Pressure-induced formation of diblock copolymer "micelles" in supercritical fluids. A combined study by small angle scattering experiments and mean-field theory. II. Kinetics of the unimer-aggregate transition

We developed a simple time-dependent mean-field theory to describe the phase separation kinetics of either homopolymers or AB-diblock copolymers in supercritical (SC) fluids. The model, previously used to describe the phase behavior of AB-block copolymers under the assumption of strong solvent selectivity for just one copolymer chain, has been extended to study the kinetics of the phase separation process. Time resolved small angle x-ray scattering (TR-SAXS) measurements have been performed on different AB-diblock copolymers containing a perfluorinated chain and dissolved in SC-CO2. The data obtained over a wide range of pressure and temperature confirm our theoretical predictions. Particularly interesting is the presence of two relaxation frequencies for the homogeneous solution --> spherical aggregate transition, where the two relaxation processes depend on the depth of the pressure jump and on temperature. The whole phenomenon could be explained as an initial SC solvent/polymer phase separation followed by a slow reorientation process to form spherical aggregates driven by the copolymer solvophilic moiety.     

Instabilities in block copolymer films induced by compressible solvents

We combine a simple lattice-gas model for fluid mixtures along with polymer mean-field theory for block copolymer melts to study the stability of thin films of diblock copolymers in the presence of compressible fluid solvents. Using a free energy analysis, the stable and unstable thicknesses of a copolymer thin film are obtained for given solvent conditions. Our results suggest that the interplay between confinement, the compressibility of the solvent, and its selectivity to polymer component can lead to significant changes on the ordering and stability of the diblock copolymer thin films. Our results are in qualitative agreement with recent experimental results.     

对称长链和近对称短链两嵌段聚合物混合体系相行为研究

利用自洽平均场理论(SCMFT)系统地研究了对称长链和近对称短链两嵌段聚合物混合体系在纳米尺度下的自组装行为.体系中具有较高聚合度的对称长链熔体处于层状相,聚合度较低的近对称短链熔体处于无序相,而其混合体系却随着两种成分的不同比例呈现出有序-无序相转变、有序-有序相转变及有序-无序两相共存等复杂的相行为,计算结果与近期类似体系的实验有着较好的吻合.同时与两种对称的两嵌段聚合物混合体系的计算结果进行了比较,得出这两种体系的异同之处.     

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.     

Concentration fluctuation effects on the phase behavior of compressible diblock copolymers

A Hartree analysis has been performed for compressible diblock copolymers of incompatible pairs to investigate the concentration fluctuation effects on their microphase separation behavior. The free energy in the Hartree analysis is obtained from the self-consistent correction to its mean-field cousin, which was recently formulated for such copolymer systems. The mean-field phase diagram is shown to be significantly affected by the fluctuation effects as the copolymer chain size N is lowered. An effective interaction chi(cRPA), which carries not only the change in contact interactions but also the compressibility difference between block components, plays a key role in understanding of the phase behavior and the pressure responses of various thermodynamic transitions for the copolymers with finite sizes. In particular, a symmetric copolymer at disorder-to-lamella transition is found to satisfy Nchi(cRPA)(q*)=10.495+41.022N(-1/3) when evaluated at a characteristic wave number q* for ordered microphases.     

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.     

Interfacial tension of evaporating emulsion droplets containing amphiphilic block copolymers: effects of solvent and polymer composition

Evaporating droplets of volatile organic solvent containing amphiphilic block copolymers may undergo hydrodynamic instabilities that lead to dispersal of copolymer micelles into the surrounding aqueous phase. As for related phenomena in reactive polymer blends and oil/water/surfactant systems, this process has been ascribed to a nearly vanishing or transiently negative interfacial tension between the water and solvent phases induced by adsorption of copolymer to the interface. In this report, we investigate the influence of the choice of organic solvent and polymer composition for a series of polystyrene-b-poly(ethylene oxide) (PS-PEO) diblock copolymers, by in situ micropipette tensiometry on evaporating emulsion drops. These measurements suggest that the sensitivity to the organic solvent chosen reflects both differences in the bare solvent/water interfacial tension as well as the propensity of the copolymer to aggregate within the organic phase. While instabilities coincident with an approach of the interfacial tension nearly to zero were observed only for copolymers with PEO content greater than 15 wt.%, beyond this point the interfacial behavior and critical concentration needed to trigger surface instability were found to depend only weakly on copolymer composition.     

