Dynamics and order-disorder transitions in bidisperse diblock copolymer blends

We employ the dynamic extension of self-consistent field theory (DSCFT) to study dynamics and order-disorder transitions (ODT) in AB diblock copolymer binary mixtures of two different monodisperse chain lengths by imitating the dynamic storage modulus G′ corresponding to any given morphology in the oscillatory shear measurements. The different polydispersity index (PDI) is introduced by binary blending AB diblock copolymers with variations in chain lengths and chain number fractions. The simulation results show that the increase of polydispersity in the minority or symmetric block introduces a decrease in the segregation strength at the ODT, (χN)_ODT, whereas the increase of polydispersity in the majority block results in a decrease, then increase and final decrease again in (χN)_ODT. To the best of our knowledge, our DSCFT simulations, for the first time, predict an increase in (χN)_ODT with the PDI in the majority block, which produces the experimental results. The simulations by previous SCFT, which generally speaking, is capable of describing equilibrium morphologies, however, contradict the experimental data. The polydispersity acquired by properly tuning the chain lengths and number fractions of binary diblock copolymer blends should be a convenient and efficient way to control the microphase separation strength at the ODT.     

Surface wetting behavior of the poly(styrene-b-isoprene-b-styrene) triblock copolymer with different chemical structures of the polyisoprene block chain

The relationship between the chemical structure of a block copolymer and its surface structure and properties is very important for the careful design of its outer surface layer. For this paper, a series of poly(styrene-b-isoprene-b-styrene) triblock copolymers (SIS), with different chemical structures in the polyisoprene block chain, were synthesized by anionic polymerization and their dynamic wetting behaviors were investigated. The dynamic contact angles of the polyisoprene homopolymer (PI) and the SIS were almost the same when the PI and the corresponding block in the SIS had similar chemical structures. The receding contact angle (θ_r) of SIS depended on the microstructure of the PI block chain, however, the advancing contact angles (θ_a) were almost the same regardless of the PI’s chemical structures. The receding contact angle (θ_r) of SIS containing 3,4-PI was far higher than that of SIS with 1,4-PI. Meanwhile, it gradually approached that of SIS with 1,4-PI as the of 3,4-PI content decreased or as the local temperature increased. Contact angle measurement is one of the most sensitive methods for providing information on the outer few angstroms of a polymer’s surface. Therefore, by designing SIS with different chemical structures in the PI block, it was confirmed that the properties and structure of the outermost layer of the SIS were controlled primarily by the PI block’s chemical structure. This demonstrates the possibility to modulate the surface structure and properties of SIS by adjusting the chemical structure of polyisoprene segment.     

Storing block-wise semantically correlated patterns in a perceptron: results from a cavity method

In this paper we calculate the storage capacity of the perceptron for block-wise semantically correlated patterns. The set of patterns is divided into blocks, each block consisting of n binary patterns. The patterns in a block have the overlap R with each other and patterns in different blocks have overlap 0. Using a cavity method, which was recently developed by F. Gerl [1], we derive a general expression for the storage capacity α(κ,R, n) for all possible values of R and n with ?1/(n ? 1) ≤ R ≤ 1. Evaluation leads to enhanced resp. reduced storage capacities for positive resp. negative correlation R. Asymptotically for n → ∞ we find that α(κ = 0, n) → nR/[2(1 ? R) In(nR√1?R)], if the logarithm in the denominator is ? 1. We are also able to interpret the various terms in the expression for α in an intuitive way.     

A variance formula related to a quantum conductance problem

Let t be a block of an Haar-invariant orthogonal (β=1), unitary (β=2) or symplectic (β=4) matrix from the classical compact groups O(n), U(n) or Sp(n), respectively. We obtain a close form for Var(tr(t^∗t)). The case for β=2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit ⁻¹(8β) for β=1,2 and 4 as the sizes of t go to infinity in a special way. Although t in our formulation comes from a block of an Haar-invariant matrix from the classical compact groups, the above limit is consistent with a formula by Beenakker, where t is a block of a circular ensemble.     

