4 Temperature Dependence of Coil Dimensions

The temperature dependence of coil dimensions is considered via the modification of the excluded volume provided via the Mayer f-function. The contributions from hard-sphere overlap and weak attraction are separated so that

f(r)  ~=  - 1;r < b
      ~
f(r)  =  U (r)∕k∫T b;r > b         ∫ ∞
   v  =  = 4π   (1)r2dr+ 4π∕kT     U(r)r2dr
               0                b
         (    Θ-) 3
   v  ≈   1 - T  b                                              (6)

where

       ∫ ∞
Θ ≈ --13    U (r)r2dr
    kb  b

The theta temperature Θ is thus explicitly linked to the chain interaction parameter and the thermal blob size via

 z  ≈   T --Θ-N 1∕2
         T
       (   T  )2
gT  ≈    T---Θ-                                    (7)