Applying the chain formation model to magnetic properties of aggregated ferrofluids

The magnetization properties of aggregated ferrofluids are calculated by combining the chain formation model developed by Zubarev with the modified mean-field theory. Using moderate assumptions for the inter- and intrachain interactions we obtain expressions for the magnetization and initial susceptibility. When comparing the results of our theory to molecular dynamics simulations of the same model we find that at large dipolar couplings (lambda>3) the chain formation model appears to give better predictions than other analytical approaches. This supports the idea that chain formation is an important structural ingredient of strongly interacting dipolar particles.

Polymer brushes under shear: molecular dynamics simulations compared to experiments

Surfaces coated with polymer brushes in a good solvent are known to exhibit excellent tribological properties. We have performed coarse-grained equilibrium and nonequilibrium molecular dynamics (MD) simulations to investigate dextran polymer brushes in an aqueous environment in molecular detail. In a first step, we determined simulation parameters and units by matching experimental results for a single dextran chain. Analyzing this model when applied to a multichain system, density profiles of end-tethered polymer brushes obtained from equilibrium MD simulations compare very well with expectations based on self-consistent field theory. Simulation results were further validated against and correlated with available experimental results. The simulated compression curves (normal force as a function of surface separation) compare successfully with results obtained with a surface forces apparatus. Shear stress (friction) obtained via nonequilibrium MD is contrasted with nanoscale friction studies employing colloidal-probe lateral force microscopy. We find good agreement in the hydrodynamic regime and explain the observed leveling-off of the friction forces in the boundary regime by means of an effective polymer–wall attraction.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Equilibrium behavior of symmetric ABA triblock copolymer melts

Melts of ABA triblock copolymer molecules with identical end blocks are examined using self-consistent field theory (SCFT). Phase diagrams are calculated and compared with those of homologous AB diblock copolymers formed by snipping the triblocks in half. This creates additional end segments which decreases the degree of segregation. Consequently, triblock melts remain ordered to higher temperatures than their diblock counterparts. We also find that middle-block domains are easier to stretch than end-block domains. As a result, domain spacings are slightly larger, the complex phase regions are shifted towards smaller A-segment compositions, and the perforated-lamellar phase becomes more metastable in triblock melts as compared to diblock melts. Although triblock and diblock melts exhibit very similar phase behavior, their mechanical properties can differ substantially due to triblock copolymers that bridge between otherwise disconnected A domains. We evaluate the bridging fraction for lamellar, cylindrical, and spherical morphologies to be about 40%–45%, 60%–65%, and 75%–80%, respectively. These fractions only depend weakly on the degree of segregation and the copolymer composition.

Effective interaction between monolayers of block copolymer compatiblizer in a polymer blend

The stability of ternary blends of two immiscible homopolymers and a block copolymer compatiblizer depends crucially on the effective interaction between the copolymermonolayers that form between the unlike homopolymer domains. Here, the interaction is calculated for blends involving A and B homopolymers of equal size with ABABdiblock copolymers of symmetric composition using both self-consistent field theory (SCFT) and strong-segregation theory (SST). If the homopolymers are larger than the copolymer molecules, an attractive interaction is predicted which would destroy the blend. This conclusion coupled with considerations regarding the elastic properties of the monolayer suggests that the optimum size of the homopolymer molecules is about 80% that of the copolymer molecule. A detailed examination of the theory demonstrates that the attraction results from the configurational entropy loss of the homopolymer molecules trapped between the copolymermonolayers. We conclude by suggesting how the monolayers can be altered in order to suppress this attraction and thus improve compatiblization.