Contour plots ethylene

The HOMOs of unsubstituted vinylidenenorbomane 47a and unsubstituted bicyclo[2.2.2]octene 48a are intrinsically comprised of similar components, i.e., the n orbital of the ethylene and the o-orbitals of the ethano bridges, the coupling being in an out-of-phase fashion (50 and 51), though the arrangement of the components is different. The contour plot (49) of the HOMO of 48a is consistent with these orbital interactions (50). 

Fig. 2. Contour plots of (Hike bonding orbitals of Zeise s anion. The contour values increase in absolute magnitude with increasing absolute values of the contour labels. The sign of the labels gives the sign of the orbital lobes. The set of contour values plotted is the same for each of the three orbitals. The interior nodes at the various atoms are not shown for clarity of presentation (a) the 5a, orbital, (b) the 6at orbital, and (c) the 7ot orbital showing significant interaction between the ethylene 7r-orbital and the Pt dx, yi orbital. [Reproduced from Rosch et at. (193), by permission of the American Chemical Society.]...

Fig. 39. Contour plot of chemical shift vs. retention time and chemigram of the on-line HPLC-NMR analysis of a technical poly(ethylene oxide) (from [210] with permission)...

Fig. 2.1. Displays of the electronic charge density in three planes of the ethylene molecule, C2H4. In the diagrams on the left, the value of the density is shown as a projection above the geometric plane the diagrams on the right are corresponding contour plots of p(r). (a) The plane containing the nuclei. Values of p(r) above an arbitrarily chosen value are not shown, (b) The plane obtained by a 90° rotation about the C-C axis of the plane shown in (a), (c) The plane perpendicular to the C-C axis at its midpoint. The values of the contours increase in magnitude from the outer contour inwards with the values given in the Appendix, Table A2. The projected positions of out-of-plane nuclei are indicated by open crosses.

In the case of small Brownian deformable droplets the interaction energy, when the continuous phase is a micellar surfactant solution of sodium nonylphenol polyoxy-ethylene-25 (SNP-25S), is illustrated in Fig. 8 as a function of the thickness, A, and film radius, R (see Fig. 3 for the definition of the geometry). The parameters of the micro-emulsion system are R = 2 im, d = 9.8 nm, (j> = 0.38, Ah = 5x10" J, <7= 7.5 mN/m, % = -135 mV, r = 1.91 nm, the electrolyte concentration 25 mM. The points on the contour plot (Fig. 8) correspond to tree local minima of -406 AbT, -140 k T and -37 k T corresponding to film containing 0, 1 and 2 micellar layers, respectively (Ivanov et al. 1999). These three possible films are thermodynamically stable and they act like barriers against the closer approach and flocculation (or coalescence) of the droplets in emulsions. 

Fig. 13.4 Contour plot of the surface of ethylene + ethylene as calculated by...

Fig. 12. Instantaneous contour plots of H2 in a turbulent ethylene diffusion flame resulting from adaptively reduced scheme with 15 species (left) in 4 sub-domains and direct integration of the full mechanism with 75 species (right). Average iso-lines are included to indicate the statistical similarities. (Lovas et al., 2010)...

Other common cross-fractionation techniques are SSF/A-Tref and SSF/ P-Tref [41,42]. In these techniques, polymers are first fractionated using SSF and the fractions are then further fractionated according to chain crystallizabilities using A-Tref or P-Tref. When P-Tref is used, further determination of comonomer content by C NMR or FTIR spectroscopy is required. Figures 19 and 20 show 3D and contour plots of bivariate distributions of molecular weight and comonomer composition obtained by SSF/P-Tref crossfractionation for an ethylene/l-pentene-4-methyl copolymer [42]. Comparing the contour plot with the equivalent contour plot of a LDPE sample (Fig. 21), one clearly notices significant differences between the bivariate distributions of these two samples. 

Fig. 4.6 Orbital symmetry in the first n n electronic transition of ethylene. Panels A, B Contour plots of the amplitudes of the HOMO (tr. A) and LUMO (tr, B) wavefunctions. C, D Contour plots of the product of the two wavefunctions. The C=C bond is aligned with the y axis, and the atomic z axes are parallel to the molecular z axis. In A-C, the plane of the drawing coincides with the yz plane in D, the plane of the drawing is parallel to the molecular xy plane and is above this plane by the Bohr radius (Uo = 0.529 A). The wavefunctions are constructed as in Fig. 2.7. Solid curves represent positive amplitudes dotted curves, negative. Distances are plotted as dimensionless multiples of and the contour intervals are O.OSOo in A and B and 0.02a in C and D. The arrows in C and D show the transition dipole in units of eA/a<, as calculated by Eq. (4.22e)...

Figure 4.17 illustrates the functions that enter into the transition gradient matrix element for the HOMO—>LUMO excitation of ethylene. Contour plots of the HOMO and LUMO (V a and tpi,) are reproduced from Fig. 4.6B in panels A and B... 

Fig. 4.17 Components of the transition matrix element of the gradient operator for excitation of ethylene. (A, B) Contour plots of the amplitudes of the HOMO and LUMO molecular orbitals in the yz plane. The C=C double bond lies on the y axis. (C, E) The derivatives of with respect to y and z, respectively. (D, F) The products of these derivatives with The y and...

Figure 1.17 Experimental and fitted data of an ethylene-propylene copolymer after stretching (a) experimental pattern, (b) fitted 3D plot, and (c) contour plot of (b) [108].

The methylene region of the contour plot of stereoirregular PP is very complex, and correlations of the C hexads with the H tetrads have been made [67]. This 2D technique was also used for ethylene-propylene copolymers [68],... 

FIG U RE 11.1 Typical contour plot to abbreviate compounding data (Vistalon 3708/Ethylene-Propylene Terpolymer, Enjay Chemical Company, 1968). Note that a compound with 200 parts each of oil and filler per 100 parts of rubber by weight (phr) still has a strength of about 1000 psi (7 MPa), quite acceptable for many mechanical applications. The compound, based on a high-molecular-weight ethylene-propylene terpolymer, also contains 5 parts zinc oxide, 1 part stearic acid, 1.5 parts sulfur, 1.5 parts tetramethylthiuram disulfide, and 0.5 parts of benzothiazyl disulfide. Cross-linking takes place at 160°C for 20 min. SRF, Semi-reinforcing furnace. 

Fig. 7.10 Display of the current density vector in the plane containing the nuclei of ethylene. The applied magnetic field is orthogonal to the plot plane and directed outward. Atom positions are marked by crosses. The maximum modulus is 1.84 (cut to 0.25) au and the step between two consecutive contours is 0.025 au. Contours of the magnetic shielding density 2 , Eq. (7.81), of hydrogen nucleus on the molecular plane of ethylene are represented in red. Solid dashed) red lines denote positive (negative) values...

---