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Polymer Analysis Polymer Physics pp 157–207Cite as

The physics of polymer dissolution: Modeling approaches and experimental behavior

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Part of the book series: Advances in Polymer Science ((POLYMER,volume 128))

Abstract

Polymer dissolution is an important phenomenon in polymer science and engineering that has found applications in areas like microlithography, controlled drug delivery, and plastics recycling. This review focuses on the modeling efforts to understand the physics of the dissolution mechanism of glassy polymers. A brief review of the experimentally observed dissolution behavior is presented, thus motivating the modeling of the mechanism of dissolution. The main modeling contributions have been classified into four broad approaches — phenomenological models and Fickian equations, external mass transfer-control based models, stress relaxation models, and anomalous transport models and scaling law-based approaches. Another approach discussed is the appropriate accommodation of molecular theories in a continuum framework. The underlying principles and the important features of each approach are discussed in depth. Details of the important models and their corresponding predictions are provided. Experimental results seem to be qualitatively consistent with the present picture.

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Abbreviations

A:

Constant of Eq. (71) dependent on polymer molecular weight, solvent viscosity and temperature

a:

Primitive path step length

ad :

Exponent in the free volume diffusivity model, Eq. (69)

B:

Constant of Eq. (77) dependent on polymer molecular weight, solvent viscosity and temperature

b:

Bond length

bi :

Body force of component i

c:

Polymer mass concentration

D:

Macroscopic diffusion coefficient

Dcoop :

Cooperative diffusion coefficient

Dp :

Stokes-Einstein diffusion coefficient

DR :

Rouse diffusion coefficient

Dself :

Self diffusion coefficient

D0 :

Preexponential factor in free volume diffusivity model, Eq. (69)

D1 :

Free volume diffusion coefficient

D12 :

Mutual diffusion coefficient

D2 :

Reptation diffusion coefficient

E:

Modulus in Maxwell element

F:

Deformation gradient tensor

F(t):

Fraction of polymer present in original tube

fg :

Free volume fraction of polymer

f1 :

Numerical factor for the diffusion coefficient of solvent in polymer, Eq. (1)

f2 :

Numerical factor for diffusion coefficient of dissolved polymer in liquid solution, Eq. (2)

ΔG:

Total change in Gibbs free energy

ΔGE :

Change in Gibbs free energy due to elastic expansion

ΔGM :

Change in Gibbs free energy due to mixing

ΔG ORseg :

Orientational contribution to the Gibbs free energy of a segment

g:

Volume fraction of polymer in an entanglement subunit

ΔH:

Enthalpy change during elastic expansion

ji :

Diffusional flux of component i

K:

Parameter of kinetic model for glass transition, Eq. (21)

k:

Boltzmann constant

kd :

Disentanglement rate

k1 :

Mass transfer coefficient

L:

Parameter of Eq. (32) dependent on c (or π)

L(t):

Average primitive path length

l:

Half thickness of thin polymer slab

Mc :

Critical molecular weight of polymer

Me :

Molecular weight between entanglements

\(\bar M\) n :

Number averaged molecular weight of the polymer

mp :

Mobility of disengaging polymer chain

Mp,∞ :

Maximum mobility of disengaging polymer chain

N:

Number of repeating units

Ne :

Number of moles of entanglements

n:

Parameter of kinetic model for glass transition, Eq. (21)

ni :

Number of moles of component i

Pe:

Peclet number

p +i :

Exchange of linear momentum between components

R:

Position of glassy-rubbery interface

Rd :

Dissolution rate

Reff :

Effective disengagement rate

R0 :

Radius of the polymer particle

r:

Radial position

rg :

Radius of gyration

S:

Position of rubbery-solvent interface

ΔS:

Entropy change

Sh:

Sherwood number

T:

Temperature

Tg :

Glass transition temperature

t:

Time

td :

Disentanglement time

trep :

Reptation time

UR :

Reference velocity scale, Eq. (16)

U∞ :

Velocity of solvent stream

Vm :

Monomer volume

V1 :

Average volume of solvent molecule

\(\bar V\) :

Molar volume of the solvent

V2 :

Average volume of a polymer chain

\(\bar V\) 2 :

Molar volume of the polymer

v:

Local swelling rate of the polymer

v1 :

Convective velocity of the solvent in the x-direction

x:

Position

\(\bar x\) n :

Ratio of polymer molar volume to solvent molar volume

Z:

Number of segments in the primitive path

α:

Isotropic expansion factor

β:

Scaling factor in expression for disentanglement time, Eq. (59)

γ:

Constant for critical stress level, Eq. (48)

δ:

Thickness of diffusion boundary layer

ε:

One-dimensional deformation

η:

Viscosity

ϑ:

Overall dissolution time

κ:

Constant appearing in Eq. (24)

μi :

Chemical potential of component i

μ 0i :

Chemical potential of pure component i

μ OP1 :

Chemical potential of solvent due to osmotic pressure

μ OR1 :

Chemical potential of solvent due to orientational contribution

νeff :

