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Synthesis, equilibrium swelling, kinetics, permeability and applications of environmentally responsive gels

  • Stevin H. Gehrke
Chapter
Part of the Advances in Polymer Science book series (POLYMER, volume 110)

Abstract

This article is a review of the research on environmentally responsive polymer gels done by Stevin H. Gehrke's research group at the University of Cincinnati. This group has studied a wide variety of responsive gels, including crosslinked cellulose ethers, poly(N-isopropylacrylamide), and radiation-crosslinked poly(vinyl methyl ether). Equilibrium swelling has been studied both experimentally and theoretically, with the general goal of learning how to control the nature of the volume transition. Conditions under which transition-inducing stimuli affect the rate of volume change have been identified and a diffusion analysis is shown to be broadly useful for correlating the kinetics. Polymer scaling theory provides a qualitative basis for understanding how polymer composition and stimulus interval influence the magnitude of the network diffusion coefficient. The response rate of gels can be several orders of magnitude greater than this if they are microporous and can absorb and expel solvent by a convective process. Diffusion coefficients of solutes in gels decline as the gel shrinks, in generally good agreement with free volume theories. Hydrophobic interactions between gels and drugs are often quite strong, especially in deswollen gels. The ability of these gels to dewater coal slurries has also been established.

Keywords

Diffusion Coefficient Crosslink Density Lower Critical Solution Temperature Volume Transition Cellulose Ether 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols and Abbreviations

APS

ammonium persulfate

C

mass of crosslinking monomer per 100 g of monomers

CMC

carboxymethylcellulose

D

diffusion coefficient

Do

diffusion coefficient in free solution

DSC

differential scanning calorimetry

DVS

divinyl sulfone

f

friction factor between network and solvent

G

shear modulus of gel

GRAS

generally recognized as safe

HPC

hydroxypropylcellulose

HPMC-E

hydroxypropylmethylcellulose, Type E

HPMC-K

hydroxypropylmethylcellulose, Type K

k

mass transfer coefficient

K

bulk modulus of gel

K

partition coefficient

Ko/w

octanol/water partition coefficient

LCST

lower critical solution temperatures

L0

initial sample thickness

Lt/L

normalized change in characteristic sample dimension

MC

methylcellulose

Mt/M

normalized approach to equilibrium mass

N

number of polymer structural units in an effective chain segment

NIPAAm

N-isopropylacrylamide

P*g

polymer cohesive energy density

PNIPAAm

poly(N-isopropylacrylamide)

P*s

solvent cohesive energy density

PVME

poly(vinyl methyl ether)

