Quantitative measurement of the polydispersity in the extent of functionalization of glass-forming calix[4]resorcinarenes.

The polydispersity in the degree of functionalization for two calix[4]resorcinarenes was determined by measuring quantitatively their molecular mass distribution with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry. A mathematical method for polydisperse materials is described that creates a calibration curve to correct the ion signal intensities in the mass spectrum to give a more reliable molecular mass distribution. Correction is required due to various sample preparation and instrumental effects that may produce a systematic mass bias in the number of oligomers measured. This method employs gravimetric mixtures of analytes with different degrees of functionalization. One calix[4]resorcinarene was found to give accurate molecular mass distributions with little correction, while another, having a very similar molecular structure, was found to exhibit strong over-counting of the oligomers having a high degree of functionalization.

A general method for quantitative measurement of molecular mass distribution by mass spectrometry.

A method is presented to test whether the conversion of the mass spectrum of a polydisperse analyte to its molecular mass distribution is quantitative. Mixtures of samples with different average molecular masses, coupled with a Taylor's expansion mathematical formalism, were used to ascertain the reliability of molecular mass distributions derived from mass spectra. Additionally, the method describes how the molecular mass distributions may be corrected if the degree of mass bias is within certain defined limits. This method was demonstrated on polydisperse samples of C(60) fullerenes functionalized with ethylpyrrolidine groups measured by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry; however, it is applicable to any polydisperse analyte and mass spectrometric method as long as spectrum resolution allows individual oligomers to be identified. Mass spectra of the derivatized fullerenes taken in positive ion mode were shown to give an accurate measurement of the molecular mass distribution while those taken in negative ion mode were not. Differences in the mechanisms for ion formation are used to explain the discrepancy. Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States of America.

Numerical optimization of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry: application to synthetic polymer molecular mass distribution measurement.

A novel approach is described for the selection of optimal instrument parameters that yield a mass spectrum which best replicates the molecular mass distribution of a synthetic polymer. The application of implicit filtering algorithms is shown to be a viable method to find the best instrument settings while simultaneously minimizing the total number of experiments that need to be performed. This includes considerations of when to halt the iterative optimization process at a point when statistically-significant gains can no longer be expected. An algorithm to determine the confidence intervals for each parameter is also given. Details on sample preparation and data analysis that ensure stability of the measurement over the time scale of the optimization experiments are provided. This work represents part of an effort to develop an absolute molecular mass distribution polymer Standard Reference Material.

Laser desorption ionization and MALDI time-of-flight mass spectrometry for low molecular mass polyethylene analysis.

Polyethylene's inert nature and difficulty to dissolve in conventional solvents at room temperature present special problems for sample preparation and ionization in mass spectrometric analysis. We present a study of ionization behavior of several polyethylene samples with molecular masses up to 4000 Da in laser desorption ionization (LDI) time-of-flight mass spectrometers equipped with a 337 nm laser beam. We demonstrate unequivocally that silver or copper ion attachment to saturated polyethylene can occur in the gas phase during the UV LDI process. In LDI spectra of polyethylene with molecular masses above approximately 1000 Da, low mass ions corresponding to metal-alkene structures are observed in addition to the principal distribution. By interrogating a well-characterized polyethylene sample and a long chain alkane, C94H190, these low mass ions are determined to be the fragmentation products of the intact metal-polyethylene adduct ions. It is further illustrated that fragmentation can be reduced by adding matrix molecules to the sample preparation.

MALDI-TOF MS analysis of a library of polymerizable cyclodextrin derivatives.

