DILUTE SOLUTION THERMODYNAMICS,
3.12 SOLUTION THERMODYNAMICS AND MOLECULAR WEIGHTS A knowledge of solution thermodynamics is critically important in
determin-ing the suitability of a solvent for a molecular weight determination. Once having decided on a suitable solvent, solution thermodynamics provides a basis for determining how an extrapolation to zero concentration is to be carried out.
Below the Flory q-temperature, polymer solutions may phase-separate. The higher the molecular weight is, the higher the upper critical solution temper-ature. At infinite molecular weight, the Flory q-temperature is reached. Thus the Flory q-temperature is defined by several different criteria:
1. It is the temperature where A2is zero for dilute solutions, and c1=–12. 2. It is the temperature where the radius of gyration approximates that of
the bulk polymer (see Chapter 5).
3. It is the temperature at which an infinite molecular weight fraction would just precipitate (see Chapter 4).
The molecular weight and polydispersity of polymers remain among the most important properties that are measured. The methods are divided into absolute methods, which determine the molecular weight from first principles, and relative methods, which depend on prior calibration. The latter are usually selected because they are fast and inexpensive. Values obtained from the several methods are summarized in Table 3.15.
While polymer molecular weights vary from about 20,000 to over 1,000,000 g/mol for linear polymers, many polymers used in commerce have
3.12 SOLUTION THERMODYNAMICS AND MOLECULAR WEIGHTS 135
Table 3.15 Summary of molecular weight methods and results
Absolute Relative Mn Mw Other
Gel permeation X X X Molecular-weight
chromatography distribution
Scattering—light, X X Rzg, A2
neutrons
Osmometry X X A2
Intrinsic viscosity [h] X Mv
Mass spectrometry X X X Best for lower molecular
weights Source: D. A. Thomas, unpublished observations.
molecular weights around 105g/mol and polydispersity indexes of about 2. This is governed by polymerization kinetics and by the balance between good physical properties and processibility.
It must be noted that sometimes the molecular weight distribution can be important in ways that are not obvious. For example, the low-molecular-weight component behaves substantially as a plasticizer, weakening the material rather than strengthening it. The high-molecular-weight tail adds much to the melt viscosity, since the melt viscosity of high-molecular-weight polymers depends on Mwto the 3.4 power (see Chapter 10). Thus most industries try to minimize the polydispersity index of their polymers.
REFERENCES
1. C. V. Uglea, Oligomer Technology and Applications, Dekker, New York, 1998.
2. R. Faust, A. Fehervari, and J. P. Kennedy, in Reactive Oligomers, F. W. Harris and H. J. Spinelli, eds., American Chemical Society, Washington, DC, 1985.