Q

equilibrium swelling degree of gel

SDS

sodium dodecyl sulfate

SMB

sodium metabisulfite

T

mass of monomers (in grams) added to 100 ml of water

T

temperature

t

time

TEAC

tetraethylammonium chloride

TEMED

N,N,N′,N′-tetramethylethylenediamine

Te

equilibrium temperature

Ti

initial temperature

Ts

spinodal temperature

Tt/T

normalized approach to equilibrium temperature

v

velocity

Zsg

correction for deviation from a geometric mean mixing rule

φ

polymer volume fraction

η

solvent viscosity

Ξ

correlation length

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9 References

  1. 1.
    Gehrke SH, Lee PI (1990) In: Tyle P (ed) Specialized drug delivery systems: manufacturing and production technology. Marcel Dekker, New York, p 333Google Scholar
  2. 2.
    Tanaka T (1981) Sci Am 244: 124PubMedGoogle Scholar
  3. 3.
    Peppas NA, Barr-Howell BD (1986) In: Peppas NA (ed) Hydrogels in medicine and pharmacy, vol I fundamentals. CRC Press, Boca Raton, FL, p 27Google Scholar
  4. 4.
    Freitas RFS, Cussler EL (1987) Chem Eng Sci 42: 97CrossRefGoogle Scholar
  5. 5.
    Gehrke SH, Cussler EL (1989) Chem Eng Sci 44: 559Google Scholar
  6. 6.
    Tanaka T, Nishio I, Sun S, Ueno-Nishio S (1982) Science 218: 467Google Scholar
  7. 7.
    Tanaka T (1978) Phys Rev Lett 40: 820CrossRefGoogle Scholar
  8. 8.
    Suzuki A, Tanaka T (1990) Nature 346: 345CrossRefGoogle Scholar
  9. 9.
    Mamada A, Tanaka T, Kungwatchakun D, Irie M (1990) Macromolecules 23: 1517CrossRefGoogle Scholar
  10. 10.
    Lee KK, Cussler EL, Marchetti M, McHugh MA (1990) Chem Eng Sci 45: 766CrossRefGoogle Scholar
  11. 11.
    Ohmine I, Tanaka T (1982) J Chem Phys 11: 5725CrossRefGoogle Scholar
  12. 12.
    Huang X, Unno H, Akehata T, Hirasa O (1988) J Chem Eng Jpn 21: 10Google Scholar
  13. 13.
    Horbett TA, Kost J, Ratner BD (1984) In: Shalaby SW, Hoffman AS, Ratner BD, Horbett TA (eds) Polymers as biomaterials. Plenum, New York, p 193Google Scholar
  14. 14.
    Sussmann MV, Katchalsky A (1970) Science 167: 45PubMedGoogle Scholar
  15. 15.
    Tatara Y (1978) Polym J 10: 563Google Scholar
  16. 16.
    Lyu LH, Gehrke SH (1989) AIChE Annual Meeting, Paper 98j, San Francisco, CAGoogle Scholar
  17. 17.
    Katchalsky A (1949) Experientia 5: 319CrossRefGoogle Scholar
  18. 18.
    Katchalsky A, Sussmann MV, Oplatka A, Steinberg I (1967) US Patent No. 3,321,908Google Scholar
  19. 19.
    Dusek, K, Patterson D (1968) J Polym Sci A-2 6: 521Google Scholar
  20. 20.
    Research Institute for Polymers and Textiles Bulletin (1989) Ibaraki, Japan p 12Google Scholar
  21. 21.
    Taylor LD, Cerankowski LD (1975) J Polym Sci, Polym Chem Edn 13: 2551Google Scholar
  22. 22.
    Hirokawa Y, Tanaka T (1984) J Chem Phys 81: 6379CrossRefGoogle Scholar
  23. 23.
    Katayama S, Hirokawa Y, Tanaka T (1984) Macromolecules 17: 2641CrossRefGoogle Scholar
  24. 24.
    Bae YH, Okano T, Kim SW (1989) J Controlled Release 9: 271CrossRefGoogle Scholar
  25. 25.
    Okano T, Bae YH, Jacobs H, Kim SW (1990) J Controlled Release 11: 255Google Scholar
  26. 26.
    Mukae K, Bae YH, Okano T, Kim SW (1990) Polym J 22: 250CrossRefGoogle Scholar
  27. 27.
