Gradient linearity

The majority of all imaging systems use the so-called linear gradients, where only the first order of the expansion of the field is used. The gradients (Gx = 8Bz/6x, Gy = Bz/ y, Gz = 8Bz/8z) should be constant over the field of view this is known as gradient linearity. 

Tests must be performed to ensure that the pump is working well pressure, flow rate, and gradient linearity. 

Similar information to that obtained dining a conjugate gradient refinement is obtainable from second derivatives (curvature)1 R 51 93. For a harmonic function the gradient (linear matrix of first derivatives, [A]) multiplied by the curvature (Hessian matrix of second derivatives, [C]) should lead directly to the shifts (AX) to be applied in order to move toward the minimum (Eq. 3.3). 

Figure 2.9 Hydrophobic-interaction chromatography of proteins. (A) Ammonium sulfate gradient from 2.16 to 0 M (B) ammonium sulfate and tetrabutylammonium bromide gradients from 2.16 to 0 M and from 0 to 10 mM, respectively (C) ammonium sulfate and tetrabutylammonium bromide gradients from 2.16 to 0 M and from 0 to 20 mM, respectively (D) ammonium sulfate and tetrabutylammonium bromide gradients from 2.16 to 0 M and from 0 to 40 mM, respectively. Chromatography conditions column, silica-bound polyether, 10 cm x 4.6 mm I.D. temperature, 25°C flow rate, 1 ml/min gradient, linear for 30 min background buffer, 50 mM phosphate, pH 6.5. Peaks a, cytochrome c b, ribonuclease A c, /3-lactoglobulin A d, lysozyme e, ovalbumin f, a-chymotrypsinogen A g, fetuin. (Reprinted from Ref. 45 with permission.)...

Applying the diffusion equations to each film and approximating the concentration gradient linearly yields an expression for the mass transfer rates across the films,... 

The combination of these two factors determines the required shape of an LSS gradient. Linear gradients were shown to result for RPLC in section 5.4, whereas a concave gradient was found to be optimal for LSC in section 6.2.2. 

Equation (2.16) consists of two contributions the molecular momentum flow tensor, it, and the convective momentum flow tensor, pvv. The term p8 represents the pressure effect, while the contribution t, for a Newtonian fluid, is related to the velocity gradient linearly through the viscosity. The convective momentum flow tensor pw contains the density and the products of the velocity components. A component of the combined momentum flow tensor of x-momentum across a surface normal to the x-direction is... 

Fig. 10. Chromatogram of a control serum ultrafiltrate sample from a normal donor using UV detection at 254 nm. Injection volume 80 1. Column reversed-phase, lO- rm particle diameter. Eluents (A) 0.02 M KHjPO<, pH 5.6 (B) 60% methanol-water. Gradient linear, 0-100% of B in 87 min, slope 0.60% methanol/min. Flow rate 1.5 ml/min. Reprinted with permission from Hartwick et at. (H7). Copyright by Elsevier Scientific Publishing Company, Amsterdam,...

Fig. 14. (A) Chromatogram of a serum sample from a patient suffering from severe depression. (B) Chromatogram of the same serum sample co-injected with inosine. (C) Purine nucleoside phosphorylase peak shift of patient serum sample. Conditions are the same as in Fig. 10 except as follows gradient linear from 1 to 40% B in 35 min. Reprinted with permission from Krstulovic et al. (K3I). Copyright by Elsevier Scientific Publishing Company, Amsterdam.

Gradient linear gradient of B in A with a linear gradient of B in A 0-18% B... 

Fig. 3-95. Gradient elution of nucleotide monophosphates, diphosphates, and triphosphates. -Separator column IonPac AS4 eluent (A) water, (B) 0.5 mol/L NaH2PO. , pH 3.4 with HjP04 gradient linear, 3% B to 100% B in 40 min flow rate 1.5 mL/min detection UV (254 ran) injection volume 50 pL solute concentrations 10 ppm each of CMP, UMP, AMP, and GMP, 20 ppm each of CDP, UDP, ADP, GDP, CTP, UTP, ATP, and GTP.

Fig. 3-110. Gradient elution of various mono- and disaccharides. - Separator column IonPac AS6A eluent (A) water, (B) 0.05 mol/L NaOH gradient linear, from 7% B to 100% B in 15 min flow rate 0.8 mL/min detection pulsed amperometry at a Au working electrode with post-column addition of NaOH injection volume 50 pL solute concentrations 15 ppm inositol (1), 40 ppm sorbitol (2), 25 ppm fucose (3) and deoxyribose (4), 20 ppm deoxyglucose (5), 25 ppm arabinose (6), rhamnose (7), galactose (8), glucose (9), xylose (10), mannose (11), fructose (12), melibiose (13), isomaltose (14), gentiobiose (15), and cellubiose (16), 50 ppm turanose (17), and maltose (18).