3. C. V. Uglea and I. I. Negulescu, Synthesis and Characterization of Oligomers, CRC Press, Boca Raton, FL, 1991.
4. P. Neogi, Diffusion in Polymers, P. Neogi, ed., Dekker, New York, 1996.
5. J. Hildebrand and R. Scott, The Solubility of Nonelectrolytes, 3rd ed., Reinhold, New York, 1949.
6. J. Brandrup, E. H. Immergut, and E. A. Grulke eds., Polymer Handbook, 4th ed., Wiley-Interscience, New York, 1999.
7. G. M. Bristow and W. F. Watson, Trans. Faraday Soc., 54, 1731, 1742 (1958).
8. H. Mark and A. V. Tobolsky, Physical Chemistry of High Polymer Systems, 2nd ed., Interscience, New York, 1950.
9. S. K. Kim and S. C. Kim, Polym. Bull., 23, 141 (1990).
10. D. Mangaraj, S. K. Bhatnagar, and S. B. Rath, Makromol. Chem., 67, 75 (1963).
11. P. A. Small, J. Appl. Chem., 3, 71 (1953).
12. K. L. Hoy, J. Paint Technol., 46, 76 (1970).
13. P. J. Flory, J. Chem. Phys., 10, 51 (1942).
14. M. L. Huggins, Ann. N.Y. Acad. Sci., 42, 1 (1942).
15. M. L. Huggins, J. Phys. Chem., 46, 151 (1942).
16. M. L. Huggins, J. Am. Chem. Soc., 64, 1712 (1942).
17. P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953.
18. G. M. Bristow and W. F. Watson, Trans. Faraday Soc., 54, 1731 (1958).
19. P. J. Flory and W. R. Krigbaum, J. Chem. Phys., 18, 1086 (1950).
20. H.-G. Elias, An Introduction to Polymer Science, VCH, New York, 1997.
21. F. Gundert and B. A. Wolf, in J. Brandrup and E. H. Immergut, eds., Polymer Handbook, 3rd ed., Wiley, New York, 1989, Sec. VII, p. 173.
22. C. A. Glover, Chap. 4 in Polymer Molecular Weights, part I, P. E. Slade Jr., ed., Dekker, New York, 1975.
23. F. W. Billmeyer Jr., Textbook of Polymer Sciences, Interscience, New York, 1962.
24. R. D. Ulrich, Chap. 2 in Polymer Molecular Weights, part I, P. E. Slade Jr., ed., Dekker, New York, 1975.
25. W. R. Krigbaum and L. H. Sperling, J. Phys. Chem., 64, 99 (1960).
26. J. Brandrup and E. H. Immergut, eds., Polymer Handbook, 2nd ed., Wiley-Interscience, New York, 1975.
27. G. Mie, Ann. Phys., 25, 377 (1908).
28. M. Smoluchowski, Ann. Phys., 25, 205 (1908).
29. M. Smoluchowski, Philos. Mag., 23, 165 (1912).
30. A. Einstein, Ann. Phys., 33, 1275 (1910).
31. P. Debye, J. Phys. Coll. Chem., 51, 18 (1947).
32. B. H. Zimm, J. Chem. Phys., 16, 1093 (1948).
33. B. H. Zimm, J. Chem. Phys., 16, 1099 (1948).
34. A. Guinier and G. Fournet, Small-Angle Scattering of X-Rays, trans. by C. B.
Walker, Wiley, New York, 1955.
35. R. G. Kirste, W. A. Kruse, and K. Ibel, Polymer, 16, 120 (1975).
36. L. H. Sperling, Polym. Eng. Sci., 24, 1 (1984).
37. K. A. Stacy, Light-Scattering in Physical Chemistry, Academic Press, Orlando, FL, 1956.
38. G. Oster, Chem. Rev., 43, 319 (1948).
39. M. Bender, J. Chem. Ed., 29, 15 (1952).
40. P. Doty and J. T. Edsall, Advances in Protein Chemistry VI, Academic Press, Orlando, 1951, pp. 35–121.
41. J. J. Rush, Current Status of Neutron-Scattering Research and Facilities in the United States, National Academy Press, Washington, DC, 1984.
42. M. Dentini, T. Coviello, W. Burchard, and V. Crescenzi, Macromolecules, 21, 3312 (1988).
43. R. G. Kirste, W. A. Kruse, and J. Schelten, Makromol. Chem., 162, 299 (1973).
44. J. Schelten, W. A. Kruse, and R. G. Kirste, Kolloid Z. Z. Polym., 251, 919 (1973).
45. J. P. Cotton, B. Farnoux, G. Jannink, J. Mons, and C. Picot, C. R. Acad. Sci. (Paris), C275, 175 (1972).
46. H. Benoit, D. Decker, J. S. Higgins, C. Picot, J. P. Cotton, B. Farnoux, G. Jannink, and R. Ober, Nature, 245, 13 (1973).
47. D. G. H. Ballard, J. Schelten, and G. D. Wignall, Eur. Polym. J., 9, 965 (1973).
48. J. P. Cotton, D. Decker, H. Benoit, B. Farnoux, J. S. Higgins, G. Jannink, R. Ober, C. Picot, and J. des Cloiseaux, Macromolecules, 7, 863 (1974).
