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.     

Synthesis and phase‐separation behavior of α,ω‐difunctionalized diblock copolymers

A series of diblock copolymers of n‐pentyl methacrylate and methyl methacrylate (PPMA/PMMA BCP) with one or two terminal functional groups was prepared by sequential anionic polymerization of PMA and MMA using an allyl‐functionalized initiator and/or and end‐capping with allyl bromide. Allyl functional groups were successfully converted into OH groups by hydroboration. The morphology in bulk was examined by temperature‐dependent small‐angle X‐ray measurements (T‐SAXS) and transmission electron microscopy (TEM) showing that functional groups induced a weak change in d‐spacings L₀ as well as in the thermal expansion behavior. T‐SAXS proved that the lamellar morphologies were stable over multiple heating/cooling cycles without order‐disorder transition (ODT) until 300 °C. While non‐functionalized BCP formed parallel lamellae morphologies, additional OH‐termination at the PMMA block forced in very thin films (ratio between film thickness and lamellar d‐spacing below 1) the generation of perpendicular lamellae morphology through the whole film thickness, as shown by Grazing‐incidence small‐angle X‐ray scattering experiments (GISAXS) measurements. Functionalized BCP were successfully used in thin films as templates for silica nanoparticles in an in‐situ sol–gel process. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Non‐equilibrium phase behavior of diblock copolymer melts and binary blends in the intermediate segregation regime

The phase behavior of intermediately segregated (χN = 45) poly(ethylene)‐poly(ethylethylene) (PE–PEE) diblock copolymers and PE–PEE binary blends are characterized using transmission electron microscopy and small‐angle X‐ray scattering. Surprisingly, the preparation‐dependent, nonequilibrium phase behavior can be overwhelming even at this degree of segregation. A pure diblock with a poly(ethylene) volume fraction of f_PE = 0.46 exhibited coexisting lamellae and perforated layers when prepared using a precipitation technique, but contained only the lamellar morphology when solvent cast. This preparation dependence was more dramatic in binary diblock copolymer blends with average compositions of 〈f_PE〉 = 0.44, 0.46, and 0.48. Precipitated blends exhibited a microphase separated structure that was disordered and bicontinuous; however, solvent cast samples exhibited either a cylindrical, coexisting cylindrical and lamellar, or lamellar morphology. This nonequilibrium behavior is attributed to the high degree of segregation and the proximity to the cylinder/lamellae phase boundary. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2229–2238, 1999     

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     

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   

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.     

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.     

Morphology and Conformation Analysis of Self‐Assembled Triblock Copolymer Melts

Summary: We used the dissipative particle dynamics method to simulate the self‐assembly of symmetric triblock copolymers of the type ABA. Depending on the volume fraction of the end blocks f_A, several mesophases including lamellar, perforated lamellar, gyroid, hexagonal cylinders and bcc spherical micelles were obtained. The order‐disorder transition (ODT) at f_A = 0.5 was found to be about χN = 19.8. The ODT for the cylindrical mesophase at symmetrical points on the phase diagram had different values, indicating asymmetry in the phase diagram. We were also able to estimate the bridge fraction in the different mesophases. They range from about 0.44 for the lamellar mesophase to about 0.75 for the spherical micelles. Our simulation results are in good agreement with previously reported theoretical calculations and experimental observations.

The hexagonal cylinders generated with the A₆B₄A₆ copolymer.     

Self-diffusion of a polystyrene-polyisoprene block copolymer

Forced Rayleigh scattering (FRS) has been used to measure the self-diffusion coefficient, D, of a lamellar-forming polystyrene-polyisoprene diblock copolymer (M_PS = 1.0 X 10⁴, M_PI = 1.3 X 10⁴) as a function of temperature. The measurements traverse the order-disorder transition (ODT), which occurs at 160°C. There is no obvious change in either D or the temperature dependence of D at the ODT, in agreement with measurements on several other systems. Electron microscopy confirms that the sample in the ordered state is quenched, with no long-range orientation of lamellae, and a typical grain size well below 1 μm. In contrast to previous measurements on a similar styrene-isoprene diblock, these FRS signals are well-described by single exponential decays; this may be largely attributed to differences in average grain size. The temperature dependence of D is modeled with several empirical expressions, based on the known monomeric friction factors for pure polystyrene and pure polyisoprene, but without quantitative success. These results underscore the need for a greater understanding of the composition and temperature dependences of local friction in polymer mixtures. © 1996 John Wiley & Sons, Inc.     

The Effect of Pressure on the Microphase Separation of Diblock Copolymer Melts Studied by Dynamic Density Functional Theory Based on Equation of State

The effect of pressure on the microphase separation of diblock copolymer melts was investigated by dynamic density functional theory based on equation of state. The results correspond well with experiment data. With the application of high pressure, all of the phase regions corresponding to the different ordered morphologies become narrower. However, the pressure dependence of the order‐disorder transition temperature (T_ODT) relies on the symmetry of the diblock copolymer. In the very non‐symmetrical case when f is small, T_ODT decreases with increasing pressure, while in the symmetrical case when f = 0.5, T_ODT increases with increasing pressure. For the latter case, the increase in the total bead number of the system at the ODT is found, which is in good accordance with the experimental phenomenon that there is an increase in volume accompanying with the transition from ordered to disordered state. In contrast to the temperature, the pressure does not influence the starting time and the duration of microphase separation.

