Effect of polydispersity on the tensile modulus of diblock copolymers in a lamellar phase

We have calculated the tensile moduli of nanomaterials having lamellar microstructures prepared through the self-assembly of a polydisperse diblock copolymer. We observed that the extensional moduli K33 provided the major contribution to the tensile modulus and that the value of K33 depended mainly on the contribution of K33(U) (the internal energy contribution to K33). We found that a larger polydispersity index (PDI) weakens the material for our polydisperse model; we attribute this phenomenon to the larger lamellar domain size at equilibrium when the polydispersity of the block increases and to the competition between short and long chains. We found that longer chains in this system strengthen the material, but shorter chains weaken it as a result of the influence of the PDI. The shear modulus contributed negligibly to the extensional moduli.     

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.     

The role of polydispersity in the lamellar mesophase of model diblock copolymers

High-resolution small angle X-ray scattering (SAXS) measurements were performed on two series of poly(ethylene-alt-propylene)-b-poly(D ,L -lactide) (PEP-PLA) diblock copolymer materials exhibiting differences in the widths of the poly(D, L -lactide) block molecular mass distributions as measured by their polydispersity indices (PDI_PLA). At symmetric compositions of PEP-PLA (f_PLA ≈ 0.5), all SAXS data were successfully fit to an established model describing the small angle scattering from lamellar mesostructures. According to this model, the increase in the PDI_PLA negligibly affected the amount of lattice disorder. The apparent asymmetry of the poly(ethylene-alt-propylene)-block lamellae (ϕ), also determined by the fitting procedure, were more substantially affected; increasing the PDI_PLA resulted in a decrease in ϕ. At asymmetric compositions of PEP-PLA (f_PLA ≈ 0.67), only the data at the highest values of the PDI_PLA could be reasonably fit to this model. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3386–3393, 2007     

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.     

On the microphase separation kinetics of symmetric diblock copolymers

Time-resolved small-angle x-ray scattering studies were performed on symmetric diblock copolymers of polystyrene and poly(methyl methacrylate), P(S-b-MMA). Freeze-dried powders of P(S-b-MMA) having a molecular weight of 8.4×10⁴ were rapidly heated to temperatures above the glass transition temperature to initiate the microphase separation. The microphase separation process was found to consist of a rapid, local microphase separation followed by a long-term coarsening process. The period characterizing the lamellar microphase separated structure was found to increase initiallv and then saturate at longer times. These results are discussed in light of recent theoretical developments.In celebration of his 65th birthday, this article is dedicated to Prof. E. W. Fischer whose methodic and thorough approach to research has been and continues to be a model for us to follow. Es freut mich, daß ich mit Herrn Fischer gearbeitet habe. Ich habe vieles von ihm gelernt. Ich hoffe, daß auch ich so fleißig sein werde, wenn ich so jung bin wie er.     

Geometric frustration phases of diblock copolymers in nanoparticles

The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.     

Elastic moduli of multiblock copolymers in the lamellar phase

We study the linear elastic response of multiblock copolymer melts in the lamellar phase, where the molecules are composed of tethered symmetric AB diblock copolymers. We use a self-consistent field theory method, and introduce a real space approach to calculate the tensile and shear moduli as a function of block number. The former is found to be in qualitative agreement with experiment. We find that the increase in bridging fraction with block number, that follows the increase in modulus, is not responsible for the increase in modulus. It is demonstrated that the change in modulus is due to an increase in mixing of repulsive A and B monomers. Under extension, this increase originates from a widening of the interface, and more molecules pulled free of the interface. Under compression, only the second of these two processes acts to increase the modulus.     

Gold nanoparticles protected with pH and temperature-sensitive diblock copolymers

Aqueous dispersions of gold nanoparticles protected with a stimuli-sensitive diblock copolymer were studied as a function of pH and temperature. Poly(methacrylic acid)-block-poly(N-isopropylacrylamide), PMAA-b-PNIPAM, copolymer was synthesized using the RAFT technique. A one-pot method utilizing the dithiobenzoate functionalized polymer was used to prepare gold nanoparticles protected with PMAA-b-PNIPAM. The gold nanoparticles coated with block copolymers, with the PNIPAM block bound to the particle surface and PMAA as an outer block form stimuli-sensitive aggregates in water. The changes in the absorption maxima of the surface plasmon resonance, SPR, of the gold particles and in the size of the aggregates were investigated as a function of pH and temperature. pH was observed to affect the size of the aggregates, whereas the effect of temperature was moderate. However, a blue shift in the SPR was observed both with decreasing pH and increasing temperature. Whereas the PMAA blocks control the colloidal stability of the particles and their aggregates, the thermo-sensitive PNIPAM blocks have a noticeable effect on the polarity of the immediate surroundings of the particles.     