Number of entanglements per polymer chain

ξ:

Distance between entanglements

π:

Osmotic pressure

ρi :

Density of component i

σ:

Stress in the rubbery polymer

σc :

Critical stress for crazing

σxx :

Normal stress component of the stress tensor

τdif :

Characteristic diffusion time

υd :

Equilibrium solubility of polymer in solvent

υi :

Volume fraction of component i

υ *1 :

Critical solvent volume fraction, at which mode of mobility changes

υ1,eq :

Equilibrium solvent volume fraction

υ1,t :

Threshold solvent volume fraction for swelling

υ2,b :

Polymer volume fraction in the bulk liquid

Φ:

Factor that determines the extent of local swelling, Eq. (37)

χ:

Polymer-solvent interaction parameter

8 References

  1. Cooper WJ, Krasicky PD, Rodriguez F (1986) J Appl Polym Sci 31: 65

    Google Scholar 

  2. Iwayanagi T, Ueno T, Nonogaki S, Ito H, Willson CG (1988). In: Electronic and photonic applications of polymers, ACS Symposium Series, Vol 218, ACS, Washington, DC, pp 109–224

    Google Scholar 

  3. O'Brien MJ, Soane DS (1989). In: Microelectronics processing: chemical engineering aspects, ACS Symposium Series, Vol 221, ACS, Washington, DC, pp 325–376

    Google Scholar 

  4. Parsonage EE, Peppas NA (1987) Brit Polym J 19: 469

    Google Scholar 

  5. Parsonage EE, Peppas NA, Lee PI (1987) J Vac Sci Technol B5: 538

    Google Scholar 

  6. Colombo P, Gazzaniga A, Sangalli ME, La Manna A (1987) Acta Pharm Technol 33: 15

    Google Scholar 

  7. Colombo P, Catellani PL, Peppas NA, Maggi L, Conte U (1992) Int J Pharm 88: 99

    Google Scholar 

  8. Conte U, Colombo P, Gazzaniga A, Sangalli ME, La Manna A (1988) Biomaterials 9: 489

    Google Scholar 

  9. Harland RS, Gazzaniga A, Sangani ME, Colombo P, Peppas NA (1988) Pharmaceut Res 5: 488

    Google Scholar 

  10. Lee PI (1987) In Controlled Release Technology: Pharmaceutical Applications, ACS Symposium Series, Vol 348, ACS, Washington, DC, pp 71–83

    Google Scholar 

  11. Pham AT, Lee PI (1993) Proceed Intern Symp Control Rel Bioact Mater 20: 220

    Google Scholar 

  12. Tsay CS, McHugh AJ (1990) J Polym Sci Polym Phys Ed 28: 1327

    Google Scholar 

  13. Yilmaz L, McHugh AJ (1988) J Appl Polym Sci 35: 1967

    Google Scholar 

  14. Kesting RE (1993) Polymeric Gas Separation Membranes, Wiley, New York, NY

    Google Scholar 

  15. Nauman EB, Lynch JC (1993) US Patent 5,198,471

    Google Scholar 

  16. Nauman EB, Lynch JC (1994) US Patent 5,278,282

    Google Scholar 

  17. Dammel RR (1993) Polym Mater Sci Eng Proceed 68: 49

    Google Scholar 

  18. Yeh TF, Reiser A, Dammel RR, Pawlowski G, Roeschert H (1993) Macromolecules 26: 3862

    Google Scholar 

  19. Huang JP, Kwei TK, Reiser A (1989) Macromolecules 22: 4106

    Google Scholar 

  20. Huang JP, Pearce EM, Reiser A, Kwei TK (1989) Polym Mater Sci Eng Proceed 60: 280

    Google Scholar 

  21. Wadke DA, Reier GE (1972) J Pharm Sci 61: 868

    Google Scholar 

  22. Koida Y, Takahata H, Kobayashi M, Samejime M (1987) Chem Pharm Bull 35: 1538

    Google Scholar 

  23. Cooney DO (1972) AIChE J 18: 446

    Google Scholar 

  24. Ozturk SS, Palsson BO, Dressman JB (1988) Pharmaceut Res 5: 272

    Google Scholar 

  25. Ozturk SS, Palsson BO, Donohue B, Dressman JB (1988) Pharmaceut Res 5: 550

    Google Scholar 

  26. Ueberreiter K (1968) In Diffusion in Polymers, Academic Press, New York, NY

    Google Scholar 

  27. Raptis G (1965) PhD Dissertation, Free University of Berlin, Berlin

    Google Scholar 

  28. Ueberreiter K, Asmussen F (1962) J Polym Sci 57: 187

    Google Scholar 

  29. Ouano AC, Carothers JA (1980) Polym Eng Sci 20: 160

    Google Scholar 

  30. Rodriguez F, Krasicky PD, Groele RJ (1985) Solid State Technol 28: 125

    Google Scholar 

  31. Cooper WJ, Krasicky PD, Rodriguez F (1985) Polymer 26: 1069

    Google Scholar 

  32. Krasicky PD, Groele RJ, Jubinsky JA, Rodriguez F (1987) Polym Eng Sci 27: 282

    Google Scholar 

  33. Krasicky PD, Groele RJ, Rodriguez F (1987) Chem Eng Comm 54: 279

    Google Scholar 

  34. Groele RJ, Rodriguez F (1989) J Coatings Tech 66: 55

    Google Scholar 

  35. Rao V, Kosbar LL, Frank CW, Pease RFW (1991) Proc SPIE 1672: 214

    Google Scholar 

  36. Rao V, Kosbar LL, Frank CW, Pease RFW (1994) In Polymers for Microelectronics, ACS Chemistry Series, ACS, Washington, DC, pp 220–234