Polymerizable cyclodextrin derivatives (PCDs) have been proposed as candidates for use in dental therapeutics (Bowen, 1996; Bowen and Reed, 1997). Here, PCD "libraries" were synthesized by quasi-random reactions of 6 moles of methacrylic anhydride plus 6 moles of cyclic glutaric anhydride per mole of beta-cyclodextrin (BCD) in solution. BCD has 21 reactive sites on each of its molecules. These proportions were based on probability calculations, which predicted that the products should have a minimum of 2 polymerizable substituents and acidic ligand groups on practically every one of the diverse product molecules. Matrix-assisted laser desorption/ionization (MALDI) time of flight (TOF) mass spectrometry (MS) gave valuable information regarding the masses of molecular ions representing the molecules that made up the PCD libraries. For the MALDI-TOF MS analyses, small samples were analyzed by the successive application of 3 solutions to the sample holder: the matrix in acetone, the products in water, and sodium trifluoroacetate in water. The resulting spectra had > 40 envelopes of mass peaks above background. The ionic-abundance peak heights had quasi-Gaussian configurations, with central peaks having masses in the neighborhood of 2000 g/mol (Daltons). Regardless of structural permutations within each peak, the range of these peaks was between about 1500 g/mol and 2900 g/mol. This range of masses was in accord with, but perhaps somewhat more narrow than, that predicted by the statistical method, which was based on equal reactivity of all hydroxyl groups. Analysis by MALDI-TOF MS gave valuable data regarding the masses, structures, and characteristics of the products formed and provided unanticipated information to facilitate improvements in future PCD syntheses.

Post-source decay in the analysis of polystyrene by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry.

Various secondary series are observed in matrix-assisted laser desorption/ionization (MALDI) time-of-flight mass spectra of polystyrene. The number and positions of the series depend on the choice of matrix and added cation. For a given treatment, series observed in linear mode are not necessarily observed in reflectron mode, and vice versa. Post-source decay analysis was used to determine that the secondary series arise at least in part from formation and decay of adducts of polystyrene with matrix species. There is some treatment-to-treatment variation, but adduct formation and decay were observed for all tested treatments. The multiplicity of secondary series makes it unclear whether post-source decay occurs for the main series (polystyrene + cation)+ ions under the conditions normally used for polystyrene analysis. Such ions do undergo post-source decay at laser fluences greater than normally used. Although only polystyrene was investigated in this work, other polymers may also produce adduct and decay series in MALDI analysis. Their presence can mask the presence of minor components in a sample, but at least as observed here, do not have a strong influence on molecular mass determinations.

The Polymer in a Cone-A Model for the Surface Free Energy of Polymer Crystal with Emergent Cilia.

A model is proposed to estimate the surface free energy of a small polymer crystal with numerous emergent cilia. For such a model the partition function of a polymer constrained to remain in a cone is computed. The partition function of the polymer in a cone is found to behave similarly to the polymer in a wedge discussed by Lauritzen and DiMarzio [1]. The estimated end surface free energy per unit area for the small extended chain crystal is found to increase with increasing area, implying the presence of cumulative surface stress in such crystals. The forces between the cilia are reduced if folds are inserted in the surface.

Behavior of An Isolated Polymer Chain Residing in a Density Gradient of Segments.

The Wiener integral (path integral, functional integral) technique is used to determine the equation describing the probability distribution of a polymer molecule immersed in a non-uniform distribution of monomer units. This result should be useful whenever there is a spatial variation of polymer density such as at an interface or surface.

The Thermodynamics of the Glassy State. I. The Heat Capacity of One-Dimensional Disordered Harmonic Systems from Moments.

Upper and lower bounds on the thermodynamic quantities of disordered one-dimensional systems are computed using the spectral moments of Domb et al. [1] and a modification of a computational technique of Wheeler and Gordon [2]. The heat capacity so produced is defined to better than 0.01 percent for all temperatures. Models for glasses in one dimension are presented. The difference in the heat capacity between a disordered state and a comparable ordered one is examined. Normal low temperature behavior of heat capacity differences between glasses and crystals is seen. From models for glasses in one dimension it is argued that when the measured heat capacity of a glass exceeds that of its crystal, the glass must have regimes of higher density than that of the crystal. Various approximation schemes and bounds for the heat capacity of glasses in one and higher dimensions are also proposed.