Poly(lactic acid) composites with poly(lactic acid)‐modified carbon nanotubes

This work reports the study of the effect of chemical functionalization of carbon nanotubes on their dispersion in poly(lactic acid). The nanotubes were functionalized by the 1,3‐dipolar cycloaddition reaction, generating pyrrolidine groups at the nanotube surface. Further reaction of the pyrrolidine groups with poly(lactic acid) was studied in solution and in the polymer melt. The former involved refluxing the nanotubes in a dimethylformamide/polymer solution; the latter was carried out by direct melt mixing in a microcompounder. The carbon nanotubes collected after each process were characterized by thermogravimetry and by X‐ray photoelectron spectroscopy, showing evidence of polymer bonded to the nanotube surface only when the reaction was carried out in the polymer melt. The composites with polymer modified nanotubes present smaller average agglomerate area and a narrower agglomerate area distribution. In addition, they show improved tensile properties at low CNT concentration and present lower electrical resistivity. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3740–3750     

The millimeter-wave spectrum of acetaldehyde in its two lowest torsional states

A large number of new millimeter-wave spectral lines of gaseous acetaldehyde have been measured at frequencies up to 250 GHz. These lines arise from rotational transitions of acetaldehyde in its two lowest (v_t = 0,1) torsional states and involve angular momentum quantum numbers J ≤ 12 and K ≤ 10. A global data set consisting of 562 lines has been obtained by combining the millimeter-wave lines with previously measured lower frequency data involving the two lowest torsional states. This data set has been analyzed via an internal axis method previously used to study the spectra of CH₃OH and CH₃SH. The root-mean-square deviation of the fit is only 685 kHz. An analogous least-squares fit to 335v_t = 0 lines yields a root-mean-square deviation of 269 kHz.     

Chern-Simons theory with finite gauge group

We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the Verlinde formula. The careful development may serve as a model for dealing with similar issues in more complicated cases.The first author is supported by NSF grant DMS-8805684, an Alfred P. Sloan Research Fellowship, a Presidential Young Investigators award, and by the O'Donnell Foundation. The second author is supported by NSF grant DMS-9207973     

Predicting thermal displacements in modular tool systems

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.