     

Twinning and growth kinetics of lamellar grains in a diblock copolymer solution

The initial stages of growth of the lamellar phase in a block copolymer solution were observed with polarizing optical microscopy (POM). Measurements were made on a poly(styrene‐b‐isoprene) diblock copolymer with block molecular weights of 15 and 13 kg/mol, respectively, dissolved in dioctyl phthalate with 70% polymer by volume. Upon cooling from above the order–disorder transition temperature, 89.5 °C, to temperatures from 87.5 to 88.5 °C, four distinct types of grain were observed: ellipsoidal single grains, twinned ellipsoidal grains, 2‐fold twinned grains, and spherulites. The relative populations were distributed as 50% single ellipsoids, 25% twinned ellipsoids, 10% 2‐fold twinned grains, and 15% spherulites. These grain types cover a range of lamellae orientation. For example, the surface of a 2‐fold twinned grain is composed of lamellar edges, whereas the spherulite surface is composed of lamellar planes. The specific grain types that arise give insight into the thermodynamic and kinetic forces governing lamellae ordering. Furthermore, growth front velocities of individual grains were measured after rapid quenches from above T_ODT. These results were compared to the predictions of Goveas and Milner. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 405–412, 2005     

Phase separation induced by shear quenching in polymer blends with a diblock copolymer

The effects of adding A–B diblock copolymer to a polymer blend (A/B) on phase‐separation kinetics and morphology have been investigated in a fixed shallow‐quench condition (ΔT = 1.5 °C) by in situ time‐resolved light scattering and phase‐contrast optical microscopy. A shear‐quench technique was used in this study instead of a conventional temperature‐quench method. Mixtures of nearly monodisperse low relative‐molecular masses of polybutadiene (M_w = 2.8 kg/mol), polystyrene (M_w = 2.6 kg/mol), and a near‐symmetric butadiene–styrene diblock copolymer (M_w = 6.3 kg/mol) as an interfacial modifier were studied. We observed that the addition of the diblock copolymer could either retard or accelerate the phase‐separation kinetics depending on the concentration of the diblock copolymer in the homopolymer blends. In contrast to the conventional temperature quench, we observed complex phase‐separation kinetics in the intermediate and late stages of phase separation by the shear‐quench technique. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 819–830, 2001     

Complex Macrophase‐Separated Nanostructure Induced by Microphase Separation in Binary Blends of Lamellar Diblock Copolymer Thin Films

The nanostructures of thin films spin‐coated from binary blends of compositionally symmetric polystyrene‐b‐polybutadiene (PS‐b‐PB) diblock copolymer having different molar masses are investigated by means of atomic force microscopy (AFM) and grazing‐incidence small‐angle X‐ray scattering (GISAXS) after spin‐coating and after subsequent solvent vapor annealing (SVA). In thin films of the pure diblock copolymers having high or low molar mass, the lamellae are perpendicular or parallel to the substrate, respectively. The as‐prepared binary blend thin films feature mainly perpendicular lamellae in a one‐phase state, indicating that the higher molar mass diblock copolymer dominates the lamellar orientation. The lamellar thickness decreases linearly with increasing volume fraction of the low molar mass diblock copolymer. After SVA, well‐defined macrophase‐separated nanostructures appear, which feature parallel lamellae near the film surface and perpendicular ones in the bulk.

     

Molecular,Nanostructural and Mechanical Characteristics of Lamellar Triblock Copolymer Blends: Effects of Molecular Weight and Constraint

While theoretical and experimental efforts have thoroughly addressed microphase‐ordered AB diblock copolymer blends with a parent homopolymer (hA or hB) or a second block copolymer, surprisingly few studies have considered comparable ABA triblock copolymers in the presence of hB or an AB diblock copolymer. In this study, we elucidate the roles of additive molecular weight and constraint by examining three matched series of miscible ABA/hB and ABA/AB blends. Self‐consistent field theory is employed to analyze molecular characteristics, e. g., segmental distributions, microdomain periods and midblock bridging fractions, as functions of blend composition. Predictions are compared to morphological characteristics discerned by transmission electron microscopy and small‐angle X‐ray scattering. The corresponding mechanical properties of these blends are measured by dynamic mechanical analysis. The results of this comprehensive work reveal that addition of hB swells the B‐lamellae of the ABA copolymer and has a generally deleterious effect on both the dynamic elastic modulus and midblock bridging fraction. In contrast, addition of a lamellar or cylindrical AB copolymer to the same ABA copolymer can promote an increase or decrease in lamellar period and bridging fraction, depending on relative block sizes.     

