Weak segregation theory and non-conventional morphologies in the ternary ABC triblock copolymers

The statistical theory of microphase separation in the ternary ABC triblock copolymers is presented and the corresponding phase diagrams are built both for the linear and miktoarm copolymers. For this purpose the Leibler weak segregation theory in molten diblock copolymers is generalized to multi-component monodisperse block copolymers with due regard for the 2nd shell harmonics contributions defined in the paper. The Hildebrand approximation for the χ-parameters is used. The physical meaning of this and alternative choices for the χ-parameters is discussed. The symmetric A_fB_1-2fC_f copolymers with the middle block non-selective with respect to the side ones are shown to undergo the continuous ODT not only into the lamellar phase but also, instead, into various non-conventional cubic phases (depending on the middle block composition it could be the simple cubic, face-centered cubic or non-centrosymmetric phase, which reveals the symmetry of I4₁ 32 space group No. 214 first predicted to appear in molten block copolymers). For asymmetric linear ABC copolymers a region of compositions is found where the weakly segregated gyroid (double gyroid) phase exists between the planar hexagonal and lamellar or one of the non-conventional cubic phases up to the very critical point. In contrast, the miktoarm (star) ABC block copolymers with one of its arm non-selective with respect to the two others are shown to reveal a pronounced tendency towards strong segregation, which is preceded by increase of stability of the conventional BCC phase and a peculiar weakly segregated BCC phase (BCC₃), where the dominant harmonics belong to the 3rd coordination sphere of the reciprocal lattice. The validity region of the developed theory is discussed and outlined in the composition triangles both for linear and miktoarm copolymers. We present also the list of the 2nd shell harmonics (SAXS reflections) allowed and prohibited in some of the non-conventional morphologies due to the weak segregation considerations and comparison of our results with the preceding SCFT treatment of the ABC copolymers by Matsen.     

Investigation of phase separation in multiblock copolymers consisting of polysulfone and a liquid crystalline polymer

Multiblock copolymers (MBCPs) consisting of polysulfone (PSU) segments and segments of the liquid crystalline poly(ethyleneterephthalate-co-oxybenzoate) (PET/HBA) form rather complex morphologies. Scanning electron microscopy (SEM), small-angle X-ray scattering (SAXS), and atomic force microscopy (AFM) investigations of two block copolymers with significantly different block molecular weights proved the existence of both macro-and microphase separation. These morphologies, existing on different length scales, were found to be superimposed in the samples. A suitable fractionation procedure was used to suppress macrophase separation. Then, it was found that microphase separation is controlled by the segment molecular weights.     

Self-assembled pattern formation of block copolymers on the surface of the sphere using self-consistent field theory

The spherical surface is spatially discretized with triangular lattices to numerically calculate the Laplace-Beltrami operator contained in the self-consistent field theory (SCFT) equations using a finite volume method. Based on this method we have developed a spherical alternating-direction implicit (ADI) scheme for the first time to help extend real-space implementation of SCFT in 2D flat space to the surface of the sphere. By using this method, we simulate the equilibrium microphase separation morphology of block copolymers including AB diblocks, ABC linear triblocks and ABC star triblock copolymers occurred on the spherical surface. In general, two classes of microphase separation morphologies such as striped patterns for compositionally symmetric block copolymers and spotted patterns for asymmetric compositions have been found. In contrast to microphase separation morphology in 2D flat space, the geometrical characteristics of a sphere has a large influence on the self-assembled morphology. For striped patterns, several of spiral-form and ring-form patterns are found by changing the ratio of the radius of a sphere to the averaging width of the stripes. The specific pattern such as the striped and spotted pattern with intrinsic dislocations or defects stems from formed periodic patterns due to microphase separation of block copolymers arranged on the curved surface.     