    Hoffman AS, Afrassiabi A, Dong LC (1986) J Controlled Release 4: 213CrossRefGoogle Scholar
  28. 28.
    Hoffman AS (1987) J Controlled Release 6: 297CrossRefGoogle Scholar
  29. 29.
    Cussler EL, Stokar MR, Varberg JE (1984) AIChE J 30: 578CrossRefGoogle Scholar
  30. 30.
    Gehrke SH, Andrews GP, Cussler EL (1986) Chem Eng Sci 41: 2153CrossRefGoogle Scholar
  31. 31.
    Trank SJ, Cussler EL (1987) Chem Eng Sci 42: 381CrossRefGoogle Scholar
  32. 32.
    Siegel RA, Firestone BA (1988) Macromolecules 21: 3254CrossRefGoogle Scholar
  33. 33.
    Firestone BA, Siegel RA (1988) Polym Commun 29: 204Google Scholar
  34. 34.
    Beltran S, Hooper HH, Blanch HW, Prausnitz JM (1990) J Chem Phys 92: 2061CrossRefGoogle Scholar
  35. 35.
    Hooper HH, Baker JP, Blanch HW, Prausnitz JM (1990) Macromolecules 23: 1096CrossRefGoogle Scholar
  36. 36.
    Yoshio N, Hirohito N, Matsuhiko M (1986) J Chem Eng Jpn 19: 274Google Scholar
  37. 37.
    Amiya T, Tanaka T (1987) Macromolecules 20: 1162CrossRefGoogle Scholar
  38. 38.
    Harsh DC, Gehrke SH (1990) In: Brannon-Peppas L, Harland R (eds) Absorbent polymer technology. Elsevier, Amsterdam, p 103Google Scholar
  39. 39.
    Huang X, Unno H, Akehata T, Hirasa O (1987) J Chem Eng Jpn 20: 123Google Scholar
  40. 40.
    Peppas NA (1987) In: Hydrogels in medicine and pharmacy, vol. 2 polymers. CRC Press, Boca Raton FL, p 1Google Scholar
  41. 41.
    Urry DW, Harris D, Long MM, Prasad KU (1986) J Peptide Protein Res 28: 649Google Scholar
  42. 42.
    Klier J, Scranton AB, Peppas NA (1990) Macromolecules 23: 4944CrossRefGoogle Scholar
  43. 43.
    Scranton AB, Klier J, Peppas NA (1991) J Polym Sci, Polym Phys Ed 29: 211Google Scholar
  44. 44.
    Scranton AB, Klier J, Aronson CL (1992) In: Harland RS, Prud'homme, RK (eds) Polyelectrolyte gels, ACS symposium series 480. American Chemical Society, Washington, DCGoogle Scholar
  45. 45.
    Gehrke SH, Palasis M, Akhtar MK (1992) Polymer Int 28: 29Google Scholar
  46. 46.
    Kabra BG, Akhtar MK, Gehrke SH (1992) Polymer 33: 990CrossRefGoogle Scholar
  47. 47.
    Ilavsky M (1981) Polymer 22: 1687CrossRefGoogle Scholar
  48. 48.
    Ilavsky M (1982) Macromolecules 15: 782CrossRefGoogle Scholar
  49. 49.
    Prange MM, Hooper HH, Prausnitz JM (1989) AIChE J 35: 803CrossRefGoogle Scholar
  50. 50.
    Marchetti M, Prager S, Cussler EL (1990) Macromolecules 23: 1760CrossRefGoogle Scholar
  51. 51.
    Marchetti M, Prager S, Cussler EL (1990) Macromolecules 23: 3445CrossRefGoogle Scholar
  52. 52.
    Harsh D, Gehrke SH (1991) J Controlled Release 17: 175CrossRefGoogle Scholar
  53. 53.
    Harsh D, Gehrke SH (1993) In: El-Nokaly M, Piatt D, Charpentier B (eds) Polymeric delivery systems. ACS symposium series 520. American Chemical Society, Washington, DC, p 105Google Scholar
  54. 54.
    Otake K, Inomata H, Konno M, Saito S (1990) Macromolecules 23: 283CrossRefGoogle Scholar
  55. 55.
    Tanaka T, Sun ST, Hirokawa Y, Katayama S, Kucera J, Hirose Y, Amiya T (1987) Nature 325: 796CrossRefGoogle Scholar
  56. 56.
    Matsuo ES, Tanaka T (1988) J Chem Phys 89: 1695CrossRefGoogle Scholar
  57. 57.
    Grimshaw PE, Grodzinsky AJ, Yarmush ML, Yarmush DM (1990) Chem Eng Sci 45: 2917CrossRefGoogle Scholar