Pathway‐Dependent Melting in a Low‐Molecular‐Weight Polyethylene‐block‐Poly(ethylene oxide) Diblock Copolymer

Summary: In a low‐molecular‐weight polyethylene‐block‐poly(ethylene oxide) (PE‐b‐PEO) diblock copolymer, two pathway‐dependent melting processes were observed: Upon slow heating, the PE lamellar crystals melted at ≈97 °C into a disordered state. However, when the temperature rapidly jumped to above the melting point (e.g., 100 °C), the PE lamellar crystals transformed directly into an ordered lamellar melt, followed by an isothermal conversion into a disordered melt. This isothermal order‐to‐disorder transition was explained by superheating of the PE crystals using a G‐T diagram.

A schematic G‐T diagram explaining the pathway‐dependent double melting for a crystalline polyethylene‐block‐poly(ethylene oxide) copolymer.     

Microdomain morphology of lamella‐forming diblock copolymer confined in a thin film

We report the self‐consistent field theory (SCFT) of the morphology of lamella‐forming diblock copolymer thin films confined in two horizontal symmetrical/asymmetrical surfaces. The morphological dependences of thin films on the polymer‐surface interactions and confinement, such as film thickness and confinement spatial structure, have been systematically investigated. Mechanisms of the morphological transitions can be understood mainly through the polymer‐surface interactions and confinement entropy, in which the plat confinement surface provides a surface‐induced effect. The confinement is expressed in the form of the ratio D/L₀, here D is film thickness, and L₀ is the period of bulk lamellar‐structure. Much richer morphologies and multiple surface‐induced morphological transitions for the lamella‐forming diblock copolymer thin films are observed, which have not been reported before. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1–10, 2009     

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.     

Perfectly‐alternating linear (AB)n multiblock copolymers: Effect of molecular design on morphology and properties

Perfectly‐alternating linear (AB)_n multiblock copolymers consist of n AB block pairs covalently linked in an alternating sequence. Although these copolymers can microphase‐order in the same fashion as their lower‐order (n = 1) diblock analogs, the 2(n ? 1) biconformational midblocks comprising each copolymer molecule have a considerable impact on microstructural characteristics and bulk properties. We have applied transmission electron microscopy, differential scanning calorimetry (DSC), and extensional rheometry to examine and compare the morphologies and properties of two series of compositionally symmetric (lamellar) poly(styrene‐b‐isoprene)_n (SI)_n (1 ≤ n ≤ 4) multiblock copolymers. In one series, chain length was held constant allowing block mass (M_b) to decrease with increasing n. In the second copolymer series, M_b remained relatively invariant. Increasing n in these two series generally promoted reductions in both the lamellar period and upper (styrenic) glass‐transition temperature, but noticeable increases in tensile modulus and yield strength. These observed trends are more pronounced in the copolymer series with constant chain length due to the coupled relationship between n and M_b. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 947–955, 2001     

Morphological behavior of model poly(ethylene‐alt‐propylene)‐b‐polylactide diblock copolymers

A set of well‐defined poly(ethylene‐alt‐propylene)‐b‐polylactide (PEP‐PLA) diblock copolymers containing volume fractions of PLA (f_PLA) ranging between 0.08 and 0.91 were synthesized by a combination of living anionic polymerization, catalytic hydrogenation, and controlled coordination‐insertion ring‐opening polymerization. The morphological behavior of these relatively low‐molecular‐weight PEP‐PLA diblock copolymers was investigated with a combination of rheology, small‐angle X‐ray scattering, and differential scanning calorimetry. The ordered microstructures observed were lamellae (L), hexagonally packed cylinders (C), spheres (S), and gyroid (G), a bicontinous cubic morphology having Ia3 d space group symmetry. The G morphology existed in only a small region between the L‐C morphologies in close proximity to the order–disorder transition (ODT). Transformations from L to G were observed upon heating in several samples. The efficacy of the reverse G to L transition in one sample was cooling rate dependent. The PEP‐PLA Flory–Huggins interaction parameter as a function of temperature χ_PEP‐PLA(T) was estimated from T_ODT's by mean‐field theory and subsequently used in the construction of the experimental PEP‐PLA morphology diagram (χN versus f_PLA). The resultant morphology diagram was symmetric there were the well‐defined L‐C morphology boundaries. The low molecular weight of the materials imparted no significant deviation from previously documented diblock systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2364–2376, 2002     

Phase‐Field Simulation of Long‐Wavelength Line Edge Roughness in Diblock Copolymer Resists

We examine stochastic computer simulations of the Leibler‐Ohta‐Kawasaki (LOK) phase‐field model 1 , 2 and demonstrate that long‐wavelength line edge roughness (LER) and line width roughness (LWR) in a lamellar diblock copolymer resist depend monotonically on quench depth and noise strength, and that the LER and LWR spectra both exhibit a peak at k₀–the characteristic wavenumber of mesophase separation in diblock copolymers. For k ⪅ k₀, we find that the LER spectrum approximately scales like k^−1.6. These observations are consistent with previous theoretical, computational, and experimental examinations LER and LWR in diblock copolymer melts, and thus the LOK phase‐field model should be considered a capable and appropriate framework for future examination of long‐wavelength LER and LWR in block copolymer resist systems.