▁the ▁c aged ▁particle ▁must ▁diff use ▁from ▁its ▁sol vent ▁c age . ▁The ▁typical ▁lifetime ▁of ▁a ▁sol vent ▁c age ▁is ▁ 1 0 − 1 1 s . ▁ ▁In ▁free ▁radical ▁polym er ization , ▁radical s ▁formed ▁from ▁the ▁decomposition ▁of ▁an ▁initi ator ▁mole c ule ▁are ▁surrounded ▁by ▁a ▁c age ▁consisting ▁of ▁sol vent ▁and / or ▁mon omer ▁mole cules . ▁ ▁Within ▁the ▁c age , ▁the ▁free ▁radical s ▁under go ▁ ▁many ▁coll isions ▁leading ▁to ▁their ▁recom bin ation ▁or ▁mut ual ▁de activ ation . ▁This ▁can ▁be ▁described ▁in ▁the ▁follow ▁reaction : ▁ ▁After ▁recom bin ation , ▁free ▁radical s ▁can ▁either ▁react ▁with ▁mon omer ▁mole cules ▁within ▁the ▁c age ▁walls ▁or ▁diff use ▁out ▁of ▁the ▁c age . ▁In ▁polym ers , ▁the ▁probability ▁of ▁a ▁free ▁radical ▁pair ▁to ▁escape ▁recom bin ation ▁in ▁the ▁c age ▁is ▁ 0 . 1 ▁- ▁ 0 . 0 1 ▁and ▁ 0 . 3 - 0 . 8 ▁in ▁liqu ids . ▁ ▁C age ▁recom bin ation ▁efficiency ▁▁ ▁The ▁c age ▁effect ▁can ▁be ▁quant it atively ▁described ▁as ▁the ▁c age ▁recom bin ation ▁efficiency ▁ ▁F c ▁where : ▁ ▁Here ▁F c ▁is ▁defined ▁as ▁the ▁ratio ▁of ▁the ▁rate ▁constant ▁for ▁c age ▁recom bin ation ▁( kc ) ▁to ▁the ▁sum ▁of ▁the ▁rate ▁constants ▁for ▁all ▁c age ▁processes . ▁According ▁to ▁mathematical