Analysis of the experimental implications of the scaling theory of polymer adsorption

Macromolecules

Volumn 31, Issue 6, 1998, Pages 1979-1988

  Klein, Jacob ^a   Rossi, Giuseppe ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b FORD RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADSORPTION; APPROXIMATION THEORY; SOLUTIONS; SOLVENTS;

SCALING THEORY;

POLYMERS;

EID: 0032027526     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma9709314     Document Type: Article

References (51)

1. Fleer, G.; Cohen-Stuart, M.; Scheutjens, J.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman and Hall; London, 1993.
2. Scheutjens, J.; Fleer, G. J. Phys. Chem. 1979, 83, 1619; 1980, 84, 178.
3. Scheutjens, J.; Fleer, G. J. Phys. Chem. 1979, 83, 1619; 1980, 84, 178.
4. de Gennes, P.-G. Macromolecules 1981, 14, 1637.
5. de Gennes, P.-G. Macromolecules 1982, 15, 492.
6. Klein, J.; Pincus, P. Macromolecules 1982, 15, 1129.
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8. Ingersent, K.; Klein, J.; Pincus, P. Macromolecules 1986, 19, 1374; 1990, 23, 548.
9. See for example: de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press; Ithaca, NY, 1978.
10. Rossi, G.; Pincus, P. A. Europhys. Lett. 1988, 5, 641.
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14. Johner, A.; Bonet Avalos, J.; van der Linden, C. C.; Semenov, A. N.; Joanny, J.-F. Macromolecules 1996, 29, 3629.
15. Klein, J.; Luckham, P. F. Nature 1984, 308, 836.
16. Klein, J.; Luckham, P. F. Macromolecules 1984, 17, 1041.
17. Luckham, P. F.; Klein, J. J. Chem. Soc., Faraday Trans. 1990, 86, 1363.
18. Luckham, P. F.; Klein, J. Macromolecules 1985, 18, 721.
19. Klein and Luckham did verify (see ref 14) that for the very dilute solutions used in their experiment, washing does not change the force vs distance profile for the saturated case.
20. For a recent study of the phase diagram of this system, see: Bekiranov, S.; Bruinsma, R.; Pincus, P. Phys. Rev. E 1997, 55, 577.
21. 3 is present at a concentration of 0.1 M: as a result, the Debye length is on the order of only 1 nm.
22. Bonet Avalos, J.; Joanny, J.-F.; Johner, A.; Semenov, A. N. Europhys. Lett. 1996, 32, 97.
23. Semenov, A. N.; Joanny, J.-F.; Johner, A.; Bonet Avalos, J. Macromolecules 1997, 30, 1479.
24. While the repulsive interaction between adsorbed layers in full equilibrium found in refs 20 and 21 represents a qualitative departure from the purely attractive behavior predicted in ref 4, an estimate of the magnitude of the repulsion shows that for colloidal size particles (radius of (0.1-1) μm), the repulsive energy is of the order of (0.1-1)kT. In view of this result, the repulsive effect is not sufficient to account for stabilization in most colloidal systems; it must then be concluded that the standard picture where stabilization effects are associated to irreversible adsorption of polymer chains on the colloidal particles is correct.
25. Note that, unless the adsorption is extremely weak, inordinately long observation times are required in order to reach experimentally the reversible adsorption regime in a surface force measurement.
26. F is the usual Flory polymer solvent interaction parameter. In practice, scaling laws for both local structure and interactions are found to be obeyed for typical systems up to polymer concentrations of several percent (see: Daoud, M.; et al. Macromolecules 1975, 8, 804; Ferry J. D. Macromolecules 1979, 13, 1719), a regime which includes most of the concentration range within adsorbed polymer layers.
27. F is the usual Flory polymer solvent interaction parameter. In practice, scaling laws for both local structure and interactions are found to be obeyed for typical systems up to polymer concentrations of several percent (see: Daoud, M.; et al. Macromolecules 1975, 8, 804; Ferry J. D. Macromolecules 1979, 13, 1719), a regime which includes most of the concentration range within adsorbed polymer layers.
