Finsler geometry of topological singularities for multi‐valued fields: Applications to continuum theory of defects

Topological singularity in a continuum theory of defects and a quantum field theory is studied from a viewpoint of differential geometry. The integrability conditions of singularity (Clairaut‐Schwarz‐Young theorem) are expressed by a torsion tensor and a curvature tensor when a Finslerian intrinsic parallelism holds for the multi‐valued function. In the context of the quantum field theory, the singularity called an extended object is expressed by the torsion when the intrinsic parallelism is related to the spontaneous breakdown of symmetry. In the continuum theory of defects, the path‐dependency of point and line defects within a crystal is interpreted by the non‐vanishing condition of torsion tensor in a non‐Riemannian space osculated from the Finsler space, and the domain is not simply connected. On the other hand, for the rotational singularity, an energy integral (J‐integral) around a disclination field is path‐independent when a nonlinear connection is single‐valued. This means that the topological expression for the sole defect (Gauss‐Bonnet theorem with genus ) is understood by the integrability of nonlinear connection.

     

Substituent effects on acidity of aryl‐substituted fluoroalkanes: a computational study

The gas‐phase acidities (GA) of various aryl‐substituted fluoroalkanes, XC₆H₄CH(R¹)R², were calculated at the B3LYP/6‐311 + G(d,p)//B3LYP/6‐311 + G(d,p). The acidity values of alkanes having a common substituent X varied significantly with the change of R¹ and R². Their changes in acidity of 1 and 2 having two strong electron‐withdrawing groups (CF₃ or C₂F₅) at the deprotonation site and 8 , 9 , 10 , 11 having no fluorine atom at β‐position were linearly correlated with the corrected number of fluorine atoms contained in the fluorinated alkyl group (R² > 0.999). On the other hand, the GA values of β‐fluorine substituted alkanes ( 3 , 4 , 5 , 6 , 7 ) deviated in a stronger acid direction from the line. The enhanced acidity was attributed to the additional stabilization of the conjugate anion caused by the β‐fluorine negative hyperconjugation. The magnitude of β‐fluorine negative hyperconjugation of the fluorinated alkyl group (ΔG^o_β‐F) given by the deviations from the line decreased with increasing electron‐withdrawing ability of substituent X on the benzene ring, indicating that β‐fluorine negative hyperconjugation competes with the electronic effect of the substituent X. The GA_el values obtained by subtraction ΔG^o_β‐F from the apparent GA value were successfully correlated in terms of the Yukawa–Tsuno equation. The obtained ρ_el and r^?_el values were linearly related to the GA_el value of the respective phenyl‐substituted fluoroalkanes, supporting our previous conclusion that the ρ and r^? values for the substituent effect caused by the electronic effects of the substituent on the acidity are determined by the thermodynamic stability of the parent ion (ring substituent = H). Copyright © 2015 John Wiley & Sons, Ltd.     

Excited‐state hydrogen bond strengthening of coumarin 153 in ethanol solvent: a TDDFT study

So far, coumarin dyes have been extensively studied with various means to understand their photophysical behaviors and photochemical properties. Here, our performing time‐dependent density functional theory calculation is aimed at exploring the excited‐state hydrogen bonding dynamics of coumarin 153 (C153) in protic ethanol (EtOH) solvent. The calculated results suggest that the excited‐state hydrogen bond C?O?H?O between C?O group and O?H group in the C153‐EtOH complex is strengthened, and the S₀ → S₁ transition of the complex corresponds to the highest occupied molecular orbital (HOMO) hopping to the lowest unoccupied molecular orbital (LUMO). The excited‐state hydrogen bond strengthening has been further confirmed by its larger binding energy in the S₁ state than in the S₀ state. In addition, because of the formation of the hydrogen bond C?O?H?O, a red shift of about 7 nm occurs in the electronic spectra of the C153‐EtOH complex, which is in good accordance with the experiment result. Copyright © 2016 John Wiley & Sons, Ltd.     

Rate constant measurements for initial addition reactions of radicals at the propagation step of photo‐polymerization as studied by pulsed EPR spectroscopy

Pulsed EPR spectroscopy was employed to determine reaction rate constants at an early stage of addition reactions in radical polymerizations triggered by four initiator radicals, which were generated by photodissociation of four parent molecules. Two monomers (tert‐butylacrylate and tert‐butylmethacrylate) were examined as reactant. Stern–Volmer analysis on the measured decay time of electron spin echo intensity of reacting radicals provides rate constants for addition reactions. We focused on rate constants for the second step reaction between monomer and adduct radical that is produced by the first step addition reaction between initiator radical and monomer. The rate constant measured by pulsed EPR was evaluated by theoretical calculations in the light of (1) enthalpy difference between product radical and reactants and (2) charge transfer interaction between reacting radical and monomer. Copyright © 2016 John Wiley & Sons, Ltd.     

High–Yield Production of Uniform Gold Nanoparticles with Sizes from 31 to 577 nm via One‐Pot Seeded Growth and Size‐Dependent SERS Property

In this work, uniform, quasi‐spherical gold nanoparticles (Au NPs) with sizes of 31–577 nm are prepared via one‐pot seeded growth with the aid of tris‐base (TB). Distinct from the seeded growth methods available in literature, the present method can be simply implemented by subsequently adding the aqueous dispersion of the 17 nm Au‐NP seeds and the aqueous solution of HAuCl₄ into the boiling aqueous TB solution. It is found that at the optimal pH range, the sizes of the final Au NPs and their concentrations are simply controlled by either the particle number of the Au seed dispersion or the concentration of the HAuCl₄ solution, while the latter enables us to produce large Au NPs at very high concentration. Moreover, as‐prepared Au NPs of various sizes are coated on glass substrates to test their surface‐enhanced Raman scattering (SERS) activities by using 4‐aminothiophenol (4‐ATP) molecules as probes, which exhibit “volcano type” dependence on the Au NP sizes at fixed excitation wavelength. Furthermore, the Au NPs with sizes of ≈97 and 408 nm exhibit the largest SERS enhancement at the excitation wavelength of 633 and 785 nm, respectively.