Adsorption at the Theta Point

Ellipsometry determines a certain average thickness th of the adsorbed layer. However, what is important for the evaluation of polymer conformations in this layer is the root-mean square thickness t. Hence, it is necessary to find a way of relating t to th. McCrackin and Colson66 studied this problem for several distributions of segments and found tnn, = th/l-5 for the exponential distribution and t - th/1.74 for the Gaussian distribution. Takahashi et al.67 showed that t = th/1.63 for the one-train and two-tail model (see Eqs. (B-110) and (B-lll)). 

Stromberg et al.68 applied ellipsometry to the adsorption of polystyrene samples with a narrow M-distribution on a chrome plate from cyclohexane solutions at 35 °C (the theta condition for polystyrene) and found that t was approximately proportional to the square root of molecular weight, M up to 1.8 x 106. These values of t were compared with the root-mean-square end-to-end distances calculated for the chains which are attached at one end to either a reflecting or an absorbing wall. They fell between the computed values for these two walls, though somewhat closer to the values for the absorbing wall. 

Peyser and Stromberg63 used the ATR method to measure the thickness of a polystyrene layer adsorbed on a quartz surface from cyclohexane solution at 35 °C and compared it with the thickness obtained by ellipsometry. Good agreement was observed although the ellipsometric measurements were made for the chrome plate. 

Gebhard and Killmann69 reported an ellipsometric study of the adsorption of polystyrene onto various metal surfaces from theta solvents, M ranging from 76 x 103 to 340 x 103. A proportionality between t,ms and M1/2 was also observed, and the adsorb-ance was found to increase with rising M. 

Recently, Takahashi et al.70) measured ellipsometrically the thicknesses of the polystyrene layers adsorbed on a chrome plate from cyclohexane at 35 °C over a very wide range of M from 10 x 103 to 13.4 x 106. The resulting adsorption isotherms are shown in Fig. 11. Initially, the adsorption isotherms rise sharply with increasing bulk polymer concentration and reach a wide plateau region. The plots of t against bulk polymer 

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