Comblike and Brushlike Polymers
Polymers in which each monomer unit has a long side chain are known as combpolymers or comblike polymers, and polymers in which each repeat unit caries two side chains, are known as brushlike polymers. Both types of polymers, particularly those that contain alkyl side chains, have been the subject of a number studies.
Polymers with long n-alkyl side chains have an intrinsic tendency for order. With increasing length of the side chain, the glass transition temperature (Tg) first decreases, as one would expect, since the side chains disrupt the packing of the polymer chains, and thus, reduce steric hindrance to segmental mobility. This in turn, lowers the Tg, but when the n-alkyl side chains reach a critical value, nc, the Tg stops to drop and shows the opposite behavior, that is for n > nc, the Tg continuously increases with increasing number of methylene groups in the side chain. This odd behavior has been recognized as early as 1954 by Greenberg and Alfrey1 and has been attributed to side-chain "crystallization", or in other words, a three-dimensional order results entirely from side chain packing.
Reimschuessel (1979)2 found that the glass transition temperature of these comb-like and brush-like polymers is for a given backbone chain structure directly related to the molecular weight (M) of the repeat unit. The decrease in Tg towards a critical value Tg,c can be described with following differential equation2:
dTg / dM = - k' · M · [Tg - Tg,c]
which on integration gives
Tg = (Tg,1 - Tg,c) · exp[k · (M2 - M12)] + Tg,c
where the subscript 1 refers to n = 1 and c to the critical value, i.e. the value corresponding to the lowest Tg,c. Reimschuessel derived following relations for the two critical parameters:
nc = 1 + 0.028 · Tg,1
Tg,c (K) = 0.97 ·Tg,1 - 8 · 10-4 · Tg,12
A somewhat more accurate fit yields
Tg,c (K) = 0.972 · Tg,1 - 7.84 · 10-4 · Tg,1
The assumption, that the critical parameters depend only on the Tg of the base polymer (n = 1) is very convenient since the Tg of the base polymer is known for many polymers.
The fitting constant k has been calculated from experimental Tgs(2). If no experimental data are available, it can be estimated with following relation:
k = 2.5 x 10-6 Vm - 3.27 x 10-4
The predicted fitting constants k together with Reimschuessel's values are listed in the table below. For most polymers, the estimated values are within the scatter range of the literature values.
| Polymer | Average k x 10-4 | Scatter x 10-4 | Estimated k x 10-4 |
| Poly(alkyl styrene) | 0.65 | 0.57 - 0.88 | 0.80 |
| Poly(alkyl vinyl ether) | 2.10 (1.45) | 1.30 - 2.10 | 1.96 |
| Poly(alkyl acrylate) | 1.60 | 1.45 - 1.80 | 1.52 |
| Poly(alkyl methacrylate) | 0.97 | 0.81 - 1.14 | 1.11 |
| Poly(alkyl itaconate) | 0.31 | 0.25 - 0.35 | 0.37 |
| Poly(alkyl phenylene ether) | 0.38 | 0.33 - 0.44 | 0.19 |
The relationships above are only applicable to polymers with short side-chains (n ≤ nc). For polymers with long side chains (n > nc), Krevelen's formula can be applied:(3)
Tg,n (K) = Tg,c + K · (n - nc) / M (n > nc)
Krevelen(3) assumed that nc is a constant for all polymers, having the value nc = 9. However, as Reimschuessel has shown, the critical number of methylene groups in the side chain, nc, depends on the Tg of the base polymer and is for several polymers noticeably larger than 9 (10 - 16)(2).
References
S. A. Greenberg and T. Alfrey, J. Am. Chem. Soc. 7, 6, 6280 (1954)
H.K. Reimschuessel, J. of Poly. Sc.: Polymer Chemistry, Edition, Vol. 17, 2447-2457 (1979)
D.W. van Krevelen and Klaas te Nijenhuis, Properties of Polymers, 4th Ed., Amsterdam (2009)