Effect of dilution on a block copolymer in the complex phase window

The phase behavior of a styrene–isoprene (SI) diblock copolymer, with block molecular weights of 1.1 × 10⁴ and 2.1 × 10⁴ g/mol, respectively, is examined in the neutral solvent bis(2-ethylhexyl) phthalate (DOP) and the styrene-selective solvent di-n-butyl phthalate (DBP). DBP is a good solvent for PS, but is near a theta solvent for PI at approximately 90°C. Small-angle X-ray scattering (SAXS), rheology, and static birefringence are used to locate and identify order–order (OOT) and order–disorder transitions (ODT); all three techniques gave consistent results. The neat polymer adopts the gyroid (G) phase at low temperatures, with an OOT to hexagonally-packed cylinders (C) at 185°C, and the ODT at 238°C. Upon dilution with the neutral solvent DOP, the C window is diminished, until for a polymer concentration ϕ = 0.65, a direct G to disorder (D) ODT is observed. These results reflect increased stability of the disordered state, based on the different concentration scalings of the interaction parameter, χ, at the OOT and ODT. The OOT follows the dilution approximation, i.e., χ_OOT ∼ ϕ⁻¹, but the ODT is found to follow a stronger concentration dependence, i.e., χ_ODT ∼ ϕ^−1.4, similar to the scaling of ϕ^−1.6 found previously for lamellar SI diblocks in toluene and DOP. Addition of the selective solvent DBP produces dramatic changes in the phase behavior relative to DOP and the melt state; these include transitions to lamellar (L) and perforated layer (PL) structures. The observed phase sequences can be understood in terms of trajectories across the SI melt phase map (temperature vs. composition): addition of a neutral solvent or increasing temperature corresponds to a “vertical” trajectory, whereas adding a selective solvent amounts to a “horizontal” trajectory. When the solvent selectivity depends on temperature, as it does for the SI/DBP system, increasing temperature results in a diagonal trajectory. For both neutral and selective solvents the domain spacing, d*, scales with ϕ and χ as anticipated by self-consistent mean-field theory. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3101–3113, 1998     

Tracer diffusion in fluctuating block copolymer melts

We present a theoretical investigation of the tracer diffusion of diblock copolymers and homopolymers in a thermally fluctuating block copolymer melt above the order-disorder transition (ODT) temperature. Entanglement effects and differences in monomeric friction coefficients are ignored; hence, the theory should be most applicable to short copolymers with rheologically similar blocks. Overall, we find that the diffusion rates of both tracer block copolymers and homopolymers in a block copolymer melt are suppressed when compared with diffusivities in a strictly homogeneous medium with the same average composition. This mobility suppression is due to thermally excited composition fluctuations in block copolymer melts near the ODT; the latter result in transient potential barriers to diffusion. We explore the dependence of the tracer diffusion coefficient on molecular weights and compositions of both matrix and tracer, as well as temperature. A comparison of our theoretical predictions to recent experiments by T. Lodge and coworkers shows qualitative agreement. © 1996 John Wiley & Sons, Inc.     

Monte-carlo simulations of the order–disorder transition depression in ABA triblock copolymers with a short terminal block

Although most ABA triblock copolymers are molecularly symmetric (i.e., the terminal blocks possess the same mass), molecularly asymmetric A1BA2 triblock copolymers are of greater fundamental interest in that they can be used to explore the transition from diblock to triblock copolymer in systematic fashion. In this study, we use a lattice Monte Carlo method known as the cooperative motion algorithm to simulate molten ABA triblock copolymers possessing a short terminal block to explore the effect of molecular asymmetry on the copolymer order–disorder transition (ODT). Reduced ODT temperatures, discerned by simultaneously analyzing several features of the simulation results, are found to compare favorably with experimental data. Of particular interest here is the initial depression in the ODT temperature for A1BA2 copolymers possessing a relatively short terminal (A2) block. This signature feature is successfully captured by the simulations and is found to be strongly dependent on composition, but weakly dependent on copolymer chain length. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