One injection for one-week controlled release: In vitro and in vivo assessment of ultrasound-triggered drug release from injectable thermoresponsive biocompatible hydrogels

Episodic release of bioactive compounds is often necessary for appropriate biological effects under specific physiological conditions. Here, we aimed to develop an injectable, biocompatible, and thermosensitive hydrogel system for ultrasound (US)-triggered drug release. An mPEG-PLGA-BOX block copolymer hydrogel was synthesized. The viscosity of 15 wt% hydrogel is 0.03 Pa*s at 25 °C (liquid form) and 34.37 Pa*s at 37 °C (gel form). Baseline and US-responsive in vitro release profile of a small molecule (doxorubicin) and that of a large molecule (FITC-dextran), from the hydrogel, was tested. A constant baseline release was observed in vitro for 7 d. When triggered by US (1 MHz, continuous, 0.4 W/cm²), the release rate increased by approximately 70 times. Without US, the release rate returned to baseline. Baseline and US-responsive in vivo release profile of doxorubicin was tested by subcutaneous injection in the back of mice and rats. Following injection into the subcutaneous layer, in vivo results also suggested that the hydrogels remained in situ and provided a steady release for at least 7 d; in the presence of the US-trigger, in vivo release from the hydrogel increased by approximately 10 times. Therefore, the mPEG-PLGA-BOX block copolymer hydrogel may serve as an injectable, biocompatible, and thermosensitive hydrogel system that is applicable for US-triggered drug release.     

Surface-grafted block copolymer gradients: Effect of block length on solvent response

We outline a method to fabricate gradient combinatorial libraries that explore architectural parameters of surface-grafted block copolymers (BCs). In addition, we demonstrate the utility of such libraries for the rapid, thorough assessment of the response of grafted BCs to solvent exposure. Our fabrication route uses surface-initiated controlled radical polymerization to produce a tethered polymer block with uniform length (in this case, poly(n-butyl methacrylate), PBMA), followed by a graded synthesis that adds a second block that varies in its length over the library (here, poly(2-(N,N′-dimethylamino)ethyl methacrylate), PDMAEMA). Our demonstration study maps the response of PBMA and PDMAEMA blocks to hexane and water, and defines regimes of behavior to this respect. Moreover, our study illuminates a narrow BC composition window that exhibits the strongest possible response to water and hexane treatment.     

Can Extra Updates Delay Mixing?

We consider Glauber dynamics (starting from an extremal configuration) in a monotone spin system, and show that interjecting extra updates cannot increase the expected Hamming distance or the total variation distance to the stationary distribution. We deduce that for monotone Markov random fields, when block dynamics contracts a Hamming metric, single-site dynamics mixes in O(n log n) steps on an n-vertex graph. In particular, our result completes work of Kenyon, Mossel and Peres concerning Glauber dynamics for the Ising model on trees. Our approach also shows that on bipartite graphs, alternating updates systematically between odd and even vertices cannot improve the mixing time by more than a factor of log n compared to updates at uniform random locations on an n-vertex graph. Our result is especially effective in comparing block and single-site dynamics; it has already been used in works of Martinelli, Toninelli, Sinclair, Mossel, Sly, Ding, Lubetzky, and Peres in various combinations.     

Fluorescence imaging assisted by surface modes on dielectric multilayers

The scaling behavior of criticality for spin-1 XXZ chains with uniaxial single-ion-type anisotropy is investigated by employing the infinite matrix product state representation with the infinite time evolving block decimation method. At criticality, the accuracy of the ground state of a system is limited by the truncation dimension χ of the local Hilbert space. We present four evidences for the scaling of the entanglement entropy, the largest eigenvalue of the Schmidt decomposition, the correlation length, and the connection between the actual correlation length ξ and the energy. The result shows that the finite scalings are governed by the central charge of the critical system. Also, it demonstrates that the infinite time evolving block decimation algorithm by the infinite matrix product state representation can be a quite accurate method to simulate the critical properties at criticality.     

