Phase Behavior Of Copolymers Research Articles

Rigidity effect on phase behavior of symmetric ABA triblock copolymers: A Monte Carlo simulation

The phase behavior of symmetric ABA triblock copolymers containing a semiflexible midblock is studied by lattice Monte Carlo simulation. As the midblock evolves from a fully flexible state to a semiflexible state in terms of increase in its persistence length, different phase behaviors are observed while cooling the system from an infinite high temperature to a temperature below T(ODT) (order-disorder transition temperature). Within the midblock flexibility range we studied (l(p)N(c)<or=0.105), a lamellar structure is formed at equilibrium state as the situation for fully flexible chains. The fraction of bridge chain is evaluated for the lamellar structures. We find that the increase in midblock rigidity indeed results in the increase in bridge chain fraction within the range from 44.9% to 51.8%. In order to elucidate phase behavior evolution observed in our simulation, a detailed conformation distribution analysis is also given. Our results bridge a gap of different phase behaviors between rod-coil block copolymer and coil-coil block copolymer and show a necessity to investigate rigidity influence on phase diagram.

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.

Phase Behavior of Gradient Copolymers

A multiblock model is developed for the study of the phase behavior of gradient copolymers. The model is able to describe gradient copolymer chains with arbitrary composition profiles. The validity of the multiblock model of gradient copolymers is established by good agreement between RPA (random phase approximation) results for a continuous composition distribution and a multiblock model. The phase behavior of gradient copolymers is examined using self-consistent mean-field theory (SCMFT) for multiblock copolymers. Phase diagrams of gradient copolymer melts with different gradient profiles are constructed by solving the SCMFT equations. It is discovered that the phase behavior depends sensitively on the gradient profiles. In particular, new triple points are observed, and the stability region of phases with curved interfaces shrinks as the gradient profile becomes smooth. For linear gradient copolymers, the lamellar phase is predicted to be the only stable ordered phase.

Micromorphology and phase behavior of cationic polyurethane segmented copolymer modified with hydroxysilane

A series of cationic waterborne polyurethane dispersions (SiPU) modified with hydroxysilane (HPMS) were successfully synthesized based on poly(oxytetramethylene) glycols (PTMG) and isophorone isocyanate (IPDI), and the films were obtained by casting the dispersions on tetrafluoroethylene (TFE) plates. Effects of HPMS content on micromorphology, particle size of the dispersions were studied, as well as thermal properties, phase behavior and surface structure of the films. The particles had the morphology of a solid sphere, with particle size varying from 17.1 nm to 114.4 nm corresponding to the increase of HPMS concentration, which can be attributed to the increase of interfacial tension. XPS spectra indicated the surface migration of Si element in the process of film forming, and the SiPU surface was mainly composed of soft segments. DSC analysis, together with TG-DTG-DTA results demonstrated the HPMS soft segment merged with the transition region of PU matrix, forming part of polyurethane backbone, but an improved microphase separation was observed when HPMS concentration greater than 15%. It was also found that incorporation of flexible HPMS prevented the degradation of polyurethane backbone, resulting in the increase of thermal stability in ultimate copolymer.

Phase Behavior of Symmetric Sulfonated Block Copolymers

Phase behavior of poly(styrenesulfonate-methylbutylene) (PSS-PMB) block copolymers was studied by varying molecular weight, sulfonation level, and temperature. Molecular weights of the copolymers range from 2.9 to 117 kg/mol. Ordered lamellar, gyroid, hexagonally perforated lamellae, and hexagonally packed cylinder phases were observed in spite of the fact that the copolymers are nearly symmetric with PSS volume fractions between 0.45 and 0.50. The wide variety of morphologies seen in our copolymers is inconsistent with current theories on block copolymer phase behavior such as self-consistent field theory. Low molecular weight PSS-PMB copolymers (<6.2 kg/mol) show order−order and order–disorder phase transitions as a function of temperature. In contrast, the phase behavior of high molecular weight PSS-PMB copolymers (>7.7 kg/mol) is independent of temperature. Due to the large value of Flory–Huggins interaction parameter, χ, between the sulfonated and non-sulfonated blocks, PSS-PMB copolymers with PSS and PMB molecular weights of 1.8 and 1.4 kg/mol, respectively, show the presence of an ordered gyroid phase with a 2.5 nm diameter PSS network. A variety of methods are used to estimate χ between PSS and PMB chains as a function of sulfonation level. Some aspects of the observed phase behavior of PSS-PMB copolymers can be rationalized using χ.

