P o l y m o l e c u l a r i t y

C o r r e c t i o n

F a c t o r s

R o l f E. B a r e i s s Bergstraesser Weg 23, D-55268 Nieder-Olm, FR Germany

A. List of Symbols Used B. Introduction Table 1. Numerical Values of Gamma Function r(x) C. Polymolecularity Correction Factors for Intrinsic Viscosity versus Molecular Weight Relationship Table 2. For M w and SZ* Table 3. For M w and LN f Table 4. For M n and SZ Table 5. For M n and LN Table 6. For M-SwDw and SZ Table 7. For M-S"D^ and LN Table 8. For M-S"D" and SZ Table 9. For M ^ D * and LN Table 10. For M-^Dz and SZ Table 11. For M-"wD] and LN Table 12. For M^w and SZ and LN Table 13. For M-S*M" Table 14. For M^]wow a n d s z and L N Table 15. For M^ol Table 16. For A ^ D ~ and SZ Table 17. For M ^ D A and LN Table 18. For M^o1 and SZ and LN Table 19. For M^o] D. Polymolecularity Correction Factors for Sedimentation Coefficient versus Molecular Weight Relationship Table 20. For s w , M w and SZ Table 21. For s w , /Vfw and LN Table 22. For s w , M n and SZ Table 23. For s w , Mn and LN Table 24. For sW/ M-5wDw and SZ Table 25. For s w , A^sIoI a n d L N Table 26. Conversion of swax into sw for SZ Table 27. Conversion of smax into sw for LN

* SZ: Schulz-Zimm distribution of molecular weight. * LN: Logarithmic normal distribution of molecular weight.

VII-216 VII-217 VII-223

VII-223 VII-223 VII-223 VII-223 VII-224 VII-224 VII-224 VII-224 VII-224 VII-225 VII-225 VII-225 VII-225 VII-225 VII-226 VII-226 VII-226 VII-226 VII-226

VII-227 VII-227 VII-227 VII-227 VII-227 VII-228 VII-228 VII-228 VII-229

E. Polymolecularity Correction Factors for Diffusion Coefficient versus Molecular Weight Relationship Table 28. For D A , Mn and SZ Table 29. For D A , M n and LN Table 30. For D A , M-SWDA and SZ Table 3 1 . For D A , M ^ D Aa n d L N Table 32. For D w , M n " and SZ Table 33. For D w , M n and LN Table 34. For D Z / /Vln and SZ Table 35. For D Z / M n and LN Table 36. For D A / Mw and SZ Table 37. For D A / M w and LN Table 38. For D w , M w and SZ Table 39. For D W / M w and LN Table 40. For O z , Mw and SZ Table 4 1 . For DZf Mw and LN F. Polymolecularity Correction Factors for Mean-Square Radius of Gyration versus Molecular Weight Relationship Table 42. For ( S 2 ) z , Mw and SZ Table 43. For (S2) 2 , M w and LN Table 44. For (S 2 )z , Mz and SZ Table 45. For (S 2 ) 2 , M1 and LN Table 46. For (S 2 ) 2 / Mn and SZ Table 47. For ( S 2 ) z , Mn and LN G. Polymolecularity Correction Factors for Second Virial Coefficient versus Molecular Weight Relationship

VII-229 VII-229 VII-229 VII-229 VII-230 VII-230 VII-230 VII-230 VII-230 Vf 1-231 VII-231 VII-231 VII-231 VII-232 VII-232

VII-232 VII-232 VII-233 VII-233 VII-233 VII-234 VII-234

VII-234

Table 48. For Af?\

Mn and SZ

VII-234

Table 49. For A{°P),

Mn and LN

VII-235

, /Vfw and SZ

VII-235

Table 50. For /^

LS)

Table 5 1 . For A^, M w and LN H. Polymolecularity Correction Factors for the Determination of the Dimensions of Macromolecules 1. Fox-Flory Relationship Table 52. For ( r 2 ) z / M n and SZ Table 53. For ( r 2 ) z , M n and LN Table 54. For ( r 2 ) z , M w and SZ Table 55. For ( r 2 ) z , M w and LN

VII-235

VII-235 VII-235 VII-235 VII-236 VII-236 VII-236

2.

