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The polymers in this category are amorphous polymers with very rigid chains The high chain rigidity is achieved in some cases by extensive crosslinking, for example, phenol formaldehyde, urea formaldehyde, and melamine formaldehyde polymers In other polymers the high rigidity is due to bulky side groups on the polymer chains resulting in high Tg values, for example, polystyrene (Tg 100 C) and poly(methyl methacrylate) (Tg 105 C) REFERENCES.



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This is a wave of frequency w traveling to the left from the left side of the point Xo and to the right from the right side of the point Xo. It is the one-dimensional analog of what happens when you throw a pebble into a pond. But even more important for our discussion now, there are no resonances in the entire spectrum of frequencies. 21 Now consider what happens if we reduce our infinite string world to a finite length L with both ends (i.e., x = -L/2 and x = L/2) fixed, so that they are always at rest. This means that instead of a Fourier transform as before, we should use a Fourier series. Moreover, this Fourier series will be a sine series because of the fixed ends [i.e., YE( -L/2, t) = YE(L/2, t) = 0] [433]. So instead of (2.76), we now write (2.80) Substituting (2.80) into (2.75), then multiplying by (2/ L) sin( mrx / L) and integrating over x along the entire string (i.e., from x = 0 to x = L now), we find that (2.81) To obtain (2.81), we also used the basic property of the delta function (2.78) and the Fourier series result: (2.82) I also leave it as an exercise to the reader working out the solution to this equation (Problem 2.5). In closed form, that is, after summing up the Fourier series (Problem





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Bershtein, V. A. and V. M. Egorov, Differential Scanning Calorimetry of Polymers: Physics, Chemistry, Analysis, Ellis-Horwood, New York, 1994. Billmeyer, F. W., Jr., Textbook of Polymer Science, Chaps. 11, 12, Wiley-Interscience, New York, 1984. Brandrup, J., E. H. Immergut, and E. A. Grulke, Polymer Handbook, 4th ed., Wiley-Interscience, New York, 1999. Carothers, W. H., J. Am. Chem. Soc., 51, 2548 (1929). Flory, P. J., Principles of Polymer Chemistry, Chap. 2, Cornell Univ. Press, Ithaca, N. Y., 1953. Heimenz, P. C., Polymer Chemistry, Marcel Dekker, New York, 1984. IUPAC, Pure Appl. Chem., 66, 2483 (1994); Pure Appl. Chem., 74, 1921 (2002). IUPAC, Compendium of Macromolecular Terminology and Nomenclature (referred to as The Purple Book), 1st ed., Blackwell Scienti c, Oxford, 1991; 2nd ed., in press. Keller, A., M. Warner, and A. H. Windle, eds., Self-order and Form in Polymeric Materials, Chapman & Hall, London, 1995. Mark, J. E., ed., Polymer Data Handbook, Oxford Univ. Press, London, 1999. Mark, J. E., A. Eisenberg, W. W. Graessley, L. Mandelkern, E. T. Samulski, J. L. Koenig, and G. D. Wignall, Physical Properties of Polymers, 2nd ed., American Chemical Society, Washington, D.C., 1993. Morawetz, H., Macromolecules in Solution, Chaps. IV-VI, Wiley-Interscience, New York, 1975. Nielsen, L. E. and R. F. Landel, Mechanical Properties of Polymers and Composites, 2nd ed., Marcel Dekker, New York, 1994.

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20Even though the force density is a delta and becomes infinite at x = xo. the displacement of the string is finite at x = xo (see Problem 2.4). 21Solution (2.79) holds only for w :I O. The pathological case of vanishing frequency. w = O. yields y(x, t) = 0 as F.(t) = A exp( t) sinwt vanishes forw = O.

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Panico, R., W. H. Powell, and J.-C. Richer, eds., A Guide to IUPAC Nomenclature of Organic Compounds, Blackwell Scienti c, Oxford, 1993. Porter, R. S. and L. H. Wang, Rev. Macromol. Chem. Phys., C35(1), 63 (1995). Potschka, M. and P. L. Dublin, eds., Strategies in Size Exclusion Chromatography, American Chemical Society, Washington, D.C., 1996. Slade, P. E., ed., Polymer Molecular Weights, Springer, Berlin, 1998. Sperling, L. H., Introduction to Physical Polymer Science, 3rd ed., Wiley-Interscience, New York, 2001. Wendlandt, W. W., Thermal Analysis, 3rd ed., Wiley, New York, 1986. Wilks, E. S., Prog. Polym. Sci., 25, 9 (2000). Woodward, A. E., Atlas of Polymer Morphology, Hanser Verlag, Munich, 1989. Wunderlich, B., Macromolecular Physics, Vols. 1 3, Academic Press, New York, 1973. Yau, W. W., J. J. Kirkland, and D. D. Bly, Modern Size Exclusion Liquid Chromatography. Practice of Gel Permeation and Gel Filtration Chromatography, Wiley, New York, 1979.

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NET 3.0; Created: 3/10/2010; Tags: Convert PDF Images. This article shows how to convert PDF to multipage TIFF in C# using PDFRasterizer.NET 3.0.

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