The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

On the chaotic character of the stochastic heat equation, II

Consider the stochastic heat equation ${\partial_t u = (\varkappa/2)\Delta u+\sigma(u)\dot{F}}$ , where the solution u := u _t (x) is indexed by ${(t, x) \in (0, \infty) \times {\bf R}^d}$ , and ${\dot{F}}$ is a centered Gaussian noise that is white in time and has spatially-correlated coordinates. We analyze the large- ${\|x\|}$ fixed-t behavior of the solution u in different regimes, thereby study the effect of noise on the solution in various cases. Among other things, we show that if the spatial correlation function f of the noise is of Riesz type, that is ${f(x)\propto \|x\|^{-\alpha}}$ , then the “fluctuation exponents” of the solution are ${\psi}$ for the spatial variable and ${2\psi-1}$ for the time variable, where ${\psi:=2/(4-\alpha)}$ . Moreover, these exponent relations hold as long as ${\alpha \in (0, d \wedge 2)}$ ; that is precisely when Dalang’s theory [Dalang, Electron J Probab 4:(Paper no. 6):29, 1999] implies the existence of a solution to our stochastic PDE. These findings bolster earlier physical predictions [Kardar et al., Phys Rev Lett 58(20):889–892, 1985; Kardar and Zhang, Phys Rev Lett 58(20):2087–2090, 1987].     

Low-temperature decomposition of methanol on Au nanoclusters supported on a thin film of Al2O3/NiAl100

With a variety of surface probe techniques, we investigated low-temperature decomposition of methanol on Au nanoclusters formed by vapor deposition onto an ordered Al(2)O(3)/NiAl(100) thin film. Upon adsorption of methanol on the Au clusters (with mean diameter 1.5-3.8 nm and height 0.45-0.85 nm) at 110 K, some of the adsorbed methanol dehydrogenates directly into carbon monoxide (CO); the produced hydrogen atoms (H) begin to desorb near 125 K whereas most of the CO desorbs above 240 K. The reaction exhibits a significant dependence on the Au coverage: the produced CO increases in quantity with the Au coverage, reaches a maximum at about 1.0-1.5 ML Au, whereas decreases with further increase of the Au coverage. The coverage-dependence is rationalized partly by an altered number of reactive sites associated with low-coordinated Au in the clusters. At least two kinds of reactive sites for the low-temperature decomposition are distinguished through distinct C-O stretching frequencies (2050 cm(-1) and 2092 cm(-1)) while the produced CO co-adsorbs with H and methanol.     

Synthesis,Characterization and Photophysical Properties of Iridium(III) Bis‐cyclometallated Complexes Containing 1,1‐Dithiolates

A series of neutral Ir(III)‐based heteroleptic complexes with a formula of [Ir(η²‐(C^∧N))₂(η²‐(S^∧S))] ((C^∧N)^‐ = ppy^‐, (S^∧S)^‐ = Et₂NCS₂^‐ ( 2a ), MeOCS₂^‐ ( 2b ), EtOCS₂^‐ ( 2c ), ⁱPrOCS₂^‐ ( 2d ); (C^∧N)^‐ = tpy^‐, (S^∧S) = Et₂NCS₂^‐ ( 3a ), MeOCS₂^‐ ( 3b ), EtOCS₂^‐ ( 3c ), ⁱPrOCS₂^‐ ( 3d ); (C^∧N)^‐ = epb^‐ , (S^∧S)^‐ = Et₂NCS₂^‐ ( 4a ), MeOCS₂^‐ ( 4a ), EtOCS₂^‐ ( 4a ); ppyH = 2‐phenylpyridine; tpyH = 2‐(4′‐tolyl)pyridine; epbH = ethyl 4‐(2′‐pyridyl)benzate) was synthesized and characterized. The crystal structure of complex 2d was also determined. The electron‐releasing substituents on (C^∧N)^‐ or (S^∧S)^‐ blueshift λ_max values.     

"Turn-on" FRET-based luminescent iridium(III) probes for the detection of cysteine and homocysteine

"Turn-on" FRET-based luminescent probes containing iridium(III) complexes for the detection of Cys and Hcy have been designed and synthesized. The relationship between the steric bulk of the probe and the corresponding emission intensity enhancement towards detection of Cys and Hcy has been studied.     

On the adjacent vertex-distinguishing acyclic edge coloring of some graphs

A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv ∈ E(G). The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by x′ _Aa (G), is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.     

Ultrafast Spectroscopy Studies on Thickness Dependence of Acoustic Phonon Modes in Silver Nanoprisms

Time-resolved transient absorption technique is used to investigate the thickness dependence of acoustic phonon modes of silver nanoprisms with two thicknesses, 7.8 ± 1.2 and 8.5 ± 0.69 nm, and a similar bisector length of 31.4 ∼ 31.6 nm. Coherent acoustic phonon signals are observed. A new acoustic phonon frequency within 7.81 cm⁻¹ ∼ 11.7 cm⁻¹ is found and this phonon mode is associated with the thickness of the nanoprism. Another phonon frequency between 1.95 cm⁻¹ and 1.71 cm⁻¹ is also observed, and its origin can be associated with the bisector length of the nanoprism.     

Preparation of cobalt-containing bulky monodentate phosphines with electron-withdrawing/donating substituents on bridged arylethynyl and their applications in Suzuki coupling reactions

Several cobalt-containing bulky monodentate phosphines (μ-PPh₂CH₂PPh₂)Co₂(CO)₄(μ,η-(^tBu)₂PCC(C₆H₄R)) (4a: R=H; 4b: R=p-F; 4cp: R=p-CF₃; 4cm: R=m-CF₃; 4d: R=p-OMe) were prepared from the reactions of (^tBu)₂PCC(R-C₆H₄) (2a: R=H; 2b: R=p-F; 2cp: R=p-CF₃; 2cm: R=m-CF₃; 2d: R=p-OMe) with Co₂(CO)₆(μ-PPh₂CH₂PPh₂) 3. Further reactions of 4a, 4b, 4cp, 4cm, and 4d with Pd(OAc)₂ yielded unique palladium complexes (μ-PPh₂CH₂PPh₂)Co₂(CO)₄(μ,η-(^tBu)₂PCC(C₆H₃R)-κC¹)Pd(μ-OAc) (5a: R=H; 5b: R=p-F; 5cp: R=p-CF₃; 5cm: R=m-CF₃; 5d: R=p-OMe, respectively). The strong electron-withdrawing substituents, -F and -CF₃, assist the ortho-metalation process during the formation of 5b, 5cp, and 5cm. The more positively charged palladium center in 5b (or 5cp, 5cm) enhances the probability for PhB(OH)₃⁻ to attack the metal center and the rate of reduction thereafter. DFT studies on the charges of these palladium centers support this assumption. The enhancement of the reaction rates of the Suzuki-Miyaura cross-coupling reactions using 5b, 5cp, and 5cm is thereby attributed to this effect.