49. G. D. Wignall, D. G. Ballard, and J. Schelten, Eur. Polym. J., 10, 861 (1974).
50. J. Schelten, D. G. H. Ballard, G. Wignall, G. Longman, and W. Schmatz, Polymer, 17, 751 (1976).
51. G. Lieser, E. W. Fischer, and K. Ibel, J. Polym. Sci. Polym. Lett. Ed., 13, 39 (1975).
52. R. G. Kirste and B. R. Lehnen, Makromol. Chem., 177, 1137 (1976).
53. G. Allen, Proc. R. Soc. London Ser. A, 351, 381 (1976).
REFERENCES 137
54. P. Herchenroeder, M. Dettenmaier, E. W. Fischer, M. Stamm, J. Hass, H. Reimann, B. Tieke, G. Wegner, and E. L. Zichny, Europhys. Conf. Abstr., C.A. 89, 198133Z (1978).
55. R. G. Kirste, W. A. Kruse, and K. Ibel, Polymer, 16, 120 (1975).
56. J. Schelten, G. D. Wignall, and D. G. H. Ballard, Polymer, 15, 682 (1974).
57. M. Helmstedt, Makromol. Chem., Macromol. Symp., 18, 37 (1988).
58. W. Burchard, Light Scattering Principles and Development, W. Brown, ed., Clarendon Press, Oxford, 1996.
59. G. Chirico, M. Placidi, and S. Cannistraro, J. Phys. Chem. B, 103, 1746 (1999).
60. W. Burchard, Makromol. Chem., Macromol. Symp., 18, 1 (1988).
61. M. Dentini, T. Coriello, W. Burchard, and V. Crescenzi, Macromolecules, 21, 3312 (1988).
62. A. Ravve, Principles of Polymer Chemistry, Plenum Press, New York, 1995.
63. G. Odian, Principles of Polymerization, 3rd ed., Wiley, New York, 1991.
64. J. Brandrup, E. H. Immergut, and E. Grulke, eds., Polymer Handbook, 4th ed., Wiley, New York, 1999.
65. G. V. Schultz, Z. Phys. Chem., B43, 25 (1939).
66. See M. Swarc, Polymerization and Polycondensation Processes, Adv. Chem. Ser.
34, American Chemical Society, Washington, DC, 1962, p. 96.
67. G. C. Odian, Principles of Polymerization, 3rd ed., Wiley, New York, 1991.
68. W. H. Stockmayer, J. Chem. Phys., 11, 45 (1943).
69. A. Einstein, Ann. Phys., 19, 289 (1906).
70. A. Einstein, Ann. Phys., 34, 591 (1911).
71. H. Mark, Der feste Korper, Hirzel, Leipzig, 1938, p. 103.
72. J. Brandrup and E. H. Immergut, eds., Polymer Handbook, 3rd ed., Wiley, New York, 1989, Sec. IV.
73. M. L. Huggins, J. Am. Chem. Soc., 64, 2716 (1942).
74. E. O. Kraemer, Ind. Eng. Chem., 30, 1200 (1938).
75. A. Yamamoto, M. Fujii, G. Tanaka, and H. Yamakowa, Polym. J., 2, 799 (1971).
76. W. W. Yau, J. J. Kirkland, and D. D. Bly, Modern Size-Exclusion Liquid Chro-matography, Wiley-Interscience, New York, 1979.
77. Waters Associates Liquid Chromatography School, Manual, LC Short Course, Waters Associates, Morristown, NJ, 1983.
78. F. M. Rabel, J. Chromatogr. Sci., 18, 394 (1980).
79. H. Pasch and B. Trathnigg, HPLC of Polymers, Springer, Berlin, 1998.
80. T. Provder, ed., Chromatography of Polymers: Characterization by SEC and FFF, American Chemical Society, Washington, DC, 1993.
81. M. Potschka and P. L. Dublin, eds., Strategies in Size Exclusion Chromatography, American Chemical Society, Washington, DC, 1966.
82. E. J. Swadesh, HPLC Practical and Industrial Applications, CRC Press, Boca Raton, FL, 1997.
83. M. Grell, D. D. C. Bradley, X. Long, T. Chamberlain, M. Inbaselain, E. P. Woo, and M. Soliman, Acta Polymerica, 49, 439 (1998).
