Basic sedimentation equilibrium

Basic Sedimentation Equilibrium Equation. Sedimentation equilibrium experiments are performed at constant temperature. The condition for sedimentation equilibrium is that the total molar potential, m, for all components i be constant everywhere in the solution column of the ultracentrifuge cell. Mathematically this can be expressed as... 

Estimation of the Ideal Values for d In c/d(r2) and dc/d . For the nonideal case we can use Equations 1-4 and 6 to obtain the basic sedimentation equilibrium equation for component i. In the Fujita notation (17) this equation is... 

There are three points to emphasize. First, the expressions for the concentration or concentration gradient distribution for non-sector-shaped centerpieces can be applied to other methods for obtaining MWD s, such as the Fourier convolution theorem method (JO, 15, 16), or to more recent methods developed by Gehatia and Wiff (38-40). The second point is that the method for the nonideal correction is general. Since these corrections are applied to the basic sedimentation equilibrium equation, the treatment is universal. The corrected sedimentation equilibrium equation (see Equation 78 or 83) forms the basis for any treatment of MWD s. Third, the Laplace transform method described here and elsewhere (11, 12) is not restricted to the three examples presented here. For those cases where the plots of F(n, u) vs. u will not fit the three cases described in Table I, it should still be possible to obtain an analytical expression for F(n, u) which is different from those in Table I. This expression for F (n, u) could then be used to obtain an equation in s using procedures described in the text (see Equations 39 and 44). Equation 39 would then be used to obtain the desired Laplace transform. 

Analysis of Mixed Associations from Conventional Sedimentation Equilibrium Experiments. In these experiments one measures a quantity Mieq (14, 28) instead of Mweq. The basic sedimentation equilibrium equation for each reactant is... 

Analysis by the Archibald Method or by Sedimentation Equilibrium Experiments at Different Speeds. Instead of using Mweq here, one uses Mwa, the apparent weight-average molecular weight. For the Archibald experiment one obtains Mwa,t at rm or r6 by the application of Equations 13-16. The extrapolation of Mwa>t to zero time gives Mwo. For sedimentation equilibrium experiments at different speeds, one can evaluate Mwa by two different methods here one uses either Equations 17 or 18. For a mixed association such as A + B AB, the basic sedimentation equilibrium equation can be written as... 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

This then is experiments. our basic, working equation in sedimentation equilibrium To obtain the weight-average molecular weight, Mw, it is ... 

It can be assumed that the corresponding functionalized grids have the same basic structure in view of the similar behavior in UV spectroscopy, the MALDI-TOF mass spectrometry and the preliminary results of sedimentation equilibrium analysis in the analytical ultracentrifuge (48). 

Four electrophoretically distinct endo-(l -> 4)-)3-D-glucanases from Trichoderma viride have been identified. Three of them (mol. wts. 3.72 x 10, 5.20 X 10, and 4.95 x 10 by sedimentation equilibrium analysis) contained D-mannose, o-glucose, D-galactose, and 2-amino-2-deoxy-D-glucose (total 4.5, 15.0, and 15.2 % respectively) and were high in acidic- and hydroxy-amino-acids and glycine, but low in basic amino-acids. 

The material within the pellet would be then more reducing than the sediment in which it lies, and would have a higher local Eh potential. Thus, the initial impetus to the process is a A Eh between sediment and pellet. The concentrations of the elements which must be present in the sea water solution to promote glauconite formation are largely governed by the type of sediment in contact with the water. Equilibrium is thus established punctually between pellet and sea water effecting a transfer of material between the two media. On a larger but still somewhat local scale the dissolution of detrital silicates in sea water provides the basic "reservoir" of material in solution and hence determines the activities of various elements in the solution. 

It is our objective in this chapter to outline the basic concepts that are behind sedimentation and diffusion. As we see in this chapter, gravitational and centrifugal sedimentation are frequently used for particle-size analysis as well as for obtaining measures of solvation and shapes of particles. Diffusion plays a much more prevalent role in numerous aspects of colloid science and is also used in particle-size analysis, as we see in Chapter 5 when we discuss dynamic light scattering. The equilibrium between centrifugation and diffusion is particularly important in analytical and preparative ultracentrifuges. 

External fields are applied widely in separation systems. The most common fields used are based on electrical and sedimentation (both centrifugal and gravitational) forces. Gradients in solvent composition and temperature maintained by actions external to the system may also be considered as external fields defined in their broadest context (see Chapter 8). All of these fields are capable of changing the equilibrium distribution of chemical components. Furthermore, they may be selective, affecting one component differently from another, a basic requirement for separation. 

The hydrological cycle involves pH variations. In fact, most natural waters have a pH between 4 and 9 that is controlled mainly by the carbon dioxide-carbonate equilibrium. For instance, as calculated in example 6.4, the pH of rainwater is around 5.7 because of its equilibrium with carbon dioxide, but as it touches the Earth and comes in contact with decomposing organic materials, it may acidify even further. On the other hand, if water comes in contact with alkaline environments, minerals or sediments — mainly carbonates (which upon dissolution in water generate strongly basic media), its pH will rise. 

Centrifugation is used for two basic purposes (1) as a preparative technique to separate one type of material from others and (2) as an analytical technique to measure physical properties (e.g., molecular weight, density, shape, and equilibrium binding constants) of macromolecules. The sedimentation constant, s, of a protein is a measure of its sedimentation rate. The sedimentation constant is commonly expressed in svedbergs (S) 1 S = 10 seconds. 

Bioinert matter represents the third basic kind of matter of the biosphere. This is a substance which is made by living organisms and inert processes simultaneously and represents the stable djmamic equilibria of both of them" (Vernadsky, 1965, 59). Vernadsky called this kind of equilibrium complex dynamic equilibrium. The bioinert natural bodies are of great importance in the biosphere. The forests, the fields, plankton, benthos, soils, marine silt and sediments, all terrestrial waters, etc, are examples of the bioinert natural bodies. When living organisms die, they also form bioinert bodies. The... 

The complex history of chert diagenesis must be considered in detail in order to try and elucidate its B isotopic evolution during diagenesis. Basically, cherts are the result of a three-stage diagenetic process the first stage is the formation of opal-A at equilibrium with seawater, followed by its dissolution and crystalhzation to opal-CT, and then by a redissolution and crystallization to microcrystaUine quartz. The transition of amorphous siliceous sediment to... 

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