Experiment Archibald

In subsequent experiments, Archibald and Moody bathed the surface of a seg-... 

Here BLS is the second virial coefficient of the polymeric solute in the original solution before ultracentrifugation. BLs is a quantity which can be obtained in light-scattering experiments (17, 25, 30) or in Archibald experiments (31), provided it is calculated from a plot of l/MWapp° vs. c. Here 1/Mw pp° is obtained from values of Mw pp (at rm or rb) that have been extrapolated to zero time. The reason for using Equation 75 is that it leads to a simple method of estimating the MWD in nonideal solutions. 

Sector-Shaped Centerpieces. Method 1. Do the Archibald experiment and calculate MWappft at rm and r6 using standard procedures (32, 34). Here MWapp/t is the value of the apparent weight-average molecular weight at rm or r6. Extrapolate these values of Mw pp)t to zero time to get MWapp° details for this extrapolation have been given by Fujita et al. (32). 

Evaluation of Mweq. Sedimentation Equilibrium Experiments and the Archibald Method. At constant temperature the condition for sedimentation equilibrium is that the total potential jZi for each associating species i (i = A, B, or AnBw) be constant at every radial position r in the solution column of the ultracentrifuge thus... 

In obtaining Equation 11 it has been assumed that the partial specific volumes v of the associating species are equal we have also assumed that the specific refractive index increments of the associating solutes are equal. In Equation 12 R is the universal gas constant (8.314 X 107 ergs/deg-mole), p is the density of the solution (gram/ml), and T is the absolute temperature. Equation 11 is also valid for the Archibald experiment but only at rm or rb, the radial positions (in the solution column of the ultracentrifuge cell) of the air-solution meniscus and of the cell... 

Equations 15 and 16 were first obtained by Kegeles and his co-workers (16, 20, 21) and they are valid only for cells with sector-shaped center-pieces. Because of convective disturbances in the solution column of the ultracentfifuge cell during the transient state when nonsector-shaped cells are used, it is customary to do Archibald experiments in cells with sectorshaped centerpieces which avoid this problem. For details on the Archibald method—pitfalls, extrapolation to zero time—one should consult the papers of LaBar (17) and Fujita et al. (22). 

Archibald Experiments, Sedimentation Equilibrium Experiments at Different Speeds, and Light Scattering Experiments The analysis of a mixed association described by Equation 1 is similar for these three... 

Analysis from Archibald Experiments or from Sedimentation Equilibrium Experiments at Different Speeds. This discussion here is illustrated by the association described by Equation 1. When vA vB and 7 b, analogs of Equations 17 and 18 will yield Mieq when extrapolated to zero time. Similarly, Mieq will also be obtained from the analog of Equation 13 when values of Mi, are extrapolated to zero time. For this situation... 

A similar equation results for cBrm. Now a priori we do not know (d In Ja/dcB), cAr, cBr, or K we do not know BAa and Bbb (see Equations 67 and 68) from measurements on pure A and pure B. We have no way of knowing ir a priori, so we cannot use equations similar to 28 or 31. Similar considerations apply if vA vB and = b- Thus, it appears at present that we are forced to use the Archibald experiment or sedimentation equilibrium experiments at different speeds to analyze mixed associations when one is restricted to Rayleigh and/or schlieren optics. 

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... 

We have shown some of the ways that mixed associations could be analyzed by light scattering, Archibald, or sedimentation equilibrium experiments. It might be appropriate at this point to make a comparison of some advantages and disadvantages of each technique. 

The sedimentation equilibrium experiment requires much smaller volumes of solution, about 0.15 ml. With six-hole rotors and multichannel centerpieces (41) it is potentially possible to do fifteen experiments at the same time. For situations where the photoelectric scanner can be used one might (depending on the extinct coefficients) be able to go to much lower concentrations. Dust is no problem since the centrifugal field causes it to go to the cell bottom. For conventional sedimentation equilibrium experiments, the analysis of mixed associations under nonideal conditions may be virtually impossible. Also, sedimentation equilibrium experiments take time, although methods are available to reduce this somewhat (42, 43). For certain situations the combination of optical systems available to the ultracentrifuge may allow for the most precise analysis of a mixed association. The Archibald experiment may suffer some loss in precision since one must extrapolate the data to the cell extremes (rm and r6) to obtain MW(M, which must then be extrapolated to zero time. Nevertheless, all three methods indicate that it is quite possible to study mixed associations. We have indicated some approaches that could be used to overcome problems of nonideality, unequal refractive index increments, and unequal partial specific volumes. 

Received January 17, 1972. Work supported by grants GM 15551 and GM 17611, National Institutes of Health. It is based on the MS theses submitted by Allen H. Pekar (nonideal, sedimentation equilibrium experiments and Archibald method) and by Peter J. Wan (light scattering) to the Graduate School of the Illinois Institute of Technology. 

Archibald, C., Malvey, P.F., 1998. Uniform-Price Auctions Update of the Treasury Experience. United States Treasury Working Paper. 

In the following year Archibald 1 published the results of four additional experiments ... 

Richards and Archibald also made three other experiments, potassium nitrate being heated with silica, and the loss in weight determined ... 

At its heart, hyperdrama is a story told in service of a moral lesson. Character, plot, tone, all serve that overriding purpose. The moral lesson might be focused on personal behavior, for example. The main character in Bunuel s The Criminal Mind of Archibald Cruz is convinced that he committed a crime (murder) as a child. We know that he did not. However, he conducts his life and relationships in an aura of guilt and in the expectation that if he becomes too close to anyone, in a love relationship for example, he will again become a murderer. The moral lesson of Bunuel s film is that we are all prisoners of our childhood experiences, whether they are negative or positive. How useful or not this imprisonment is goes to the core of Bunuel s goal in this film. 

An exact analytic solution to the diffusion equation with constant D and s was given in 1938 by W.J. Archibald for the problem posed (Fujita 1975). However, it is sufficiently complex that its use in application to sedimentation experiments is difficult. To simplify the form of the solution, H. Faxen, as far back as 1929, had introduced the approximation of considering the sector cell to be infinitely extended, corresponding to We shall outline the solution... 

In 1974-75 Archibald and Moody compared mucosal flows measured with microspheres and with aminopyrine in similar preparations when acid secretion was not stimulated, when it was inhibited by isoproterenol, and when it was stimulated by histamine. In these as in the thiocyanate experiments, the mucosa was always bathed with 150 mN HCl. In the unstimulated stomach aminopyrine clearance was only 46% of microsphere-measured mucosal flow in the isoprotereonl-inhibited stomach it was 34% and in the histamine-stimulated stomach it was 88%. When Archibald and Moody plotted the ratio of microsphere-measured flow to aminopyrine-measured flow against the rate of acid secretion, they saw that at low secretion rates the ratio was high and that it approached 1.25 0.06 SEM at high flows (Fig. 8-11). ... 

In the mid-nineteenth century three individuals, working independently, laid the conceptual foundations for the structural theory of matter. August Kekuld, Archibald Scott Couper, and Alexander M. Butlerov each suggested that substances are defined by a specific arrangement of atoms. As an example, consider the structures of ammonium cyanate and urea from Wohler s experiment ... 

From our own experience, and wisdom gleaned from the likes of Peter Smith, Thomas Archibald, and Alfred Hassner, we say get ready for the arrival of more azides in applied chemistry. They may be late bloomers, but they re coming on strong. In fact, the best evidence for the ascendancy of organic azides in synthesis is right here, in this outstanding collection of reviews on the topic edited by Stefan Erase and Klaus Banert. 

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