共聚物组成对线形苯乙烯-丁二烯-苯乙烯嵌段共聚物粘弹弛豫与相形态的影响

研究了不同组成的苯乙烯-丁二烯-苯乙烯嵌段共聚物(SBS)的相形态与粘弹弛豫.用透射电子显微镜(TEM)表征了SBS的形态,结果显示,几种SBS均呈层状结构,随着苯乙烯含量的降低,聚苯乙烯(PS)相的尺寸稍有减小,而聚丁二烯(PB)相尺寸明显增大.用动态流变学方法考察了不同温度下SBS嵌段大分子的弛豫行为,结果表明,苯乙烯含量减少,PS相玻璃化转变和有序-无序转变温度均降低;苯乙烯含量少的,在有序-无序转变过程中呈现出高且宽的损耗峰,表明有序-无序转变过程中能量的耗散主要由两相溶合时分子链间的内摩擦所决定,分子链越长,内摩擦越大,能量耗散越大.     

Integral equation theory of randomly coupled multiblock copolymer melts: effect of block size on the phase behavior

The phase behavior of randomly coupled multiblock copolymer melts is studied using the polymer reference interaction site model integral equation theory. The molecules are modeled as flexible chains with random sequences of two types of blocks, each of which consists of the same number (R) of monomer beads. In the random copolymer (R=1) limit the theory predicts macrophase separation as the temperature is decreased for all values of the monomer correlation length lambda. For R>2, however, the theory predicts a microphase separation for values of lambda less than some critical value which increases as the block size increases.     

分子量多分散性对AB二嵌段共聚物相行为的影响

采用Monte Carlo方法研究了分子量多分散性对AB型嵌段共聚物相行为的影响. 通过调整嵌段共聚物中组分含量, 考察了整体多分散性和单嵌段多分散性对嵌段共聚物共混物的有序-无序转变(Order-disorder transition, ODT)、 形貌及链尺寸的影响. 研究结果表明, 多分散度的增大使无序相向较大χN区域略微移动, 形成的片层结构厚度增加. 在形成微观有序形貌后, 较大分散度时各亚组分的链会得到更大的伸展, 表明分子链堆积受挫的程度减小, 因此, 涨落作用受到的抑制作用减小, 无序相区向更低温度区域移动.     

Dynamic heterogeneity in diblock copolymer systems

Dynamic light scattering from diblock copolymers in melt and solution in a non-selective solvent reveals different mechanisms for relaxing the composition and orientation fluctuations near the order to disorder transition (ODT). For the former, internal relaxation and copolymer chain diffusion are the main relaxation processes whereas the latter relate to collective orientation of the copolymer chains near the ODT and induced form anisotropy of coherently ordered microstructures below ODT.     

Single chain conformations in the system of symmetric and asymmetric diblock copolymers

A theory which describes a local structure and global properties of a diblock copolymer melt has been developed in the framework of the one‐loop self‐consistent approximation. We have derived expressions for the sizes of a single diblock macromolecule and its parts. Two different behaviors of single macromolecule conformations in the disordered melt have been obtained depending on the asymmetry of chains and morphologies occurring in ordered states after the order‐disorder transition (ODT). In the nearly symmetric melt, 0.35 < f ⪇ 0.5 (f is a composition), the blocks of both types shrink a little initially as the temperature decreases and then, at some temperature, they begin to swell. In strongly asymmetric melts, f < 0.35, the block of a macromolecule which consists of the monomers of minority type shrinks monotonically, while the other block monotonically swells. We have found nearly Gaussian behavior of the individual blocks and stretching near the chemical bond joining the blocks. Near the ODT the chains are stretched with a magnitude which is of the order of a few percent of their Gaussian sizes. We have calculated the peak position in the scattering curve as a function of the Flory‐Huggins interaction parameter, composition and degree of polymerization. Less then 5% change in the size of copolymer molecules lead to a 25% shift of the scattering peak in comparison to the Gaussian limit. We have found a good quantitative agreement of our theoretical results with the experimental neutron scattering data.     

Dynamic light scattering from ternary polymer blends: critical behavior and bicontinuous microemulsions

We have used dynamic light scattering to study the dynamics of ternary polymer blends consisting of poly(dimethylsiloxane) (PDMS) and poly(ethylethylene) (PEE) homopolymers and a PDMS‐PEE diblock copolymer nearly symmetric in composition. The intensity autocorrelation functions for the binary blend are single‐exponential, and the associated correlation length ξ scales with reduced temperature ϵ in accordance with the Ising universality class (i.e., ξ ∼ ϵ^−ν, with ν = 0.63). An addition of copolymer depresses the critical temperature, but also increases the magnitude of ν. For compositions within the microemulsion channel, ξ exhibits a distinct maximum with decreasing temperature, near the Lifshitz line obtained from the static structure factor. For a particular composition, there is a “re‐entrant” microemulsion, as the system passes into and then out of the phase‐separated region upon cooling.     