Morphological transition behavior ofABCstar copolymers by varying the interaction parameters

We employ dissipative particle dynamics (DPD) to examine the effects of composition and interaction parameter on the resulting phase behavior of ABC star copolymers. Here, we assume that the interaction parameters among the three components are equal. When the three components have comparable volume fractions, our DPD results illustrate that the unique formation of various types of three-phase separated polygonal cylinders is mainly dominated by the composition but not influenced by the interaction parameter. In contrast, when two of the three components are minor, the resulting morphology type is greatly influenced by the interaction parameter. Generally speaking, with an increase in the interaction parameter, the two minority components first act like one component and the system forms a one-length-scale ordered microstructure. Then a further segregation between the two minority components within the large-length-scale phase can be induced as the interaction parameter keeps increasing. In general, our DPD results, a systematic study of the morphological transition behavior obtained by varying the interaction parameter and composition, bridge the gap between the previous theoretical results in the strong and weak segregation regimes via Monte Carlo and two-dimensional self-consistent mean-field methods, respectively.

Phase behavior of tri-block copolymers in solution: Mesoscopic simulation study

The microphase separation dynamics of tri-block copolymers Pluronic EO17PO60EO17 (P103), EO19PO43EO19 (P84) and EO19PO29EO19 (P65) was simulated in aqueous solution by a dynamic variant of mean-field density functional theory for Gaussian chains. For a Pluronic copolymer with smaller ratio of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) (P103, P84 and P65) at low concentration, with an increase of the concentration, the micellar phases change from spherical micelles and micellar clusters, to disk-like micelles for the P103 and P84 solutions, and from spherical micelles to worm-like micelles for the P65 solution. In the P103 and P84 systems, the spherical micelles and micellar clusters can be divided clearly by order parameter, and in the P65 solution the phase separation of worm-like micelle with simulation time is shown clearly by the 3D density field of the PO block. With a decrease of the ratio of hydrophobic PPO and PEO (from P103, P84 to P65), the critical micellar concentration (cmc) increases. It was found that the cmc were 4vol.% for P103, 7vol.% for P84 and 43vol.% for P65. It was concluded that mesoscopic simulation can be considered as an adjunct to experimentation and can provide mesoscopic information otherwise inaccessible (or, not easily accessible) from experimentation.

Self-assembling of hydrophobic-hydrophilic copolymers in hydrophobic nanocylindrical tubes: Formation of channels

By employing Monte Carlo simulations, the phase behavior of hydrophobic-hydrophilic copolymers confined in hydrophobic nanocylindrical tubes has been investigated by changing the hydrophobic-hydrophilic distribution, the ratio of the hydrophobic to hydrophilic segments, the hydrophobicity of the tube surface, and the tube diameter. The ratio of hydrophobic to hydrophilic segments, the number of blocks in a chain, and the number of segments in a block affected the generation of channels in the central region. Such channels were formed when the hydrophobicity of the tube surface was sufficiently strong for its attraction for the hydrophobic segments to overcome the attraction between the hydrophobic segments. When the numbers of hydrophobic and hydrophilic beads in a chain are constant, the number of blocks has opposite effects in small and large tubes. In the former, the formation of channels is stimulated by a larger number of blocks, while in the latter, it is stimulated by a smaller number of blocks.

Phase Behaviour and Thermal Stability of Imide-Containing Siloxane-Urethane Copolymers

Imide-containing siloxane-urethane copolymers (I-PU copolymers) were synthesized from 4,4'-diphenylmethane diisocyanate (MDI), OH-terminated polydimethylsiloxane (PDMS) and pyromellitic dianhydride (PMDA). The hard segment consisted of urethane and imide segments and the soft segment was PDMS. The DSC of I-PU copolymers suggests that they had a high degree of phase separation in their low hard segment contents and phase mixing in high hard segment contents. DMA indicates similar phase behaviour and shows that incorporating imide segments into the copolymers can maintain the high modulus at high temperature. The progress of degradation of I-PU copolymers was determined by TGA and standard kinetics methods and there were three stages at around 250~425 °C, 425~560 °C and 560~700 °C, respectively. The first stage was dominated by the hard-segment structure and content. Incorporating imide segments into PU raises the characteristic temperatures of degradation in the first stage. The second stage resulted from the degradation of the PDMS soft segment to form oligomers by the interchange reaction. The degradation of the imide segment leads to the third stages because the maximum rate of degradation in DTG curves increases with the imide content.

WITHDRAWN: Influences of selective solvents on phase behavior of symmetric diblock copolymers

This article has been withdrawn at the request of the author. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy .

Phase Behavior of Weakly-segregated Multiblock Copolymers with Two-scale Periodic Architecture

AbstractThe phase behavior of a melt of periodic two-scale multiblock copolymers has been theoretically studied in the framework of the Weak-Segregation Limit theory. The effect of the structural symmetry of the macromolecules on the vertex functions of the Landau free energy expansion is considered in detail. The existence of a thermodynamically stable mesophase with a two length-scale space periodicity has been revealed for a melt of monodisperse periodic heteropolymers.

Side‐chain crystallization behavior of graft copolymers consisting of an amorphous main chain and crystalline side chains. II. Poly(n‐hexyl methacrylate)‐graft‐poly(ethylene glycol)

AbstractThe phase behavior and crystallization of graft copolymers consisting of poly(n‐hexyl methacrylate) (PHMA) as an amorphous main chain and poly(ethylene glycol) (PEG) as crystallizable side chains (HMAxwith 15 ≤x≤ 73, wherexrepresents the weight percentage of PEG) were investigated. Small‐angle X‐ray scattering profiles measured above the melting temperature of PEG suggested that a microdomain structure with segregated PHMA and PEG domains was formed in HMA40 and HMA46. This phase behavior was qualitatively described by a calculated phase diagram based on the mean‐field theory. Because of the segregation of PEG into microdomains, the crystallization temperature of the PEG side chains in HMAxwas higher than that in poly(methyl acrylate)‐graft‐poly(ethylene glycol) having a similar value ofx, which was considered to be in a disordered state above the melting temperature. In HMAxwithx≤ 40, PEG crystallization was strongly restricted, probably because the PEG microdomains were isolated in the PHMA matrix. As a result, the growth of PEG spherulite was not observed because the PEG crystallization occurred after vitrification of the PHMA segregated domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 129–137, 2007

Effects of solvent immiscibility on the phase behavior and microstructural length scales of a diblock copolymer in the presence of two solvents

We employ self-consistent mean-field theory to study the phase behavior and the microstructural sizes of AB diblock copolymers in the presence of a neutral solvent S1 and a slightly B-selective solvent S2. In particular, the effects of copolymer volume fraction phiC, the solvent ratio, and the immiscibility parameter between two solvents chiS1S2, are examined. We find that increasing chiS1S2 not only enlarges the ordered microphase region in the concentrated solutions, but also induces a less concentrated homogeneous solution to form an ordered structure and even undergo a macrophase separation. This is due to the fact that increasing chiS1S2 enhances the preferentially of S1 for A and S2 for B and, thereafter, the effective segregation between A and B. Hence, we observe that the structural length results obtained by varying chiS1S2 resemble a consequence of varying the solvent selectivity in the diblock copolymer solutions when only one solvent is added. For example, when chiS1S2 is small, the domain spacing decreases with decreasing phiC while at larger values of chiS1S2, it first shows a decreasing trend and then an increasing behavior with decreasing phiC.

New liquid-crystalline homo-and copolymers with phenyl benzoate side groups and a chiral center in a flexible spacer

The phase behavior and structure of liquid-crystalline homo-and copolymers based on structurally isomeric units belonging to the family of phenyl benzoates that differ in orientation of an ester link situated between benzene rings have been studied with X-ray diffraction, scanning calorimetry, and polarization optical microscopy. The orientation of this link in the monomer unit affects the temperature of phase transition, the type of the smectic phase, and the packing mode of side mesogenic groups in smectic layers of homopolymers. When monomer units commensurable with the monomer units of the basic component in terms of geometry but not identical to them in terms of smectogenity are randomly incorporated into macromolecules of the LC polymer, the resulting copolymer is characterized by layered packing not typical of either of the components.

Effects of Polydispersity on Phase Behavior of Diblock Copolymers

The influence of polydispersity on the phase behavior of diblock copolymer melts is studied using a self-consistent field theoretic model. A perturbation theory is developed for the polydisperse sy...

Phase behavior and microstructural length scales of a diblock copolymer in the presence of a selective solvent

We employ self-consistent mean-field (SCMF) theory in studying the phase behavior as well as the microstructural domain sizes for a diblock copolymer in the presence of a selective solvent. First we examine the effects of solvent addition on the formation of fcc and bcc packed spheres. As has been found in experiments, the so-called “normal” spheres, i.e., formed by the minority blocks, tend to pack into the bcc array, while the “inverted” spheres formed by the majority blocks favor the fcc packing. Upon increasing the solvent selectivity and/or solvent amount, the formed inverted spheres tend to pack from bcc to fcc. This thermotropic transition of bcc → fcc upon increasing the solvent selectivity is induced by the fact that the intermicellar interactions vary from long-range to short-range via a combination of the solvent exclusion from the cores and an increase in the aggregation number. In analyzing the effects of solvent addition on the microstructural sizes, the SCMF results have successfully captured the crossover behavior of characteristic domain spacing from decreasing with added solvent to increasing by increasing the solvent selectivity. Further, the variation of the characteristic domain spacing when the systems transform to a more curved structure changes from a discontinuous decreasing behavior to even a discontinuous increasing behavior upon increasing the solvent selectivity and/or the formation of inverted structures.

