Kraemer function

In both of these equations c is the polymer concentration in g/dl. The Kraemer function is based on the relative viscosity, which is a ratio of the solution viscosity [r ) and the viscosity of the pure solvent The Huggins function uses the specific viscosity, ri p, which is defined in terms of the relative viscosity as follows ... 

Altmann L, Sveinsson K, Kraemer U, et al. 1998. Visual functions in 6-year-old children in relation to lead and mercury levels. Neurotoxicology and Teratology 20(1) 9-17. 

Figure 1. The summative-fractionation parameter H (ideal-fractionation assumption) as a function of polydispersity K w/Kln for the Poisson, Schulz-Zimm exponential, Lansing-Kraemer logarithmic-normal, and rectangular...

Fractionation Data and Distribution Analysis of HEC After One Hour of Cellulase Attack. The results of the gel chromatographic separation of HEC after one hour of enzymic hydrolysis are given in Table II. These fractionation data did not correspond to any of the distribution functions mentioned by Peebles (41) and by Tung (42). In the middle of the distribution it corresponded to the Lansing-Kraemer distribution functions, but deviations occurred at the low- and high-molecular-weight ends. 

The broadness of the distribution is given by the parameter j, obtained from the slope (tan 0) of the log-normal plot where tan d = 7A/2. The polydispersity ratio (Af /Afp = exp(7 /2) no and x are constants in the distribution function not determinable from the log-normal line. (Special cases of the general distribution function have also been employed, e.g., the Lansing and Kraemer relationship where x = 0 [304] and the Wesslau relationship [305], where x = —1). Fractionation data can also be adequately represented by other exponential distributions such as that of Tung [306] W(n) dn = abn exp(—an ) dn. (W(n) = 1 — exp(—an )). Fig. 14a(c). 

Meyer and coworkers have investigated the viscosities of amylose and amylopectin fractions obtained by hot water extraction. Such fractions probably are not pure (see page 261). They have shown that the reduced viscosity, of their corn amylose triacetate in chloroform or in tetrachloroethane varies as a linear function of the concentration, C, whereas the reduced viscosity of corn amylopectin triacetate does not. Amylose triacetate exhibits a considerably higher viscosity than amylopectin triacetate of equal molecular weight. This is probably E. O. Kraemer, Ind, Eng. Chem., 40, 1200 (1038). 

W.-J. Shen, S. Patel, and F. B. Kraemer, Hormone-sensitive lipase functions as an oligomer. Biochemistry, 2000, 39, 2392-2398. 

References about immobilized enzyme reactors for environmental purposes are scarce (Katchalski-Katzir and Kraemer 2000). The concept is based on the immobilization of the enzyme onto a support by covalent binding or ionic interaction. The feasibility of the immobilized enzyme reactors is determined by the following requirements i) the specific activity of the derivative (units of enzyme per g of support) should be as high as possible ii) the support or membrane should be applied with a secondary function, such as the separation of substrates or products and iii) the support should have good mechanical resistance and minimum interaction with the substrates or products. Additionally, the immobilization process should be simple and inexpensive. 

It can also be shown (Kraemer et al.,1991) that the activity decay function described equation 1.5b, which relates the catalyst activity to the amount of coke on the catalyst, has the following... 

This section reviews examples of results obtained from the catalytic cracking runs conducted in the Riser Simulator. These runs show the ability of the Riser Simulator to assess catalyst performance. First, the trends in conversion of gas oils, yields of products and gasoline research octane numbers will be discussed for both the commercial feedstocks and for the pure light oil mixtures used. Then the kinetic parameters obtained from the 3-lump model and an 8-lump model using various decay functions are presented. Additional details about product distribution are provided in Kraemer (1991). 

Figure 10. Conversion of feedstock A on GX-30 catalyst as a function of reaction time and temperature (Kraemer 1991).

Kraemer Kristin, Cooper Susan, Wignall Steve, Reding Nicholas, Krishnan Rajesh, Korlacki Rafal, et al. Functionalized barium titanate nanocomposite capacitors for energy storage. In MRS fall meeting exhibit, November 28-December 2, 2011, Boston, Massachusetts 2011. 

For precise laboratory measurements, the intrinsic viscosity is determined by the extrapolation to zero concentration of data obtained at several concentrations. This procedure will be subject to large uncertainty if the function plotted is not linear with concentration. Several methods have been proposed for carrying out the extrapolation, but those most commonly used are the Huggins plot, based on Eq. 2.112, and the Kraemer plot, based on Eq. 2.113. 

---