Extension of integral equation theory to microphase separation of block copolymers

The confined polymer reference interaction site model (Wall-PRISM) integral equation theory was applied to investigate the microphase separation behaviour of copolymers at a solid surface or in bulk. In particular, the effects of the solid surface on polymer conformation were taken into account for constructing a set of novel bridge functionals for different segments to improve the theory. After the integration of the bridge functionals, the theory can well reproduce the simulated density profiles at different microphase domains of flexible–flexible, flexible–rigid, and linear–branched copolymers. As a consequence, the application scope of the inhomogeneous theoretical approach has been extensively extended. This work provides a prospective way to quantitatively predict the density profiles in microphase separation for block copolymers with sophisticated conformation.     

Complex nanostructured materials from segmented copolymers prepared by ATRP

The development of new controlled/living radical polymerization processes, such as Atom Transfer Radical Polymerization (ATRP) and other techniques such as nitroxide mediated polymerization and degenerative transfer processes, including RAFT, opened the way to the use of radical polymerization for the synthesis of well-defined, complex functional nanostructures. The development of such nanostructures is primarily dependent on self-assembly of well-defined segmented copolymers. This article describes the fundamentals of ATRP, relevant to the synthesis of such systems. The self-assembly of block copolymers prepared by ATRP is illustrated by three examples. In the first, block copolymers of poly(butyl acrylate) with polyacrylonitrile phase separate, leading to spherical, cylindrical or lamellar morphologies, depending on the block copolymer composition. At a higher temperature, polyacrylonitrile block converts to nanostructured carbon clusters, whereas poly(butyl acrylate) block serves as a sacrificial block, aiding the development of designed nanostructures. In the second example, conductive nanoribbons of poly(n-hexylthiophene) surrounded by a matrix of organic polymers are formed from block copolymers prepared by ATRP. The third example describes an inorganic-organic hybrid system consisting of hard nanocolloidal silica particles (20 nm) grafted by ATRP with well-defined polystyrene-poly(benzyl acrylate) block copolymer chains (1000 chains per particle). Silica cores in this system are surrounded by a rigid polystyrene inner shell and softer polyacrylate outer shell. Received 9 July 2002 Published online: 11 March 2003     

Enantiomeric PLA–PEG block copolymers and their stereocomplex micelles used as rifampin delivery

A novelty approach to self-assembling stereocomplex micelles by enantiomeric PLA–PEG block copolymers as a drug delivery carrier was described. The particles were encapsulated by enantiomeric PLA–PEG stereocomplex to form nanoscale micelles different from the microspheres or the single micelles by PLLA or PDLA in the reported literatures. First, the block copolymers of enantiomeric poly(l-lactide)–poly(ethylene–glycol) (PLLA–PEG) and poly(D-lactide)–poly(ethylene–glycol) (PDLA–PEG) were synthesized by the ring-opening polymerization of l-lactide and d-lactide in the presence of monomethoxy PEG, respectively. Second, the stereocomplex block copolymer micelles were obtained by the self-assembly of the equimolar mixtures of enantiomeric PLA–PEG copolymers in water. These micelles possessed partially the crystallized hydrophobic cores with the critical micelle concentrations (cmc) in the range of 0.8–4.8 mg/l and the mean hydrodynamic diameters ranging from 40 to 120 nm. The micelle sizes and cmc values obviously depended on the hydrophobic block PLA content in the copolymer. Compared with the single PLLA–PEG or PDLA–PEG micelles, the cmc values of the stereocomplex micelles became lower and the sizes of the stereocomplex micelles formed smaller. And lastly, the stereocomplex micelles encapsulated with rifampin were tested for the controlled release application. The rifampin loading capacity and encapsulation efficiency by the stereocomplex micelles were higher than those by the single polymer micelles, respectively. The drug release time in vitro was depending on the composites of the block copolymers and also could be controlled by the polymer molecular weight and the morphology of the polymer micelles.     