The relation between the microphase separation transition and the glass transition in diblock copolymers

The microphase separation transition (MST) has been studied for short chain diblock copolymers poly(styrene-b-isoprene) and poly(styrene-b-mma). A detailed analysis of small-angle x-ray scattering (SAXS) profiles in the homogeneous phase allows determination of the interaction parameter and the spinodal temperature T_s of the MST. T_s for the PS/PI diblocks is found to be lower than the glass transition temperature of their hard blocks. This results in a coupling of the MST and the glass transition. Using both structural (SAXS) and thermal differential scanning calorimetry (DSC) methods it is shown that an endothermal peak found in the DSC diagrams is related to the combined effect of the MST and the glass transition. © 1992 John Wiley & Sons, Inc.     

Nanoreactors based on self-assembled amphiphilic diblock copolymers for the preparation of ZnO nanoparticles

A self-assembled diblock copolymer containing styrene (S), methyl methacrylate and a certain percentage of hydrophilic segment of poly(methacrylic acid) (i.e., poly(styrene)-block-poly(methyl methacrylate/methacrylic acid) was synthesized via the ATRP method in two steps. This was followed by a partial hydrolysis of the methyl ester linkages of the methyl methacrylate block under acidic conditions. The resultant block copolymer had a narrow molecular weight dispersity (Р< 1.3) and was characterized using FT-IR and Raman spectroscopy as well as size exclusion chromatography. The block copolymer was used as a nanoreactor for inorganic nanoparticles (ZnO). The incorporation of a single source precursor, such as ZnCl₂, into the self-assembled copolymer matrix and the conversion into ZnO nanostructures was carried out in the liquid phase using wet chemical processing techniques. We report the synthesis and characterization of nanocomposites with dual characteristics due to the functionalities incorporated into the matrix. The optical properties were determined by UV–Vis and fluorescence, the crystallinity was studied using X-ray diffraction, and the thermal stability and studies of the cyclic voltammetry were obtained by thermogravimetric analyzes and potentiodynamic electrochemical measurements, respectively. The structural, topographical and morphological characterizations of the ZnO composite in relation to the precursor block copolymer were analyzed via scanning electron microscopy, transmission electron microscopy and atomic force microscopy.     

Simple synthesis of zwitterionic diblock copolymers for the application on metal nanoparticles preparation

AB diblock copolymers of poly(2-(dimethylamino)ethyl metharylate-block-potassiurn acrylate) were prepared via reversible addition-fragmentation chain transfer (RAFT) polymerization. The structure of the block polymer was determined by the nuclear magnetic resonance (NMR) spectroscopy and the gel permeation chromatography. Moreover, it has also been shown that the diblock copolymers exhibit aggregate as function of the pH according to the result of ¹H-NMR spectroscopy, FT-IR absorption spectra, UV-vis transmittance spectroscopy, transmission electron microscopy and ultrasonic particle size analyzer. The result was attributed that such AB diblock copolymers were tailored to undergo pH-induced self-assembly. Furthermore, the aggregate can be as template of metal nanoparticles preparation, and the sizes of the aggregate, in turn, strongly control nanoparticle sizes.     

Recognition-mediated assembly of nanoparticles into micellar structures with diblock copolymers

Polystyrene-based diblock copolymers, featuring diaminotriazine functionality on one of the blocks were used to assemble complementary uracil-functionalized nanoparticles into micellar aggregates. The size of these self-assembled aggregates was controlled by block length, as determined in solution (using dynamic light scattering), and in thin films (using transmission electron microscopy).     

Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers

Using the self-consistent field theory (SCFT), we investigate the phase behavior of a mixture of diblock copolymers and nanoparticles with monodisperse polymer chains tethered to their surfaces. We assume the size of the nanoparticles to be much smaller than that of the attached polymer chains and therefore model the particles with their grafted polymer "shell" as star polymers. The polymer chains attached to the particles are of the same species as one of the blocks of the symmetric diblock copolymer. Of primary interest is how to tune the shell of the particle by changing both the length and number of tethered polymers in order to achieve higher loading of nanoparticles within an ordered structure without macrophase separation occurring. We find that the phase behavior of the system is very sensitive to the size of the particle including its tethered shell. The region of microphase separation is increased upon decreasing the star polymer size, which may be achieved by shortening and/or removing tethered polymer chains. To explore the possible structures in these systems we employ SCFT simulations that provide insight into the arrangement of the different species in these complex composites.     

Influence of electric field on the phase transitions of the hexagonal cylinder phase of diblock copolymers.

