Gradient revolution

Schafer, L. 1983. The Ab Initio Gradient Revolution in Structural Chemistry the Importance of Local Molecular Geometries and the Efficacy of Joint Quantum Mechanical and Experimental Procedures. J. Mol. Struct. 100, 51-73. 

Schafer, L. 1983. The ab initio gradient revolution in structural chemistry The importance of local molecular geometries and the efficacy of joint quantum mechanical and experimental procedures. J. Molec. Struct. 100 51-73. 

Fig. 2.9.2 Radiofrequency, field gradient and current distributions requires a three-dimen-ionic current pulse sequences for two-dimen- sional imaging sequence [see Figure 2.9.1(a)] sional current density mapping. TE is the Hahn and multiple experiments with the orientation spin-echo time, Tc is the total application time of the sample relative to the magnetic field of ionic currents through the sample. The 180°- incremented until a full 360°-revolution is pulse combined with the z gradient is slice reached. The polarity of the current pulses...

At low rotor revolution numbers an equilibrium state can be reached between sedimentation and diffusion. Now, a time-independent concentration gradient is established, i.e., (dddt) = 0. Under these conditions, the Svedberg equation becomes ... 

In the ultracentrifuge, solutions can be rotated at speeds up to 80,000 revolutions per minute, which provides force fields larger than the force of gravity by a factor of 3 x 105. Under these conditions, much larger concentration gradients can be obtained. 

The catalysts to be deposited are inserted into the sputter plant as the so-called targets. The shuttle carries the titer-plate and revolves below the metal targets (Figure 3.4). In every rotation up to three sublayers are deposited. For a binary system, the sublayer thickness was 10 nm in each revolution. The thickness gradients were realized by aperture orifices which shaped the particle beam (Figure 3.5). 

Fig. 2 Chromatograms obtained by high-speed CCC. (A) Separation of a set of dipeptides by gradient elution. Experimental conditions are as follows apparatus type-J multilayer CPC prototype with a 10-cm revolution radius column multilayer coil,...

These phenomena can be interpreted in terms of molecular orientation by the velocity gradient in the flowing liquid, opposed by the rotary Brownian movement which produces disorientation and a tendency toward a purely random distribution. The intensity of this Brownian movement is charaterized by the rotary diffusion constants, 0, discussed in the preceding section. The fundamental treatment of this problem, for very thin rod-shaped particles, was given by Boeder (5) the treatment has been generalized, and extended to rigid ellipsoids of revolution of any axial ratio, by Peterlin and STUARTi 56), [98), (99) and by Snell-MAN and Bj5knstAhl (J9J). The main features of their treatment are as follows 1 ... 

The discussion will be restricted to molecules which can be described as ellipsoids of revolution. We shall denote the semi-axis of revolution by a, the equatorial semi-axis by b. The orientation of a molecule may thus be completely described by the orientation of the a semiaxis the frame of reference is shown in Fig. 4. The center of the coordinate system is located in the center of gravity of the ellipsoid. The velocity gradient in the liquid, indicated in Fig. 4, tends to rotate the molecule clockwise. The orientation of the a semi-axis of the molecule is specified by the angles and 0, as defined in the figure and the accompanying legend. 

Fig. 4. Orientation of an ellipsoidal molecule in a flowing liquid of constant velocity gradient. The positive Z axis points perpendicularly upward from the plane of the paper. The projection of the axis of revolution of the ellipsoid on the XV plane is denoted by aa. The movement of the Liquid is parallel to the X axis, and is described by the equation GY, where is the velocity and G is the velocity gradient. The significance of the angle

The components of co, co and due to the velocity gradient, have been evaluated for ellipsoids of revolution by Jeffery (55) from the fundamental equations of hydrodynamics ... 

E. coU cells in a capillary tube can also be powered by an external voltage. In alkalophilic strains of Bacillus and some Vibrio species a sodium ion gradient will substitute. Several hundred protons or Na+ ions must pass through the motor per revolution. Some estimates, based on energy balance, are over 1000. However, Na+-dependent rotation at velocities of up to 1700 Hz has been reported for the polar flagellum of Vibrio alginolyticus. It is difficult to understand how the bacterium could support the flow of 1000 Na+ per revolution to drive the flagellum. ... 

It is well known that interfacial reaction rates increase as stirring speed is increased until reaching a plateau around 600-1700 rpm (revolutions per minute) [25]. On the other hand, PTC reaction rates are independent of the stirring speed above 200-350 rpm, necessary to level concentration gradients at the interphase. When neutral reagents are involved, it is thus possible to exclude the contribution of interfacial phenomena to the PTC processes. 

Fig. 2 Chromatograms obtained by high-speed CCC. (A) Separation of a set of dipeptides by gradient elution. Experimental conditions are as follows apparatus type-J multilayer CPC prototype with a 10 cm revolution radius column multilayer coil, 1.6 mm I.D., 130 m length, 285 ml total capacity sample dipeptide mixture 70 mg solvent system linear gradient between the starting medium of 1-butanol/ dichloroacetic acid/0.1 M ammonium formate (1 0.01 1) and the ending medium of 1-butanol/O.l M ammonium formate (1 1) mobile phase for 4 hr lower aqueous phase flow rate—214 ml/hr revolution 800 rpm detection 280 nm retention of stationary phase 55% of the total column capacity. (B) Separation of bacitracins by high-speed CCC. Bacitracins A and F are separated in peaks 18 and 22, respectively. Separation conditions are as follows apparatus Shimadzu type-J multilayer CPC (model HSCCC-IA Shimadzu Corporation, Kyoto, Japan) with a 10 cm revolution radius column multilayer cod, 1.6 mm I.D., 325 ml capacity sample 50 mg solvent system chloroform/ethanol/methanol/water (5 3 3 4) mobile phase lower organic phase flow rate 3 ml/min detection 254 nm.

Shear rate (shear-strain rate, velocity gradient) n. The rate of change of shear strain with time. In concentric-cylinder flow where the gap between the cylinders is much smaller than the cylinder radii, shear rate is almost uniform throughout the fluid and is given by 7r(i i + R2)N/ R2 — Ri), where Ri and are the radii of the cylinders, one rotating, the other stationary, and N is the rotational speed in revolutions per second. The universally used unit of shear rate is s . In tube flow, the shear rate varies from zero at the center to its maximum at the tube wall where, for a Newtonian liquid, it... 

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