  58. 58.
    Chou LY, Blanch HW, Prausnitz JM (1992) J Appl Poly Sci 45: 1411CrossRefGoogle Scholar
  59. 59.
    Gehrke SH, Lyu LH, Yang MC (1989) Polym Prepr 30: 482Google Scholar
  60. 60.
    Tanaka T, Fillmore DJ (1979) J Chem Phys 70: 1214CrossRefGoogle Scholar
  61. 61.
    Gehrke SH, Akhtar MK (1990) In: 33rd IUPAC international symposium on macromolecules. July 8–13, Montreal, CanadaGoogle Scholar
  62. 62.
    Tanaka T, Sato E, Hirokawa Y, Hirotsu S, Peetermans J (1985) Phys Rev Lett 55: 2455CrossRefPubMedGoogle Scholar
  63. 63.
    Li Y, Tanaka T (1990) J Chem Phys 92: 1365CrossRefGoogle Scholar
  64. 64.
    Li Y, Tanaka T (1991) In: De Rossi D, Kajiwara K, Osada Y, Yamauchi A (eds) Polymer gels: Fundamentals and biomedical applications. Plenum Press, New York, p 41Google Scholar
  65. 65.
    Kabra B, Gehrke S (1991) Polym Commun 32: 322Google Scholar
  66. 66.
    Tatara Y, Mori M (1972) Trans Jpn Soc Mech Eng 38: 2807Google Scholar
  67. 67.
    Chiarelli P, Umezawa K, De Rossi D (1991) In: De Rossi D, Kajiwara K, Osada Y, Yamauchi A (eds) Polymer gels: Fundamentals and biomedical applications. Plenum, New York, p 195Google Scholar
  68. 68.
    Leung BK, Robinson J (1990) J Membr Sci 52: 1CrossRefGoogle Scholar
  69. 69.
    Feil H, Bae YH, Feijen J, Kim SW (1991) J Membr Sci 64: 283CrossRefGoogle Scholar
  70. 70.
    Palasis M, Gehrke SH (1992) J Controlled Release 18: 1CrossRefGoogle Scholar
  71. 71.
    De Rossi D, Kajiwara K, Osada Y, Yamauchi A (eds) (1991) Polymer gels: Fundamentals and biomedical applications. Plenum, New YorkGoogle Scholar
  72. 72.
    Urry DW, Harris RD, Prasad KU (1988) J Am Chem Soc 110: 3303CrossRefGoogle Scholar
  73. 73.
    Suzuki M (1989) Kobunshi Ronbunshu 46: 603Google Scholar
  74. 74.
    Tatara Y (1987) Adv Robotics 2: 69Google Scholar
  75. 75.
    Bishop JE (1990) In: The Wall Street Journal, August 13, p B1Google Scholar
  76. 76.
    De Rossi DE, Galletti PM, Dario P, Richardson PD (1983) ASAIO J 6: 1Google Scholar
  77. 77.
    De Rossi DE, Parrini P, Chiarelli P, Buzzigoli G (1985) Trans Am Soc Artif Intern Organs 31: 60PubMedGoogle Scholar
  78. 78.
    De Rossi DE, Chiarelli P, Buzzigoli G, Domenici C, Lazzeri L (1986) Trans Am Soc Artif Intern Organs 32: 157Google Scholar
  79. 79.
    Chiarelli P, De Rossi D (1988) Progr Colloid Polym Sci 78: 4Google Scholar
  80. 80.
    Stinson S (1990) Chem Eng News, January 8, p 30Google Scholar
  81. 81.
    Shiga T, Hirose Y, Okada A, Kurauchi T (1990) Polym Prepr 30: 310Google Scholar
  82. 82.
    Sheppard NF, Lee HL, Madrid Y, Melcher JR, Langer RS (1988) Annual AIChE Meeting, paper 120i, Washington DCGoogle Scholar
  83. 83.
    Osada Y, Umezawa K, Yamauchi A (1988) Makromol Chem 189: 597CrossRefGoogle Scholar
  84. 84.
    Umezawa K, Osada Y (1987) Chem Lett 1795Google Scholar
  85. 85.
    Gillmore VE (1989) Popular Sci 235: 24Google Scholar
  86. 86.
    Wald ML (1992) In: The New York Times, August 16, p F9Google Scholar
  87. 87.
    Tanaka T (1992) In: Harland RS, Prud'homme RK (eds) Polyelectrolyte gels, ACS symposium series 480. American Chemical Society, Washington, DC, p 1Google Scholar