Surface ordering of a rod-coil block molecule on the water subphase

We investigate the surface ordering and orientation of a synthetic rigid-flexible block molecule containing a rigid penta-p-phenylene and poly(propylene oxide) flexible chains at the air–water interface. This supramolecular amphiphile self-organizes into a honeycomb-like structure in the bulk, but it behaves differently with the conventional amphiphilies at the air–water interface. Surface pressure–area isotherms, TEM and AFM results show that the rod-coil molecule forms a stable monolayer at the air–water surface. After monolayer collapses, the molecule exhibits island morphology with the (10) layer spacing of 18 nm. From these results, we discuss the self-assembling mechanism of microphase separation between the rigid moiety and the flexible segments on the water subphase.     

Self-organization of triblock copolymer patterns obtained by drying and dewetting

Self-organized block copolymer structures derived from dewetting of thin films are becoming important in nanotechnology because of the various spontaneous and regular sub-micrometric surface patterns that may be obtained. Here, we report on the self-organization of a poly(styrene)-b-poly(ethene-co-butene-1)-b-poly(styrene) triblock copolymer during drying of its solution over a mica substrate. Regular submicrometric arrangements with long-range order were formed at critical polymer concentrations, consisting of parallel ribbons and hexagonal arrays of dots (droplets). This variety of highly ordered structures is explained by the interplay between forming mechanisms, mainly due to “fingering instabilities” at the three-phase line of the copolymer solution during drying. The thickness of the structures was “quantized” due to the microphase separation of the block copolymer. The formation of hexagonal patterns may be attributed to Marangoni instability at the liquid film surface prior to dewetting.     

Structure of colloidal complexes obtained from neutral/poly- electrolyte copolymers and oppositely charged surfactants

We report on the phase behavior and scattering properties of colloidal complexes made from block copolymers and surfactants. The copolymer is poly(sodium acrylate)-b-poly(acrylamide), hereafter abbreviated as PANa-PAM, with molecular weight 5000 g/mol for the first block and 30000 g/mol for the second. In aqueous solutions and neutral pH, poly(sodium acrylate) is a weak polyelectrolyte, whereas poly(acrylamide) is neutral and in good-solvent conditions. The surfactant is dodecyltrimethylammonium bromide (DTAB) and is of opposite charge with respect to the polyelectrolyte block. Combining dynamical light scattering and small-angle neutron scattering, we show that in aqueous solutions PANa-PAM diblocks and DTAB associate into colloidal complexes. For surfactant-to-polymer charge ratios Z lower than a threshold (Z(C) approximately 0.3), the complexes are single surfactant micelles decorated by few copolymers. Above the threshold, the colloidal complexes reveal an original core-shell microstructure. We have found that the core of typical radius 100-200 A is constituted from densely packed surfactant micelles connected by the polyelectrolyte blocks. The outer part of the colloidal complex is a corona and is made from the neutral poly(acrylamide) chains. Typical hydrodynamic sizes for the whole aggregate are around 1000 A. The aggregation numbers expressed in terms of numbers of micelles and copolymers per complex are determined and found to be comprised between 100-400, depending on the charge ratio Z and on the total concentration. We have also shown that the sizes of the complexes depend on the exact procedure of the sample preparation. We propose that the driving mechanism for the complex formation is similar to that involved in the phase separation of homopolyelectrolyte/surfactant systems. With copolymers, the presence of the neutral blocks prevents the macroscopic phase separation from occurring.     

非对称半结晶两嵌段共聚物的微相分离与结晶行为的模拟退火研究

利用模拟退火方法研究非对称半结晶两嵌段共聚物熔体分别在弱分离和强分离条件下的结晶过程.考察微相分离作用和结晶作用的相对强度对柱状组成的两嵌段共聚物平衡形态的影响.研究结果表明,当嵌段间的相互排斥作用较弱时,结晶便破坏了柱状畴;当此相互作用足够强时,结晶过程可以有效地被限制在熔体微相分离所形成的柱状畴内.另外,介于上述两种情形之间还存在一个模板区域,此时熔体形成的柱状畴大部分被保留下来,但在局部会变形或连通.这些结果和文献报道的实验结果一致.当嵌段间的相互排斥作用非常强时,结晶被抑制,微相分离主导最终形态,观察到了非晶态结构.     