28. F is the usual Flory polymer solvent interaction parameter. In practice, scaling laws for both local structure and interactions are found to be obeyed for typical systems up to polymer concentrations of several percent (see: Daoud, M.; et al. Macromolecules 1975, 8, 804; Ferry J. D. Macromolecules 1979, 13, 1719), a regime which includes most of the concentration range within adsorbed polymer layers.
29. It can be shown explicitly (see ref 3) that the inclusion of long-ranged van der Waals fields does not perturb the form of the self-similar concentration profile deduced using the short ranged interactions alone.
30. Edwards, S. F. Proc. Phys. Soc. London 1966, 88, 255. See also A. K. Dolan and S. F. Edwards, Proc. Roy. Soc. (London) A 1975, 343, 427 for an early application of the self-consistent mean field method to the problem of interactions between polymer bearing surfaces.
31. Edwards, S. F. Proc. Phys. Soc. London 1966, 88, 255. See also A. K. Dolan and S. F. Edwards, Proc. Roy. Soc. (London) A 1975, 343, 427 for an early application of the self-consistent mean field method to the problem of interactions between polymer bearing surfaces.
32. Jones, I. S.; Richmond, P. J. Chem. Soc., Faraday Trans. 2 1977, 73, 1062.
33. 0 rather than by m. Finally an overall minus sign is missing in the left-hand side of both eq 5 in ref 8 and eq 28 in ref 9.
34. Note that both the reduced functions F(ω) and the reduced surface energy G(ω) (defined in eq 13) are dimensionless quantities.
35. d axis of Figure 7 is incorrect, so that the actual value of F(ω) for saturated plates is much smaller than that shown in Figure 7 of ref 4. References 8 and 9 have the correct results for F(ω).
36. Tabor, D.; Winterton, R. H. S. Proc. R. Soc. London, Ser. A 1969, 312, 435.
37. Israelachvili, J. N.; Tabor, D. Proc. R. Soc. London, Ser. A 1972, 331, 19.
38. Derjaguin, B. V. Kolloid-Z. 1934, 69, 155.
39. i, so that it is appropriate to identify the lhs of eq 18 with the quantity G(ω) defined in eq 13.
40. 3.
41. Note that this force-distance curve (1.2 M PEO, Figure 1b, curve c) cannot be used for comparison with the predictions of the model. This is because the part of the curve measured covers only the onset of interactions, and - as for the other M values used - this regime is not described by the scaling model.
42. F of PEO in water are given in Kawaguchi, M.; Masaaki, M.; Takahashi, A. Macromolecules 1984, 17, 2063.
43. onset. The reasons for this have been considered in some detail earlier in ref 39 and have to do with the sensitivity of the SFB in picking up the initial interactions of the outer segments of the opposing adsorbed layers.
44. Klein, J.; Luckham, P. F. Macromolecules 1986, 19, 2007.
45. While this expression for the osmotic pressure was derived originally for an athermal solvent, it has been shown that in a number of cases it applies well, using the appropriate values of α, also for moderate to good solvents in the semidilute regime (see: Ferry, J. D., loc cit in ref 24).
46. (a) Cosgrove, T.; Vincent, B.; Crowley, T. L.; Cohen-Stuart, M. A. In Polymer Adsorption and Dispersion Stability, Goddard, E. D., Vincent, B., Eds.; ACS Symposium Series 240; American Chemical Society, Washington, DC, 1984; pp 147-160.
47. (b) Cosgrove, T.; Crowley, T. L.; Ryan, K.; Webster J. R. P. Colloids Surf. 1990, 51, 255.
48. Lee, E. M.; Thomas, R. K.; Rennie, A. R. Europhysics Lett. 1990, 13, 135.
49. These values of the volume fraction at the wall are somewhat higher than the expected range of concentrations for semidilute solutions, though we note that, in other polymer/good solvent systems, scaling behaviour has been observed to persist up to comparable concentrations (see: Daoud, M.; et al., loc cit in ref 24).
50. 00 ≅ Γ = 4 ± 1.5 nm. We should however note that the adsorbance values for PEO on latex particles in water estimated in the study of ref 41 are lower than for PEO on mica.
51. Klein, J. J. Chem. Soc., Faraday Trans. 1 1983, 79, 99.