Segregation Strength Research Articles

Density functional theory for inhomogeneous polymer systems. II. Application to block copolymer thin films

We use polymer reference interaction site model (PRISM)-based density functional theory (DFT) to study the structures and morphologies of block copolymer thin films. The polymers are modeled as freely jointed chains, allowing numerical solution of the nonlinear DFT equations. The use of PRISM with DFT allows the inclusion of compressibility and local packing effects due to the finite size of the monomers. We also employ a pseudo-arclength continuation algorithm to locate phase transitions and new morphologies. We study symmetric diblock copolymers confined between two parallel surfaces which both attract one component of the diblock, for two different values of AB segregation strength and for various surface interactions. The predicted equilibrium morphologies are in good qualitative agreement with previous self-consistent field calculations and are consistent with experiment. We are able to resolve the detailed packing structure near the surfaces. We find that packing effects enhance the stability of the perpendicular morphologies.

Real-time determination of the segregation strength of indium atoms in InGaAs layers grown by molecular-beam epitaxy

The surface segregation of indium (In) atoms was investigated during the growth of InGaAs layers by reflection high-energy electron diffraction (RHEED). We observed that the decay constant of the RHEED-oscillation amplitude during growth depends on the growth conditions and is related, in a very simple way, to the segregation coefficient of the In atoms in the InGaAs layers.

Isothermal Crystallization Kinetics and Melting Behavior of Poly(oxyethylene)-b-poly(oxybutylene)/Poly(oxybutylene) Blends

Poly(oxyethylene-b-oxybutylene) block copolymers of various chain lengths (EmBn) were blended with poly(oxybutylene) homopolymer (Bh), materials having different segregation strengths and morphologies (lamellae, cylinder, and sphere) were obtained. The isothermal crystallization kinetics and melting behavior of the blends were studied using differential scanning calorimetry (DSC) and synchrotron small-angle X-ray scattering (SAXS), respectively. Two types of crystallization are identified: confined crystallization occurring at lower temperature with Avrami exponent close to 1.0, having a strong dependence of crystallization halftime on crystallization temperature and a smooth change of q* in crystallization; breakout crystallization occurring at higher temperature with an Avrami exponent much bigger than 1.0 and a step change in q*. The relative segregation strength χc/χODT has an important influence on the crystallization mechanism, and confined crystallization is observed at χc/χODT > 3 whereas breakou...

In-situ determination of indium segregation in InGaAs/GaAs quantum wells grown by molecular beam epitaxy

The surface segregation of indium atoms during the growth of InGaAs/GaAs heterostructures has been investigated in situ by reflection high-energy electron diffraction (RHEED). We pointed out that strong damping of the RHEED oscillations during the deposition of InGaAs on GaAs was related to the segregation strength of indium atoms in the InGaAs layer. A simple model shows that the decay constant of the RHEED oscillations may be used to determine accurately the segregation coefficient R, as confirmed by photoluminescence (PL) measurements.

Effect of Selective Perfluoroalkylation on the Segregation Strength of Polystyrene−1,2-Polybutadiene Block Copolymers

A series of partially fluorinated (C6F13H-modified) polystyrene-b-1,2-polybutadiene (PS-b-1,2-PB) copolymers were prepared by the reaction of a model PS-b-1,2-PB copolymer with n-C6F13I followed by substitution of hydrogen for the iodine by hydrogenolysis. The morphologies and domain spacings of the ordered samples at 120 and 195 °C were determined as a function of C6F13H modification extent using small-angle X-ray scattering (SAXS). From the domain spacings an effective interaction parameter (χeff) between the PS and partially C6F13H-modified 1,2-PB blocks was estimated. The χeff at 120 °C increases significantly with fluorination, from ca. 0.05 (0 mol % C6F13H modification) to ca. 0.75 (80 mol % C6F13H modification). The order−disorder transition temperature (TODT) for a partially C6F13H-modified PS-b-1,2-PB (25 mol %) was determined to be 186 ± 3 °C, using rheology and static birefringence. From self-consistent mean-field theory χeff for this block copolymer is estimated to be 0.16 at TODT, which agree...

Modes of Crystallization in Block Copolymer Microdomains: Breakout, Templated, and Confined

We examined the melt and solid-state structures of a series of diblock copolymers containing polyethylene as the minority block, with a rubbery hydrocarbon majority block. When the interblock segregation strength during crystallization is sufficiently high (approximately 3 times the segregation strength at the order−disorder transition), crystallization can be effectively confined within spherical domains formed by microphase separation in the melt; the process is homogeneously nucleated, and the resulting kinetics are first-order (Avrami n = 1). Below this critical interblock segregation strength, crystallization disrupts the spherical microdomains, resulting in sigmoidal kinetics (n > 1). Cylinder-forming materials are more complex: there exists a range of intermediate segregation strength where crystallization is templated but not wholly confined within the nanoscale domains prescribed by microphase separation; while the melt morphology is generally retained on cooling, local distortions and connections between cylinders occur due to crystallization. These intercylinder connections allow the material initially contained within several cylinders to be crystallized by a single nucleus, producing sigmoidal kinetics and a dramatic acceleration of the overall crystallization rate, despite the general preservation of the cylindrical structure.