Interconversion of Different Averages of the Mean-Square Radius of Gyration Table 56. (S2) w from (S2)z for SZ Table 57. (S 2 ) w from (S2)z for LN Table 58. (S2) n from (S2) 2 for SZ Table 59. (S 2 ) n from (5 2 } z for LN 3. Interconversion of Different Averages

VII-236 VII-236 VII-237 VII-237 VII-238

^A = (E 1 V^r 0 T 2

of the Mean-Square End-to-End Distance VII-238 Table 60. (r 2 ) n from [(r 2 ) 3 / 2 ] 2 / 3 for SZ

VII-238

Dz

Table 62. ( r 2 ) w from [(r 2 ) 3 / 2 ] 2 / 3 for SZ

VII-239

[/] e i k

2 3/2 2/3

Table 61. (r ) n from [(r ) 2

]

2 3/2 2/3

Table 63. ( r ) w from [(r )

]

2

2 3/2 2/3

2

2 3/2 2/3

Table 64. (r ) z from [(r )

]

for LN

VII-239

for SZ

VII-239

Table 65. (r ) z from [(r ) ] for LN 4. The Effect of Polymolecularity on the Radius of Gyration of Stiff Polymer Chains _ Table 66. q (sz) (£ w ) for SZ Table 67. c/( LN )(l w ) for LN I. Polymolecularity Correction Factors for the Determination of Unperturbed Dimensions of Macromolecules 1. Burchard-Stockmayer-Fixman Procedure Table 68. For Mw, SZ and LN Table 69. For Mn and SZ Table 70. For M n and LN 2. Cowie- By water Procedure Table 71. CB, 1: For M W / s w and SZ Table 72. CB, 2: For M w , s w and SZ Table 73. CB, 1: For Mw, s w and LN Table 74. CB, 2: For /Vfw, s w and LN 3. Baumann-Stockmayer-Fixman Procedure Table 75. q^: For M w and SZ Table 76. q £ § 2 ) i : For (S 2 ) z and SZ L

Table 77. qJ ^:For M w and LN 2

VII-240 VII-240 VII-240

VII-240 VII-240 VII-240 VII-240 VII-241 VII-241 VII-241 VII-241 VII-241 VII-241 VII-242 VII-242 VII-242

Table 80. q ^ ^ : For (S 2 ) z and SZ

VII-243

w andLN

Table 82. q^s*)/ For (S ) z and LN References ' *

LIST OF SYMBOLS USED a

exponent in D = KoM ° exponent in s = KsMas exponent in [rj\ — K^Maw

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VII-243 VII-243 VII-244

diffusion coefficient of component / weight-average diffusion coefficient Dw = X)1-WiD1z-average diffusion coefficient intrinsic frictional coefficient in the theta state integers 1,2,..., i degree of coupling in Schulz-Zimm distributions of the molecular weight

/:-(M w /M n -ir l

Mn

constant in D = KDMaD constant for the determination of unperturbed dimensions Jf0 = $e((r2)0/M)3/2 a$ constant in s — KsM constant in (S2) = K{si)Ml^ constant in [77] = K^Maw reduced contour length L — L'/A""1 contour length number-, weight-, z-average L molecular weight1 any average of the molecular weight molecular weight from D molecular weight of component / molecular weight of compound j molecular weight of median in logarithmic normal distributions number-average molecular weight

Ms M(S2) Mso My

molecular weight from s molecular weight from (S2) molecular weight from s and D viscosity-average molecular weight

KD Ko K5 K{si) K[^ L V Ln, L w , L z M M av Mo Mi Mj Mm

Mv = (E,- vw(Af y)x/a™

VII-242

VII-243 VII-243

2

aD as a[v]

VII-239

Table 78. q ^ 2 ) : For (S ) 2 and LN 4. Baumann-Kurata-Stockmayer Procedure Table 79. q ^ ^ For Mw and SZ Table 81. g ^ n /F o r ^

A.

VII-238

D1 £)w

for LN

2

J.

A2 second virial coefficient P LS ^2° '' ^2 ^ ^ 2 from osmotic pressure, light scattering, resp. B,Bf,B" constants D diffusion coefficient DA "area average" diffusion coefficient

Mw

weight-average molecular weight

Ms[v] MfylD rii A^L P0 q #B

molecular weight from s and [77] molecular weight from [77] and D mole fraction of component i Avogadro number constant in [ / ] e - Po(r2)lo/2 polymolecularity correction factor q for Baumann-Stockmayer-Fixman procedure q for Burchard-Stockmayer-Fixman equation

#BSF

According to IUPAC recommendations (1,2), "molecular weight" is understood to be the relative molecular mass, the numerical values of which are identical to those of the molar mass in g/mol and therefore molecular weight is denoted here with the same symbol as the molar mass, viz. M.