84. C. S. Patrickios, A. B. Lowe, S. P. Armes, and N. C. Billingham, J. Polym. Sci., Part A, Polym. Chem., 36, 617 (1998).
85. J. F. Miravet and J. M. J. Frechet, Macromolecules, 31, 3461 (1998).
86. B. Fried and J. Sherma, Thin-Layer Chromatography: Techniques and Applica-tions, 2nd ed., Dekker, New York, 1986.
87. R. P. W. Scott, Introduction to Analytical Gas Chromatography, 2nd ed., Dekker, New York, 1998.
88. K. Anton and C. Berger, eds., Supercritical Fluid Chromatography with Packed Columns: Techniques and Applications, Dekker, New York, 1998.
89. Annon., Ann. ASTM Stds., 08.03, 433 (1998).
90. S. D. Kim, P. Suwanmala, A. Klein, and L. H. Sperling, J. Mater. Sci., 36, 2787 (2001).
91. T. C. Ward Jr., Chem. Ed., 58, 867 (1981).
92. C. W. Bielawski, D. Benitez, and R. H. Grubbs, Science, 297, 2041 (2002).
93. B. H. Zimm and W. H. Stockmayer, J. Chem. Phys., 17, 1301 (1949).
94. C. M. L. Atkinson and R. Dietz, Eur. Polym. J., 15, 21 (1979).
95. J. L. Koenig, Spectroscopy of Polymers, 2nd ed., Elsevier, Amsterdam, 1999.
96. P. O. Danis, D. E. Karr, J. W. J. Simonsick Jr., and D. T. Wu, Macromolecules, 28, 1229 (1995).
97. M. W. F. Nielen, Mass Spectrometry Rev., 18, 309 (1999).
98. H. S. Creel, Trends in Polym. Sci. (TRIP), 1, 336 (1993).
99. S. D. Hanton, Chem. Rev., 101, 527 (2001).
100. S. D. Hanton, I. Z. Hyder, J. R. Stets, K. G. Ovens, W. R. Blair, C. M. Guttman, and A. A. Giuseppetti, J. Am. Soc. Mass Spectrom., 15, 168 (2004).
101. M.-F. Llauro, J. Loiseau, F. Boisson, F. Delolme, C. Ladavier, and J. Claverie, J.
Polym. Sci., Part A: Polym. Chem., 42, 5439 (2004).
102. C. M. Guttman, S. J. Wetzel, W. R. Blair, B. M. Fanconi, J. E. Girard, R. J.
Goldschmidt, W. E. Wallace, and D. L. VanderHart, Anal. Chem., 73, 1252 (2001).
103. C. I. Carr and B. H. Zimm, J. Chem. Phys., 18, 1616 (1950).
104. A. Oth, J. Oth, and V. Desreux, J. Polym. Sci., 10, 551 (1953).
GENERAL READING
W. Brown, ed., Light Scattering Principles and Development, Clarendon Press, Oxford, 1996.
E. Katz, R. Eksteen, P. Schoenmaders, and N. Miller, eds., Handbook of HPLC, Dekker, New York, 1999.
G. Montaudo and R. P. Lattimer, Eds., Mass Spectrometry of Polymers, CRC Press, Boca Raton, FL, 2002.
H. Pasch and B. Trathnigg, HPLC of Polymers, Springer, Berlin, 1998.
H. Pasch and W. Schrepp, MALDI-TOF Mass Spectrometry of Synthetic Polymers, Springer-Verlag, Berlin, 2003.
M. E. Rogers and T. E. Long, eds., Synthetic Methods in Step-Growth Polymers, Wiley-Interscience, Hoboken, NJ, 2003.
GENERAL READING 139
D. W. van Krevelen, Properties of Polymers, 3rd ed., Elsevier, Amsterdam, 1990 (Additive group contributions.).
STUDY PROBLEMS
1. Calculate the solubility parameter of polyisobutene from Table 3.3. How does this value compare with that shown in Figure 3.2?
2. What is the free energy of mixing of one mole of polystyrene, M = 2 ¥ 105g/mol, with 1 ¥ 104liters of toluene, at 298 K?