Fig. 3-114. Separation of a-, / -, and y-cyclodextrin. -Separator column CarboPac PA-1 eluent (A) 0.1 mol/L NaOH, (B) 0.1 mol/L NaOH + 0.5 mol/L NaOAc gradient linear, 100% A to 100% B in 20 min flow rate 1 vaU min detection and injection volume see Fig. 3-105 solute concentrations 500 ppm each of a- (1), ft- (2), and y-cyclo-dextrin (3).

Fig. 3-162. Separation of lanthanides by anion exchange. - Separator column Ion Pac CS5 eluent (A) 0.1 mol/L oxalic acid, (B) 0.1 mol/L diglycolic acid, (C) water gradient linear 80% A in 8 min to 26% A and 23% B all other chromatographic conditions see Fig. 3-161.

Fig. 3-166. Separation of tetraethylenepentamine (technical grade). - Chromatographic conditions see Fig. 3-165 gradient linear, 30% B for 2 min isocratically, then to 100% B in 15 min injection volume 50 pL solute concentration 20 ppm.

Fig. 5-38. Separation of fatty alcohol sulfates with various chain lengths. - Separator column IonPac NS1 (10 pm) eluent (A) 0.02 mol/L NH4OH / acetonitrile (80 20 v/v), (B) 0.02 mol/L NH4OH / acetonitrile (20 80 v/v) gradient linear, 100% A to 100% B in 25 min flow rate 1 mL/ min detection suppressed conductivity injection volume 50 jiL solute concentrations 1. 80 mg/ L Rewopol NLS 28 II. 80 ppm each of octyl sulfate (1), decyl sulfate (2), dodecyl sulfate (3), tetradecyl sulfate (4), and hexadecyl sulfate (5).

Fig. 5-42. Separation of a fatty alcohol polyglycolether sulfosuccinate (Rewopol SBFA 30). — Separator column Hypersil 5 MOS eluent (A) 0.001 mol/L NaOAc / acetonitrile (78 22 v/v), (B) 0.001 mol/L NaOAc / acetonitrile (60 40 v/v) gradient linear 100% A isocratically for 10 min, then in 20 min to 100% B flow rate 1 mL/min detection direct conductivity injection volume 50 pL solute concentration 1000 mg/L of the raw material (taken from [44]).

Fig. 6-26. Analysis of polyphosphoric acid upon application of DC plasma detection. - Separator column 150 mm x 4.1 mm I.D. PRP-1 eluent (A) 0.01 mol/L tetraethylammonium nitrate (pH 9), (B) 0.01 mol/L tetraethylammonium nitrate + 0.1 mol/L KN03 (pH 9.0) gradient linear, 1% B to 40% B in 18 min flow rate 1.2 mL/min detection DC plasma emission wavelength 214.9 nm injection 20 pL of a solution with ca. 60 pg P external standard 8.24 pg P as orthophosphate (taken from [52]).

Fig. 8-87. Analysis of water-soluble vitamins. - Separator column Spherisorb ODS 2 (5 pm) eluent (A) 0.1 mol/L KOAc (pH 4.2 with HOAc), (B) water/methanol/acetonitrile (50 10 40 v/v/v) gradient linear, 6% B in 30 min to 100% B flow rate 2 mL/min detection UV (254 nm) injection volume 50 pL solute concentrations 5 nmol each of ascorbic acid (1), nicotinic acid (2), thiamine (3), pyridoxine (4), nicotinic add amide (5), p-aminobenzoic add (6), cyanocobala-mine (7), and riboflavine (8).

Fig. 8-100. Gradient elution of catecholamines with amperometric detection. — Separator column Zorbax ODS eluent (A) 0.005 mol/L triethylamine / methanol, (B) 0.07 mol/L KH2P04 + 0.005 mol/L triethylamine + 0.001 mol/L sodium butanesulfonate (pH 3) gradient linear, 5% A in 20 min to 56% A flow rate 1 mL/min detection amperometry at a GC working electrode oxidation potential +0.8 V injection volume 50 pL solute concentrations 4 ppm each of norepinephrine (1), epinephrine (2), 3,4-dihydroxybenzyl-amine (3), dopamine (4), seratonine (5), 5-hydroxy-3-indolylacetic acid (6), and homovanillic acid (7).

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