  88. 88.
    Urry DW (1990) Polymeric Materials Eng Sci 63: 329Google Scholar
  89. 89.
    Cornejo-Bravo JM, Siegel RA (1990) Proc Intern Symp Contr Rel Bioact Mat 17: 174Google Scholar
  90. 90.
    Grimshaw PE, Grodzinsky AJ, Yarmush ML, Yarmush DM (1989) Chem Eng Sci 44: 827CrossRefGoogle Scholar
  91. 91.
    Grodzinsky AJ, Grimshaw PE, Yarmush ML (1990) Proc Intern Symp Contr Rel Bioact Mat 17: 108Google Scholar
  92. 92.
    Afrassiabi A, Hoffman AS, Cadwell LA (1987) J Membr Sci 33: 191CrossRefGoogle Scholar
  93. 93.
    Dong LC, Hoffman AS (1992) J Controlled Release 19: 171CrossRefGoogle Scholar
  94. 94.
    Dong LC, Hoffman AS (1990) J Controlled Release 13: 21CrossRefGoogle Scholar
  95. 95.
    Mukae K, Bae YH, Okano T, Kim SW (1990) Polym. J 22: 206CrossRefGoogle Scholar
  96. 96.
    Bae YH, Okano T, Kim SW (1989) J Controlled Release 9: 271CrossRefGoogle Scholar
  97. 97.
    Bae YH, Okano T, Kim SW (1991) Pharm Res 8: 531CrossRefPubMedGoogle Scholar
  98. 98.
    Bae YH, Okano T, Kim SW (1991) Pharm Res 8: 624CrossRefPubMedGoogle Scholar
  99. 99.
    Kwon IC, Bae YH, Kim SW (1991) Nature 28: 291CrossRefGoogle Scholar
  100. 100.
    Kwon IC, Bae YH, Okano T, Kim SW (1991) J Controlled Release 17: 149CrossRefGoogle Scholar
  101. 101.
    Horbett TA, Ratner BD, Kost J, Singh M (1984) In: Anderson JM, Kim SW (eds) Recent advances in drug delivery systems. Plenum, New York, p 209Google Scholar
  102. 102.
    Horbett TA, Ratner BD (1988) Proceedings Pharm Tech Conference '88. East Rutherford, NJ, p 356Google Scholar
  103. 103.
    Kost J, Horbett TA, Ratner BD (1985) J Biomed Mater Res 19: 1117CrossRefPubMedGoogle Scholar
  104. 104.
    Albin GW, Horbett TA, Miller SR, Ricker NL (1987) J Controlled Release 6: 267CrossRefGoogle Scholar
  105. 105.
    Osada Y, Takeuchi Y (1981) J Polym Sci, Poly Lett Ed 19: 303Google Scholar
  106. 106.
    Osada Y, Takeuchi Y (1983) Polym J 15: 279Google Scholar
  107. 107.
    Osada Y, Hasebe M (1985) Chem Lett 12: 85Google Scholar
  108. 108.
    Huang X, Akehata T, Unno H, Hirasa O (1989) Biotech Bioeng 34: 102CrossRefGoogle Scholar
  109. 109.
    Hirasa O, Ito, S, Yamauchi A, Fujishige S, Ichijo H (1991) In: DeRossi D, Kajiwara K, Osada Y, Yamauchi A (eds) Polymer gels: Fundamentals and biomedical applications. Plenum Press, New York, p 241Google Scholar
  110. 110.
    Dong LC, Hoffman AS (1986) J Controlled Release 4: 223CrossRefGoogle Scholar
  111. 111.
    Gehrke SH (1986) Kinetics of gel volume change and its interaction with solutes. Thesis, University of Minnesota, Minneapolis, MNGoogle Scholar
  112. 112.
    Kabra BG, Gehrke SH, Hwang ST, Ritschel W (1991) J Appl Polym Sci 42: 2409CrossRefGoogle Scholar
  113. 113.
    Gehrke SH (1992) to appear in: Lee PI (ed) Fundamental aspects of polymers in pharmaceutics. Elsevier, AmsterdamGoogle Scholar
  114. 114.
    Gehrke SH, Johnson JF, Robeson J, Vaid N (1991) Biotech Prog 7: 355CrossRefGoogle Scholar
  115. 115.
    Gehrke SH, Lyu, LH, Barnthouse K (1992) submittedGoogle Scholar
  116. 116.
    Lyu LH (1990) Dewatering fine coal slurries by gel extraction. Thesis, University of Cincinnati, Cincinnati, OHGoogle Scholar
