Polymer Solution Limit of Superheat T Falls to that of Solvent To as r –> ∞

Jennings and Middleman [1] measured the limit of superheat of polystyrene in cyclohexane and Jennings [2] derived the following equation for the effect, found in Jennings [3].

T – To = (3 k To2 w2 MWo) / (σo ao MW2)

Looking at the data in [1] one can see that the rise in superheat is falling to that of the cyclohexane as the molecular weight of the polystyrene rises. In this paper, the author takes the partial derivative of T, solution limit of superheat, and shows that ∂ T / ∂ ln MW2 –> 0 as r –> ∞. r is the ratio of molar volume of polymer to that of solvent. An image of the apparatus used to measure the temperature of the superheated solution is presented from Holden and Katz [4]. Figures 1, 2 and 3 of the 1985 Jennings and Middleman data are here. In a previous paper, Jennings [5], Jennings proved that, ∂ σ / ∂ r = 0 comes from r = ∞. I take the above equation to:

∂T / ∂ln MW2 = - (3 k To2 ρo w2) / (σo ao r ρ2).

Notice that the left side goes to zero as r goes to infinity. This is the tendency in the Jennings and Middleman data.