Crowding effect induced phase transition of amphiphilic diblock copolymer in solution

The crowding agent induced phase transition of amphiphilic block copolymers in solution was explicitly considered. The influence of the size and the volume fraction of the crowding agent on the phase separation of amphiphilic diblock copolymers is investigated by using self-consistent field theory (SCFT) method. The concentration of the disorder to order transition of the block copolymer decreases when the size of the crowding agent is larger than that of the solvent. The higher volume fraction of the crowding agent will induce the transition of the block copolymer from disorder to order state at a lower concentration. The relation between the size and the volume fraction of the crowding agent is elucidated. When the size of the crowding agent is larger, its volume fraction of the disorder to order transition of the block copolymer will be lower. The conformation of the crowding agent considered as a polymer chain is also studied and compared.     

Effect of molecular architecture on phase behavior of graft copolymers

Influence of molecular architecture on phase behavior of graft copolymer melts was studied by using a reciprocal-space self-consistent filed theory (SCFT). The phase diagrams were examined as functions of the architectural parameters describing the graft copolymers (i.e., the number of grafts and the position of first junction). In comparison with the well-known phase diagram of diblock copolymers, the phase diagrams of the graft copolymers are asymmetric. When the number of grafts or the position of first junction varies, the boundaries of order-order transitions have shifts due to the variation in the chain stretching energy. The change in molecular architecture also significantly alters the domain spacing of ordered structures but has weak impact on the density distributions of graft copolymers. For comparison of the theoretical predictions with the existing experimental results, the phase diagrams of graft copolymers were also calculated at strong segregation. The SCFT calculations can accurately capture the characteristics of the phase behavior of graft copolymer melts.     

Physical deposition behavior of charged amphiphilic diblock copolymers: Effect of charge distribution and electric field

Coarse-grained molecular dynamics simulations are used to investigate physical deposition behavior of charged amphiphlic diblock copolymers. The effects of solvent selectivity, charge distribution in amphiphlic diblock copolymers, and electric field strength on deposition conformations are studied qualitatively. Flat amphiphilic bilayers, which consist of hydrophilic monolayer and hydrophobic brush, are formed by physical deposition of charged amphiphlic diblock copolymers in nonselective solvents. For physically deposited amphiphlic diblock copolymers in selective solvents, amphiphilic bilayers consist of disc-shaped hydrophilic monolayers and hydrophobic nanospheres are found. This study sheds light on the formation of various amphiphlic diblock copolymer deposition conformations in different solvents and interaction mechanism of different components. Furthermore, the evolution of physical deposition process of charged amphiphlic diblock copolymers layer offers new insight to the controlling of amphiphilic bilayer thickness, hydrophobic nanosphere size, and interface property of depositional amphiphlic diblock copolymers.     

嵌段序列对聚合物囊泡形成过程影响的Monte Carlo模拟

采用Monte Carlo模拟方法研究了具有相同链长和组分比的不同嵌段序列的AB两嵌段共聚物与ABA三嵌段共聚物在选择性溶剂中形成囊泡的动力学过程. 模拟结果表明, AB两嵌段共聚物囊泡的形成与ABA三嵌段共聚物囊泡的形成的动力学过程不同. 在慢速退火条件下, ABA三嵌段共聚物囊泡是通过亲水链段向胶束的表面和中心扩散而形成的, 而AB两嵌段共聚物囊泡则由片层弯曲闭合而形成. 相对而言, 退火速度对AB两嵌段共聚物囊泡形成的动力学过程没有显著影响, 其改变仅影响亲水链段与疏水链段发生相分离的难易程度. 当退火速度较快时, 亲水链段和疏水链段发生相分离的速度较快且相分离发生在囊泡形成之前; 而当退火速度较慢时亲水链段和疏水链段之间的相分离在囊泡形成之后仍在进行.     

Insights into poly(3‐hexylthiophene)‐b‐poly(ethylene oxide) block copolymer: Synthesis and solvent‐induced structure formation in thin films

We report the synthesis, characterization, and solvent‐induced structure formation in thin films of an amphiphilic rod‐coil conjugated block copolymer, poly(3‐hexylthiophene)‐b‐poly(ethylene oxide). The diblock copolymers were prepared by a facile click reaction and their characterizations as well as thermal, crystalline, optical properties, and self‐assembly behavior have been investigated in detail. A series of morphologies including two‐phase separated nanostructure, nanofibrils, and their mixed morphology could be obtained depending on the selectivity of solvents to different blocks. Structural analyses demonstrate there is a subtle balance between microphase separation of copolymer and the π‐π stacking of the conjugated P3HT and such balance can be controlled by changing the solvents of different selectivity in solution and the length of P3HT block. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A theoretical and simulation study of the self-assembly of a binary blend of diblock copolymers