The effects of Lowe-Andersen temperature controlling method on the polymer properties in mesoscopic simulations

Lowe-Andersen (LA) temperature controlling method [C. P. Lowe, Europhys. Lett. 47, 145 (1999)] is applied in a series of mesoscopic polymer simulations to test its validity and efficiency. The method is an alternative for dissipative particle dynamics simulation (DPD) technique which is also Galilean invariant. It shows excellent temperature control and gives correct radial distribution function as that from DPD simulation. The efficiency of LA method is compared with other typical DPD integration schemes and is proved to be moderately efficient. Moreover, we apply this approach to diblock copolymer microphase separation simulations. With LA method, we are able to reproduce all the results from the conventional DPD simulations. The calculated structure factors of the microphases are consistent with the experiments. We also study the microphase evolution dynamics with increasing chiN and find that the bath collision frequency Gamma does not affect the order of appearing phases. Although the thermostat does not affect the surface tension, the order-disorder transition (ODT) is somewhat sensitive to the values of Gamma, i.e., the ODT is nonmonotonic with increasing Gamma. The dynamic scaling law is also tested, showing that the relation obeys the Rouse theory with various Gamma.     

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)相似文献   

Diffusion in microstructured block copolymer melts

Forced Rayleigh scattering has been employed to measure tracer and self-diffusion in block copolymer melts, for both entangled and unentangled systems, and in both the ordered and disordered states. It is shown that entanglements are particularly effective in retarding the motion of copolymers parallel to the interface between microdomains. The mechanisms of “activated reptation” and “block retraction” are proposed for parallel diffusion. The importance of large amplitude composition fluctuations in the disordered state near the ordering transition is also demonstrated, for both copolymer and homopolymer tracers; the results suggest that copolymer tracers are more affected than homopolymers of comparable molecular weight.     

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.     

Renormalized one-loop theory of correlations in disordered diblock copolymers

A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)] is used to calculate corrections to the random phase approximation (RPA) for the structure factor S(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity S(q?), peak position q?, and single-chain statistics for symmetric and asymmetric copolymers as functions of χ(e)N, where χ(e) is an effective Flory-Huggins interaction parameter and N is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity S(q?) upon χ(e)N for symmetric diblock copolymers in the limit of strong scattering, or large χ(e)N, but to yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of S(q?) and a decrease of q? for large values of χ(e)N, relative to the RPA predictions, but an enhancement of S(q?) and an increase in q? for small χ(e)N. The decrease in q? near the ODT is shown to be unrelated to any change in single-chain statistics, and to be a result of inter-molecular correlations. Conversely, the predicted increase in q? at small values of χ(e)N is a direct result of non-Gaussian single-chain statistics.     

Synthesis,surface accumulation,and micellar properties of amphiphilic block copolymers

Amphiphilic block copolymers, i.e., poly(methyl methacrylate)-b-poly(2-dimethylethylammoniumethyl methacrylate), were synthesized by the reaction between two prepolymers. Carboxyl-terminated poly(methyl methacrylate) and hydroxyl-terminated poly(2-dimethylaminoethyl methacrylate) were prepared by radical polymerization of the corresponding monomers in the presence of thioglycolic acid and 2-mercaptoethanol as a chain transfer agent, respectively. Two condensation methods, i.e., DCC and the acid chloride method, were used for the reactions of these prepolymers. The subsequent quarternization produced the amphiphilic block copolymers. Surface property of poly(methyl methacrylate) films containing this amphiphilic block copolymer was examined by measuring contact angles for water. The addition of only 0.5 wt% of the block copolymer was sufficient to make poly(methyl methacrylate) surfaces hydrophilic. The block copolymer formed a polymeric micelle in acetone–water mixed solvent.     