Kinetics of the growth of domain blocks in KDP-type ferroelectric crystals

The process of the domain-block structure formation at the ferroelectric phase transition in KDP-type crystals is investigated. An effective Hamiltonian of the system is constructed; the growth of domain blocks in the vicinity of the Curie point is numerically simulated using the Monte Carlo method, and the temperature interval of the domain block growth is determined. It is shown that the asymptotic dependence of the mean block size on time has the form R(t) ～ √t/lnt. In the framework of an equivalent mathematical model combining the Ising and Kosterlitz-Thouless two-dimensional models, a kinetic equation that approximately describes the evolution of the domain-block size distribution function is derived.     

Dielectric properties of thin films of partially deuterated betaine phosphite with large- and small-block structures

Ferroelectric thin films of partially deuterated betaine phosphite (DBPI) have been grown by evaporation on NdGaO₃ substrates with a preliminarily deposited structure of interdigitated electrodes. The block structure of the films is a texture in which the polar axis b is oriented in the plane of the film and the a* axis is perpendicular to this plane. Typical dimensions of the single-crystal blocks in DBPI films substantially exceeds the distance between the interdigitated electrodes (d = 50 μm). However, DBPI films in which the block structure has characteristic dimensions of the order of d have also been grown. Investigations of the dielectric properties of the films have demonstrated that the dimensions of the block structure have little effect on the behavior of a small-signal dielectric response, which, in the phase transition region, is characterized by a strong anomaly of the capacitance of the structure at T = T _c and by a glass-like behavior of the capacitance C and dielectric loss tangent tanδ in the temperature range of 120–200 K. By contrast, the low-frequency strong-signal dielectric response (dielectric hysteresis loops) in the structures with small blocks differs significantly from that observed for large-block structures. The difference in the frequency behavior of the hysteresis loops in the large-block and small-block structures is associated with the limitation of motion of domain walls in the case of small blocks.     

Ellipsometry measurements of glass transition breadth in bulk films of random, block, and gradient copolymers

Bulk films of random, block and gradient copolymer systems were studied using ellipsometry to demonstrate the applicability of the numerical differentiation technique pioneered by Kawana and Jones for studying the glass transition temperature (T _g) behavior and thermal expansivities of copolymers possessing different architectures and different levels of nanoheterogeneity. In a series of styrene/n -butyl methacrylate (S/nBMA) random copolymers, T _g breadths were observed to increase from ～ 17^° C in styrene-rich cases to almost 30^° C in nBMA-rich cases, reflecting previous observations of significant nanoheterogeneity in PnBMA homopolymers. The derivative technique also revealed for the first time a substantial increase in glassy-state expansivity with increasing nBMA content in S/nBMA random copolymers, from 1.4×10^-4 K-1 in PS to 3.5×10^-4 K-1 in PnBMA. The first characterization of block copolymer T _g ’s and T _g breadths by ellipsometry is given, examining the impact of nanophase-segregated copolymer structure on ellipsometric measurements of glass transition. The results show that, while the technique is effective in detecting the two T _g ’s expected in certain block copolymer systems, the details of the glass transition can become suppressed in ellipsometry measurements of a rubbery minor phase under conditions where the matrix is glassy; meanwhile, both transitions are easily discernible by differential scanning calorimetry. Finally, broad glass transition regions were measured in gradient copolymers, yielding in some cases extraordinary T _g breadths of 69- 71^° C , factors of 4-5 larger than the T _g breadths of related homopolymers and random copolymers. Surprisingly, one gradient copolymer demonstrated a slightly narrower T _g breadth than the S/nBMA random copolymers with the highest nBMA content. This highlights the fact that nanoheterogeneity relevant to the glass transition response in selected statistical copolymers can be comparable to or exceed that observed in moderately phase-segregated gradient copolymers.     

Block error rate of FSO links over non-Kolmogorov turbulence with exponentiated Weibull distribution

In this paper, we model block error rate (BLER) performance of optical wireless communication systems in strong turbulence slant channels with very slow fading and additive Gaussian noise, using the Exponentiated Weibull distribution models. In a communication system, which transmits data in blocks of N bits, the BLER probability P(M, N) of more than M bit errors in a block is particularly useful in evaluating the wireless optical channel performance. The joint effects of the beam wander and spread, pointing errors and the spectral index of non-Kolmogorov turbulence on system's performance are included. The obtained results can be essential for the designing of such links under real circumstances.     

