Ordering transition of block copolymer films

It is well-known that a bulk, symmetric, A-b-B diblock copolymer forms a lamellar morphology, with period L, below an order-disorder transition (T(ODT)) temperature, for chiN < 10.5; chi is the Flory-Huggins interaction parameter and N is the degree of polymerization of the copolymer. The ordering temperatures of poly(styrene-b-methyl methacrylate) (PS-b-PMMA) thin film diblock copolymers of thickness h 相似文献   

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.     

Continuous Thermodynamic Integration in Field‐Theoretic Simulations of Structured Polymers

This work explores the use of continuous thermodynamic integration in field‐theoretic simulations of a symmetric diblock copolymer melt. Free energies of the lamellar and disorder phases are evaluated by thermodynamic integration from a reference state (an Einstein crystal, λ = 0) to a diblock copolymer (λ = 1). This is followed by integration over the interaction parameter, χ_b , to locate the order–disorder transition (ODT). Then the equilibrium lamellar spacing and free energy cost of stretching and compressing lamellae are examined. The ODT, lamellar spacing, and compression modulus are consistent with previous calculations, though found faster and more precisely. The above quantities do not depend on simulation box size, suggesting that finite‐size effects are small and simulating two lamellar periods is sufficient to accurately evaluate bulk behavior. Furthermore, the statistical uncertainty in the ODT increases quickly with system size, suggesting that small systems may lead to more precise results.     

Effects of confinement on the order-disorder transition of diblock copolymer melts

The effects of confinement on the order-disorder transition of diblock copolymer melts are studied theoretically. Confinements are realized by restricting diblock copolymers in finite spaces with different geometries (slabs, cylinders, and spheres). Within the random phase approximation, the correlation functions are calculated using the eigenvalues and eigenfunctions of the Laplacian operator inverted Delta(2) in the appropriate geometries. This leads to a size-dependent scattering function, and the minimum of the inverse scattering function determines the spinodal point of the homogeneous phase. For diblock copolymers confined in a slab or in a cylindrical nanopore, the spinodal point of the homogeneous phase (chiN)(s) is found to be independent of the confinement. On the other hand, for diblock copolymers confined in a spherical nanopore, (chiN)(s) depends on the confinement and it oscillates as a function of the radius of the sphere. Further understanding of the finite-size effects is provided by examining the fluctuation modes using the Landau-Brazovskii model.     

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.     

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.     

Phase behavior of diblock copolymers; pressure and temperature dependence studied by small-angle neutron scattering

The structure factor of a poly(ethylene-propylene)poly(dimethylsiloxane) diblock copolymer has been measured by SANS as a function of temperature and pressure. In contradiction to the random phase approximation the conformational compressibility exhibits a pronounced maximum at the order-disorder phase transition. The phase boundary shows an unusual shape: with increasing pressure it first decreases and then increases. Its origin is an increase in, respectively, the entropic and the enthalpic part of the Flory-Huggins interaction parameter. The Ginzburg parameter describing the limit of the mean-field approximation is not influenced by pressure.     

Double-Gyroid Network Morphology in Tapered Diblock Copolymers

We report the formation of a double-gyroid network morphology in normal-tapered poly(isoprene-b-isoprene/styrene-b-styrene) [P(I-IS-S)] and inverse-tapered poly(isoprene-b- styrene/isoprene-b-styrene) [P(I-SI-S)] diblock copolymers. Our tapered diblock copolymers with overall poly(styrene) volume fractions of 0.65 (normal-tapered) and 0.67 (inverse-tapered), and tapered regions comprising 30 volume percent of the total polymer, were shown to self-assemble into the double-gyroid network morphology through a combination of small angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). The block copolymers were synthesized by anionic polymerization, where the tapered region between the pure poly(isoprene) and poly(styrene) blocks was generated using a semi-batch feed with programmed syringe pumps. The overall composition of these tapered copolymers lies within the expected network-forming region for conventional poly(isoprene-b-styrene) [P(I-S)] diblock copolymers. Dynamic mechanical analysis (DMA) clearly demonstrated that the order-disorder transition temperatures (T(ODT)'s) of the network-forming tapered block copolymers were depressed when compared to the T(ODT) of their non-tapered counterpart, with the P(I-SI-S) showing the greater drop in T(ODT). These results indicate that it is possible to manipulate the copolymer composition profile between blocks in a diblock copolymer, allowing significant control over the T(ODT), while maintaining the ability to form complex network structures.     

Calculating the free energy of self-assembled structures by thermodynamic integration

We discuss a method for calculating free energy differences between disordered and ordered phases of self-assembling systems utilizing computer simulations. Applying an external, ordering field, we impose a predefined structure onto the fluid in the disordered phase. The structure in the presence of the external, ordering field closely mimics the structure of the ordered phase (in the absence of an ordering field). Self-consistent field theory or density functional theory provides an accurate estimate for choosing the strength of the ordering field. Subsequently, we gradually switch off the external, ordering field and, in turn, increase the control parameter that drives the self-assembly. The free energy difference along this reversible path connecting the disordered and the ordered state is obtained via thermodynamic integration or expanded ensemble simulation techniques. Utilizing Single-Chain-in-Mean-Field simulations of a symmetric diblock copolymer melt we illustrate the method and calculate the free energy difference between the disordered phase and the lamellar structure at an intermediate incompatibility chiN=20. Evidence for the first-order character of the order-disorder transition at fixed volume is presented. The transition is located at chi(ODT)N=13.65+/-0.10 for an invariant degree of polymerization of N=14 884. The magnitude of the shift of the transition from the mean field prediction qualitatively agrees with other simulations.     