Pure diblock copolymer melts exhibit a narrow range of conditions at which bicontinuous and cocontinuous phases are stable; such conditions and the morphology of such phases can be tuned by the use of additives. In this work, we have studied a bidisperse system of diblock copolymers using theory and simulation. In particular, we elucidated how a short, lamellar-forming diblock copolymer modifies the phase behavior of a longer, cylinder-forming diblock copolymer. In a narrow range of intermediate compositions, self-consistent field theory predicts the formation of a gyroid phase although particle-based simulations show that three phases compete: the gyroid phase, a disordered cocontinuous phase, and the cylinder phase, all having free energies within error bars of each other. Former experimental studies of a similar system have yielded an unidentified, partially irregular bicontinuous phase, and our simulations suggest that at such conditions the formation of a partially transformed network phase is indeed plausible. Close examination of the spatial distribution of chains reveals that packing frustration (manifested by chain stretching and low density spots) occurs in the majority-block domains of the three competing phases simulated. In all cases, a double interface around the minority-block domains is also detected with the outer one formed by the short chains, and the inner one formed by the longer chains.     

Dynamic structure factor of homogeneous diblock copolymers solutions

The dynamics of homogeneous diblock copolymer solutions in the mean field regime sensitively depends on the composition polydispersity at constant chain length polydispersity. It was observed by photon correlation spectroscopy that the decay of the order parameter fluctuations in high molecular mass diblock copolymers solutions in a common solvent can change from a pure relaxational to a pure diffusive character. A rationalization of this behavior is presented.     

Bilayers and interdigitation in block copolymer vesicles

Amphiphilic block copolyethers assemble into membranes with thickness between 2.4 and 7.5 nm. The vesicular morphology has been confirmed by small-angle X-ray scattering combined with electron microscopy for diblock copolymers and triblock copolymers of both architectures. The scaling of the membrane thicknesses with the length of the hydrophobic block is in good agreement with the strong segregation theory for block copolymer melts, indicating a mixed and stretched conformation of the hydrophobic chain inside the vesicle membrane. This result is in contrast to previously published results where the hydrophobic membranes were observed to have bilayer geometry and polymer chains that are relatively unperturbed from their ideal Gaussian dimensions.     

Dewetting instability during the formation of polymersomes from block-copolymer-stabilized double emulsions

We investigate the formation of polymer vesicles, or polymersomes, of polystyrene-block-poly(ethylene oxide) diblock copolymers using double emulsion droplets of controlled architecture as templates. To engineer the structure of the polymersomes, it is important to consider the concentration of diblock copolymer in the middle phase of the double emulsion. We describe how the presence of excess polymer can induce a transition from complete wetting to partial wetting of the middle phase, resulting in polymer shells with inhomogeneous thicknesses.     

Effect of particle surface selectivity on composite nanostructures in nanoparticle/diblock copolymer mixture dilute solution

In this study the phase behavior of nanoparticle/diblock copolymer composites in dilute solution has been investigated by the hybrid particle-field (HPF) method. We focus on the influence of particle surface selectivity (i.e. hydrophobic and hydrophilic) on the distribution of nanoparticles in the micelles formed by the diblock copolymers. These two types of particle surface selectivity are simulated systematically. The different competition between the energy from enthalpy and the energy from entropy has been observed in the two kinds of composite systems. Our simulation results show that the particle surface selectivity is a crucial factor for determining the thermodynamic properties in the complex dilute solution, and the morphologies of micelles are controlled by the volume fraction of the nanoparticles. The change of particle distribution in various micelles enriches the composite microstructures that can be formed by nanoparticle and diblock copolymer.     

