Molecular dynamics simulations of electrostatic layer-by-layer self-assembly

Electrostatic assembly of multilayered thin films through sequential adsorption of polyions in layer-by-layer fashion utilizes the strong electrostatic attraction between oppositely charged molecules. We perform molecular dynamics simulations of multilayers of flexible polyelectrolytes around a charged spherical particle. Our simulations establish that the charge reversal after each deposition step is a crucial factor for the steady layer growth. The multilayers appear to be nonequilibrium structures.     

Free Partially Commutative Lie Superalgebras: Dimensions of Homogeneous Components

We consider dimensions of various homogeneous components in free partially commutative Lie (p-)superalgebras and offer a computational algorithm for finding them. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15, 2000.     

Reaction of 5-oxo-2-phenyl-4,4-bis(trifluoromethyl)-4,5-dihydro-1,3,2-benzodioxaphosphepine with chloral. The synthesis and spatial structure of 5-carbaphosphatrane containing a four-membered ring

Phosphorylation of 2-hydroxyphenyl 2,2,2-trifluoro-1-hydroxy-1-(trifluoromethyl)ethyl ketone with dichloro(phenyl)phosphine gave 5-oxo-2-phenyl-4,4-bis(trifluoromethyl)-4,5-di-hydro-1,3,2-benzodioxaphosphepine. Heating of the latter initiated an intramolecular interaction of the P atom with the carbonyl group. Hydrolysis of the intermediate product yielded 3-hydroxy-2-oxo-2-phenyl-3-[2,2,2-trifluoro-1-hydroxy-1-(trifluoromethyl)ethyl]-2,3-di-hydro-1,2λ⁵-benzo[d]oxaphosphole. The reaction was highly stereoselective (P_RC_S/P_SC_R). The reaction of the starting phosphepine with chloral proceeded highly stereoselectively (P_RC_SC_S/P_SC_RC_R) to give a 5-carbaphosphatrane derivative containing a four-membered ring, namely, 1-phenyl-3-trichloromethyl-10,10-bis(trifluoromethyl)-6,7-benzo-2,4,8,9-tetraoxa-1λ⁵-phosphatricyclo[3.3.2.0¹,⁵]decene. The trigonal bipyramid of the 5-carbaphosphatrane derivative is made up of the equatorial O atoms and the apical C atoms.     

Chains are more flexible under tension

The mechanical response of networks, gels, and brush layers is a manifestation of the elastic properties of the individual macromolecules. Furthermore, the elastic response of macromolecules to an applied force is the foundation of the single-molecule force spectroscopy techniques. The two main classes of models describing chain elasticity include the worm-like and freely-jointed chain models. The selection between these two classes of models is based on the assumptions about chain flexibility. In many experimental situations the choice is not clear and a model describing the crossover between these two limiting classes is therefore in high demand. We are proposing a unified chain deformation model which describes the force-deformation curve in terms of the chain bending constant K and bond length b. This model demonstrates that the worm-like and freely-jointed chain models correspond to two different regimes of polymer deformation and the crossover between these two regimes depends on the chain bending rigidity and the magnitude of the applied force. Polymer chains with bending constant K>1 behave as a worm-like chain under tension in the interval of the applied forces f ≤ Kk(B)T/b and as a freely-jointed chain for f ≥ Kk(B)T/b (k(B) is the Boltzmann constant and T is the absolute temperature). The proposed crossover expression for chain deformation is in excellent agreement with the results of the molecular dynamics simulations of chain deformation and single-molecule deformation experiments of biological and synthetic macromolecules.     

Regular 4‐critical graphs of even degree

In 1960, Dirac posed the conjecture that r‐connected 4‐critical graphs exist for every r ≥ 3. In 1989, Erd?s conjectured that for every r ≥ 3 there exist r‐regular 4‐critical graphs. In this paper, a technique of constructing r‐regular r‐connected vertex‐transitive 4‐critical graphs for even r ≥ 4 is presented. Such graphs are found for r = 6, 8, 10. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 103–130, 2004     

2-(2-Hydroxyphenyl)imidazolidines and their O-phosphorylated derivatives

2-(2-Hydroxyaryl)imidazolidines were synthesized by reaction of aromatic carbonyl compounds with N,N′-dialkylethylenediamines. The title compounds were also prepared using the corresponding Schiff bases instead of carbonyl compounds. Phosphorylation of 2-(2-hydroxyphenyl)imidazolidines with phosphoryl and phosphorothioyl chlorides and phosphorochloridites was accomplished. The reaction of O-phosphorylsalicylaldehyde with N,N′-dialkylethylenediamines also afforded 2-(2-hydroxyphenyl)imidazolidines.     

Conjugation effects of various linkers on Gd(III) MRI contrast agents with dendrimers: optimizing the hydroxypyridinonate (HOPO) ligands with nontoxic, degradable esteramide (EA) dendrimers for high relaxivity

One essential requirement for more sensitive gadolinium-based MRI contrast agents is to slow the molecular tumbling of the gadolinium(III) ion, which increases the gadolinium's relaxivity (i.e., its ability to speed up the NMR relaxation of nearby water molecules). One route to this is through conjugation to high-molecular-weight polymers such as dendrimers. In this work, amine-functionalized TREN-bis(1,2-HOPO)-TAM-ethylamine and TREN-bis(1-Me-3,2-HOPO)-TAM-ethylamine ligands have been synthesized and attached to biocompatible 40 kDa esteramide (EA)- and poly-l-lysine (PLL)-based dendrimers capable of binding up to eight gadolinium complexes. These conjugates have T(1) relaxivities of up to 38.14 ± 0.02 mM(-1) s(-1) per gadolinium at 37 °C, corresponding to relaxivities of up to 228 mM(-1) s(-1) per dendrimer molecule. This relaxivity expressed on a "per Gd" basis is several times that of the small-molecule complexes and an order of magnitude higher than that of current commercial agents. Because of their high performance and low toxicity, these macromolecules may constitute an attractive complement to currently available gadolinium(III)-based contrast agents.