Orientation fluctuations in diblock copolymers

Depolarized light scattering and dielectric relaxation spectroscopy reveal pertinent composition fluctuations effects on the orientation dynamics in diblock copolymers near the ordering transition (ODT). The main evidence stems from the broadening of the block relaxation function and collective chain orientation in the disordered state near ODT as well as a slow relaxation process below ODT.     

Monte Carlo simulation on symmetric ABA/AB copolymer blends in confined thin films

The effects of blend composition on morphology, order-disorder transition (ODT), and chain conformation of symmetric ABA/AB copolymer blends confined between two neutral hard walls have been investigated by lattice Monte Carlo simulation. Only lamellar structure is observed in all the simulation morphologies under thermodynamic equilibrium state, which is supported by theoretical prediction. When the composition of AB diblock copolymer (phi) increases, both lamellar spacing and the corresponding ODT temperature increase, which can be attributed to the variation of conformation distribution of the diblock and the triblock copolymer chains. In addition, both diblock and triblock copolymer, chains with bridge conformation extend dramatically in the direction parallel to the surface when the system is in ordered state. Finally, the copolymer chain conformation depends strongly on both the blend composition and the incompatibility parameter chiN.     

Coarse graining in block copolymer films

We present few ordering mechanisms in block copolymer melts in the coarse-graining approach. For chemically homogeneous or modulated confining surfaces, the surface ordering is investigated above and below the order–disorder temperature. In some cases, the copolymer deformation near the surface is similar to the copolymer morphology in bulk grain boundaries. Block copolymers in contact with rough surfaces are considered as well, and the transition from lamellae parallel to perpendicular to the surface is investigated as a function of surface roughness. Finally, we describe how external electric fields can be used to align block copolymer mesophases in a desired direction, or to induce an order–order phase transition, and dwell on the role of mobile dissociated ions on the transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2725–2739, 2006     

Dynamic mechanical and rheological properties of binary S–(S/B)–S triblock copolymer blends

The rheology and dynamic mechanical properties of binary block copolymer blends consisting of a symmetrical triblock copolymer with thermoplastic elastomeric behavior (LN4) and an asymmetrical thermoplastic triblock copolymer (LN3) were investigated. TEM images of the blends show a systematic variation in the morphologies from worms (～20–0 wt % LN3) to cylinders (～60–30 wt % LN3) to lamellae (100–70 wt % LN3) as a function of LN3 content. DMA analysis has revealed that the increase in LN3 content leads to a decrease in miscibility between the PS end blocks and the S/B middle block. The frequency and temperature dependence of the storage modulus (G′), loss modulus (G″), and complex viscosity (|η*|) has been studied for LN4 (weakly segregated) and LN3 (strongly segregated) from their master curves. By comparing the rheological properties of these blend compositions at low‐frequency regime, it is observed that with the increase in LN3 content the shear modulus and complex viscosity increase. Blend compositions with 70–100 wt % of LN3 show nonterminal behavior at reduced frequencies due to the presence of highly ordered microdomains when compared to blends with ～0–20 wt % of LN3 content. van Gurp–Palmen plots were constructed to observe the transition from liquid‐ to solid‐like behavior in the vicinity of order‐to‐disorder transition (ODT) temperature. ODT temperature increases as the thermoplastic LN3 content increases which are also confirmed by the Han plots. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 329–343, 2008     

Bicomponent Block Copolymers Derived from One or More Random Copolymers as an Alternative Route to Controllable Phase Behavior

Block copolymers have been extensively studied due to their ability to spontaneously self‐organize into a wide variety of morphologies that are valuable in energy‐, medical‐, and conservation‐related (nano)technologies. While the phase behavior of bicomponent diblock and triblock copolymers is conventionally governed by temperature and individual block masses, it is demonstrated here that their phase behavior can alternatively be controlled through the use of blocks with random monomer sequencing. Block random copolymers (BRCs), i.e., diblock copolymers wherein one or both blocks are a random copolymer comprised of A and B repeat units, have been synthesized, and their phase behavior, expressed in terms of the order–disorder transition (ODT), has been investigated. The results establish that, depending on the block composition contrast and molecular weight, BRCs can microphase‐separate. We also report that large variation in incompatibility can be generated at relatively constant molecular weight and temperature with these new soft materials. This sequence‐controlled synthetic strategy is extended to thermoplastic elastomeric triblock copolymers differing in chemistry and possessing a random‐copolymer midblock.