Low-frequency lattice vibrations in β-alumina

The elastic constants of M β-alumina (M = Na, K, Rb, Ag and TL) are obtained from polarized Brillouin scattering spectra. The frequency versus wave-vector dispersion curves near the Γ-point are calculated from the elastic constants obtained in the harmonic approximation by using a rigid ion model in which a spinel block composed of Al³⁺ and O^2- is considered as one rigid ion. The vibrational frequency or the attempt frequency of the mobile ion in β-alumina is related not only to the mass of the mobile ion but also to the force constant between the spinel block and the mobile ion, which participates in the elastic constant C₄₄.     

Amphiphilic polysilane-methacrylate block copolymers — Formation and interesting properties —

Several polysilane block copolymers have been prepared by the newly developed method, anionic polymerization of masked disilenes. Especially amphiphilic block copolymers of poly(1,1-dimethyl-2,2-dihexyldisilene) and poly methacrylate are focused. Poly(1,1-dimethyl-2,2-dihexyldisilene)-b-poly(2-hydroxyethyl methacrylate) (PMHS-b-PHEMA) is the first example of the amphiphilic polysilane copolymer that can form micelles in polar solvents. Poly(1,1-dimethyl-2,2-dihexyldisilene)-b-poly(methacrylic acid) (PMHS-b-PMAA) is more polar than (PMHS-b-PHEMA), soluble in water to form micelles. The cross-linking reaction of (PMHS-b-PMAA) with 1,10-diaza-4,7-dioxadecane and 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride afforded the first shell cross-linked micelles (SCM) of polysilane. In addition to interesting properties, SCM is indicated to be able to form hollow sphere particles (hollow shell cross-linked micelles, HSCM) by a photochemical process. Reversible encapsulation of guest molecules by SCM and HSCM is demonstrated. Finally, SCM can be used as the template for the synthesis of metal nanoparticles, which may be used as catalysts.     

General features of lipid organization

In block systems made of long chair molecules (lipids, detergents, copolymers), attached by one end at an interface, the steric interactions impose a non zero chain alignment even if the chains are very flexible. This may explain why, in recent experiments on deuterated lammellar lipids, the quadrupolar order parameter S appears to be the same for most of the CD₂ groups.     

Frequency-domain channel estimation and equalization for shallow-water acoustic communications

A new frequency-domain channel estimation and equalization (FDE) scheme, combined with a new group-wise phase correction scheme, is proposed for single-carrier (SC) underwater acoustic communications systems employing single transducer and multiple hydrophones. The proposed SC-FDE scheme employs a 2N-point Fast Fourier Transform (FFT) to estimate and equalize the channel in frequency domain, where N is the number of symbols in a data block. Both the frequency-domain channel estimation and equalization are designed by the linear minimum mean square error criterion. Initial channel estimation is performed by a pilot signal block and later updates are achieved using the detected data blocks. The proposed phase correction scheme utilizes a few pilot symbols in each data block to estimate the initial phase shift and then correct it for the block to combat the large phase rotation due to the instantaneous Doppler drifts in the acoustic channels. Time-varying instantaneous phase drifts are re-estimated and compensated adaptively by averaging the phase variation across a group of symbols. The proposed SC-FDE and phase correction method is applied to the AUVFest’07 experimental data measured off the coast of Panama City, Florida, USA, June 2007. With the Quadrature Phase Shift Keying (QPSK) modulation and a symbol rate of 4 ksps, the proposed scheme achieves an average uncoded bit error rate on the order of 1×10^?4 for fixed-to-fixed channels with the source–receiver range of 5.06 km. For the moving-to-fixed source–receiver channels where the source–receiver range is 1–3 km, the multipath delay spread is 5 ms, the average Doppler shifts are ±20 Hz, and the maximum instantaneous Doppler drifts from the mean is ±4 Hz, the proposed scheme achieves an average uncoded bit error rate on the order of 1×10^?3.     

