymer on the blend morphology was examined as a function of the block copolymer molecular weight (M_n,bcp), concentration, and viscosity ratio (η_r). When blended together with the PS and PDMS homopolymers, most of the block copolymer appeared as micelles in the PS matrix. Even when the copolymer was preblended into the PDMS dispersed phase, block copolymer micelles in the PS matrix phase were observed with transmission electron microscopy after mixing. Adding 16 kg/mol PS–PDMS block copolymer dramatically reduced the PDMS particle size, but the morphology, as examined by scanning electron microscopy, was unstable upon thermal annealing. Adding 156 kg/mol block copolymer yielded particle sizes similar to those of blends with 40 or 83 kg/mol block copolymers, but only blends with 83 kg/mol block copolymer were stable after annealing. For a given value of M_n,bcp, a minimum PDMS particle size was observed when η_r ～ 1. When η_r = 2.6, thermally stable, submicrometer particles as small as 0.6 μm were observed after the addition of only 3% PS–PDMS diblock (number‐average molecular weight = 83 kg/mol) to the blend. As little as 1% 83 kg/mol block copolymer was sufficient to stabilize a 20% dispersion of 1.1‐μm PDMS particles in PS. Droplet size reduction was attributed to the prevention of coalescence caused by small amounts of block copolymer at the interface. The conditions under which block copolymer interfacial adsorption and interpenetration were facilitated were explained with Leibler's brush theory. © 2002 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 346–357, 2002; DOI 10.1002/polb.10098     

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     

Poly[(R)‐3‐hydroxybutyrate)]/poly(styrene) blends compatibilized with the relevant block copolymer

A novel triblock copolymer PS–PHB–PS based on the microbial polyester Poly[(R)‐3‐hydroxybutyrate)] (PHB) and poly(styrene) (PS) was prepared to be used as compatibilizer for the corresponding PHB/PS blends. It was prepared in a three‐step procedure consisting of (i) transesterification reaction between ethylene glycol and a high‐molecular‐weight PHB, (ii) synthesis of bromo‐terminated PHB macroinitiator, and (iii) atom transfer radical polymerization polymerization of styrene initiated by the PHB‐based macroinitiator. Fourier transform infrared, gel permeation chromatography, ¹H‐, and ¹³C‐NMR spectroscopies were used to determine the molecular structure and/or end‐group functionalities at each step of the procedure. Although thermogravimetric analysis showed that the block copolymer underwent a stepwise thermal degradation and had better thermal stability than their respective homopolymers, differential scanning calorimetry displayed that the PHB block in the copolymer could not crystallize, and thus generating a total amorphous structure. Atomic force microscopy images indicated that the block copolymer was phase segregated in a well‐defined morphological structure with nanodomain size of ～40 nm. Contact angle measurements proved that the wettability properties of the block copolymer were in between those of the PHB and PS homopolymers. Blends analyzed for their morphology and thermal properties showed good miscibility and had well‐defined morphological features. Polymer blends exhibited lower crystallinity and decreased stiffness which was proportional to the amount of compatibilizer content in the blends. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

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.     

Dynamic properties of microemulsions modified with homopolymers and diblock copolymers: the determination of bending moduli and renormalization effects

The properties of bicontinuous microemulsions, consisting of water, oil, and a surfactant, can be modified by the addition of diblock copolymers (boosting effect) and homopolymers (inverse boosting effect) or a combination of both. Here, the influence of the addition of homopolymers (PEP(X) and PEO(X), X=5k or 10k molecular weight) on the dynamics of the surfactant layer is studied with neutron spin echo spectroscopy (NSE). Combining the results with the previous findings for diblock copolymers allows for a better separation of viscosity and bending modulus effects. With the addition of homopolymers, a significant increase of the relaxation rate compared to the pure microemulsion has been observed. The influence on the bending rigidity kappa is measured with NSE experiments. Homopolymer addition reduces kappa by up to Deltakappa approximately -0.5k(B)T, whereas the diblock copolymer yields an increase of kappa by approximately 0.3k(B)T. Comparison of the bending moduli that are obtained by analysis of the dynamics to those obtained from small angle neutron scattering (SANS) sheds light on the different renormalization length scales for NSE and SANS. Variation of the surfactant concentration at otherwise constant conditions of homopolymer or diblock-copolymer concentration shows that NSE results are leading to the pure bending rigidity, while the renormalized one is measured with SANS.     

