Absorption/Expulsion of Oligomers and Linear Macromolecules in a Polymer Brush

The absorption of free linear chains in a polymer brush was studied with respect to chain size $L$ and compatibility $\chi$ with the brush by means of Monte Carlo (MC) simulations and Density Functional Theory (DFT) / Self-Consistent Field Theory (SCFT) at both moderate, $\sigma_g = 0.25$, and high, $\sigma_g = 1.00$, grafting densities using a bead-spring model. Different concentrations of the free chains $0.0625 \le \phi_o \le 0.375$ are examined. Contrary to the case of $\chi = 0$ when all species are almost completely ejected by the polymer brush irrespective of their length $L$, for $\chi < 0$ we find that the degree of absorption (absorbed amount) $\Gamma(L)$ undergoes a sharp crossover from weak to strong ($\approx 100$) absorption, discriminating between oligomers, $1\le L\le 8$, and longer chains. For a moderately dense brush, $\sigma_g = 0.25$, the longer species, $L > 8$, populate predominantly the deep inner part of the brush whereas in a dense brush $\sigma_g = 1.00$ they penetrate into the "fluffy" tail of the dense brush only. Gyration radius $R_g$ and end-to-end distance $R_e$ of absorbed chains thereby scale with length $L$ as free polymers in the bulk. Using both MC and DFT/SCFT methods for brushes of different chain length $32 \le N \le 256$, we demonstrate the existence of unique {\em critical} value of compatibility $\chi = \chi^{c}<0$. For $\chi^{c}(\phi_o)$ the energy of free chains attains the {\em same} value, irrespective of length $L$ whereas the entropy of free chain displays a pronounced minimum. At $\chi^{c}$ all density profiles of absorbing chains with different $L$ intersect at the same distance from the grafting plane. The penetration/expulsion kinetics of free chains into the polymer brush after an instantaneous change in their compatibility $\chi$ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length $L$: I ($1\le L\le 8$), II ($8 \le L \le N$), and III ($L > N$), in which the time of absorption $\tau$ grows with $L$ at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of $\Gamma \propto t^\alpha$ with power $\alpha \propto -\ln \phi_o$ whereby penetration of the free chains into the brush gets {\em slower} as their concentration rises

Soliton topology versus discrete symmetry in optical lattices

We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general ``charge rule'' using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing in the case of Bessel lattices allows us to derive also a overall stability rule for the allowed vortex solitons.Comment: 4 pages, 3 figures. To appear in Phys. Rev. Let

Spectrophotometric Procedure for Fast Reactor Advanced Coolant Manufacture Control

The paper describes a spectrophotometric procedure for fast reactor advanced coolant manufacture control. The molar absorption coefficient of dimethyllead dibromide with dithizone was defined as equal to 68864 ± 795 lmole{-1}cm{-1}, limit of detection as equal to 0.583 10{-6} g/ml. The spectrophotometric procedure application range was found to be equal to 37.88-196.3 g. of dimethyllead dibromide in the sample. The procedure was used within the framework of the development of the method of synthesis of the advanced coolant for fast reactors