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Using Eq. 3-163 with Eqs. 3-160 and 3-161, one can calculate the ratio M = M s as a function of t=ts for a xed value of r. A semilog plot of such data for r 3 is shown in Fig. 3-11. To obtain ts the steady-state polymerization rate Rp s is rst measured at constant illumination (no pulsing). Then the average rate Rp is measured as a function of r and t. The data are plotted as the rate ratio Rp = Rp s versus log t. Alternately, one can plot the data as the rate ratio Rp = Rp 1 since this ratio is related to Rp = Rp s through Eq. 3-159. The theoretical plot (e.g., Fig. 3-11) for the same r value is placed on top of the experimental plot and shifted on the abscissa (x axis) until a best t is obtained. The displacement on the abscissa of one plot from the other yields log ts since the abscissa for the theoretical plot is log t log ts . The experimental determination of ts allows the calculation of kp , kt , ktr , and kz . kp =kt and 1=2 kp =kt , obtained from Eqs. 3-157 and 3-25 (non-steady-state and steady-state experiments, respectively), are combined to yield the individual rate constants kp and kt . Quantities such as



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,"out r, . , <:' ~)] B "11,1 (k) =tK.vvace iK..r.e II [. kzZ-t'2 rll (B) SllluSln (k zZ-U COS, sin tll(B) . ~ .

Fig. 3-11 Semilog plot of 2[M]/[M]s versus t=ts . After Matheson et al. [1949] (by permission of American Chemical Society, Washington, DC).

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(2.184)

Rt and M s are calculated from Eqs. 3-22 and 3-23, respectively. ktr and kz are calculated from the values of chain transfer and inhibition constants. The measurement of ts also allows an evaluation of the validity of the usual steady-state assumption in radical chain polymerization from the relationship [Flory, 1953]

,"out r, , <:' ~)]. B "11.2 (k) = -Zvvac eiK..r.e II [ k zZ-t'2 rll (B) SllluCOS (k zZ-u Sill, COS tll(B) . ~





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M Rp tanh t=ts M s Rp s 3-164

(2.185)

The time required for M and Rp to reach their steady-state values is calculated as 65, 6.5, and 0.65 s, respectively, for ts values of 10, 1, and 0.1 s. Thus, in the usual polymerization the steady-state assumption is valid after a minute or so at most. 3-8c PLP-SEC Method

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An examination of the literature, including the Polymer Handbook [Brandrup et al., 1999], often shows fairly wide disparities in the values of various rate constants. Much of this is due to experimental dif culties with the rotating sector method as well as the fact that different workers studied polymerizations under widely different reaction conditions. There has been a concerted effort in recent years to bring some order to the situation. A group of polymer scientists organized under the auspices of the IUPAC Working Party on Modeling of Kinetics and Processes of Polymerization has made good progress in this direction by standardization of the reaction conditions for measuring rate constants and the use of the PLPSEC method. Unlike the rotating sector method, the PLP-SEC method allows the measurement of kp directly without the need to couple it to the termination rate constant. The PLP-SEC method, like the rotating sector method, involves a non-steady-state photopolymerization [Beuermann, 2002; Beuermann and Buback, 2002; Kornherr et al., 2003; Nikitin et al., 2002]. Under pulsed laser irradiation, primary radicals are formed in very short times ($10 ns pulse width) compared to the cycle time ($1 s). The laser pulse width is also very short compared to both the lifetimes of propagating radicals and the times for conversion of primary radicals to propagating radicals. The PLP-SEC method for measuring kp requires that reaction conditions be chosen so that no signi cant chain transfer is present. The rst laser pulse generates an almost instantaneous burst of primary radicals at high

multiblock polyurethanes similar to TPU. Spandex typically differs from TPU in containing urea linkages instead of urethane in the hard blocks. These are obtained by using a diamine (instead of diol) to chain-extend isocyanate-terminated polyurethane prepolymers (synthesized from macroglycol and excess diisocyanate). Spandex bers can undergo large, reversible deformations and are used in the manufacture of undergarments. The various multiblock polyurethanes are often referred to as segmented polyurethanes. Other important thermoplastic elastomers are the multiblock polyetheresters (trade names: Hytrel, Lomod ) and polyetheramides (trade names: Pebax, Estamid, Grilamid ). 2-13c-3 Polymer Blends and Interpenetrating Polymer Networks

(2.186)

Polymer blends and interpenetrating polymer networks (IPNs) are different from copolymers but like copolymers are used to bring together the properties of different polymers [Paul et al, 1988] The total of all polymer blends (produced by both step and chain reactions) is estimated at about 3% of the total polymer production about 3 billion pounds per year in the United States There is considerable activity in this area since new products can be obtained and markets expanded by the physical mixing together of existing products No new polymer need be synthesized Polycarbonate is blended with a number of polymers including PET, PBT, acrylonitrile butadiene styrene terpolymer (ABS) rubber, and styrene maleic anhydride (SMA) copolymer The blends have lower costs compared to polycarbonate and, in addition, show some property improvement.

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