Derivatives Of Experimental Data Research Articles

On derivatives of surface charge curves of minerals

Surface titrations of minerals in aqueous electrolyte solutions are used as building blocks for surface complexation modelling. However, these potentiometric data may contain less model relevant information than previously and presently assumed. In the literature, derivative analyses have been applied to experimental surface charge versus pH curves and four or more p K values were extracted for goethite or aluminium oxide. Derivative analysis of specific surface charge versus pH curves calculated for various published model variants for goethite shows that not more than the net-zero proton surface charge condition can be extracted from computer generated data. Generated data can be produced in density and precision superior to experimental data, but yield only relatively little output from such derivative analysis compared to what has previously been extracted from derivatives of experimental data. For the generated goethite data and for all model variants only the point of zero could be extracted. For the various goethite model variants tested a nearly symmetrical peak appeared at the point of zero charge in the derivative curve. A different pattern could be obtained for generic models, for which two sites with unequal sites densities and different p K values were assumed. Variation of these parameters could result in derivatives of the charging curves with two maxima or one maximum and a broad tailing. In the literature, curves with features nearly identical to these generated curves have been interpreted by up to four p K values (i.e., four different sites within a 1-p K model). It is concluded that the interpretation of the generated data is in all cases hampered by the overwhelming electrostatic contributions to the free energy of proton ad/desorption. In no case except for the one-site 1-p K model was it possible to extract the input p K value(s) from the derivatives. Plausible explanations for the discrepancy between generated data and published experimental data are discussed.

Fluidlike behavior of dielectric permittivity in a wide range of temperature above and below the nematic-isotropic transition.

Singular behavior of the static dielectric permittivity of n-alkyloxycyanobiphenyls (CnH2n+1O-Ph-Ph-C [triple bond] N, n=6, 7) was studied above and below the nematic clearing point (T(I-N)). On approaching the clearing point, the evolution of principal components of the nematic permittivity tensor, epsilon(parallel) and epsilon(perpendicular), is described by the order parameter exponent beta approximately 0.25. The mean value of the nematic permittivity epsilon(mean)=(epsilon(parallel)+2epsilon(perpendicular))/3 exhibits a singular behavior similar to that observed in the isotropic phase and that for the diameter of the coexistence curve in binary mixtures. The derivative of experimental data d(epsilon)iso(T)/dT and d(epsilon)mean(T)/dT shows the specific-heat-like behavior with universal exponents alpha=alpha' approximately 0.5. Results obtained confirm the hypothesis of the fluidlike, pseudospinodal, and tricritical behavior of the isotropic to nematic phase transition. [A. Drozd-Rzoska, Phys. Rev. E 59, 5556 (1999)].

Model-independent method of data analysis

Many experiments or observations measure physical quantities indirectly so that considerable data reduction is required for their interpretation. We present an approach to this problem of data analysis which is based on the transformation of the measurements into the result of a hypothetical experiment designed to measure the physical quantity directly. The method, which greatly appeals to physical intuition, gives the estimates of the desired physical quantity as a direct measurement of that quantity averaged over a resolution function. We are guided to this result by an examination of the characteristics common to all experiments rather than by the introduction of arbitrary mathematical criteria. Even though we approach the problem of data analysis from an entirely new point of view, the mathematics in much of the development parallels that of the method of Backus and Gilbert. No apriori assumptions are made about the physical quantity being estimated and in this sense the method is model independent. The method is applied to the test problem of determining the second derivative of experimental data.

Methods for Determining the First and Second Derivatives of Experimental Data

Methods for Determining the First and Second Derivatives of Experimental Data