Wavelet based ILU preconditioners for the numerical solution by PUFEM of high frequency elastic wave scattering

Daubechies family of wavelets combined to the Incomplete Lower–Upper (ILU) factorization are considered as preconditioners for a block sparse linear system arising from the approximation of the time harmonic elastic wave equations by the Partition of Unity Finite Element Method (PUFEM). After applying the discrete wavelet transform (DWT) to each dense block in the final matrix and the known right-hand side, due to the local enrichment by pressure (P) and shear (S) plane waves, the resulting linear system is solved by the restarted Generalized Minimum RESidual method (GMRES) with ILU preconditioners allowing fill-in elements in the L and U matrix factors. A reordering algorithm of the vertices based on Gibbs method is also introduced. It leads to a significant reduction of the bandwidth of the wave based Finite Element (FE) matrix and enables the ILU preconditioners to be more effective. To study the performance of the proposed preconditioners, a problem of a horizontal S plane wave scattered by a rigid circular body in an infinite elastic medium is considered. The numerical tests show the good performance of the DWT based ILU preconditioners in improving the rate of convergence of GMRES, for high numbers of approximating P and S plane waves, on coarse mesh grids containing multi-wavelength sized elements. Moreover, the Haar DWT enhances the scalability with respect to the problem size, when the number of the nodal points increases, of the ILU preconditioner which uses the threshold strategy in the control of the fill-in elements. Despite the high level of the conditioning, a good accuracy may be achieved for a discretization level of around 1.9 degrees of freedom per S wavelength, which is far below the rule of thumb of 10 nodal points per wavelength, adopted for the conventional FE.     

The Fisher-Hartwig Formula and Entanglement Entropy

Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use the Fisher-Hartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.     

The Dunkl Oscillator in the Plane II: Representations of the Symmetry Algebra

The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the Schwinger–Dunkl algebra sd(2), are investigated. The algebra sd(2) has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra \({\mathfrak{u}(2)}\) . Two of the symmetry generators, J ₃ and J ₂, are respectively associated to the separation of variables in Cartesian and polar coordinates. Using the parabosonic creation/annihilation operators, two bases for the representations of sd(2), the Cartesian and circular bases, are constructed. In the Cartesian basis, the operator J ₃ is diagonal and the operator J ₂ acts in a tridiagonal fashion. In the circular basis, the operator J ₂ is block upper-triangular with all blocks 2 × 2 and the operator J ₃ acts in a tridiagonal fashion. The expansion coefficients between the two bases are given by the Krawtchouk polynomials. In the general case, the eigenvectors of J ₂ in the circular basis are generated by the Heun polynomials, and their components are expressed in terms of the para-Krawtchouk polynomials. In the fully isotropic case, the eigenvectors of J ₂ are generated by little ?1 Jacobi or ordinary Jacobi polynomials. The basis in which the operator J ₂ is diagonal is considered. In this basis, the defining relations of the Schwinger–Dunkl algebra imply that J ₃ acts in a block tridiagonal fashion with all blocks 2 × 2. The matrix elements of J ₃ in this basis are given explicitly.     

Second-order terms in the phonon-phason dynamic matrix of an icosahedral quasicrystal

They fourth-order terms (in the wave vector components) of the phonon-phason dynamic matrix are obtained for an icosahedral quasicrystal. In this order, the dynamic matrix has nine independent coefficients: three phonon-phonon, three phason-phonon, and three phason-phason coefficients. The number of independent coefficients in the phonon block of the constructed dynamic matrix is greater by unity than that for an isotropic medium. The corresponding features of acoustic phonon dispersion in the i-AlPdMn alloy are considered. It is shown that when the fourth-order terms are taken into account, the intensity of diffuse scattering in the vicinity of Bragg reflections decreases in accordance with the law α/(q ²+βq ⁴), where q is the distance to a reflection in the reciprocal space and coefficients α and β depend on the direction of vector q.