A Phase Diagram for the Binary Blends of Nearly Symmetric Diblock Copolymers. 2. Parameter Space of Temperature and Blend Composition†

2001 ◽  
Vol 34 (18) ◽  
pp. 6506-6518 ◽  
Author(s):  
Daisuke Yamaguchi ◽  
Hirokazu Hasegawa ◽  
Takeji Hashimoto
Keyword(s):  
Phase Diagram ◽  
Parameter Space ◽  
Diblock Copolymers ◽  
Binary Blends ◽  
Blend Composition

COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

2007 ◽  
Vol 17 (09) ◽  
pp. 3071-3083 ◽  
Author(s):  
J. M. GONZÀLEZ-MIRANDA
Keyword(s):  
Phase Diagram ◽  
Bifurcation Diagram ◽  
Parameter Space ◽  
Neuron Model ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Rapid Responses ◽  
Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

The Ordered Bicontinuous Double Diamond Structure in Binary Blends of Diblock Copolymer and Homopolymer.

1989 ◽  
Vol 171 ◽  
Author(s):  
Karen I. Winey ◽  
Edwin L. Thomas
Keyword(s):  
Molecular Weight ◽  
Diblock Copolymer ◽  
Diblock Copolymers ◽  
Composition Range ◽  
Volume Fraction ◽  
Diamond Structure ◽  
Binary Blends ◽  
Resultant Effect ◽  
Strong Segregation ◽  
Double Diamond

ABSTRACTWe report the observation of the ordered bicontinuous double diamond (OBDD) structure in binary blends of poly(styrene-isoprene) diblock copolymer and homopolystyrene. The overall polystyrene volume fraction range is 64 - 67 PSvol% for the OBDD structure in binary blends of a lamellar diblock (SI 27/22) and a homopolymer (14.0 hPS). This composition range is approximately within the polystyrene volume fraction range established for pure diblock copolymers in the strong segregation regime having the OBDD structure. Ordered lamellae are observed at approximately 65 PSvol% when the homopolystyrene molecular weight is greater than the molecular weight of the polystyrene block of the copolymer. This observation is discussed in terms of the decreased degree of mixing between the homopolymer and the corresponding block and the resultant effect on the interfacial curvature.

scholarly journals Phase Behavior of Melts of Diblock-Copolymers with One Charged Block

Polymers ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1027 ◽  
Author(s):  
Alexey A. Gavrilov ◽  
Alexander V. Chertovich ◽  
Igor I. Potemkin
Keyword(s):  
Phase Diagram ◽  
Phase Behavior ◽  
Electrostatic Interactions ◽  
Diblock Copolymers ◽  
Volume Fraction ◽  
Microphase Separation ◽  
Dissipative Particle Dynamics ◽  
Homogeneous Structure ◽  
Electrostatic Energy ◽  
Ordered Structures

In this work, we investigated the phase behavior of melts of block-copolymers with one charged block by means of dissipative particle dynamics with explicit electrostatic interactions. We assumed that all the Flory–Huggins χ parameters were equal to 0. We showed that the charge- correlation attraction solely can cause microphase separation with a long-range order; a phase diagram was constructed by varying the volume fraction of the uncharged block and the electrostatic interaction parameter λ (dimensionless Bjerrum length). The obtained phase diagram was compared to the phase diagram of “equivalent” neutral diblock-copolymers with the non-zero χ-parameter between the beads of different blocks. The neutral copolymers were constructed by grafting the counterions to the corresponding co-ions of the charged block with further switching off the electrostatic interactions. Surprisingly, the differences between these phase diagrams are rather subtle; the same phases in the same order are observed, and the positions of the order-disorder transition ODT points are similar if the λ-parameter is considered as an “effective” χ-parameter. Next, we studied the position of the ODT for lamellar structure depending on the chain length N. It turned out that while for the uncharged diblock copolymer the product χcrN was almost independent of N, for the diblock copolymers with one charged block we observed a significant increase in λcrN upon increasing N. This can be attributed to the fact that the counterion entropy prevents the formation of ordered structures, and its influence is more pronounced for longer chains since they undergo the transition to ordered structures at smaller values of λ, when the electrostatic energy becomes comparable to kbT. This was supported by studying the ODT in diblock-copolymers with charged blocks and counterions cross-linked to the charged monomer units. The ODT for such systems was observed at significantly lower values of λ, with the difference being more pronounced at longer chain lengths N. The fact that the microphase separation is observed even at zero Flory–Huggins parameter can be used for the creation of “high-χ” copolymers: The incorporation of charged groups (for example, ionic liquids) can significantly increase the segregation strength. The diffusion of counterions in the obtained ordered structures was studied and compared to the case of a system with the same number of charged groups but a homogeneous structure; the diffusion coefficient along the lamellar plane was found to be higher than in any direction in the homogeneous structure.

scholarly journals Exploring the phase diagram of fully turbulent Taylor–Couette flow

2014 ◽  
Vol 761 ◽  
pp. 1-26 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Siegfried Grossmann ◽  
Detlef Lohse
Keyword(s):  
Phase Diagram ◽  
Reynolds Number ◽  
Couette Flow ◽  
Parameter Space ◽  
Coriolis Force ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Aspect Ratios ◽  
Cylinder Rotation

AbstractDirect numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to $3\times 10^{5}$, corresponding to Taylor numbers of $\mathit{Ta}=4.6\times 10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.

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