Phase Behavior of Styrene−Isoprene Diblock Copolymers in Strongly Selective Solvents

The phase behavior of polystyrene−polyisoprene diblock copolymers diluted with solvents strongly selective for polyisoprene was investigated using variable-temperature small-angle X-ray scattering. Tetradecane was employed as a model selective solvent; its addition induced lyotropic order−order transitions, with as many as five ordered phases found in solutions of one diblock as tetradecane content was varied. The mesophases observed for tetradecane solutions of 10 different diblocks can be partially collapsed into a single two-dimensional map of segregation strength vs overall polystyrene content, as if the selective solvent simply alters the volume fraction of the soluble block. Among strongly selective solvents (tetradecane, tributylamine, squalane), measurable and even large differences in diblock−solvent phase behavior are revealed, in both the locations of lyotropic order−order transitions and the thermotropic order−disorder transition. The addition of squalane to polystyrene-rich diblocks actually ...

Predicting Performance of Self-Compacting Concrete Mixtures Using Artificial Neural Networks

This paper shows that artificial neural networks (ANN) can be used to effectively predict the performance of self-compacting concrete (SCC) mixtures. Inspired by the internal operation of the human brain, the ANN method has learning, self-organizing, and auto-improving capabilities. Thus, it can capture complex interactions among input/output variables in a system without any prior knowledge of the nature of these interactions, and without having to explicitly assume a model form. Indeed, such a model form is generated by the data points themselves. The database assembled, the architecture of the network selected, and the training process of the ANN model used are described. Initial tests show that the ANN method can accurately predict the slump flow, filling capacity, segregation, and compressive strength test results of SCC mixtures. A model for the acceptance or rejection of SCC mixtures based on knowledge of their mixture proportions is proposed and may be used after sufficient development of a more comprehensive database on an industrial scale for the proportioning of SCC with tailor-made properties.

Phase Behavior of Styrene−Isoprene Diblock Derivatives with Varying Conformational Asymmetry

At present, diblock copolymer phase behavior in the long-chain limit is considered to be governed by three factors: the volume fraction of one block, φ; the segregation strength of the diblock, χN; and the conformational asymmetry parameter, e. This implies that the phase diagrams for polymers of different chemistry but similar molecular weight should evolve simply and smoothly as e is varied. We present here partial phase diagrams (covering the cylinder−gyroid−lamella region) for two derivatives of the well-known styrene−isoprene diblocks: styrene−(ethylene-alt-propylene) and vinylcyclohexane−(ethylene-alt-propylene), all of similar molecular weights. Comparison of the S/I, VCH/EP, and S/EP phase diagrams reveals that the phase behavior does not vary simply with e. In particular, the shape and extent of the gyroid region differ greatly between the three chemistries; in the S/EP system, this region disappears into a cusp at moderate segregation strengths (χN ≈ 24). Our findings indicate that factors oth...

Microphase-separated structure of 1,3-cyclohexadiene/butadiene triblock copolymers and its effect on mechanical and thermal properties

We report the effect of microphase-separated structure on the mechanical and thermal properties of several poly(1,3-cyclohexadiene-block-butadiene-block-1,3-cyclohexadiene) triblock copolymers (PCHD-block-PBd-block-PCHD) and of their hydrogenated derivatives: poly(cyclohexene-block-ethylene/butylene-block-cyclohexene) triblock copolymers (PCHE-block-PEB-block-PCHE). Both mechanical strength and heat-resistant temperature (ex. Vicat Softening Temperature: VSPT) tended to increase with an increase in the 1,3-cyclohexadiene (CHD)/butadiene ratio. On the other hand, heat resistance of the hydrogenated block copolymer was found to be higher than that of the unhydrogenated block copolymer. However, the mechanical strength was lower than those of the unhydrogenated block copolymer with the same ratio of CHD to butadiene. To clarify the relationship between the higher order structures of those block copolymers and their properties, we observed the microphase-separated structure by transmission electron microscope (TEM). Hydrogenated block copolymers were found to have more finely dispersed microphase-separated structures than those of the unhydrogenated block copolymers with the same CHD/Bd ratios through the use of TEM and the small-angle X-ray scattering (SAXS) technique. Those results indicated that the segregation strength between the PCHE block sequence and the PEB block sequence increased, depending on hydrogenation of the unhydrogenated precursor. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 13–22, 2001

