[xshadow]

Hi all !!
Please help me with this doubt....


My textbook says that in bulk polymerization there is the "gel effect" that causes an "autoacceleration" of the  rate of polymerization (radical one)

Wikipedia explain well this:
 "a decrease in the termination rate was the basis of the phenomenon (the increase  of  rate of polymerization ) . This decrease in termination rate, kt, is caused by the raised viscosity of the polymerization region when the concentration of previously formed polymer molecules increases. Before autoacceleration, chain termination by combination of two free radical chains is a very rapid reaction that occurs at very high frequency (about one in 104 collisions).[1] However, when the growing polymer molecules - with active free radical ends - are surrounded in the highly viscous mixture consisting of a growing concentration of "dead" polymer, the rate of termination becomes limited by diffusion. "


BUT my doubt is this:
in free radical polymerization the rate of polymerization can be defined as:

r_p = K_p * [M·][M] = K_p*(v_i/2k_t)^1/2 * [M·][M]
(so the rate of polymerization is equal to the propagation one)

Now if rate of  termination reaction decreases (due to the high viscosity) I have MORE M· in the reaction environment at a certain time ...
So [M·] increases for a same time than usual....BUT if I have more growing chains I should consume MORE  monomer molecules in the same time..
So [M] should decrease more than usual


I have two opposite effects...and if the rate of reaction,r_p, is  proportional to the product [M·] * [M]  , how can say that the total effect is the rising of the rate of reaction r_p ??



Any suggestion??
Thanks

[mjc123]

I should consume MORE  monomer molecules in the same time..

That is saying exactly the same as "the rate of reaction increases". Of course if you increase the rate of reaction you will use up monomer faster and so eventually the rate will slow down, but that is true of any way of increasing the rate, e.g. increasing the temperature - rate will initially be faster, but the reaction will be over sooner - so I can't see the problem. Remember too that generally [M·] is much smaller than [M], so if the gel effect causes [M·] to rise by, say, a factor of 3, it will take some time for [M] to be reduced by a factor of 3.