Simulations of a weakly conducting droplet under the influence of an alternating electric field

We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is the same as the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio $(K_r)$ and permittivity ratio $(S)$ of the droplet to the surrounding fluid. In contrast, our simulations for weakly conducting media show that this equivalence between alternating and direct electric fields does not hold for $K_r \ne S$. Moreover, for a range of parameters, the deformation obtained using the alternating and direct electric fields is qualitatively different, i.e. for low $K_r$ and high $S$, the droplet becomes prolate under alternating electric field but deforms to an oblate shape in the case of the equivalent direct electric field. A parametric study is conducted by varying the time period of the applied alternating electric field, the permittivity and the electrical conductivity ratios. It is observed that while increasing $K_r$ has a negligible effect on the deformation dynamics of the droplet for $K_r<S$, it enhances the deformation of the droplet when $K_r>S$ for both alternating and direct electric fields. We believe that our results may be of immense consequence in explaining the morphological evolution of droplets in a plethora of scenarios ranging from nature to biology.Comment: 10 pages, 8 figure

Ligand Effects on the Regioselectivity of Rhodium-Catalyzed Hydroformylation: Density Functional Calculations Illuminate the Role of Long-Range Noncovalent Interactions

Density functional theory calculations have been performed to gain insight into the origin of ligand effects in rhodium (Rh)-catalyzed hydroformylation of olefins. In particular, the olefin insertion step of the Wilkinson catalytic cycle, which is commonly invoked as the regioselectivity-determining step, has been examined by considering a large variety of density functionals (e.g., B3LYP, M06-L); a range of substrates, including simple terminal (e.g., hexene, octene), heteroatom-containing (e.g., vinyl acetate), and aromatic-substituted (e.g., styrene) alkenes, and different ligand structures (e.g., monodentate PPh₃ ligands and bidentate ligands such as DIOP, DIPHOS). The calculations indicate that the M06-L functional reproduces the experimental regioselectivities with a reasonable degree of accuracy, while the commonly employed B3LYP functional fails to do so when the equatorial–equatorial arrangement of phosphine ligands around the Rh center is considered. The different behavior of the two functionals is attributed to the fact that the transition states leading to the Rh–alkyl intermediates along the pathways to isomeric aldehydes are stabilized by the medium-range correlation containing π–π (ligand–ligand) and π–CH (ligand–substrate) interactions that cannot be handled properly by the B3LYP functional due to its inability to describe nonlocal interactions. This conclusion is further validated using the B3LYP functional with Grimme’s empirical dispersion correction term: i.e., B3LYP-D3. The calculations also suggest that transition states leading to the linear Rh–alkyl intermediates are selectively stabilized by these noncovalent interactions, which gives rise to the high regioselectivities. In the cases of heteroatom- or aromatic-substituted olefins, substrate electronic effects determine the regioselectivity; however, these calculations suggest that the π–π and π–CH interactions also make an appreciable contribution. Overall, these computations show that the steric crowding-induced ligand–ligand and ligand–substrate interactions, but not intraligand interactions, influence the regioselectivity in Rh-catalyzed hydroformylation when the phosphine ligands are present in an equatorial–equatorial configuration in the Rh catalyst

Importance of Long-Range Noncovalent Interactions in the Regioselectivity of Rhodium-Xantphos-Catalyzed Hydroformylation

M06-L-based quantum chemical calculations were performed to examine two key elementary steps in rhodium (Rh)-xantphos-catalyzed hydroformylation: carbonyl ligand (CO) dissociation and the olefin insertion into the Rh–H bond. For the resting state of the Rh-xantphos catalyst, HRh­(xantphos)­(CO)₂, our M06-L calculations were able to qualitatively reproduce the correct ordering of the equatorial–equatorial (<i>ee</i>) and equatorial–axial (<i>ea</i>) conformers of the phosphorus ligands for 16 derivatives of the xantphos ligand, implying that the method is sufficiently accurate for capturing the subtle energy differences associated with various conformers involved in Rh-catalyzed hydroformylation. The calculated CO dissociation energy from the <i>ea</i> conformer (Δ<i>E</i> = 21–25 kcal/mol) was 10–12 kcal/mol lower than that from the <i>ee</i> conformer (Δ<i>E</i> = 31–34 kcal/mol), which is consistent with prior experimental and theoretical studies. The calculated regioselectivities for propene insertion into the Rh–H bond of the <i>ee</i>-HRh­(xantphos)­(propene)­(CO) complexes were in good agreement with the experimental l:b ratios. The comparative analysis of the regioselectivities for the pathways originating from the <i>ee</i>-HRh­(xantphos)­(propene)­(CO) complexes with and without diphenyl substituents yielded useful mechanistic insight into the interactions that play a key role in regioselectivity. Complementary computations featuring xantphos ligands lacking diphenyl substituents implied that the long-range noncovalent ligand–ligand and ligand–substrate interactions, but not the bite angles per se, control the regioselectivity of Rh-diphosphine-catalyzed hydroformylation of simple terminal olefins for the <i>ee</i> isomer. Additional calculations with longer chain olefins and the simplified structural models, in which the phenyl rings of the xantphos ligands were selectively removed to eliminate either substrate–ligand or ligand–ligand noncovalent interactions, suggested that ligand–substrate π-HC interactions play a more dominant role in the regioselectivity of Rh-catalyzed hydroformylation than ligand–ligand π–π interactions. The present calculations may provide foundational knowledge for the rational design of ligands aimed at optimizing hydroformylation regioselectivity

Unnat Sabji Paudhashala Prabandhan

Not AvailableIt is an extension leaflet in the Hindi language on 'Unnat Sabji Paudhashala Prabandhan' (Improved Vegetable Nursery Management).AICRP-VC (Anusuchit Jati Upyojana