Kinetics of microphase segregation in one-dimensional symmetric diblock copolymer systems

An analytical one-dimensional model of the microphase separation in symmetric diblock copolymers is developed. Three stages of the process of the microphase segregation of a quenched diblock copolymer system into a lamella structure are predicted. The first stage involves a fast increase of the amplitude of the quasi-periodical lamella structure (with the average wave vector q₀) up to a nearly equilibrium value; the second stage is a slow phase diffusion process which is characterized by increasing coherency of the lamella structure; the third stage is the slow process of the lamella swelling, which is driven by the thermally activated process of the spontaneous deletion of excessive lamellas, the lamella size increasing from the initial value 2π/q ₀ to the equilibrium 2π/q _eq > 2π/q ₀ during the process. The last two stages are described with the specially introduced coarse-grained “amplitude-phase” approximation. It is shown that the relaxation of the gradient of the phase of the lamellar structure is the slowest relaxation process and, thus, can be used as an effective order parameter of the lamellar structure at the later stages of the microphase segregation. Received 10 March 2000 and Received in final form 5 June 2000     

Molecular mobility of confined phases in model mesoporous (MCM-41) and microporous (AlPO4-5 zeolite) host materials

This paper discusses the self-assembly of block copolymers into vesicular morphology. After a brief state of art of the field, a system based on an amphiphilic poly(butadiene)-b-poly(-L-glutamic acid) (PB-b-PGA) diblock copolymer in aqueous solution is discussed in detail. The aggregation behavior of this block copolymer has been investigated by means of fluorescence spectroscopy, dynamic (DLS) and static (SLS) light scattering as well as transmission electron microscopy (TEM). The diblock copolymer was found to form well-defined vesicles in water. The size of these so-called polymersomes or peptosomes could be reversibly manipulated as a function of both pH and ion strength. Depending on the pH of the aqueous solution, the hydrodynamic radii of these vesicles were found to vary from 100 nm to 150 nm. By cross-linking the 1,2-vinyl double bonds present in the polybutadiene block, the ability to transform a transient supramolecular self-organized aggregate into a permanent “shape-persistent stimuli-responsive nanoparticle” has been demonstrated. Received 25 June 2002 and Received in final form 22 October 2002 Published online: 11 March 2003     

Recent trends in the tuning of polymersomes’ membrane properties

“Polymersomes” are vesicular structures made from the self-assembly of block copolymers. Such structures present outstanding interest for different applications such as micro- or nano-reactor, drug release or can simply be used as tool for understanding basic biological mechanisms. The use of polymersomes in such applications is strongly related to the way their membrane properties are controlled and tuned either by a precise molecular design of the constituting block or by addition of specific components inside the membrane (formulation approaches). Typical membrane properties of polymersomes obtained from the self-assembly of “coil coil” block copolymer since the end of the nineties will be first briefly reviewed and compared to those of their lipidic analogues, named liposomes. Therefore the different approaches able to modulate their permeability, mechanical properties or ability to release loaded drugs, using macromolecular engineering or formulations, are detailed. To conclude, the most recent advances to modulate the polymersomes’ properties and systems that appear very promising especially for biomedical application or for the development of complex and bio-mimetic structures are presented.     

Surface energies and self-assembly of block copolymers on grafted surfaces

We present a theoretical analysis of the self-assembly of diblock copolymers on surfaces grafted with random copolymers. Our results demonstrate that the surface energies of homopolymeric components on grafted surfaces differ from the corresponding values for self-assembled morphologies. Moreover, grafted random copolymers are shown to adapt their conformations in response to the morphology of the overlaying block copolymer film to create chemical inhomogeneities which modulate the interfacial interactions. Consequently, the surface energy differences between the different components on the grafted substrate do not serve as a useful measure to predict the stability of self-assembly of the diblock copolymer film.     