Use of Viscosity-Modifying Admixture to Reduce Top- Bar Effect of Anchored Bars Cast with Fluid Concrete

With the increasing use of highly fluid concrete to facilitate the casting and consolidation of congested reinforced concrete sections, it is essential to ensure adequate stability of fresh concrete to reduce micro-structural defects at the interface between the hardened cement paste and embedded reinforcement. Accumulation of bleed water under the reinforcement and minute separation of fresh paste from the reinforcement caused by segregation and settlement can significantly reduce bond with anchored or overlapped reinforcement. The reduction in bond with horizontally embedded bars located in the upper sections of structural elements as opposed to those located near the bottom is known as the top-bar effect (top-bar factor). This paper aims at investigating the effectiveness of incorporating viscosity-modifying admixture to enhance the stability of high-slump concrete and reduce the top-bar factor of anchored bars. A total of 25 specimens measuring 500 mm, 700 mm, and 1,100 mm in height were cast with various mixtures with slump values of 220 mm and 190 mm and self-consolidating mixtures with slump flow values of 600-690 mm. The specimens were prepared to evaluate the effect of viscosity-modifying admixture content, specimen height, and mode of consolidation on external bleeding, surface settlement, segregation, and relative bond strength to horizontally embedded bars. The findings indicate that regardless of the slump, specimen height, and mode of consolidation, the reduction in surface settlement (that is related to bleeding and segregation) resulting from incorporating a viscosity-modifying admixture (welan gum) can significantly reduce the top-bar factor. Highly stable, self-consolidating concrete with low settlement had low top-bar factors comparable to specimens cast with 190- and 200-mm slump concrete. The use of 0.07% welan gum in concrete made without any silica fume developed greater stability and lower top-bar factor than similar concrete containing 0.035% of welan gum and 8% silica fume replacement.

Dynamics of Structure Formation and Crystallization in Asymmetric Diblock Copolymers

The crystallization behavior of a series of ethylene-b-(3-methyl-1-butene) diblocks (E/MB) is investigated via simultaneous, time-resolved small-angle and wide-angle X-ray scattering. All the diblocks contain 26−27 wt % E, but possess varying molecular weights and hence varying segregation strengths in the melt, ranging from homogeneous to strongly segregated. Crystallization from homogeneous or weakly segregated melts at typical rates yields a semicrystalline solid consisting of alternating E and MB lamellae. By contrast, a strongly segregated diblock shows crystallization within the E cylinders that are present in the melt, even for slow crystallization rates and at temperatures where both blocks are well above their glass transition temperatures. Modest differences in intercylinder spacing between the melt at high temperatures and solid at low temperatures are shown to arise from the temperature dependence of the intercylinder spacing in the melt. Because chain diffusion in these block copolymer melts is not always fast on the crystallization time scale, the value of the melt spacing that is “frozen in” upon crystallization depends on the specimen’s thermal history. Despite the marked differences in the final structure between polymers where crystallization is constrained to cylinders and those where it “breaks out” to form lamellar microdomains, the kinetics are not remarkably different, at least in these polyethylene-based systems.

Architectural effects on the stability limits ofABC block copolymers

The random phase approximation has been used to extend the Leibler theory for the stability limit of a homogeneous melt of A-B diblock copolymers to examine the onset of microphase and macrophase separation in a variety of ABC block copolymer systems. The stability limit is located by the divergence of the collective structure factor of the melt. We introduce and analyze three models for ABC block copolymers: linear triblocks, random comb copolymers where a fixed number of A and B teeth are placed randomly along a C backbone, and statistical comb copolymers, with A or B teeth spaced regularly, but with sequences constructed using a two parameter Markov process. We compute order-disorder stability boundaries for the segregation strength parameter XAB N at threshold as a function of XAC N, XBC N, composition, and other model parameters, and compare the results for the three different architectural models. An interesting reentrant order-disorder transition is located in several model phase diagrams, and is associated with a peculiar situation in which more incompatibility causes less segregation. In the case of statistical combs, macrophase separation into two liquid phases can be favored over microphase separation.

Temperature Dependence of Interfacial Tension of Demixed Polymer Blend Melts: Polystyrene/Poly(dimethylsiloxane)s

Interfacial tension of polystyrene/poly(dimethylsiloxane) blends with different molecular weights have been measured as a function of temperature by sessile drop method. The results are described as a scaled relation of reduced interfacial tension vs. reduced segregation strength, χ/χc−1, where χ is the segmental interaction parameter and χc is χ at the critical temperature. The scaled relation is discussed on the basis of mean-field theory, and a semi-empirical expression has been presented for the scaled relation covering a wide temperature range.

