Light-scattering studies on phase separation in a binary blend with addition of diblock copolymers

Time-resolved light-scattering measurements have been conducted to investigate the influence of a diblock copolymer additive on the phase boundaries and the kinetics of the phase separation of a polymer blend. The blend studied was a polystyrene-d₈/polybutadiene (PSD/PB) mixture with a diblock copolymer composed of the same homopolymers. It was observed that the critical temperature of the blend, which has an upper critical solution temperature (UCST), decreased with increasing copolymer content and the kinetics of the phase separation via a spinodal decomposition mechanism slowed down in the presence of the copolymer. The features of the spinodal peak position and intensity as a function of time with and without copolymer additive were analyzed for near and off-critical compositions in various temperature jumps. The intermediate and late-stage growth rates do not follow a universal scaling function with the addition of diblock copolymers. © 1995 John Wiley & Sons, Inc.     

Design of bicontinuous polymeric microemulsions

Recent experiments suggest that thermodynamically stable, bicontinuous microemulsions can be achieved in symmetric ternary blends of two homopolymers and a diblock copolymer by formulating alloys with compositions near mean-field isotropic Lifshitz points. We argue that practical application of this design criterion may require use of homopolymers of unequal molecular weights and block copolymers of different architecture. We demonstrate the existence of, and explicitly locate, mean-field isotropic Lifshitz points in ternary blends with homopolymer molecular weight asymmetry and either AB diblock or ABA triblock copolymer architectures. These calculations considerably expand the parameter space for observing bicontinuous microemulsions and allow for more flexibility in tailoring melt rheological properties and solid-state mechanical properties. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2775–2786, 1997     

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.     

Calculation of phase diagrams not requiring the derivatives of the Gibbs energy demonstrated for a mixture of two homopolymers with the corresponding copolymer

A method is presented which allows the calculation of phase diagrams (spinodal, binodal and tie lines) on the basis of the Gibbs energy of mixing ΔG. No derivatives of ΔG with respect to the composition variables are required. This method is particularly useful in cases where the composition dependence of ΔG is very complex and no analytical representation of the derivatives can be given. The method is applied to a ternary mixture of two homopolymers with a copolymer consisting of the same monomers. The sequence distribution of the copolymer is kept constant between random and purely alternating, and phase diagrams are calculated for different chemical compositions of the copolymer. The complex phase separation behavior resulting for a 1 : 1 copolymer becomes much simpler as one monomeric unit starts to predominate in the copolymer.     

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     

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.     

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.     

Calculation of critical points not requiring the derivatives of the Gibbs energy demonstrated for a mixture of two homopolymers with the corresponding copolymer

The method for the calculation of phase diagrams (spinodal, binodal and tie lines) exclusively on the basis of the Gibbs energy of mixing, ΔG, with no need of calculating its derivatives with respect to the composition variables was extended to determine the critical conditions and the condition of the stability of the critical points. The method is applied to a ternary mixture of two homopolymers with a copolymer consisting of the same monomers. The sequence distribution of the copolymer is kept constant between random and purely alternating, and phase diagrams are calculated for different chemical compositions of the copolymer. Three critical lines were found within a very small interval of the copolymer composition.     

Molecular weight dependence of diblock copolymer segregation at a polymer/polymer interface

Utilizing forward recoil spectrometry (FRES), we have determined the segregation isotherm which describes the interfacial excess z_i^* of diblock copolymers of poly (d₈-styrene-b-2-vinylpyridine) (dPS-PVP) at the interface between the homopolymers PS and PVP as a function of ?_∞, the volume fraction of diblock copolymer remaining in the host homopolymer. All the samples were analyzed after annealing at temperatures and times sufficient to achieve equilibrium segregation. The effect of the degree of polymerization of both the diblock copolymers and the host homopolymers on the segregation isotherm is investigated. When the degree of polymerization of the homopolymer is much larger than that of the diblock copolymer, the normalized interfacial excess (z_i^*/R_g), where R_g is the radius of gyration of an isolated block copolymer chain, is a universal function of that portion of the block copolymer chemical potential due to chain stretching. The existence of such a universal function is predicted by theory and its form is in good agreement with self-consistent mean field calculations. Using these results, one can predict important aspects of the block copolymer segregation (e.g., the saturation interfacial excess) without recourse to the time-consuming numerical calculations. © 1994 John Wiley & Sons, Inc.     