Interdiffusion measurements of modified poly(arylether sulfone)s using nuclear reaction analysis

The interdiffusion and miscibility behavior of three different types of modified poly(arylether sulfone)s with deuterated poly(arylether sulfone) is studied by depth profiling using the nuclear reaction D(³He, α)p. The diffusion coefficients are found to be in the range of 10⁻¹⁵ and 10⁻¹⁴ cm²/s at 195°C. A random copolymer of poly(arylether sulfone) containing 4,4-bis-(4′-hydroxyphenyl)valeric acid units is only partially miscible with deuterated poly(arylether sulfone) when the comonomer content is 8.8 mol %, whereas blends with comonomer contents of 1.7 and 4.5 mol % are miscible as indicated by complete interdiffusion. The transition from miscibility to immiscibility is caused by repulsive interactions of copolymer segments and can be explained in terms of a mean-field theory of random copolymer blends. Also, poly(arylether sulfone)s grafted with 0.4 wt % maleic anhydride or having pyromellitic anhydride endgroups are miscible with deuterated poly(arylether sulfone)s. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2083–2091, 1997     

Stress–strain behavior of low‐density polyethylene/poly(methyl methacrylate) blends with modulated interfaces with a hydrogenated polybutadiene‐block‐poly(methyl methacrylate) diblock copolymer

The stress–strain diagrams and ultimate tensile properties of uncompatibilized and compatibilized hydrogenated polybutadiene‐block‐poly(methyl methacrylate) (HPB‐b‐PMMA) blends with 20 wt % poly(methyl methacrylate) (PMMA) droplets dispersed in a low‐density polyethylene (LDPE) matrix were studied. The HPB‐b‐PMMA pure diblock copolymer was prepared via controlled living anionic polymerization. Four copolymers, in terms of the molecular weights of the hydrogenated polybutadiene (HPB) and PMMA sequences (22,000–12,000, 63,300–31,700, 49,500–53,500, and 27,700–67,800), were used. We demonstrated with the stress–strain diagrams, in combination with scanning electron microscopy observations of deformed specimens, that the interfacial adhesion had a predominant role in determining the mechanism and extent of blend deformation. The debonding of PMMA particles from the LDPE matrix was clearly observed in the compatibilized blends in which the copolymer was not efficiently located at the interface. The best HPB‐b‐PMMA copolymer, resulting in the maximum improvement of the tensile properties of the compatibilized blend, had a PMMA sequence that was approximately half that of the HPB block. Because of the much higher interactions encountered in the PMMA phase in comparison with those in HPB (LDPE), a shorter sequence of PMMA (with respect to HPB but longer than the critical molecular weight for entanglement) was sufficient to favor a quantitative location of the copolymer at the LDPE/PMMA interface. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 22–34, 2005     

Styrene and isoprene friction factors in styrene–isoprene matrices

Monomeric friction factors, Ξ, for polystyrene (PS), polyisoprene (PI), and a polystyrene–polyisoprene (SI) diblock copolymer have been determined as a function of temperature in four poly(styrene-b-isoprene-b-styrene-b-isoprene) tetrablock copolymer matrices. The Rouse model has been used to calculate the friction factors from tracer diffusion coefficients measured by forced Rayleigh scattering. Within the experimental temperature range the tetrablock copolymers are disordered, allowing for measurement of the diffusion coefficient in matrices with average compositions determined by the tetrablock copolymers (23, 42, 60, and 80% styrene by volume). Remarkably, for a given matrix composition the styrene and isoprene friction factors are essentially equivalent. Furthermore, at a constant interval from the system glass transition temperature, T_g, all of the friction factors (obtained from homopolymer, diblock copolymer, and tetrablock copolymer dynamics) agree to within an order of magnitude. This is in marked contrast to results for miscible polymer blends, where the individual components generally have distinct composition dependences and magnitudes at constant T − T_g. The homopolymer friction factors in the tetrablock matrices were systematically slightly higher than those of the diblock, which in turn were slightly higher than those of the homopolymers in their respective melts, when all compared at constant T − T_g. This is attributed to the local spatial distribution of styrene and isoprene segments in the tetrablocks, which presents a nonuniform free energy surface to the tracer molecules. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3079–3086, 1998     

Control of pore size and pore uniformity in films based on self‐assembling block copolymers

Blends of self‐assembling polystyrene‐block‐poly(4‐vinyl pyridine) (PS‐b‐P4VP) diblock‐copolymers and poly(4‐vinyl pyridine) (P4VP) homopolymers were used to fabricate isoporous and nanoporous films. Block copolymers (BCP) self‐assembled into a structure where the minority component forms very uniform cylinders, while homopolymers, resided in the core of the cylinders. Selective removal of the homopolymers by ethanol immersion led to the formation of well‐ordered pores. In films without added homopolymer, just immersion in ethanol and subsequent swelling of the P4VP blocks was found to be sufficient to create pores. Pore sizes were tuned between 10 and 50 nm by simply varying the homopolymer content and the molecular weight of the block‐copolymer. Uniformity was lost when the average pore size exceeded 30 nm because of macrophase separation. However, preparation of films from low M_W diblock copolymers showed that it is possible to have excellent pore size control and a high porosity, while retaining a low pore size distribution. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1568–1579