A Simple Field-Theoretic Simulation Method for Compressible Block Copolymer Systems

A simple field-theoretic simulation method based on a compressible random-phase approximation (RPA) theory has been suggested to understand the self-assembly behavior and its pressure responses of compressible block copolymer systems. Finite compressibility is incorporated in the free energy functional for the dissipative dynamics through effective RPA interactions that account for the excluded volume and the attractive nonbonded interactions. It was shown that basic equation-of-state parameters completely characterizing given block components readily yield stable and metastable morphologies without any presumed symmetry over a wide range of temperature−pressure−composition space for copolymer melts in unconfined or confined geometry. It was demonstrated that the simulation tool is capable of predicting in a unified way block copolymer phase behavior, not only exhibiting nanoscale ordering either upon cooling or reversely upon heating, but also revealing barotropicity and baroplasticity.

Modeling the phase behavior of commercial biodegradable polymers and copolymer in supercritical fluids

Biodegradable polymers have received much attention as materials for reducing environmental problems caused by conventional plastic wastes. In this work, the thermodynamic behavior of binary and ternary systems composed by commercial biodegradable polymers and high-pressure fluids [poly( d, l-lactide) + dimethyl ether, poly( d, l-lactide) + carbon dioxide, poly( d, l-lactide) + chlorodifluoromethane, poly( d, l-lactide) + difluoromethane, poly( d, l-lactide) + trifluoromethane, poly( d, l-lactide) + 1,1,1,2-tetrafluoroethane, poly(butylene succinate) + carbon dioxide and poly( d, l-lactide) + dimethyl ether + carbon dioxide] and binary systems formed by commercial biodegradable copolymers and supercritical fluids [poly(butylene succinate-co-butylene adipate) + carbon dioxide] were studied. The Perturbed Chain-SAFT (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic EoS were used to model the liquid–fluid equilibrium (LFE) for these binary systems, by fitting one temperature-dependent binary interaction parameter. For comparison, the same data were also modeled by using the traditional Peng–Robinson (PR) cubic EoS. The three pure-component parameters of PC-SAFT and SL EoS and two pure-component of PR EoS were regressed by fitting pure-component data (liquid pressure–volume–temperature data for polymers and copolymer and vapor pressure and saturated liquid molar volume for fluids). The estimation of pure-component and binary interaction parameters was performed by using the modified maximum likelihood method with an objective function that includes the cloud point pressure. An excellent agreement was obtained with the PC-SAFT EoS, while the performance of the SL and PR EoS was less satisfactory.

Phase Behavior of Triblock Copolymers Varying in Molecular Asymmetry

The transformation from A(1)B diblock copolymer to A(1)BA(2) triblock copolymers varying in molecular asymmetry is investigated as the A(2) end block is progressively grown via chemical synthesis. Dynamic rheological measurements show that the order-disorder transition (ODT) temperatures of two copolymer series differing in composition and molecular weight decrease when the A(2) block is short relative to the A(1) block, and then increase as the length of the A(2) block is increased further. The resultant ODT minimum, predicted by mean-field theory, is attributed to mixing between long B and short A(2) blocks.

Equilibrium Phase Behavior of Triblock Copolymer + Salt + Water Two-Phase Systems at Different Temperatures and pH

Data on phase equilibrium of aqueous two-phase systems formed by mixture of triblock copolymer, potassium phosphate, and water were measured as a function of three temperatures (283.15 K, 298.15 K, and 313.15 K), two pH values (7 and 12), and two copolymer molar masses (L35 of 1900 g mol-1 and F68 of 8400 g mol-1). The effect of the temperature was more pronounced on the behavior of the ATPS formed by the L35 copolymer as compared with that induced by the F68 copolymer. Temperature variation affected more intensively the tie line slope than the binodal position. The pH increase shifted the binodal curve to higher copolymer and phosphate concentrations corresponding to a decrease in the region of two-phase coexistence. The effect of the molar masses on the behavior of the phase diagrams for both copolymers was offset by the effects associated with the hydrophobicity of the macromolecules.