Self-assembly in block polyelectrolytes

The self-consistent field theory (SCFT) complemented with the Poisson-Boltzmann equation is employed to explore self-assembly of polyelectrolyte copolymers composed of charged blocks A and neutral blocks B. We have extended SCFT to dissociating triblock copolymers and demonstrated our approach on three characteristic examples: (1) diblock copolymer (AB) melt, (2) symmetric triblock copolymer (ABA) melt, (3) triblock copolymer (ABA) solution with added electrolyte. For copolymer melts, we varied the composition (that is, the total fraction of A-segments in the system) and the charge density on A blocks and calculated the phase diagram that contains ordered mesophases of lamellar, gyroid, hexagonal, and bcc symmetries, as well as the uniform disordered phase. The phase diagram of charged block copolymer melts in the charge density--system composition coordinates is similar to the classical phase diagram of neutral block copolymer melts, where the composition and the Flory mismatch interaction parameter χ(AB) are used as variables. We found that the transitions between the polyelectrolyte mesophases with the increase of charge density occur in the same sequence, from lamellar to gyroid to hexagonal to bcc to disordered morphologies, as the mesophase transitions for neutral diblocks with the decrease of χ(AB). In a certain range of compositions, the phase diagram for charged triblock copolymers exhibits unexpected features, allowing for transitions from hexagonal to gyroid to lamellar mesophases as the charge density increases. Triblock polyelectrolyte solutions were studied by varying the charge density and solvent concentration at a fixed copolymer composition. Transitions from lamellar to gyroid and gyroid to hexagonal morphologies were observed at lower polymer concentrations than the respective transitions in the similar neutral copolymer, indicating a substantial influence of the charge density on phase behavior.     

Thermoreversible gelation of poly(ethylene oxide) biodegradable polyester block copolymers. II

Poly(ethylene oxide)-b-poly(L-lactic acid) (PEO-PLLA) diblock copolymers were synthesized via a ring opening polymerization from poly(ethylene oxide) and l -lactide. Stannous octoate was used as a catalyst in a solution polymerization with toluene as the solvent. Their physicochemical properties were investigated by using infrared spectroscopy, ¹H-NMR spectroscopy, gel permeation chromatography, and differential scanning calorimetry, as well as the observational data of gel-sol transitions in aqueous solutions. Aqueous solutions of PEO-PLLA diblock copolymers changed from a gel phase to a sol phase with increasing temperature when their polymer concentrations are above a critical gel concentration. As the PLLA block length increased, the gel-sol transition temperature increased. For comparison, diblock copolymers of poly(ethylene oxide)-b-poly(l -lactic acid-co-glycolic acid) [PEO-P(LLA/GA)] and poly(ethylene oxide)-b-poly(dl -lactic acid-co-glycolic acid) [PEO-P(DLLA/GA)] were synthesized by the same methods, and their gel-sol transition behaviors were also investigated. The gel-sol transition properties of these diblock copolymers are influenced by the hydrophilic/hydrophobic balance of the copolymer, block length, hydrophobicity, and stereoregularity of the hydrophobic block of the copolymer. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2207–2218, 1999     

Preparation and characterization of MPEG–PCL diblock copolymers with thermo‐responsive sol–gel–sol phase transition

MPEG–PCL diblock copolymers consisting of methoxy polyethylene glycol (MPEG, 750 g/mol) and poly(?‐caprolactone) (PCL) were synthesized by ring‐opening polymerization. Aqueous solutions of the synthesized diblock copolymers were prepared by dissolving the MPEG–PCL diblock copolymers at concentrations in the range of 0–20 wt %. When the PCL molecular weight was 3000 or greater, the polymer was only partially soluble in water. As the temperature was increased from room temperature, the diblock copolymer solutions showed two phase transitions: a sol‐to‐gel transition and a gel‐to‐sol transition. The sol‐to‐gel phase transition temperature decreased substantially with increasing PCL length. The sol–gel–sol transition with the increase in temperature was confirmed by monitoring the viscosity as a function of temperature. The temperature ranges of the phase transitions measured by the tilting method were in full agreement with those determined from the viscosity measurements. The maximum viscosity of the copolymer solution increased with increasing hydrophobicity of the diblock copolymer and with increasing copolymer concentration. X‐ray diffraction (XRD) and differential scanning calorimetry (DSC) analyses revealed that the diblock copolymers exhibited crystalline domains that favored the formation of an aggregated gel because of the tight aggregation and strong packing interactions between PCL blocks. Scanning electron micrographs of the diblock copolymer solutions in the sol state showed interconnected polyhedral pore structures, whereas those of the gel state revealed a fibrillar‐like morphology. Atomic force microscope (AFM) studies of the sol and gel surfaces showed that the sol surface was covered with fine globular particles, whereas the gel surface was covered with particles in micron‐scale irregular islets. These findings are consistent with uniform mixing of the diblock copolymer and water in the sol state, and aggregation of PCL blocks in the gel state. In conclusion, we confirm that the MPEG–PCL diblock copolymer solution exhibited a sol–gel–sol transition as a function of temperature. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5413–5423, 2006