Dilution

Abstract: Deuterium or tritium labeled water traditionally has been used for the measurement of total body water by application of the dilution principle. However, these methods have not enjoyed wide clinical use. The use of deuterium is hampered by the tedious and time consuming nature of the analysis while the use of tritium involves a radiation hazard. In addition, exchange of the label with nonaqueous hydrogen in the body raises questions about the accuracy of total body water values. To determine if water labeled with the stable isotope 18O can yield faster and more accurate results, total body water was measured simultaneously using water labeled with both 18O and 2H. The 18O and 3H dilutions were measured by mass spectrometry. The relative precision of the body water value using the 18O method was 2% for both serum and breath analysis. The 18O was fully equilibrated within 2 to 3 hr after administration, and results from the analysis of breath CO2 could be readily obtained within 1 hr after sampling. The H2(18)O dilution space averaged 3.0% (SE = 0.4) less than the 2HHO dilution space, because the latter exchanges with nonaqueous hydrogen. For this reason, the H2(18)O dilution should be a more accurate measure of total body water than the 3HHO dilution.

Abstract: Data in the literature on the thermodynamic behaviour of solute elements in liquid dilute iron as the solvent have been collected and collated. The results have been expressed in terms of the first- and second-order free-energy interaction coefficients. Those based on composition in wt.-%, ei j and ri j are tabulated and the source materials are referenced. The thermodynamic properties of many alloying elements at infinite dilution in liquid iron are also tabulated.

Abstract: A detailed interpretation of the kinetics of homogeneous nucleation and growth of crystals of a linear homopolymer from dilute solution is given. The probability of forming both nuclei with folded chains, and conventional bundlelike nuclei, from dilute solution is analyzed. It is predicted that at sufficiently high dilution, critical nuclei of length lp* will be formed from single polymer molecules by sharp folding of the chain backbone. The step height of the nucleus is given approximately by lp*=4σe/Δf . Here σe is the free energy required to form a unit area of the loop-containing end surfaces, and Δf is the free energy difference per unit volume of crystal between the crystalline and solution states. The quantity Δf is approximately proportional to the degree of supercooling ΔT. The growth of these nuclei is then analyzed. After growth, the resulting crystal is flat and platelike, the loops formed by the chain folds being on the upper and lower surfaces. Kinetic factors determine that the distance between the flat surfaces in the grown crystal will vary over only a narrow range about a value that is in the vicinity of 1*=4σe /Δf. (Neglecting effects due to edge free energies, the theoretical upper and lower limits are 1*=4σe /Δf and 1*=2σe /Δf, respectively.) In some cases the predicted temperature dependence of the step height of the grown crystal, 1* = const./ΔT, may be modified by the existence of a constant term resulting from the presence of an edge free energy ϵp . A grown loop-type crystal is predicted to be stable in comparison with a bundlelike crystal of the same shape and volume in a sufficiently dilute solution. The logarithm of the nucleation rate is approximately proportional to 1/(ΔT)2 near the melting point. The exponent n in the free growth rate law is predicted under various assumptions. To the extent that comparison is possible, the predictions given agree with the experimental results obtained by Keller and O'Connor and others on single crystals of unbranched polyethylene grown from dilute solution. A survey is given of homogeneous nucleation in bulk polymers, where the conventional bundlelike nucleus containing segments from many different molecules is valid, and the essential results compared with those calculated for the dilute solution case. The theory given for loop nuclei is both general and precise enough at the critical points to suggest that, on crystallization from sufficiently dilute solution, crystals of a definite step height are commonly to be expected for other crystallizable linear polymers than polyethylene, provided loop formation is sterically possible.

Abstract: SUMMARY The isotope dilution method for measuring gross rates of N mineralization, immobilization, and nitrification was applied to intact soil cores so that the effects of soil mixing were avoided. Soil cores were injected with solutions of either 15NH4+ or 15NO4−; gross mineralization rates were calculated from the decline in “N enrichment of the NH: pool during a 24-h incubation; gross nitrification rates were calculated from the decline in 15N enrichment of the NO−3 pool; gross rates of NH4+ and NO3− consumption were calculated from disappearance of the 15N label. The assumptions required for application of this method to intact cores are evaluated. Sensitivity analysis revealed that homogeneous mixing of added “N with ambient pools was not a necessary assumption but that bias in distribution of added label, coincident with a non-random distribution of microbial processes, would cause significant errors in rate estimates. Rate estimates were also sensitive to errors in initial 15N and 14N pool size estimates, In a silt loam soil from a grassland site, abiotic processes consumed over 30% of the added 15NH4+ within minutes of adding the label to sterilized soil. Extracting a subset of soil cores at the beginning of an incubation is recommended for obtaining initial pool size estimates. Gross immobilization is probably stimulated by addition of inorganic 15N substrate and, therefore, is overestimated by the isotope dilution method. As an alternative method, a non-linear equation is given for calculating the gross immobilization rate from the appearance of 15N in chloroform-labile microbial biomass; but incomplete extraction of biomass N may result in low estimates. Details of the isotope dilution methodology (injection rates, concentrations, experimental artefacts, etc.) are described and discussed. When care is taken to understand the underlying assumptions and sources of error, the isotope dilution method provides a powerful tool for measuring gross rates of microbial transformations of soil nitrogen in intact soil cores.