  117. 117.
    Gehrke SH, Lyu LH (1990) Final project report: Dewatering fine coal slurries by gel extraction. Ohio Coal Development Office, Columbus, OhioGoogle Scholar
  118. 118.
    Gehrke SH, Yang MC, Kabra BG, Lyu LH, Akhtar MK (1989) Proceed Intern Symp Control Rel Bioact Mater 16: 209Google Scholar
  119. 119.
    Gehrke SH, Akhtar MK (1992) submittedGoogle Scholar
  120. 120.
    Akhtar MK, Gehrke SH (1992) submittedGoogle Scholar
  121. 121.
    Akhtar MK (1990) Volume change kinetics in near critical gels. Thesis, University of Cincinnati, Cincinnati OHGoogle Scholar
  122. 122.
    Palasis M, Gehrke SH (1990) Proceed Intern Symp Contr Rel Bioact Mater 17: 385Google Scholar
  123. 123.
    Palasis M (expected, 1993) Permeability of responsive polymer gels. Thesis, University of Cincinnati, Cincinnati OHGoogle Scholar
  124. 124.
    Harsh DC, Gehrke SH (1989) Proceed Intern Symp Contr Rel Bioact Mater 16: 383Google Scholar
  125. 125.
    Harsh DC (1992) Controlling swelling characteristics of novel cellulose ether gels. Thesis, University of Cincinnati, Cincinnati OHGoogle Scholar
  126. 126.
    Kabra BG (expected, 1993) Relationships between synthesis, structure, and swelling properties of responsive polymer gels. Thesis, University of Cincinnati, Cincinnati OHGoogle Scholar
  127. 127.
    Gehrke SH, Agrawal G, Yang MC (1992) In: Harland RS, Prud'homme, RK (eds) Polyelectrolyte gels, ACS symposium series 480. American Chemical Society, Washington, DC, p 211Google Scholar
  128. 128.
    Hrouz J, Ilavsky M, Ulbrich K, Kopecek J (1981) Eur Polym J 17: 361CrossRefGoogle Scholar
  129. 129.
    Ilavsky M, Hrouz J, Ulbrich K (1982) Polym Bull 7: 107Google Scholar
  130. 130.
    Hirotsu S, Hirokawa Y, Tanaka T (1987) J Chem Phys 87: 1392CrossRefGoogle Scholar
  131. 131.
    Trank SJ, Johnson DW, Cussler EL (1989) Food Tech. 43: 78Google Scholar
  132. 132.
    Dualeh AJ, Steiner CA (1992) In: Harland RS, Prud'homme, RK (eds) Polyelectrolyte gels, ACS symposium series 480. American Chemical Society, Washington, DC, p 42Google Scholar
  133. 133.
    Doelker E (1990) In: Brannon-Peppas L, Harland RS (eds) Absorbent polymer technology. Elsevier, Amsterdam, p 125Google Scholar
  134. 134.
    Doelker E (1986) In: Peppas NA (ed) Hydrogels in medicine and pharmacy, vol. II polymers. CRC Press, Boca Raton, FL, p 115Google Scholar
  135. 135.
    Butler RW, Klug ED (1980) In: Davidson RL (ed) Handbook of water-soluble gums and resins. McGraw-Hill, New York, p 1Google Scholar
  136. 136.
    Brannon-Peppas L (1990) In: Brannon-Peppas L, Harland RS (eds) Absorbent polymer technology. Elsevier, Amsterdam, p 67Google Scholar
  137. 137.
    Brannon-Peppas L, Peppas NA (1988) Polym Bull 20: 285CrossRefGoogle Scholar
  138. 138.
    Sanchez IC, Lacombe RH (1976) J Phys Chem 80: 2352CrossRefGoogle Scholar
  139. 139.
    Lacombe RH, Sanchez IC (1976) J Phys Chem 80: 2568CrossRefGoogle Scholar
  140. 140.
    Sanchez IC, Lacombe RH (1978) Macromolecules 11: 1145CrossRefGoogle Scholar
  141. 141.
    Sanchez IC, Balazs AC (1989) Macromolecules 22: 2325CrossRefGoogle Scholar
  142. 142.
