Long-Range Order and Orientation of Cylinder-Forming Block Copolymers on Chemically Nanopatterned Striped Surfaces

2006 ◽  
Vol 39 (10) ◽  
pp. 3598-3607 ◽  
Author(s):  
Erik W. Edwards ◽  
Mark P. Stoykovich ◽  
Harun H. Solak ◽  
Paul F. Nealey
Keyword(s):  
Block Copolymers ◽  
Long Range ◽  
Range Order ◽  
Long Range Order

Long-Range Order Self-Assembly of Conjugated Block Copolymers at Inclined Air–Liquid Interfaces

2020 ◽  
Vol 12 (4) ◽  
pp. 5099-5105 ◽  
Author(s):  
Saejin Oh ◽  
Seulki Kang ◽  
Ma. Helen M. Cativo ◽  
Myungjae Yang ◽  
Sung-Hee Chung ◽  
...  
Keyword(s):  
Block Copolymers ◽  
Long Range ◽  
Self Assembly ◽  
Range Order ◽  
Long Range Order ◽  
Liquid Interfaces

Long-Range Order of Supramolecular Structures in Amorphous Butadiene-Styrene Block Copolymers

1972 ◽  
Vol 45 (6) ◽  
pp. 1564-1581 ◽  
Author(s):  
G. Kämpf ◽  
H. Krömer ◽  
M. Hoffmann
Keyword(s):  
Block Copolymers ◽  
Long Range ◽  
Colloidal Particles ◽  
Supramolecular Structures ◽  
Range Order ◽  
Long Range Order ◽  
X Ray Diffraction ◽  
The Matrix ◽  
The One ◽  
Butadiene Styrene

Abstract The various methods for determining quantitatively the dimensions of morphological structures from electron micrographs as well as evaluation of small-angle electron and x-ray diffraction are reviewed briefly. In continuation of previous work, the types of long-range order of supramolecular structures observed in two-block butadiene-styrene (BS) copolymers of very uniform molecular structure are discussed. By phase separation, aggregates of the one type of block with uniform shapes and sizes are formed which are arranged strictly periodically in the matrix consisting of the other type of block. Apart from “lattice imperfections”, special regard is given to the formation of boundaries between regions with long-range order of domains. The macroscopic lattices observed in BS block copolymers are compared with the latticelike arrays of colloidal particles found in other systems of a completely different chemical nature.

Guide Pattern for Long-Range-Order Nanofabrication of Self-Assembled Block Copolymers

2010 ◽  
Vol 459 ◽  
pp. 124-128 ◽  
Author(s):  
Takashi Akahane ◽  
Miftakhul Huda ◽  
You Yin ◽  
Sumio Hosaka
Keyword(s):  
Electron Beam ◽  
Block Copolymer ◽  
Block Copolymers ◽  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
Self Assembled ◽  
Guide Lines

In this paper, we report two kinds of guide patterns precisely created by electron beam drawing. These guide patterns are expected to precisely control the arrangement of nanodots self-assembled from block copolymer (BCP) in order to obtain long-range-order nanofabrication. The first guide pattern is comprised only of a post lattice. The second guide pattern adds guide lines to the post lattice. The added guide lines are expected to better control the location and orientation of the BCP nanodots. We succeeded in fabricating these two kinds of guide patterns for 22-nm- and 33-nm-pitch BCP nanodots.

Amphiphilic Polymer Conetworks Based on End-Linked “Core-First” Star Block Copolymers: Structure Formation with Long-Range Order

2015 ◽  
Vol 4 (10) ◽  
pp. 1163-1168 ◽  
Author(s):  
Eleni J. Kepola ◽  
Elena Loizou ◽  
Costas S. Patrickios ◽  
Epameinondas Leontidis ◽  
Chrysovalantis Voutouri ◽  
...  
Keyword(s):  
Block Copolymers ◽  
Structure Formation ◽  
Long Range ◽  
Amphiphilic Polymer ◽  
Range Order ◽  
Long Range Order ◽  
Star Block Copolymers

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

Time-Resolved, Laser-Induced Phase Transformation in Aluminum

1984 ◽  
Vol 35 ◽  
Author(s):  
S. Williamson ◽  
G. Mourou ◽  
J.C.M. Li
Keyword(s):  
Point Defect ◽  
Long Range ◽  
Rapid Heating ◽  
Range Order ◽  
Nucleation Theory ◽  
Long Range Order ◽  
Time Resolved ◽  
Aluminum Films ◽  
Thin Aluminum ◽  
Initial Nucleus

ABSTRACTThe technique of picosecond electron diffraction is used to time resolve the laser-induced melting of thin aluminum films. It is observed that under rapid heating conditions, the long range order of the lattice subsists for lattice temperatures well above the equilibrium point, indicative of superheating. This superheating can be verified by directly measuring the lattice temperature. The collapse time of the long range order is measured and found to vary from 20 ps to several nanoseconds according to the degree of superheating. Two interpretations of the delayed melting are offered, based on the conventional nucleation and point defect theories. While the nucleation theory provides an initial nucleus size and concentration for melting to occur, the point defect theory offers a possible explanation for how the nuclei are originally formed.

scholarly journals Finite temperature off-diagonal long-range order for interacting bosons

2020 ◽  
Vol 102 (18) ◽  
Author(s):  
A. Colcelli ◽  
N. Defenu ◽  
G. Mussardo ◽  
A. Trombettoni
Keyword(s):  
Long Range ◽  
Finite Temperature ◽  
Range Order ◽  
Long Range Order
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