We have used the cell dynamic simulations (CDS) method to study the evolution of asymmetric and symmetric diblock copolymers under electric fields. For symmetric diblock copolymers, long-range-ordered lamellar phases form readily under electric fields. For asymmetric diblock copolymers, sphere-to-cylinder phase transitions occur rapidly when strong electric fields are applied, but it takes longer for the system to form hexagonal cylinder structures. The results of these simulations suggest that the sphere phase is stable under weak electric fields, but a threshold electric intensity exists for the sphere-to-cylinder phase transition. In addition, we also studied the kinetic pathways of the transition of the lamellar phase to the hexagonal cylinder phase of the asymmetric diblock copolymers under electric fields. Hexagonal cylinder structures form when the lamellar phase is subjected to a sudden temperature jump. The scattering functions suggest that the hexagonal cylinder structures are very regular and possess very few flaws.     

Tilt grain boundaries in a diblock copolymer ordered nanocomposite lamellar phase

A hybrid self-consistent field theory/density functional theory method is applied to predict tilt (kink) grain boundary structures between lamellar domains of a symmetric diblock copolymer with added spherical nanoparticles. Structures consistent with experimental observations are found and theoretical evidence is provided in support of a hypothesis regarding the positioning of nanoparticles. Some particle distributions are predicted for situations not yet examined by experiment.     

Isotropic-nematic phase transition in athermal solutions of rod-coil diblock copolymers

We present a hybrid method to investigate the isotropic-nematic (I-N) transition in athermal solutions of rod-coil copolymers. This method incorporates the scaled-particle theory for semiflexible chains with two-chain Monte Carlo simulation for the osmotic second virial coefficient and for the angle-dependent excluded volume. We compare the theoretical prediction with Monte Carlo simulations for fused rod-coil copolymers and find good agreement for both the equation of state and the orientational order parameter. The theory is also used to examine the effects of the bond length, the chain length, and the chain composition on orientational ordering in athermal solutions of rod-coil block copolymers. It predicts I-N transition in rod-coil copolymers with fixed rod length but a variable flexible tail in good agreement with experiments.     

Polymerization-induced phase separation in gradient copolymers

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Microphase separation transition and ordering kinetics in thin films of diblock copolymers

Using x-ray reflectivity measurements, we have investigated the structure of films of a symmetric diblock copolymer of polystyrene-b-polyisoprene (M _w =15700). The film thickness is in the range of 1 m. In equilibrium the films consist of lamellae with a thickness of 15.3 nm. They are nearly completely oriented parallel to the substrate. The evolution of oriented structure is studied by time-dependent experiments. The time constants of the structure formation depend strongly on the annealing temperature. An enhancement of the diffuse intensity in the range of Yoneda scattering is evidence for an additional surface structure.     

Simulations of the gyroid phase in diblock copolymers with the Gaussian disphere model

Pure melts of asymmetric diblock copolymers are studied by means of the off-lattice Gaussian disphere model with Monte-Carlo kinetics. In this model, a diblock copolymer chain is mapped onto two soft repulsive spheres with fluctuating radii of gyration and distance between centers of mass of the spheres. Microscopic input quantities of the model such as the combined probability distribution for the radii of gyration and the distance between the spheres as well as conditional monomer number densities assigned to each block were derived in the previous work of F. Eurich and P. Maass [J. Chem. Phys. 114, 7655 (2001)] within an underlying Gaussian chain model. The polymerization degree of the whole chain as well as those of the individual blocks are freely tunable parameters thus enabling a precise determination of the regions of stability of various phases. The model neglects entanglement effects which are irrelevant for the formation of ordered structures in diblock copolymers and which would otherwise unnecessarily increase the equilibration time of the system. The gyroid phase was reproduced in between the cylindrical and lamellar phases in systems with box sizes being commensurate with the size of the unit cell of the gyroid morphology. The region of stability of the gyroid phase was studied in detail and found to be consistent with the prediction of the mean-field theory. Packing frustration was observed in the form of increased radii of gyration of both blocks of the chains located close to the gyroid nodes.     

Microphase separation in the melts of diblock copolymers composed of linear and amphiphilic blocks

Computer-aided simulation performed via two independent methods (the Monte Carlo method and method of dissipative particle dynamics) is performed for studying the effect of microphase separation in concentrated solutions of diblock copolymers composed of linear blocks A and amphiphilic blocks A-graft-B. The type of microstructures generated by strong incompatibility between units A and B is shown to be controlled by the ratio of block lengths. For example, in the case of short amphiphilic blocks, elongated micelles with correlated mutual alignment are formed. In the case of longer amphiphilic blocks, lamellar structures are produced; with an increase in the length of this block, these structures are transformed into sequences of lamellas containing parallel layers, lamellas with intersecting layers, and perforated lamellas. When the system contains long amphiphilic blocks, bicontinuous structures arise.