Temperature Dependence of Interfacial Tension of Polymer Melts

Abstract A unique behavior of interfacial tension of polymer melts is that, in an ordinary temperature region of strong segregation, the entropy effect of chain molecules on the composition-gradient term in the free energy at the interface can make the interfacial tension increase with increasing temperature. To confirm this role of the entropy, interfacial tension of polystyrene/poly(dimethylsloxane) was measured as a function of temperature, and was found to increase with increasing temperature. Using temperature dependence of the segment-segment interaction parameter, which was evaluated from experimental coexistence curves, it was shown that the entropy effect was responsible for this positive temperature dependence of the interfacial tension. The experimental result was also discussed on the basis of scaled expressions of interfacial tension as a function of segregation strength covering weak, strong, and very strong segregation regimes.

Particulate segregation and mechanical properties in transient liquid phase bonded metal matrix composite material

AbstractThefactors determining particulate segregation and joint shear strength in transient liquid phase (TLP) bonded aluminium based metal matrix composite (Mj1C) material are examined in the present paper. Three situations are evaluated during TLP bonding, namely, where the liquid width is unrestrained at the bonding temperature, where the liquid width is maintained constant, and where liquid is continuously expelled from the bondline region during the joining operation. Similar experimental and numerically calculated liquid width values are found during unrestrained liquid width TLP bonding (at the start of the isothermal solidification period). However, the calculated rate constant during isothermal solidification is smaller than in experimental testing. When liquid is expelled from the joint interface during TLP bonding at 853 K, the liquid width attains a constant value of ~55 μm. Although the completion time for isothermal solidification is substantially decreased when liquid is expelled from the ...

Particulate segregation and mechanical properties in transient liquid phase bonded metal matrix composite material

Thefactors determining particulate segregation and joint shear strength in transient liquid phase (TLP) bonded aluminium based metal matrix composite (Mj1C) material are examined in the present paper. Three situations are evaluated during TLP bonding, namely, where the liquid width is unrestrained at the bonding temperature, where the liquid width is maintained constant, and where liquid is continuously expelled from the bondline region during the joining operation. Similar experimental and numerically calculated liquid width values are found during unrestrained liquid width TLP bonding (at the start of the isothermal solidification period). However, the calculated rate constant during isothermal solidification is smaller than in experimental testing. When liquid is expelled from the joint interface during TLP bonding at 853 K, the liquid width attains a constant value of ~55 μm. Although the completion time for isothermal solidification is substantially decreased when liquid is expelled from the joint interface, particulate segregation is still observed in joints produced using 15 and 25 μm thick copper insert metals. Particulate segregation could only be prevented through the use of very thin (<15 μm) copper insert metals. Joint shear strength increases when the thickness of the copper insert metal is decreased and when the applied load increases during liquid expulsion bonding. Higher joint shear strength results from decreased particulate segregation in completed joints.MST/2037

Morphologies of strongly segregated polystyrene-poly(dimethylsiloxane) diblock copolymers

Five polystyrene—poly(dimethylsiloxane) (PS/PDMS) diblocks were synthesized by sequential anionic polymerization, and their morphologies characterized by small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). All materials are microphase-separated in toluene-cast films, and estimates of the interaction parameter χ indicate that these materials are all strongly segregated. The experimentally determined phase diagram is strongly skewed towards low styrene volume fractions, even more than the styrene—isoprene (SI) diblock phase diagram, even though little conformational asymmetry should exist in the PS/PDMS system. The PS/PDMS diblocks form substantially larger microdomain structures than the analogous SI diblocks, reflecting the stronger segregation strength.

Modeling crack growth processes in fusion reactor materials

Models for the effect of the chemical environment on crack growth processes in austenitic and ferritic stainless were evaluated. The effect of impurity segregation, yield strength, and hydrogen on crack growth of HT-9 and radiation induced phosphorus segregation on the intergranular stress corrosion of 316SS have been evaluated. Moderate increases in impurity segregation and/or yield strength caused significant decreases in the K IC and K TH of HT-9, while less than a 10 fold increase in the intergranular stress corrosion crack growth rate of 316SS was predicted for a fluence of 100 dpa using the radiation induced phosphorus segregation data of Brimhall et al. and the stress corrosion model of Parkins. Therefore, while radiation induced impurity segregation is greater in 316SS than HT-9, the effect of impurity segregation may be more pronounced in HT-9. The effect of hydrogen on fatigue crack thresholds was evaluated using a model by Tien which describes the threshold as a function of surface energy. A reduction in the surface energy by hydrogen adsorption was found to cause a decrease in the fatigue threshold a small but comparable amount to that observed for 2-1/4Cr-lMo steel.