    Google Scholar 

  37. Manjkow J, Papanu JS, Hess DW, Soane DS, Bell AT (1987) J Electrochem Soc 134: 2003

    Google Scholar 

  38. Manjkow J, Papanu JS, Hess DW, Soane DS, Bell AT (1987) J Appl Phys 62: 682

    Google Scholar 

  39. Papanu JS, Hess DW, Soane DS, Bell AT (1989) J Electrochem Soc 136: 1195

    Google Scholar 

  40. Papanu JS, Hess DW, Soane DS, Bell AT (1989) J Electrochem Soc 136: 3077

    Google Scholar 

  41. Papanu JS, Hess DW, Soane DS, Bell AT (1990) J Appl Polym Sci 39: 803

    Google Scholar 

  42. Drummond RK, Boydston GL, Peppas NA (1990) J Appl Polym Sci 39: 2267

    Google Scholar 

  43. Tu YO, Ouano AC (1977) IBM J Res Develop 21: 131

    Google Scholar 

  44. Tu YO (1977) Quart Appl Math 35: 269

    Google Scholar 

  45. Ouano AC, Tu YO, Carothers JA (1977) In Structure-Solubility Relationships in Polymers, Academic Press, New York, NY

    Google Scholar 

  46. Devotta I, Ambeskar VD, Mandhare AB, Mashelkar RA (1994) Chem Eng Sci 49: 645

    Google Scholar 

  47. Ranade VV, Mashelkar RA (1995) AIChE J 41: 666

    Google Scholar 

  48. Devotta I, Badiger MV, Rajamohanan PR, Ganapathy S, Mashelkar RA (1995) Chem Eng Sci 50: 2557

    Google Scholar 

  49. Zielinski JM, Duda JL (1992) AIChE J 38: 405

    Google Scholar 

  50. Astarita G, Sarti GC (1978) Polym Eng Sci 18: 388

    Google Scholar 

  51. Lee PI, Peppas NA (1987) J Contr Rel 6: 207

    Google Scholar 

  52. Lee HR, Lee YD (1991) Chem Eng Sci 46: 1771

    Google Scholar 

  53. Brochard F, de Gennes PG (1983) Phys Chem Hydrodynamics 4: 313

    Google Scholar 

  54. Doi M, Edwards SF (1986) The Theory of Polymer Dynamics, Oxford University Press, Oxford

    Google Scholar 

  55. Herman MF, Edwards SF (1990) Macromolecules 23: 3662

    Google Scholar 

  56. de Gennes PG (1971) J Chem Phys 55: 571

    Google Scholar 

  57. Papanu JS, Soane DS, Bell AT, Hess DW (1989) J Appl Polym Sci 38: 859

    Google Scholar 

  58. de Gennes (1979) Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, New York

    Google Scholar 

  59. Peppas NA, Wu JC, von Meerwall, ED (1994) Macromolecules 27: 5626

    Google Scholar 

  60. Wu JC, Peppas NA (1993) J Polym Sci Polym Phys Ed 31: 1503

    Google Scholar 

  61. Narasimhan B, Peppas NA (1996) J Polym Sci Polym Phys Ed, 34: 947

    Google Scholar 

  62. Flory PJ (1953) Principles of Polymer Chemistry, Cornell University Press, Ithaca, New York

    Google Scholar 

  63. des Cloizeaux J, Jannink G (1989) Polymers in Solution: Their Modeling and Structure, Oxford University Press, Oxford

    Google Scholar 

  64. Edwards SF (1982) Proc Royal Soc London A385: 267

    Google Scholar 

  65. Narasimhan B, Peppas NA (1996) Macromolecules, 29: 3283

    Google Scholar 

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Authors and Affiliations

  1. School of Chemical Engineering, Purdue University, 47907-1283, West Lafayette, IN, USA

    Balaji Narasimhan & Nikolaos A. Peppas

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  1. Balaji Narasimhan
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  2. Nikolaos A. Peppas
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© 1997 Springer-Verlag

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Narasimhan, B., Peppas, N.A. (1997). The physics of polymer dissolution: Modeling approaches and experimental behavior. In: Polymer Analysis Polymer Physics. Advances in Polymer Science, vol 128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61218-1_8

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  • DOI: https://doi.org/10.1007/3-540-61218-1_8

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  • Print ISBN: 978-3-540-61218-6

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