Monte Carlo phase diagram for diblock copolymer melts

A partial phase diagram is constructed for diblock copolymer melts using lattice-based Monte Carlo simulations. This is done by locating the order-disorder transition (ODT) with the aid of a recently proposed order parameter and identifying the ordered phase over a wide range of copolymer compositions (0.2相似文献   

The effects of nanoparticles on the lamellar phase separation of diblock copolymers

The phase separation of diblock copolymers containing some energetically neutral/biased nanoparticles is studied by means of large-scale dissipative particle dynamics (DPD) simulations. The effects of the volume fraction of nanoparticles, the size of nanoparticles, and the interaction strength between nanoparticles and blocks on the lamellar phase separation of diblock copolymers are investigated. When these effects are up to a critical value, the diblock copolymer nanocomposites can form a new bicontinuous morphology, which is well consistent with the experimental results. It is also found that the degree of order of phase separation for a given system increases slightly and then decreases abruptly until the bicontinuous morphology is formed as the volume fraction of nanoparticles increases. Furthermore, we discuss the microphase transition through the position distributions of nanoparticles and present a phase diagram in terms of the nanoparticle volume fraction, size, and surface interaction strength.     

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.     

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.     

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.     

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.     

Understanding self-assembly of rod-coil copolymer in nanoslits

Rod-coil diblock copolymers are a special kind of molecule containing a rigid rod and a flexible part. We present a systematic study on self-assembly of the rod-coil copolymers in nanoslits using a hybrid density functional theory. The self-assembly of the rod-coil molecule is driven by the bulk concentration, and there exists a critical bulk concentration beyond which the rod-coil molecule self-assembled into ordered lamellar structures in the slit, otherwise it is in a disordered state. By monitoring the effect of the interaction (epsilon(TT)(*)) of molecular tail on the self-assembly, we found that in the nanoslit of H=13sigma, it is at epsilon(TT)(*)=8 rather than epsilon(TT)(*)=10 or epsilon(TT)(*)=12 that the minimal critical bulk concentration occurs. It may be because the strong tail-tail interaction leads to aggregation of the copolymer molecules in bulk phase, and the resulting supramolecular structures are fairly difficult to enter the slit due to the depletion effect. At a fixed slit, the structural evolution of the self-assembled film with the bulk concentration is observed, including trilayer and five-layer lamellar structures, smectic-A, smectic-C, and a mixture of smectic-A and smectic-C liquid crystal phases and so on. We found that the critical bulk concentration, corresponding to the disordered-ordered phase transition, greatly depends on the separation between two walls, and it changes periodically with the increase of the slit width. In addition, it is also found that the molecular flexibility is one of key factors determining the self-assembled structure in the slit, and the critical bulk density increases with the molecular flexibility.     

Morphological change of asymmetric oxyethylene/oxybutylene block copolymers induced by montmorillonite

Two oxyethylene/oxybutylene block copolymers (E(40)B(79) and E(47)B(62)), which exhibit body-centered cubic sphere (bcc) and hexagonally packed cylindrical (hex) melt morphologies in bulk, respectively, were blended with nanoclay of montmorillonite (MMT). The effects of MMT on the morphology and crystallization of E(40)B(79) and E(47)B(62) were studied with small-angle x-ray scattering, wide-angle x-ray diffraction, and differential scanning calorimeter. It is found that the E block in the block copolymers can intercalate into the galleries of MMT, leading to a larger layer spacing than that of neat MMT. The preferential absorption of the E block onto MMT plates induces the formation of a new lamellar structure, irrespectively of original morphology in the bulk. There is, however, coexistence of the new lamellar structure with regions retaining the melt morphology. The order-disorder transition temperature (T(ODT)) of the block copolymer is increased by MMT for E(40)B(79), but it remains unchanged for E(47)B(62). Crystallinity of the block copolymers is also greatly suppressed by the addition of MMT.     

Influence of chain architecture on phase behaviour of styrene-(styrene/butadiene)-styrene triblock copolymers and their binary blends

The phase behaviour of symmetric (LN4) and asymmetric (LN3) triblock copolymers based on styrene-b-(styrene-co-butadiene)-b-styrene (S-SB-S) and their blends have been studied using transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) and were correlated with rheological properties. A direct control over the final morphology and segregation strength for the block copolymer blends was achieved by blending of LN3 and LN4. The interaction parameter (χ) for LN4 is extracted by fitting the SAXS patterns at temperatures well above the ODT in consistency with Leibler mean-field structure-function for ABA triblock copolymers. A weak temperature dependency of χ has been observed which revealed that the phase behaviour in LN4 is mainly controlled by the entropic term. In the low frequency regime a non-terminal flow behaviour was observed in LN3 revealing the persistence of ordered structure within the experimental temperature range whereas a terminal flow behaviour with composition fluctuation was observed in LN4. G′ vs. G″ plots indicated a solid-like elastic melt behaviour for LN3 whereas presence of ODT over a broad temperature range was observed for LN4. ODT is observed to increase non-linearly with increase in LN3 content in the blends. ODT behaviour of the blends further reveals that the blends shift from weak-segregation to intermediate-segregation strength with the increase in LN3 content. The improvement in the state of ordering along with the change in morphology with the increase of LN3 content is attributed to co-surfactant effect between the PS end-blocks of LN3 and LN4 inside PS-rich phase.     

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     

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.