Pressure-induced formation of diblock copolymer “micelles” in supercritical fluids. A combined study by small angle scattering experiments and mean-field theory. I. The critical micellization density concept

2004 ◽  
Vol 120 (7) ◽  
pp. 3489-3498 ◽  
Author(s):  
A. Raudino ◽  
F. Lo Celso ◽  
A. Triolo ◽  
R. Triolo
Keyword(s):  
Field Theory ◽  
Supercritical Fluids ◽  
Diblock Copolymer ◽  
Small Angle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Small Angle Scattering ◽  
Angle Scattering ◽  
Copolymer Micelles

Structure of Cd-Ga Melts Part 2: X-Ray Small-Angle Scattering

1980 ◽  
Vol 35 (9) ◽  
pp. 938-945 ◽  
Author(s):  
Gerhard Hermann ◽  
Georg Rainer-Harbach ◽  
Siegfried Steeb
Keyword(s):  
Critical Point ◽  
Small Angle ◽  
Lattice Gas ◽  
Critical Concentration ◽  
Mean Field Theory ◽  
Mean Field ◽  
Small Angle Scattering ◽  
Correlation Lengths ◽  
X Ray ◽  
Angle Scattering

Abstract X-ray small-angle scattering experiments were performed on nine melts of the Cd-Ga system at different temperatures up to 440°C. Evaluation of the data follows the Ornstein-Zernike theory of critical scattering, thus yielding correlation lengths ξ of concentration fluctuations and the long-wavelength limit Sec (0) of the Bhatia-Thornton structure factor. Studies of the concentration and temperature dependence of ξ and SCC (0) indicate that the critical point occurs at cc = 50.0 ± 1-0 at % Ga and Tc - 295.2 ± 0-1° C. For a melt with the critical concentration, SCC (0) increases up to 3500 times the ideal S1dCC (0)=CACB-This indicates a strong segregation tendency. In the vicinity of the critical point of the Cd-Ga system, experimental correlation lengths ξ > 100 A were obtained. The critical-point exponents ν and γ were determined. It follows that the behaviour of a critical Cd-Ga melt satisfies the prediction of the classical mean-field theory for higher temperatures, whereas, within experimental accuracy, the lattice-gas predictions are satisfied upon approaching the critical temperature.

Mean Field Theory of Diblock Copolymer on Curved Manifolds

2014 ◽  
Vol 346 (1) ◽  
pp. 22-31 ◽  
Author(s):  
Daming Li ◽  
Kewei Liang ◽  
Thomas Gruhn
Keyword(s):  
Field Theory ◽  
Diblock Copolymer ◽  
Mean Field Theory ◽  
Mean Field ◽  
Curved Manifolds
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