    Welty JR, Wicks CE, Wilson RE (1984) Fundamentals of momentum, heat, and mass transfer, 3rd edn. John Wiley, New YorkGoogle Scholar
  143. 143.
    Perry RH, Green D (1984) Chemical engineering handbook, 6th edn. McGraw-Hill, New YorkGoogle Scholar
  144. 144.
    Carslaw AS, Jaeger JC (1959) The conduction of heat in solids, 2nd edn. Oxford Clarendon Press, OxfordGoogle Scholar
  145. 145.
    Helfferich F (1965) J Phys Chem 69: 1178Google Scholar
  146. 146.
    Helfferich F (1962) Ion Exchange. McGraw-Hill, New YorkGoogle Scholar
  147. 147.
    Dana PR, Wheelock TD (1974) Ind Eng Chem Fund 13: 20CrossRefGoogle Scholar
  148. 148.
    Levenspiel O (1972) Chemical Reaction Engineering, 2nd edn. John Wiley, New YorkGoogle Scholar
  149. 149.
    Crank J (1975) The mathematics of diffusion, 2nd edn. Oxford University Press, LondonGoogle Scholar
  150. 150.
    Meares P (1968) In: Crank J, Park G (eds) Diffusion in polymers. Academic, London, p 373Google Scholar
  151. 151.
    Tanaka T, Hocker LO, Benedek GB (1973) J Chem Phys 59: 5151CrossRefGoogle Scholar
  152. 152.
    de Gennes. PG (1979) Scaling concepts in polymer physics. Cornell Unoversity Press, Ithaca, New YorkGoogle Scholar
  153. 153.
    Billovits GF, Durning CJ (1989) Chem Eng Commum 82: 21Google Scholar
  154. 154.
    Peters A, Schosseler F, Candau SJ (1989) In: Glass J (ed) Polymer in aqueous media: performance through association. Advances in chemistry series 223. American Chemical Society, Washington, DC, p 45Google Scholar
  155. 155.
    Chatterjee PK, Nguyen HV (1985) In: Chatterjee PK (ed) Absorbency. Textile science and technology, vol. 7. Elsevier Science Publishers, Amsterdam, p 29Google Scholar
  156. 156.
    Williams JM, Wrobleski DA (1989) Langmuir 4: 656CrossRefGoogle Scholar
  157. 157.
    Barby D, Haq Z (1982) European Patent 0,060,138Google Scholar
  158. 158.
    Williams JM, Wilkerson KR (1990) Polymer 31: 2162CrossRefGoogle Scholar
  159. 159.
    Yasuda, H, Peterlin A, Colton CK, Smith KA, Merrill EW (1969) Die Makromol Chem 126: 177CrossRefGoogle Scholar
  160. 160.
    Schnitzer JE (1988) Biophys J 54: 1065PubMedGoogle Scholar
  161. 161.
    Peppas NA, Reinhart (1983) J Membr Sci 15: 275CrossRefGoogle Scholar
  162. 162.
    Lustig SR, Peppas NA (1988) J Appl Polym Sci 36: 735CrossRefGoogle Scholar
  163. 163.
    Dearden JC, Tomlinson E (1971) J Pharm Pharmac 73: 735Google Scholar
  164. 164.
    Hansch C, Anderson S (1967) J Org Chem 32: 2583CrossRefGoogle Scholar
  165. 165.
    Ruckenstein E, Lesins V (1988) In: Mizrahi A (ed) Downstream processes: equipment and techniques. Alan R. Liss, New York, p 246Google Scholar
  166. 166.
    Luck WA (1980) In: Rowland SP (ed) Water in polymers, ACS symposium series 127. American Chemical Society, Washington DC, p 43Google Scholar
  167. 167.
    Scopes RK (1987) Protein purification: principles and practice, 2nd edn. Springer, Berlin Heidelberg New YorkGoogle Scholar
  168. 168.
    Hashman T, Palasis M (1988) unpublished researchGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Stevin H. Gehrke
    • 1
  1. 1.Department of Chemical EngineeringUniversity of CincinnatiCincinnatiUSA

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