Michael Marth

An analytical relation between relaxation time spectrum and molecular weight distribution

In this article it is shown that the relaxation time spectrum can be analytically related to the molecular weight distribution regarding a recently derived generalized mixing rule. This analytical relation greatly reduces the computational effort to determine the molecular weight distribution from the relaxation time spectrum. In this mixing rule a generalized mixing parameter β has been introduced. This parameter has been controversially discussed in the literature. The value of β has been determined theoretically by [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] as β=1 and [Europhys. Lett. 5, 437–442 (1988); 6, 475 (1988)] and [Polym. Prepr. (Am. Chem. Soc. Div. Polym. Chem.) 28, 185–186 (1987)] (β=2) and experimentally by [J. Rheol. 42, 1153–1173 (1998)] (β=3.84). In this article the influence of β on shape and position of peaks in bimodal molecular weight distributions is emphasized.In this article it is shown that the relaxation time spectrum can be analytically related to the molecular weight distribution regarding a recently derived generalized mixing rule. This analytical relation greatly reduces the computational effort to determine the molecular weight distribution from the relaxation time spectrum. In this mixing rule a generalized mixing parameter β has been introduced. This parameter has been controversially discussed in the literature. The value of β has been determined theoretically by [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] as β=1 and [Europhys. Lett. 5, 437–442 (1988); 6, 475 (1988)] and [Polym. Prepr. (Am. Chem. Soc. Div. Polym. Chem.) 28, 185–186 (1987)] (β=2) and experimentally by [J. Rheol. 42, 1153–1173 (1998)] (β=3.84). In this article the influence of β on shape and position of peaks in bimodal molecular weight distributions is emphasized.

A unifying view on some experimental effects in tapping-mode atomic force microscopy

Several experimental effects that occur in tapping-mode atomic force microscopy are examined: apparent hysteresis effects in force probes and frequency sweeps and distortions in imaging. It is found through examinations of the phase space that they can all be reduced to one common cause: the existence of more than one stable state of the tip vibration for certain parameters. It is shown that the experimental effects can be explained considering only the phase space under the assumption that measurement noise exists. Numerical simulations confirm the theoretical and experimental findings.

On the Rouse spectrum and the determination of the molecular weight distribution from rheological data

Maier et al. [Maier, D., et al., J. Rheol. 42, 1153–1173 (1998)] examined the reconstruction of binary molecular weight distributions from rheological data for a series of polystyrene mixtures using a generalized mixing rule recently introduced [Anderssen, R. S. and D. W. Mead, J. Non-Newtonian Fluid Mech. 76, 299–306 (1998)]. They found an unexpected high value for β(β=3.84±0.1), the mixing parameter, which is 1 for the reptation and 2 for the double reptation or entanglement models. This result can be understood when the relaxation time spectrum is decomposed into a Rouse and an entanglement part and only the latter is used for determination of the molecular weight distribution. Applying a procedure which separates the Rouse processes from the spectrum determined from measured dynamic shear moduli, β values are found which are in accordance with the double reptation theory and which give very good agreement between molecular weight distributions determined by size-exclusion chromatography and by rheolog...

Optimization of surface acoustic wave sensor arrays and application to high performance liquid chromatography

Abstract Some issues regarding the optimization of sensor arrays are discussed. The criteria considered here are based on Lorbers figures of merit and nonlinear generalizations thereof. Especially, it is discussed how the averaging over the analyte space should be performed for nonlinear data and what optimization criterion should be used. A genetic algorithm is used as optimization algorithm. These considerations are used for sensor selection and sensor reduction of surface acoustic wave sensor devices applied in preparative process high performance liquid chromatography.

Influence of correlated errors on the estimation of the relaxation time spectrum in dynamic light scattering

An important step in analyzing data from dynamic light scattering is estimating the relaxation time spectrum from the correlation time function. This estimation is frequently done by regularization methods. To obtain good results with this step, the statistical errors of the correlation time function must be taken into account [J. Phys. A 6, 1897 (1973)]. So far error models assuming independent statistical errors have been used in the estimation. We show that results for the relaxation time spectrum are better if correlation between statistical errors is taken into account. There are two possible ways to obtain the error sizes and their correlations. On the one hand, they can be calculated from the correlation time function by use of a model derived by Schätzel. On the other hand, they can be computed directly from the time series of the scattered light. Simulations demonstrate that the best results are obtained with the latter method. This method requires, however, storing the time series of the scattered light during the experiment. Therefore a modified experimental setup is needed. Nevertheless the simulations also show improvement in the resulting relaxation time spectra if the error model of Schätzel is used. This improvement is confirmed when a lattice with a bimodal sphere size distribution is applied to experimental data.

Early transition detection-A dynamic extension to common classification methods

Abstract An extension for classification methods in order to process time-dependent data is introduced. It is based on the detection of transitions from one steady state to another one by examination of the time derivatives of classification vectors. The method is called Early Transition Detection (ETD). It is shown that it can be used in conjunction with a number of common classification methods like SIMCA or Artificial Neural Nets and it is successfully tested on simulated and on real data.

Two improvements of early transition detection

Two improvements of early transition detection (ETD) are presented. One improvement allows for transitions to be detected if they occur on very different timescales. The other extends ETD to be applicable together with unsupervised classification methods. Both improvements are successfully tested on data obtained from sensor array measurements. Copyright

Some aspects of data analysis of multi-angle dynamic light scattering

In dynamic light scattering the signal to noise ratio may become very low because of short measurement times or low intensities. Then the analysis of the data becomes a central point and it is worthwhile to accept some numerical efforts and an increased calculation time caused by more sophisticated data analysis. In the following three aspects of an improved data analysis are discussed for multi-angle dynamic light scattering. In the first part of this paper, the influence of the correlation of the errors of the autocorrelation time function is considered. With decreasing measurement time the errors of the autocorrelation time function increase. The more the errors increase, however, the more important the error model becomes. On the other hand, with increasing number of photons the correlations of the errors of the autocorrelation time function become important: The non-diagonal elements of the covariance matrix of the data errors increase and may become of the order of the diagonal elements. In the second part the sensitivity of the nonlinear simultaneous multi-angle regularization to aberrations in the experimental set-up is investigated. Therefore, for a given bimodal radii distribution and different scattering angles data were simulated taking into account the finite aperture of the detector as well as the laser light backscattered at the back of the cuvette. This improved model is compared with the classical model, which neglects these aberrations in the experimental setup. Finally, the advantage of the simultaneous regularization method over averaging over single-angle results is demonstrated. Estimating of the radii distribution from all multi-angle data at once leads to a higher solution compared to averaging over the single-angle results.

Using properties of random matrices for target factor analysis of sensor array data

Target factor analysis is an important issue in the analysis of sensor array data as it allows one to test whether measurements contain only the substances with which a chemical sensor system was calibrated. In this paper a new approach based on the properties of random matrices is presented. The problem is first transformed to a pseudorank estimation problem by forming a combined calibration – prediction data matrix. Then the largest eigenvalue of the estimated measurement error matrix of this matrix is compared with maximum values obtained from pure random matrices. The test is statistically exact and especially useful for sensor array data. The largest eigenvalue test is compared with Malinowski’s F‐test on simulated data and tested on real data from chemical sensor arrays.