Designed chemical structures for supramolecular assembly in polymers

One of the goals of synthetic polymer chemistry, and maybe the most important one, is the synthesis of macromolecules having tailored macroscopic properties. The synthetic strategies involved in the preparation of new polymeric materials usually utilize the formation of covalent bonds. In recent years the ability of molecules to self-organize has gained increased attention for the development of new materials. Self-assembly can be de.ned as a spontaneous intermolecular process involving noncovalent bonds (e.g. electrostatic or solvophobic interactions, hydrogen bonds) that results in the formation of, usually, thermodynamically stable supramolecular structures with well-defined order in the nm to μm scale. A plethora of self-organizing systems can be found in nature e.g. double-helical structures of DNA and bilayers of lipids in cell membranes. In natural systems their organization is closely linked to their biological function. These systems continue to provide inspiration to synthetic chemists. Control over the self-assembling process of synthetic macromolecules opens new fascinating opportunities for fabrication of functional materials for technological applications where manipulation of macroscopic properties is essential e.g. electronic devices, microsensors, separation membranes, catalysts and biomaterials. However, the information needed for self-assembly in a macromolecular system is always stored, in various ways, in its detailed primary chemical structure. It is this structure that defines the nature and strength of the interactions that are more probable to be developed in the system. This special issue contains papers concerned with the evolution of self assembly processes and structures of macromolecules, both in solution and in bulk state, through the control of the macromolecular architecture, the selective and functionalization of polymers with functional groups, the introduction of amphiphilicity and of conformational asymmetry in the di.erent parts of block copolymers, by using specific interactions between polymers and low molecular weight compounds or by changes occurring in the physicochemical properties of the environment around polymer chains. By use of well-developed polymerization routes, especially anionic and controlled free radical polymerization techniques, new synthetic macromolecules can be produced and used successfully in the formation of complex, self assembled nanostructures (i.e. block copolymer mesophases, micelles and vesicles from block copolymers, nanoobjects, etc.), in many cases responsive to their environment and having an internal structural hierarchy. These features allow for their use in immerging technologies and applications. Obviously a wide field like that of self-assembly in polymer containing systems cannot be fully covered in the limited space of a single special issue. However we hope that by the works presented here we have given a flavor of some of the issues that attract current scientific interest in this field. We also hope that we have shown the degree of concerted effort and collaboration that is often required, between scientists of different disciplines, theoreticians and experimentalists, in order to design, synthesize, study and understand self-organizing polymeric systems. It is our goal to initiate discussion in this, to our opinion, interesting and important field. The European Physical Journal E-Soft Matter aims in becoming a place where more related studies will be published, and especially on the synthesis of designed polymeric chemical structures, in the framework of multidisciplinarity that characterizes this Journal and the field of Soft Matter in general. Martin M?ller (Editor) Stergios Pispas (Guest Editor)     

Microphase separation in weakly charged hydrophobic polyelectrolytes

Aqueous solutions of a well-defined poly(N-isopropylacrylamide-co-sodium 2-acrylamido-methylpropanesulfonate) (NIPAM/NaAMPS in a 95/5 molar ratio) have been investigated by means of small-angle neutron scattering (SANS) and rheological experiments as a function of temperature ( 25^° C T 60^° C) and polymer concentration ( 0.5wt% C 12wt%). The solutions remain optically transparent and isotropic over the whole temperature range, in contrast with the homopolyNIPAM which precipitates above its lower critical solution temperature (LCST = 32^° C). Upon addition of salt, the systems undergo a micro-macrophase separation. At temperatures above 45^° C, the SANS spectra exhibit a sharp peak at a scattering wave vector, q _max, which increases slightly with temperature. At high temperature ( T∼ 60^° C), the scattered intensity follows a power law I(q) ∼q ^-4 in the asymptotic regime, characteristic of two-density media with sharp interfaces, and q _max is found to vary with polymer concentration as q _max∼C ^0.22. Estimates of the typical sizes give values between 40 ? and 200 ?. These results provide a strong evidence of a thermally induced microphase separation, which is corroborated by the very sharp increases of the viscosity (over 2 decades) and of the stress relaxation time of the solutions, occurring in the temperature range where the scattering peak is observed. The results are discussed and compared with the theoretical models proposed for weakly charged polyelectrolytes in a poor solvent. Received 1 October 2001     