Study of the phase behavior of a diblock copolymer in an ionic liquid: Outlook for use of the integral-equation theory

It is shown that the integral-equation theory may be used to study the phase behavior of a diblock copolymer in an ionic liquid with allowance made for the solvent structure. Features of microphase separation are exemplified via calculation of the mean-field spinodal temperature and order-disorder transition temperature as functions of the copolymer concentration at two different lengths of the cationic tail of the ionic liquid. The need to allow for the solvent structure during construction of the theory of the phase behavior of block copolymers in ionic liquids is substantiated.     

Phase behavior of binary blends of diblock copolymer/homopolymer confined in spherical nanopores

Binary blends of a diblock copolymer (AB) and an incompatible homopolymer (C) confined in spherical cavities are studied using a simulated annealing technique. The phase behavior of the blends is examined for four typical cases, representing the different selectivity of the pore surface to the A, B, and C species. The internal morphology of the spherical polymeric particles is controlled by the homopolymer volume fraction, the degree of confinement, and the composition of the copolymer. Inside a particle, the homopolymers segregate to form one or, under some conditions, two domains; thus, the homopolymers may act as an additional controlling parameter of the shape and symmetry of the copolymer domain. A rich array of confinement-induced novel diblock copolymer morphologies is predicted. In particular, core-shell particles with the copolymers as the shell wrapping around a homopolymer core or a copolymer-homopolymer combined core and Janus-like particles with the copolymers and the homopolymers on different sides are obtained.     

Phase behavior of ABC-triblock copolymers with two inherently miscible blocks

 The phase behavior of ternary poly-1,4-isoprene-block-poly-1,2-butadiene-block-polystyrene (ABC) triblock copolymers based on a compatible diblock copolymer attached to an incompatible C-block of different lengths is investigated by differential scanning calorimetry, transmission electron microscopy and dynamic mechanical analysis. It is shown that the system behaves like a binary diblock copolymer of a mixed AB-block and a microphase separated C-block. Received: 10 June 1997 Accepted: 19 August 1997     

Scattering Function and Spinodal Transition of Linear and Nonlinear Block Copolymers Based on a Unified Molecular Model

This work uses a block copolymer architecture [(A'B)_n A_2]_m to unify the scattering function and spinodal transition of typical AB-type block copolymers. The key roles of block number, junction points and asymmetry ratios of block length are(1) to determine the form factor of each block copolymer at the molecular scale;(2) to affect the entropy loss across the spinodal transition and may result in deflection of spinodal curves. The common features are validated in typical linear and nonlinear block copolymers, including AB diblock, asymmetric A'BA triblock,miktoarm stars of AB_n, A_n B_n,(AB)_n,(A'B)_n A, A'BA_m, and multi-graft combs of(B_n A_2)m and [(A'B)_n A_2]_m. The explicit scattering functions and form factors of various block copolymers can be directly applied in radiation experiments(i.e. neutron or X-ray scattering) to unravel the effect of molecular architecture in solution and microphase separation in disordered melt. The molecular model used in this study is also helpful to guide the chemical synthesis to explore more potentially interesting block copolymers.     

On phase equilibria,interfacial tension and phase growth in ternary polymer blends

A gradient squared free energy functional of the Landau-Ginzburg type is combined with Flory-Huggins theory to calculate minimum domain sizes, concentration profiles and interfacial tensions in ternary polymer blends. The dynamic equations governing spinodal decomposition are linearized to show that the minimum size for growth is identical to the thermodynamic minimum on phase volume. It is shown that unseparated, third components are enriched at the interface, reduce interfacial tension, increase stability and increase the minimum domain sizes. Enrichment of the third component at the interface causes concentrations at the major components to lie outside their binodal limits at a distance from the interface. Although the effects are most pronounced when the third component is a compatibilizer, the general phenomena remain true even when the third component is relatively incompatible. Generalizations to blends of N components are presented, and a robust method for calculating multicomponent phase diagrams is described.     

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     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

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     

Synthesis of High χ–Low N Diblock Copolymers by Polymerization-Induced Self-Assembly

Polymerization-induced self-assembly (PISA) enables the scalable synthesis of functional block copolymer nanoparticles with various morphologies. Herein we exploit this versatile technique to produce so-called “high χ–low N” diblock copolymers that undergo nanoscale phase separation in the solid state to produce sub-10 nm surface features. By varying the degree of polymerization of the stabilizer and core-forming blocks, PISA provides rapid access to a wide range of diblock copolymers, and enables fundamental thermodynamic parameters to be determined. In addition, the pre-organization of copolymer chains within sterically-stabilized nanoparticles that occurs during PISA leads to enhanced phase separation relative to that achieved using solution-cast molecularly-dissolved copolymer chains.