It is possible by calculation to predict the Tg of a copolymer given the copolymer composition and the Tg of the homopolymers of the acrylic monomers used.
J______ Wmi Wm2
Tg " Tgmi Tgm2
Wmi is the weight fraction of monomer 1 in the copolymer WfTi2 is the weight fraction of monomer 2 in the copolymer Tgmi is the Tg of a homopolymer of monomer 1 in °K Tgm2 is the Tg of a homo polymer of monomer 2 in °K
For example:
An acrylic copolymer of composition 70% methyl methacrylate (Tg 105°C) and 30% butyl acrylate (Tg -56°C) would have the following Tg:
1_____________ 0.7 0,3
Tg copolymer- (273+105) (273 — 56)
= 0.00185 + 0.00138
——— — —— = 0.00323
Tg copolymer
Tg copolymer = 309.6 °K = 36.6 °С
The above example illustrates the effect, on the final copolymer Tg, of using a “soft” monomer (butyl acrylate) and a “hard” monomer (methyl methacrylate) in combination.
The above equation assumes a linear relationship between weight composition and Tg. This is normally the case with acrylic polymers. However, some monomer combinations do show differences between the calculated and theoretical values of Tg.
As the equation used to calculate Tg is an approximation, this approach to calculating Tg is most valid where relative comparisons of monomer combinations are required.
It should be remembered, however, that these equations are intended only as a guideline for the formulator. Having achieved an initial starting point based on Tg, it will be necessary, in most cases, to modify the type and ratio of “hard” and “soft” monomers to achieve other desirable performance properties in the final surface coating.
A reasonable agreement can be achieved between the theoretical and practical values of Tg by using the Fox-Johnston equation.
For a copolymer of monomers A and B, the following equation can be expected to give good agreement with the practical results.
J_ Waa Wbb Wab
Tg TgAA + TgBB + TgAB
Waa is weight fraction of homopolymer AA in the final product Wbb is weight fraction of homopolymer BB in the final product Wab is weight fraction of copolymer AB in the final product TgAA is Tg of homopolymer of monomer A TgBB is Tg of homopolymer of monomer В TgAB is Tg of copolymer of monomers AB
At the glass transition point of an acrylic polymer, significant rotation in the backbone and side chain stops. The properties of a polymer alter considerably as the polymer passes through this temperature zone. Below its Tg the polymer is rigid, hard, brittle and glass like. Above its Tg the polymer is softer, rubbery and flexible.
Polymers with Tg below 20-25°C are soft and flexible at ambient temperatures with the possibility of cold flow occurring, particularly on warm days, whereas polymers with a Tg above 25°C tend to be hard and brittle at ambient temperature.