The segregation of poly(styrene-b-isoprene) diblock copolymers to the surface of a polystyrene melt: the effect of the ratio of block lengths

The effect of the ratio of block lengths on the interfacial partitioning of poly(styrene-block-1,4 isoprene) diblock copolymers from their mixtures with polystyrene homopolymer melt is investigated utilizing a series of copolymers with almost constant molecular weight but different compositions. The concentration profile of the copolymer is measured directly using the nuclear reaction analysis technique; a segregation of the diblock is found at both the air/polymer surface, due to the lower surface energy of polyisoprene, and at the substrate/polymer interface. No significant effect of the block length ratio on the free-surface excess was observed. The block molecular weights have apparently led to dangling chain conformations in the non-overlapping mushroom and in the overlapping mushroom regimes whereas the brush regime was not accessible; no indications of a real border between the two former regimes was found. Received: 20 July 1998 / Received in final form and Accepted: 11 September 1998     

Microphase separation at two length scales

The possibility of microphase separation at two different length scales in monodisperse AB block copolymer melts consisting of a homopolymer A block and either a linear alternating AB copolymer block (poly(A)_m-block-poly(B-alt -A)_n) or an AB comb copolymer block poly(A)_m-block-poly(A-graft-B)_n, is investigated. An analysis of the structure factor reveals that in the parameter space of n and m three different cases can be distinguished: I) The structure factor has only one minimum corresponding to the short length scale (i.e. the characteristic length of the repeating unit of the alternating or comb block). II) The structure factor has only one minimum corresponding to the long length scale (the characteristic length of the blocks). III) Two minima are present leading to a competition between microphase separation at the short and the long length scale. Depending on the choice of n and m, one of these three possibilities will occur. Received 25 August 2000     

Membrane-water structural interactions in reverse osmosis transport

Reverse-osmotic water permeabilities, equilibrium water sorption levels, and rates of approach to sorption equilibrium were measured for a series of polymers, including hydroxyethyl methacrylate (HEMA), copolymers of HEMA and ethyl methacrylate (EMA), cellulose acetate, cellulose nitrate, and poly(urethans). Pronounced equilibrium solvent clustering behavior was observed for these systems as vapor saturation was approached in sorption experiments. However, clustering tendency was not found to be a function of total membrane water content at saturation but rather appears to be a function of the chemical nature of the polymer in question. Moreover, clustering of water molecules in (relatively) hydrophobic membranes resulted in low effective diffusivities (reverse osmotic permeability divided by equilibrium water content) whereas clustering in hydrophilic membranes led to higher effective water diffusivities. Clustering tendency was not as strong in the case of the weakly interacting membranes (i.e., the cellulose acetates). These conclusions were supported by theoretical diffusivity calculations. Predictions were based on analyses of transient sorption data, employing a dual-mode sorption model, and considering ordinary Fickian diffusion with simultaneous first-order reversible penetrant localization at water-binding sites in the polymer matrices. Means were found for correcting these diffusivity predictions to those values obtained experimentally under reverse osmosis conditions by accounting for the nonideality of the water flux under the latter conditions.     

Scaling concepts for polymer brushes and their test with computer simulation

After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of “dimples”. Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulations are briefly described, and an outlook on related experiments is given. Dedicated to Prof. H.E. Stanley on the occasion of his 60th birthday Received 11 March 2002 and Received in final form 3 June 2002